We identify a relation between the dynamics of ultracold Rydberg gases in which atoms experience strong dipole blockade and spontaneous emission, stochastic process that models certain wireless random-access networks. then transfer insights techniques initially developed for these networks to realm gases, explain how gas can be driven into crystal formations using our understanding Finally, we propose method determine Rabi frequencies (laser intensities) such particles are excited with...

Several recent experiments have established by measuring the Mandel $Q$ parameter that number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to blockade occurs due strong interatomic interactions between highly excited atoms. Because this effect, system can end up a state which all particles are either or blocked: jamming limit. We analyze appropriately constructed random-graph models capture and derive formulae for mean variance...

This paper considers cluster detection in Block Markov Chains (BMCs). These chains are characterized by a block structure their transition matrix. More precisely, the $n$ possible states divided into finite number of $K$ groups or clusters, such that same exhibit rates to other states. One observes trajectory chain, and objective is recover, from this observation only, (initially unknown) clusters. In paper, we devise clustering procedure accurately, efficiently provably detects We first...

We prove two universal approximation theorems for a range of dropout neural networks. These are feed-forward networks in which each edge is given random $\{0,1\}$-valued filter, that have modes operation: the first output multiplied by its resulting output, while second expectation leading to deterministic output. It common use mode during training and testing prediction. Both following form: Given function approximate threshold $\varepsilon>0$, there exists network $\varepsilon$-close...

We analyze the convergence rate of gradient flows on objective functions induced by Dropout and Dropconnect, when applying them to shallow linear Neural Networks (NNs) ---which can also be viewed as doing matrix factorization using a particular regularizer. algorithms such these are thus regularization techniques that use {0,1} -valued random variables filter weights during training in order avoid coadaptation features. By leveraging recent result nonconvex optimization conducting careful...

We develop a gradient algorithm for optimizing the performance of product-form networks through online adjustment control parameters. The use standard algorithms finding optimal parameter settings is hampered by prohibitive computational burden calculating in terms stationary probabilities. proposed approach instead relies on measuring empirical frequencies various states simulation or operation so as to obtain estimates gradient. Besides reduction effort, further benefit lies natural...

We consider Markovian many-server systems with admission control operating in a Quality-and-Efficiency-Driven (QED) regime, where the relative utilization approaches unity while number of servers grows large, providing natural Economies-of-Scale. In order to determine optimal policy, we adopt revenue maximization framework, and suppose that rate attains maximum when no customers are waiting idling. When function scales properly system size, show nondegenerate optimization problem arises...

We study the recovery of one-dimensional semipermeable barriers for a stochastic process in planar domain. The considered acts like Brownian motion when away from and is reflected upon contact until sufficient but random amount interaction has occurred, determined by permeability, after which it passes through. Given sequence samples, we wonder one can determine location shape barriers. This paper identifies several different regimes, available observation period time between with...

Clustering algorithms frequently require the number of clusters to be chosen in advance, but it is usually not clear how do this. To tackle this challenge when clustering within sequential data, we present a method for estimating data trajectory Block Markov Chain. Chains are that exhibit block structure their transition matrix. The considers matrix counts transitions between different states trajectory, and transforms into spectral embedding whose dimension set via singular value...

Abstract All analog signal processing is fundamentally subject to noise, and this also the case in next generation implementations of Optical Neural Networks (ONNs). Therefore, we propose first hardware-based approach mitigate noise ONNs. A tree-like an accordion-like design are constructed from a given Network (NN) that one wishes implement. Both designs have capability resulting ONNs give outputs close desired solution. To establish latter, analyze mathematically. Specifically, investigate...

Motivated by applications in service systems, we consider queueing systems where each customer must be handled a server with the right skill set. We focus on optimizing routing of customers to servers order maximize total payoff customer--server matches. In addition, dependent parameters are assumed unknown priori. construct machine learning algorithm that adaptively learns while maximizing and prove it achieves polylogarithmic regret. Moreover, show is asymptotically optimal up logarithmic...

We investigate the convergence and rate of stochastic training algorithms for Neural Networks (NNs) that have been inspired by Dropout (Hinton et al., 2012). With goal avoiding overfitting during NNs, dropout consist in practice multiplying weight matrices a NN componentwise independently drawn random with $\{0, 1 \}$-valued entries each iteration Stochastic Gradient Descent (SGD). This paper presents probability theoretical proof fully-connected NNs differentiable, polynomially bounded...

This paper quantifies the asymptotic order of largest singular value a centered random matrix built from path Block Markov Chain (BMC). In BMC there are n labeled states, each state is associated to one K clusters, and probability jump depends only on clusters origin destination. Given X0,X1,…,XTn started equilibrium, we construct Nˆ that records number transitions between pair states. We prove if ω(n)=Tn=o(n2), then ‖Nˆ−E[Nˆ]‖=ΩP(Tn/n). also Tn=Ω(nlnn), ‖Nˆ−E[Nˆ]‖=OP(Tn/n) as n→∞; Tn=ω(n),...

A block Markov chain is a whose state space can be partitioned into finite number of clusters such that the transition probabilities only depend on clusters. Block chains thus serve as model for with communities. This paper establishes limiting laws singular value distributions empirical matrix and frequency associated to sample path whenever length Θ(n2) n size space. The proof approach split two parts. First, we introduce class symmetric random matrices dependent entries called...

We develop an online gradient algorithm for optimizing the performance of product-form networks through adjustment control parameters. The use standard algorithms finding optimal parameter settings is hampered by prohibitive computational burden calculating in te

We characterize the achievable range of performance measures in product-form networks where one or more system parameters can be freely set by a network operator. Given and configurable parameters, we identify which controlled target values attained. also discuss an online optimization algorithm, allows operator to so as achieve metrics. In some cases, algorithm implemented distributed fashion, give several examples. Finally, conditions that guarantee convergence under assumption metrics are...

This paper considers cluster detection in Block Markov Chains (BMCs). These chains are characterized by a block structure their transition matrix. More precisely, the $n$ possible states divided into finite number of $K$ groups or clusters, such that same exhibit rates to other states. One observes trajectory chain, and objective is recover, from this observation only, (initially unknown) clusters. In we devise clustering procedure accurately, efficiently, provably detects We first derive...

We consider an exploration algorithm where at each step, a random number of items become active while related get explored. Given initial $N$ growing to infinity and building on strong homogeneity assumption, we study using scaling limits Markovian processes statistical properties the proportion nodes in time. This is companion paper that rigorously establishes claims heuristics presented [5]. [5] Jaron Sanders, Matthieu Jonckheere, Servaas Kokkelmans. Sub-Poissonian statistics jamming...