Related papers: Order recognition by Schubert polynomials generate…
Generation of irregular time series based on physical processes is indispensable in computing and artificial intelligence. In this report, we propose and experimentally demonstrate the generation of Schubert polynomials, which is the…
We develop numerical homotopy algorithms for solving systems of polynomial equations arising from the classical Schubert calculus. These homotopies are optimal in that generically no paths diverge. For problems defined by hypersurface…
Prime-based ordering which is proved to be admissible, is the encoding of indeterminates in power-products with prime numbers and ordering them by using the natural number order. Using Eiffel, four versions of Buchberger's improved…
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…
The first quantum technologies to solve computational problems that are beyond the capabilities of classical computers are likely to be devices that exploit characteristics inherent to a particular physical system, to tackle a bespoke…
We present an application of Hilbert quasi-polynomials to order domains, allowing the effective check of the second order-domain condition in a direct way. We also provide an improved algorithm for the computation of the related Hilbert…
We describe random generation algorithms for a large class of random combinatorial objects called Schur processes, which are sequences of random (integer) partitions subject to certain interlacing conditions. This class contains several…
Mechanisms for one-dimensional photon sorting are theoretically studied in the framework of a couple mode method. The considered system is a nanopatterned structure composed of two different pixels drilled on the surface of a thin gold…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However,…
This paper shows a proof-of-concept that, given a typical 3-channel images but in a randomly permuted channel order, a model (termed as Chanel-Orderer) with ad-hoc inductive biases in terms of both architecture and loss functions can…
Exceptional points are complex-valued spectral singularities that lead to a host of intriguing features such as loss-induced transparency - a counterintuitive process in which an increase in the system's overall loss can lead to enhanced…
We discuss uniform sampling algorithms that are based on stochastic growth methods, using sampling of extreme configurations of polymers in simple lattice models as a motivation. We shall show how a series of clever enhancements to a…
Learning to hash pictures a list-wise sorting problem. Its testing metrics, e.g., mean-average precision, count on a sorted candidate list ordered by pair-wise code similarity. However, scarcely does one train a deep hashing model with the…
Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we…
The need to increase data transfer rates constitutes a key challenge in modern information-driven societies. Taking advantage of the transverse spatial modes of light to encode more information is a promising avenue for both classical and…
Quasiprobability representation is an important tool for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear…
Disordered nanostructures are commonly encountered in many nanophotonic systems, from colloid dispersions for sensing, to heterostructured photocatalysts. Randomness, however, imposes severe challenges for nanophotonics modeling, often…
Schubert polynomials were discovered by A. Lascoux and M. Sch\"utzenberger in the study of cohomology rings of flag manifolds in 1980's. These polynomials generalize Schur polynomials, and form a linear basis of multivariate polynomials. In…
The manipulation and sorting of chiral nanoparticles are of fundamental importance in multidisciplinary fields ranging from biochemistry to nanophotonics. In this study, we propose a novel and controllable chirality sorting mechanism for…