Results for "Loukas P. Petrou"
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Metric Map Merging using RFID Tags & Topological InformationNov 17 2017A map merging component is crucial for the proper functionality of a multi-robot system performing exploration, since it provides the means to integrate and distribute the most important information carried by the agents: the explored-covered space and ... More Optical control of carrier wavefunction in magnetic quantum dotsJan 16 2018Spatially indirect Type-II band alignment in magnetically-doped quantum dot (QD) structures provides unexplored opportunities to control the magnetic interaction between carrier wavefunction in the QD and magnetic impurities. Unlike the extensively studied, ... More Formal Verification of a Programmable HypersurfaceJul 17 2018A metasurface is a surface that consists of artificial material, called metamaterial, with configurable electromagnetic properties. This paper presents work in progress on the design and formal verification of a programmable metasurface, the Hypersurface, ... More Fault Adaptive Routing in Metasurface Controller NetworksOct 15 2018HyperSurfaces are a merge of structurally reconfigurable metasurfaces whose electromagnetic properties can be changed via a software interface, using an embedded miniaturized network of controllers, thus enabling novel capabilities in wireless communications. ... More Graph reduction with spectral and cut guaranteesAug 31 2018Dec 29 2018Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity measure used ... More Towards Federated Learning at Scale: System DesignFeb 04 2019Mar 22 2019Federated Learning is a distributed machine learning approach which enables model training on a large corpus of decentralized data. We have built a scalable production system for Federated Learning in the domain of mobile devices, based on TensorFlow. ... More Frequency Analysis of Temporal Graph SignalsFeb 14 2016This letter extends the concept of graph-frequency to graph signals that evolve with time. Our goal is to generalize and, in fact, unify the familiar concepts from time- and graph-frequency analysis. To this end, we study a joint temporal and graph Fourier ... More Stationary time-vertex signal processingNov 01 2016The goal of this paper is to improve learning for multivariate processes whose structure is dependent on some known graph topology. Typically, the graph information is incorporated to the learning process via a smoothness assumption postulating that the ... More Particle Acceleration in Multiple Dissipation RegionsFeb 25 2004The sharp magnetic discontinuities which naturally appear in solar magnetic flux tubes driven by turbulent photospheric motions are associated with intense currents. \citet{Par83} proposed that these currents can become unstable to a variety of microscopic ... More Spectrally approximating large graphs with smaller graphsFeb 21 2018How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard ... More Predicting the evolution of stationary graph signalsJul 12 2016An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have been successful ... More The Marcinkiewicz multiplier condition for bilinear operatorsOct 08 2000This article is concerned with the question of whether Marcinkiewicz multipliers on $\mathbb R^{2n}$ give rise to bilinear multipliers on $\mathbb R^n\times \mathbb R^n$. We show that this is not always the case. Moreover we find necessary and sufficient ... More The Kato-Ponce InequalityMar 21 2013In this article we develop a simplistic approach to revisit the classical Kato-Ponce inequality, which is also known as 'fractional Leibniz rule.' As a consequence, we derive the validity of this inequality even in quasi-Banach spaces $L^p$ for $p<1$ ... More Approximating Spectral Clustering via Sampling: a ReviewJan 29 2019Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of these algorithms' ... More On Fourier transforms of radial functions and distributionsDec 22 2011Feb 18 2013We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier transform of any radial ... More Multilinear interpolation between adjoint operatorsNov 12 2001Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies ... More A Note on Fault Tolerant Reachability for Directed GraphsNov 24 2015In this note we describe an application of low-high