Related papers: Partition Rank and Partition Lattices
We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
Some variants of the (block) Gauss--Seidel iteration for the solution of linear systems with $M$-matrices in (block) Hessenberg form are discussed. Comparison results for the asymptotic convergence rate of some regular splittings are…
MacMahon enumerated the plane partitions in an $a \times b \times c$ box. These are in bijection to lozenge tilings of a hexagon, to certain perfect matchings, and to families of non-intersecting lattice paths. In this work we consider more…
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
Algorithms for partition refinement are actively studied for a variety of systems, often with the optimisation called Hopcroft's trick. However, the low-level description of those algorithms in the literature often obscures the essence of…
We give short elementary expositions of combinatorial proofs of some variants of Euler's partitition problem that were first addressed analytically by George Andrews, and later combinatorially by others. Our methods, based on ideas from a…
In [2] a new factorization for infinite Hessenberg banded matrices was introduced. In this note we prove that this kind of factorization can also be used for finite matrices. In addition, a new method for solving banded linear systems is…
Recently, Schneider and Schneider defined a new class of partitions called sequentially congruent partitions, in which each part is congruent to the next part modulo its index, and they proved two partition bijections involving these…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of two dimensional zonotopes, using dynamical systems and order theory. We show that the sets of partitions ordered with a simple…
The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, $Z$, is then linear in the number of categories, which is…
In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear algebra can hardly be…
We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices,…
This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine…
We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show…
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases. We formulate irreducibility and symmetry properties of a…
The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control…