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Family of replica matrices, related to general ultrametric spaces with general measures, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed. Replica symmetry breaking…
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…
Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors…
We continue the study of prime simple modules for quantum affine algebras from the perspective of $q$-fatorization graphs. In this paper we establish several properties related to simple modules whose $q$-factorization graphs are afforded…
We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…
In this paper, we present several new constructions of differentially 4-uniform permutations over $\F_{2^{2m}}$ by modifying the values of the inverse function on some subsets of $\F_{2^{2m}}$. The resulted differentially 4-uniform…
Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…
Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…
In this paper, we study the dynamics of degenerating sequences of rational maps on Riemann sphere $\hat{\mathbb{C}}$ using $\mathbb{R}$-trees. Given a sequence of degenerating rational maps, we give two constructions for limiting dynamics…
Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…
Traversals are commonly seen in tree data structures, and performance-enhancing transformations between tree traversals are critical for many applications. Existing approaches to reasoning about tree traversals and their transformations are…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…
In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
We extend classical results on simple varieties of trees (asymptotic enumeration, average behavior of tree parameters) to trees counted by their number of leaves. Motivated by genome comparison of related species, we then apply these…
We consider the Steiner tree problem in hyperbolic geometry in the context of the AdS/CFT duality between large-$c$ conformal blocks on the boundary and particle motions in the bulk. The Steiner trees are weighted graphs on the Poincare…
We extend useful properties of the $H\to\gamma\gamma$ unintegrated dual amplitudes from one- to two-loop level, using the Loop-Tree Duality formalism. In particular, we show that the universality of the functional form -- regardless of the…
The computation of feedback control using Dynamic Programming equation is a difficult task due the curse of dimensionality. The tree structure algorithm is one the methods introduced recently that mitigate this problem. The method computes…
The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…