orders in fault-tolerant network design. Baswana et al. [DISC 2015] study the following reachability problem. We are given a flow graph $G = (V, A)$ with start vertex $s$, and a spanning tree $T =(V, ... More Dominator Tree Certification and Independent Spanning TreesOct 31 2012Mar 07 2013How does one verify that the output of a complicated program is correct? One can formally prove that the program is correct, but this may be beyond the power of existing methods. Alternatively one can check that the output produced for a particular input ... More Extrapolating paths with graph neural networksMar 18 2019We consider the problem of path inference: given a path prefix, i.e., a partially observed sequence of nodes in a graph, we want to predict which nodes are in the missing suffix. In particular, we focus on natural paths occurring as a by-product of the ... More Simplified Models for Dark Matter Searches at the LHCJun 09 2015Mar 23 2016This document outlines a set of simplified models for dark matter and its interactions with Standard Model particles. It is intended to summarize the main characteristics that these simplified models have when applied to dark matter searches at the LHC, ... More On maximal functions for Mikhlin-Hoermander multipliersJan 08 2005Given Mikhlin-H\"ormander multipliers $m_i$, $i=1,..., N$, with uniform estimates we prove an optimal $\sqrt{\log(N+1)}$ bound in $L^p$ for the maximal function $\sup_i|\cF^{-1}[m_i\hat f]|$ and related bounds for maximal functions generated by dilations. ... More Join-Reachability Problems in Directed GraphsDec 22 2010For a given collection G of directed graphs we define the join-reachability graph of G, denoted by J(G), as the directed graph that, for any pair of vertices a and b, contains a path from a to b if and only if such a path exists in all graphs of G. Our ... More Incremental $2$-Edge-Connectivity in Directed GraphsJul 24 2016In this paper, we initiate the study of the dynamic maintenance of $2$-edge-connectivity relationships in directed graphs. We present an algorithm that can update the $2$-edge-connected blocks of a directed graph with $n$ vertices through a sequence of ... More Analytical Model of Spin-Polarized Semiconductor LasersJun 25 2008We formulate an analytical model for vertical-cavity surface-emitting lasers (VCSELs) with injection (pump) of spin-polarized electrons. Our results for two different modes of carrier recombination allow for a systematic analysis of the operational regimes ... More Impulsive electron acceleration by Gravitational WavesDec 05 2003We investigate the non-linear interaction of a strong Gravitational Wave with the plasma during the collapse of a massive magnetized star to form a black hole, or during the merging of neutron star binaries (central engine). We found that under certain ... More L^p bounds for a maximal dyadic sum operatorDec 11 2002We prove $L^p$ bounds in the range $1<p<\infty$ for a maximal dyadic sum operator on $\rn$. This maximal operator provides a discrete multidimensional model of Carleson's operator. Its boundedness is obtained by a simple twist of the proof of Carleson's ... More On the norm of the operator $aI+bH$ on $L^p(\mathbb R)$Feb 16 2017Mar 12 2018We provide a direct proof of the following theorem of Kalton, Hollenbeck, and Verbitsky \cite{HKV}: let $H$ be the Hilbert transform and let $a,b$ be real constants. Then for $1<p<\infty$ the norm of the operator $aI+bH$ from $L^p(\mathbb R)$ to $L^p(\mathbb ... More Certain Multi(sub)linear square functionsApr 14 2015Let $d\ge 1, \ell\in\Z^d$, $m\in \mathbb Z^+$ and $\theta_i$, $i=1,\dots,m $ are fixed, distinct and nonzero real numbers. We show that the $m$-(sub)linear version below of the Ratnakumar and Shrivastava \cite{RS1} Littlewood-Paley square function $$T(f_1,\dots ... More The Fourier transform of multiradial functionsJul 31 2013We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\Phi(x)=\phi(|x_1|, \dots, |x_m|)$, $x_i\in \mathbf R^{n_i}$, in terms of the Fourier transform of the function $\phi$ on $\mathbf R^{r_1}\times ... More Fractional Transport in Strongly Turbulent PlasmasJul 05 2017We analyze statistically the energization of particles in a large scale environment of strong turbulence that is fragmented into a large number of distributed current filaments. The turbulent