Related papers: Subtraction-free complexity, cluster transformatio…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…
We give a comprehensive review of recent developments on using the pure spinor formalism to compute massless superstring scattering amplitudes at tree level. The main results of the pure spinor computations are placed into the context of…
Dimensional reduction is a key issue in finite temperature field theory. For example, when following the QCD Free Energy from low to high scales across the critical temperature, ultrasoft degrees of freedom can be captured by a 3d SU(3)…
A corner is a triple of points in $\Bbb{Z}^2$ of the form $(x,y),(x+d,y),(x,y+d)$ where $d\neq 0$. One can think of them as being 2D-analogues to 3-term arithmetic progressions. In this short note, we extend ideas of Green-Wolf from this…
An attempt is described to extend the notion of Schur functions from Young diagrams to plane partitions. The suggestion is to use the recursion in the partition size, which is easily generalized and deformed. This opens a possibility to…
The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to…
Kernels are key in machine learning for modeling interactions. Unfortunately, brute-force computation of the related kernel sums scales quadratically with the number of samples. Recent Fourier-slicing methods lead to an improved linear…
Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…
Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…
Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the…
Scattering amplitudes of the spin-4/3 fractional superstring are shown to satisfy spurious state decoupling and cyclic symmetry (duality) at tree-level in the string perturbation expansion. This fractional superstring is characterized by…
Modern understanding of symmetry in quantum field theory includes both invertible and non-invertible operations. Motivated by this, we extend Nielsen's geometric approach to quantum circuit complexity to incorporate non-invertible gates.…
In this paper, we study the form over the minimum spanning tree problem (MST) from which we will derive an intuitively generalized model and new methods with the upper bound of runtimes of logarithm. The new pattern we made has taken…
Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and…
We study complex zeros of the partition function of 2-spin systems, viewed as a multivariate polynomial in terms of the edge interaction parameters and the uniform external field. We obtain new zero-free regions in which all these…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…