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Related papers: Random sampling of plane partitions

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An efficient method for obtaining low-density hyperplane separators in the unsupervised context is proposed. Low density separators can be used to obtain a partition of a set of data based on their allocations to the different sides of the…

Machine Learning · Statistics 2021-08-10 David P. Hofmeyr

In this work we give an efficient construction of unitary $k$-designs using $\tilde{O}(k\cdot poly(n))$ quantum gates, as well as an efficient construction of a parallel-secure pseudorandom unitary (PRU). Both results are obtained by giving…

We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…

Optimization and Control · Mathematics 2021-03-04 Dimitris Bertsimas , Michael Lingzhi Li

This work presents a technique for particle size generation and placement in arbitrary closed domains. Its main application is the simulation of granular media described by disks. Particle size generation is based on the statistical…

The existing algorithms for processing skyline queries cannot adapt to big data. This paper proposes two approximate skyline algorithms based on sampling. The first algorithm obtains a fixed size sample and computes the approximate skyline…

Databases · Computer Science 2020-10-16 Xingxing Xiao , Jianzhong Li

We study nested partitions of $R^d$ obtained by successive cuts using hyperplanes with fixed directions. We establish the number of measures that can be split evenly simultaneously by taking a partition of this kind and then distributing…

Metric Geometry · Mathematics 2014-10-14 Roman Karasev , Edgardo Roldán-Pensado , Pablo Soberón

Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population…

Methodology · Statistics 2017-11-21 Giuseppe Di Benedetto , François Caron , Yee Whye Teh

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

Probability · Mathematics 2013-08-16 Richard Arratia , Simon Tavare

We consider a new kind of straight and shifted plane partitions/Young tableaux --- ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the…

Combinatorics · Mathematics 2012-05-31 Greta Panova

In this paper, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our…

Number Theory · Mathematics 2017-04-14 Ali H. Al-Saedi

The paper deals with a 3-parameter family of probability measures on the set of partitions, called the z-measures. The z-measures first emerged in connection with the problem of harmonic analysis on the infinite symmetric group. They are a…

Probability · Mathematics 2007-05-23 Alexei Borodin , Grigori Olshanski

We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics induces a distribution over random partitions. The community has therefore assumed that the best…

Methodology · Statistics 2021-08-03 Garritt L. Page , Fernando A. Quintana , David B. Dahl

Random sequential adsorption (RSA) is a time-dependent packing process, in which particles of certain shapes are randomly and sequentially placed into an empty space without overlap. In the infinite-time limit, the density approaches a…

Soft Condensed Matter · Physics 2018-05-01 G. Zhang

Consider an opaque medium which contains 3D particles. All particles are convex bodies of the same shape, but they vary in size. The particles are randomly positioned and oriented within the medium and cannot be observed directly. Taking a…

Applications · Statistics 2024-06-24 Thomas van der Jagt , Geurt Jongbloed , Martina Vittorietti

In this paper, we consider the planted partition model, in which $n = ks$ vertices of a random graph are partitioned into $k$ "clusters," each of size $s$. Edges between vertices in the same cluster and different clusters are included with…

Data Structures and Algorithms · Computer Science 2017-08-28 Sam Cole , Shmuel Friedland , Lev Reyzin

Let $S$ be a finite set of geometric objects partitioned into classes or \emph{colors}. A subset $S'\subseteq S$ is said to be \emph{balanced} if $S'$ contains the same amount of elements of $S$ from each of the colors. We study several…

Computational Geometry · Computer Science 2017-08-22 Sergey Bereg , Matias Korman , Rodrigo I. Silveira , Ferran Hurtado , Dolores Lara , Jorge Urrutia , Mikio Kano , Carlos Seara , Kevin Verbeek

Sampling from very large spatial populations is challenging. The solutions suggested in recent literature on this subject often require that the randomly selected units are well distributed across the study region by using complex…

Methodology · Statistics 2017-10-26 Roberto Benedetti , Federica Piersimoni

We use confocal microscopy to study a random close packed sample of colloidal particles. We introduce an algorithm to estimate the size of each particle. Taking into account their sizes, we compute the compressibility of the sample as a…

Soft Condensed Matter · Physics 2011-12-08 Rei Kurita , Eric R. Weeks

We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…

Computational Geometry · Computer Science 2024-10-23 Mikkel Abrahamsen , Nichlas Langhoff Rasmussen

Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…

Discrete Mathematics · Computer Science 2011-06-24 Giovanni Rossi