environment is generated through strongly perturbed, 3D, resistive ... More A remark on an endpoint Kato-Ponce inequalityNov 18 2013This note introduces bilinear estimates intended as a step towards an $L^\infty$-endpoint Kato-Ponce inequality. In particular, a bilinear version of the classical Gagliardo-Nirenberg interpolation inequalities for a product of functions is proved. Rough Bilinear Singular IntegralsSep 21 2015Sep 22 2015We study the rough bilinear singular integral, introduced by Coifman and Meyer , $$ T_\Omega(f,g)(x)=p.v. \! \int_{\mathbb R^{n}}\! \int_{\mathbb R^{n}}\! |(y,z)|^{-2n} \Omega((y,z)/|(y,z)|)f(x-y)g(x-z) dydz, $$ when $\Omega $ is a function in $L^q(\mathbb ... More Waves and instabilities in an anisotropic universeOct 19 2001The excitation of low frequency plasma waves in an expanding anisotropic cosmological model which contains a magnetic field frozen into the matter and pointing in the longitudinal direction is discussed. Using the exact equations governing finite-amplitude ... More Fast Approximate Spectral Clustering for Dynamic NetworksJun 12 2017Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a ... More Particle Acceleration and Heating by Turbulent ReconnectionApr 18 2016Jul 21 2016Turbulent flows in the solar wind, large scale current sheets, multiple current sheets, and shock waves lead to the formation of environments in which a dense network of current sheets is established and sustains "turbulent reconnection". We constructed ... More 2-Edge Connectivity in Directed GraphsJul 11 2014Jul 31 2014Edge and vertex connectivity are fundamental concepts in graph theory. While they have been thoroughly studied in the case of undirected graphs, surprisingly not much has been investigated for directed graphs. In this paper we study $2$-edge connectivity ... More Compensating strong coupling with large chargeOct 14 2016Oct 25 2016We study some (conformal) field theories with global symmetries in the sector where the value of the global charge $Q$ is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone's theorem ... More Online Balanced RepartitioningNov 06 2015Jul 18 2016This paper initiates the study of deterministic algorithms for collocating frequently communicating nodes in a distributed networked systems in an online fashion. In particular, we introduce the Balanced RePartitioning (BRP) problem: Given an arbitrary ... More Spinner: Scalable Graph Partitioning in the CloudApr 15 2014Feb 02 2015Several organizations, like social networks, store and routinely analyze large graphs as part of their daily operation. Such graphs are typically distributed across multiple servers, and graph partitioning is critical for efficient graph management. Existing ... More Forecasting Time Series with VARMA Recursions on GraphsOct 19 2018Graph-based techniques emerged as a choice to deal with the dimensionality issues in modeling multivariate time series. However, there is yet no complete understanding of how the underlying structure could be exploited to ease this task. This work provides ... More The multilinear strong maximal functionFeb 06 2010Mar 08 2011A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this ... More Anomalous biased diffusion in networksAug 01 2013We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the packet/particle to travel ... More 2-Vertex Connectivity in Directed GraphsSep 22 2014Feb 19 2015We complement our study of 2-connectivity in directed graphs, by considering the computation of the following 2-vertex-connectivity relations: We say that two vertices v and w are 2-vertex-connected if there are two internally vertex-disjoint paths from ... More Conditions for Boundedness into Hardy spacesFeb 08 2017We obtain boundedness from a product of Lebesgue or Hardy spaces into Hardy spaces under suitable cancellation conditions for a large class of multilinear operators that includes the Coifman-Meyer class, sums of products of linear Calderon-Zygmund operators ... More Multilinear Multiplier Theorems and ApplicationsNov 25 2015Dec 16 2016We obtain new multilinear multiplier theorems for symbols of restricted smoothness which lie locally in certain Sobolev spaces. We provide applications concerning the boundedness of the commutators of Calder\'on and Calder\'on-Coifman-Journ\'e. Statistical Properties of Dissipative MHD