Jaron Sanders

• MSc
• Professor (Assistant) at Eindhoven University of Technology

We study the recovery of one-dimensional semipermeable barriers for a stochastic process in a planar domain. The considered process acts like Brownian motion when away from the barriers and is reflected upon contact until a sufficient but random amount of interaction has occurred, determined by the permeability, after which it passes through. Given...

All analog signal processing is fundamentally subject to noise, and this is also the case in next generation implementations of optical neural networks (ONNs). Therefore, we propose the first hardware-based approach to mitigate noise in ONNs. A tree-like and an accordion-like design are constructed from a given NN that one wishes to implement. Both...

We establish sharp concentration inequalities for sums of dependent random matrices. Our results concern two models. First, a model where summands are generated by a $\psi$-mixing Markov chain. Second, a model where summands are expressed as deterministic matrices multiplied by scalar random variables. In both models, the leading-order term is prov...

A block Markov chain is a Markov chain whose state space can be partitioned into a finite number of clusters such that the transition probabilities only depend on the clusters. Block Markov chains thus serve as a model for Markov chains with communities. This paper establishes limiting laws for the singular value distributions of the empirical tran...

This paper quantifies the asymptotic order of the largest singular value of a centered random matrix built from the path of a Block Markov Chain (BMC). In a BMC there are n labeled states, each state is associated to one of K clusters, and the probability of a jump depends only on the clusters of the origin and destination. Given a path X0,X1,…,XTn...

Motivated by theoretical advancements in dimensionality reduction techniques we use a recent model, called Block Markov Chains, to conduct a practical study of clustering in real-world sequential data. Clustering algorithms for Block Markov Chains possess theoretical optimality guarantees and can be deployed in sparse data regimes. Despite these fa...

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. Dropout algorithms such as these are thus regularization techniques that use {0,1} -valued r...

We analyze the convergence rate of gradient flows on objective functions induced by Dropout and Dropconnect, when applying them to shallow linear Neural Networks(NN) ---which can also be viewed as doing matrix factorization using a particular regularizer. Dropout algorithms such as these are thus regularization techniques that use 0,1-valued random...

This paper quantifies the asymptotic order of the largest singular value of a centered random matrix built from the path of a Block Markov Chain (BMC). In a BMC there are $n$ labeled states, each state is associated to one of $K$ clusters, and the probability of a jump depends only on the clusters of the origin and destination. Given a path $X_0, X...

We prove two universal approximation theorems for a range of dropout neural networks. These are feed-forward neural networks in which each edge is given a random $\{0,1\}$-valued filter, that have two modes of operation: in the first each edge output is multiplied by its random filter, resulting in a random output, while in the second each edge out...

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. Dropout algorithms such as these are thus regularization techniques that use 0,1-valued rando...

We investigate the convergence and convergence rate of stochastic training algorithms for Neural Networks (NNs) that, over the years, have spawned from Dropout (Hinton et al., 2012). Modeling that neurons in the brain may not fire, dropout algorithms consist in practice of multiplying the weight matrices of a NN component-wise by independently draw...

We study a model for the accumulation of errors in multi-qubit quantum computations, as well as a model describing continuous errors accumulating in a single qubit. By modeling the error process in a quantum computation using two coupled Markov chains, we are able to capture a weak form of time-dependency between errors in the past and future. By s...

This paper considers cluster detection in Block Markov Chains (BMCs). These Markov chains are characterized by a block structure in their transition matrix. More precisely, the $n$ possible states are divided into a finite number of $K$ groups or clusters, such that states in the same cluster exhibit the same transition rates to other states. One o...

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become explored. Given an initial number of vertices $N$ growing to infinity, we study statistical...

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become explored. Given an initial number of vertices $N$ growing to infinity, we study statistical...

The Quality-and-Efficiency-Driven (QED) regime provides a basis for solving asymptotic dimensioning problems that trade off revenue, costs and service quality. We derive bounds for the optimality gaps that capture the differences between the true optimum and the asymptotic optimum based on the QED approximations. Our bounds generalize earlier resul...

The Quality-and-Efficiency-Driven (QED) regime provides a basis for solving asymptotic dimensioning problems that trade off revenue, costs and service quality. We derive bounds for the optimality gaps that capture the differences between the true optimum and the asymptotic optimum based on the QED approximations. Our bounds generalize earlier resul...

Several recent experiments have established by measuring the Mandel Q parameter that the number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to the Rydberg blockade that occurs due to the strong interatomic interactions between highly-excited atoms. Because of this blockade effect, the syst...

We consider an exploration algorithm where at each step, a random number of items become active while related items get explored. Given an initial number of items $N$ growing to infinity and building on a strong homogeneity assumption, we study using scaling limits of Markovian processes statistical properties of the proportion of active nodes in t...

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

We consider Markovian many-server systems with admission control operating in a QED regime, where the relative utilization approaches unity while the number of servers grows large, providing natural Economies-of-Scale. In order to determine the optimal admission control policy, we adopt a revenue maximization framework, and suppose that the revenue...

We identify a relation between the dynamics of ultracold Rydberg gases in which atoms experience a strong dipole blockade and spontaneous emission, and a stochastic process that models certain wireless random-access networks. We then transfer insights and techniques initially developed for these wireless networks to the realm of Rydberg gases, and...

We develop many-server asymptotics in the QED regime for models with admission control. The admission control, designed to reduce the incoming traffic in periods of congestion, scales with the size of the system. For a class of Markovian models with this scaled control, we identify the QED limits for two stationary performance measures. We also der...

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 a product-form network and a set of configurable parameters, we identify which performance measures can be controlled and which target values can be attained. We also discuss an onl...

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 a product-form network and a set of configurable parameters, we identify which performance measures can be controlled and which target values can be attained. We also discuss an onl...

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

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