scholarly journals Noncolliding Brownian motion with drift and time-dependent Stieltjes-Wigert determinantal point process

2012 ◽  
Vol 53 (10) ◽  
pp. 103305 ◽  
Author(s):  
Yuta Takahashi ◽  
Makoto Katori
Keyword(s):  
Brownian Motion ◽  
Point Process ◽  
Time Dependent ◽  
Determinantal Point Process ◽  
Brownian Motion With Drift ◽  
Noncolliding Brownian Motion

scholarly journals Fast optimization of cache-enabled Cloud-RAN using determinantal point process

2021 ◽  
Vol 46 ◽  
pp. 101292
Author(s):  
Ashraf Bsebsu ◽  
Gan Zheng ◽  
Sangarapillai Lambotharan
Keyword(s):  
Point Process ◽  
Determinantal Point Process ◽  
Fast Optimization ◽  
Cloud Ran

scholarly journals Couplings for determinantal point processes and their reduced Palm distributions with a view to quantifying repulsiveness

2021 ◽  
Vol 58 (2) ◽  
pp. 469-483
Author(s):  
Jesper Møller ◽  
Eliza O’Reilly
Keyword(s):  
Finite Number ◽  
Point Process ◽  
Point Processes ◽  
Parametric Models ◽  
Determinantal Point Processes ◽  
Determinantal Point Process ◽  
The Difference ◽  
Weaker Conditions ◽  
Palm Distributions

AbstractFor a determinantal point process (DPP) X with a kernel K whose spectrum is strictly less than one, André Goldman has established a coupling to its reduced Palm process $X^u$ at a point u with $K(u,u)>0$ so that, almost surely, $X^u$ is obtained by removing a finite number of points from X. We sharpen this result, assuming weaker conditions and establishing that $X^u$ can be obtained by removing at most one point from X, where we specify the distribution of the difference $\xi_u: = X\setminus X^u$. This is used to discuss the degree of repulsiveness in DPPs in terms of $\xi_u$, including Ginibre point processes and other specific parametric models for DPPs.

scholarly journals High-performance sampling of generic determinantal point processes

2020 ◽  
Vol 378 (2166) ◽  
pp. 20190059 ◽  
Author(s):  
Jack Poulson
Keyword(s):  
Point Process ◽  
Spectral Decomposition ◽  
High Performance ◽  
Point Processes ◽  
Cholesky Factorization ◽  
Determinantal Point Processes ◽  
Determinantal Point Process ◽  
Decomposition Approach ◽  
Map Inference ◽  
Sampling Schemes

Determinantal point processes (DPPs) were introduced by Macchi (Macchi 1975 Adv. Appl. Probab. 7 , 83–122) as a model for repulsive (fermionic) particle distributions. But their recent popularization is largely due to their usefulness for encouraging diversity in the final stage of a recommender system (Kulesza & Taskar 2012 Found. Trends Mach. Learn. 5 , 123–286). The standard sampling scheme for finite DPPs is a spectral decomposition followed by an equivalent of a randomly diagonally pivoted Cholesky factorization of an orthogonal projection, which is only applicable to Hermitian kernels and has an expensive set-up cost. Researchers Launay et al. 2018 ( http://arxiv.org/abs/1802.08429 ); Chen & Zhang 2018 NeurIPS ( https://papers.nips.cc/paper/7805-fast-greedy-map-inference-for-determinantal-point-process-to-improve-recommendation-diversity.pdf ) have begun to connect DPP sampling to LDL H factorizations as a means of avoiding the initial spectral decomposition, but existing approaches have only outperformed the spectral decomposition approach in special circumstances, where the number of kept modes is a small percentage of the ground set size. This article proves that trivial modifications of LU and LDL H factorizations yield efficient direct sampling schemes for non-Hermitian and Hermitian DPP kernels, respectively. Furthermore, it is experimentally shown that even dynamically scheduled, shared-memory parallelizations of high-performance dense and sparse-direct factorizations can be trivially modified to yield DPP sampling schemes with essentially identical performance. The software developed as part of this research, Catamari ( hodgestar.com/catamari ) is released under the Mozilla Public License v.2.0. It contains header-only, C++14 plus OpenMP 4.0 implementations of dense and sparse-direct, Hermitian and non-Hermitian DPP samplers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

scholarly journals A generalized perspective of Fourier and Fick’s laws: Magnetized effects of Cattaneo-Christov models on transient nanofluid flow between two parallel plates with Brownian motion and thermophoresis

2020 ◽  
Vol 9 (1) ◽  
pp. 201-222 ◽  
Author(s):  
Usha Shankar ◽  
Neminath B. Naduvinamani ◽  
Hussain Basha
Keyword(s):  
Brownian Motion ◽  
Joule Heating ◽  
Concentration Field ◽  
Double Diffusion ◽  
Diffusion Models ◽  
Time Dependent ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Casson Nanofluid ◽  
Highly Nonlinear

AbstractPresent research article reports the magnetized impacts of Cattaneo-Christov double diffusion models on heat and mass transfer behaviour of viscous incompressible, time-dependent, two-dimensional Casson nanofluid flow through the channel with Joule heating and viscous dissipation effects numerically. The classical transport models such as Fourier and Fick’s laws of heat and mass diffusions are generalized in terms of Cattaneo-Christov double diffusion models by accounting the thermal and concentration relaxation times. The present physical problem is examined in the presence of Lorentz forces to investigate the effects of magnetic field on double diffusion process along with Joule heating. The non-Newtonian Casson nanofluid flow between two parallel plates gives the system of time-dependent, highly nonlinear, coupled partial differential equations and is solved by utilizing RK-SM and bvp4c schemes. Present results show that, the temperature and concentration distributions are fewer in case of Cattaneo-Christov heat and mass flux models when compared to the Fourier’s and Fick’s laws of heat and mass diffusions. The concentration field is a diminishing function of thermophoresis parameter and it is an increasing function of Brownian motion parameter. Finally, an excellent comparison between the present solutions and previously published results show the accuracy of the results and methods used to achieve the objective of the present work.

Examples of Stationary Sequences with Approximate Negative Dependence

2019 ◽  
pp. 305-318
Author(s):  
Florence Merlevède ◽  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Spectral Density ◽  
Point Process ◽  
Point Processes ◽  
Random Variables ◽  
Stationary Processes ◽  
Negative Dependence ◽  
Stationary Sequences ◽  
Determinantal Point Process ◽  
Dependent Random Variables ◽  
Associated Sequences

In this chapter, we treat several examples of stationary processes which are asymptotically negatively dependent and for which the results of Chapter 9 apply. Many systems in nature are complex, consisting of the contributions of several independent components. Our first examples are functions of two independent sequences, one negatively dependent and one interlaced mixing. For instance, the class of asymptotic negatively dependent random variables is used to treat functions of a determinantal point process and a Gaussian process with a positive continuous spectral density. Another example is point processes based on asymptotically negatively or positively associated sequences and displaced according to a Gaussian sequence with a positive continuous spectral density. Other examples include exchangeable processes, the weighted empirical process, and the exchangeable determinantal point process.

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