AcceleratorsMar 07 2005We use exact orbit integration to investigate particle acceleration in a Gauss field proxy of magnetohydrodynamic (MHD) turbulence. Regions where the electric current exceeds a critical threshold are declared to be `dissipative' and endowed with super-Dreicer ... More Autoregressive Moving Average Graph FilteringFeb 14 2016Sep 21 2016One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We ... More The bilinear Bochner-Riesz problemDec 17 2012Apr 03 2013Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers $(1-|\xi|^2-|\eta|^2)^\delta_+$ and we make some advances in this investigation. We obtain an optimal result ... More The Hörmander multiplier theorem I: The Linear CaseJul 09 2016We discuss $L^p(\mathbb R^n)$ boundedness for Fourier multiplier operators that satisfy the hypotheses of the H\"ormander multiplier theorem in terms of an optimal condition that relates the distance $|\frac 1p-\frac12|$ to the smoothness $s$ of the associated ... More Multilinear generalized Radon transforms and point configurationsApr 19 2012Aug 19 2013We study multilinear generalized Radon transforms using a graph-theoretic paradigm that includes the widely studied linear case. These provide a general mechanism to study Falconer-type problems involving $(k+1)$-point configurations in geometric measure ... More High-dimensional approximate $r$-netsJul 16 2016The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean distance. For ... More Normal and Anomalous Diffusion: A TutorialMay 05 2008The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is made clear. ... More Multicommutators and Multiplier TheoremsNov 25 2015May 12 2016For all $k,n\in \mathbb N$, we obtain the boundedness of the $n$th dimensional Calder\'on-Coifman-Journ\'e-type multicommutator $\mathscr{C}_k^{(n)}(f,a_1,\dots, a_k)(x),$ given by \[\mathrm{p.v.}\int_{\mathbb R^{nk}} \!\! f(x-y_1-\cdots -y_k) \! \bigg(\! ... More High-dimensional approximate $r$-netsJul 16 2016May 06 2017The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean distance. For ... More Towards Communication-Aware Robust TopologiesMay 19 2017We currently witness the emergence of interesting new network topologies optimized towards the traffic matrices they serve, such as demand-aware datacenter interconnects (e.g., ProjecToR) and demand-aware overlay networks (e.g., SplayNets). This paper ... More Non-supersymmetric heterotic model buildingJul 23 2014Oct 17 2014We investigate orbifold and smooth Calabi-Yau compactifications of the non-supersymmetric heterotic SO(16)xSO(16) string. We focus on such Calabi-Yau backgrounds in order to recycle commonly employed techniques, like index theorems and cohomology theory, ... More Towards stationary time-vertex signal processingJun 22 2016Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods ... More Compensating strong coupling with large chargeOct 14 2016We study (conformal) field theories with global symmetries in the sector where the value of the global charge $Q$ is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone's theorem in ... More An Experimental Study of Dynamic DominatorsApr 10 2016Motivated by recent applications of dominator computations, we consider the problem of dynamically maintaining the dominators of flow graphs through a sequence of insertions and deletions of edges. Our main theoretical contribution is a simple incremental ... More Repair Strategies for Storage on Mobile CloudsMar 01 2017We study the data reliability problem for a community of devices forming a mobile cloud storage system. We consider the application of regenerating codes for file maintenance within a geographically-limited area. Such codes require lower bandwidth to ... More Sources of Solar Energetic ParticlesMar 19 2019Solar Energetic Particles (SEP) are an integral part of the physical processes related with Space Weather. We present a review for the acceleration mechanisms related to the explosive phenomena (flares and/or CMEs) inside the solar corona. For more than ... More Finding Dominators via Disjoint Set UnionOct 08 2013The problem of finding dominators in a directed graph has many important applications, notably in global optimization of computer code. Although linear and near-linear-time algorithms exist, they use sophisticated data structures. We develop an algorithm ... More