In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The can be due problems the acquisition process or because user manually identified unwanted outliers. Our works even with a small amount samples and it propagate structure fill larger regions. methodology is built on recent studies about matrix completion using trace norm. contribution our paper extend case tensor by proposing first definition norm for then building working algorithm. First, that...

A distributed algorithm is described for solving a linear algebraic equation of the form Ax = b assuming has at least one solution. The simultaneously solved by m agents each agent knows only subset rows partitioned matrix [A b], current estimates equation's solution generated its neighbors, and nothing more. Each recursively updates estimate utilizing neighbors. Neighbor relations are characterized time-dependent directed graph N(t) whose vertices correspond to arcs depict neighbor...

Advances in wired and wireless technology have necessitated the development of theory, models, tools to cope with new challenges posed by large-scale control optimization problems over networks. The classical methodology works under premise that all problem data are available a central entity (a computing agent or node). However, this does not apply large networked systems, where each (node) network typically has access only its private local information view structure. This review surveys...

Abstract Open physical systems with balanced loss and gain, described by non-Hermitian parity-time $$\left( {{\cal P}{\cal T}} \right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow time, thus spontaneously breaks the $${\cal T}$$ -symmetry. Such -symmetry-breaking...

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task formulation, in which are induced by cardinality regularization term constraint, respectively. This formulation non-convex; we convert it into its convex surrogate, can be routinely solved via semidefinite programming for small-size problems. propose to employ general projected gradient scheme efficiently solve such surrogate; however, optimization...

Thyroid ultrasonography is a widely used clinical technique for nodule diagnosis in thyroid regions. However, it remains difficult to detect and recognize the nodules due low contrast, high noise, diverse appearance of nodules. In today's practice, senior doctors could pinpoint by analyzing global context features, local geometry structure, intensity changes, which would require rich experience accumulated from hundreds thousands case studies. To alleviate doctors' tremendous labor...

For the purposes of this paper, “gossiping” is a distributed process whose purpose to enable members group autonomous agents asymptotically determine, in decentralized manner, average initial values their scalar gossip variables. This paper discusses several different deterministic protocols for gossiping which avoid deadlocks and achieve consensus under assumptions. First considered <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML"...

This paper considers the discrete-time version of Altafini's model for opinion dynamics in which interaction among a group agents is described by time-varying signed digraph. Prompted an idea from [3], exponential convergence system studied using graphical approach. Necessary and sufficient conditions with respect to each possible type limit states are provided. Specifically, under assumption repeatedly jointly strong connectivity, it shown that 1) certain two-clustering will be reached...

This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over network consisting of multiple groups individuals. Limiting behaviors the are characterized by analyzing equilibria system and their stability. Specifically, when possibly different directed infection graphs, may have following: first, unique equilibrium, healthy state, is globally stable, implying that both will eventually be eradicated, second, including state dominant virus almost...

In this paper we propose an algorithm to estimate missing values in tensors of visual data. The can be due problems the acquisition process, or because user manually identified unwanted outliers. Our works even with a small amount samples and it propagate structure fill larger regions. methodology is built on recent studies about matrix completion using trace norm. contribution our extend case tensor by laying out theoretical foundations then building working algorithm. First, definition for...

Two asynchronous distributed algorithms are presented for solving a linear equation of the form Ax=b with at least one solution. The is simultaneously and asynchronously solved by m agents assuming that each agent knows only subset rows partitioned matrix [A\ \ b], estimates equation's solution generated its neighbors, nothing more. Neighbor relationships characterized time-dependent directed graph whose vertices correspond to arcs depict neighbor relationships. Each recursively updates...

The recently proposed DeGroot-Friedkin model describes the dynamical evolution of individual social power in a network that holds opinion discussions on sequence different issues. This paper revisits model, and uses nonlinear contraction analysis, among other tools, to establish several novel results. First, we show for with constant topology, each individual's converges its equilibrium value exponentially fast, whereas previous results only concluded asymptotic convergence. Second, when...

This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze behavior dynamic. As result, new convergence rate results obtained that capture graph structure in novel way. In particular, exponential is established with exponent order $1-O(1/(m\log_{2}m))$ special tree-like regular graphs. Also, over time-varying graphs, which...

Models of spreading processes over nontrivial networks are commonly motivated by modeling and analysis biological networks, computer human contact networks. However, learning the spread parameters such models has not yet been explored in detail, have validated real data. In this paper, we present several different from literature explore their relationships to each other; for one these processes, a sufficient condition asymptotic stability healthy equilibrium, show that is necessary...

Distributed averaging (also known as average consensus) is an algorithm that builds on neighbor to interactions with the ultimate goal of convergence all initial node values or some value close average. We analyze in this paper performance distributed algorithms where information exchanged between neighboring agents subject deterministic uniform quantization (i.e., real sent by nodes their neighbors are truncated). With such quantization, precise cannot be achieved general, but would it,...

We propose a mathematical model to study coupled epidemic and opinion dynamics in network of communities. Our captures SIS dynamics, whose evolution is dependent on the opinions communities toward epidemic, vice versa. In particular, we allow both cooperative antagonistic interactions, representing similar opposing perspectives severity respectively. an opinion-dependent reproduction number characterize mutual influence between spreading dissemination over networks. Through stability...

Quantum networks are considered as a promising future platform for quantum information exchange and applications, which have capabilities far beyond the traditional communication networks. Remote entanglement is an essential component of network. How to efficiently design multi-routing protocol fundamental yet challenging problem. In this paper, we study routing problem simultaneously maximize number quantum-user pairs their expected throughput. Our approach formulate two sequential integer...

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task formulation, in which are induced by cardinality regularization term constraint, respectively. This formulation non-convex; we convert it into its convex surrogate, can be routinely solved via semidefinite programming for small-size problems. propose to employ general projected gradient scheme efficiently solve such surrogate; however, optimization...

Consider a network whose nodes have some initial values, and it is desired to design an algorithm that builds on neighbor interactions with the ultimate goal of convergence average all node values or value close average. Such called generically "distributed averaging", our in this paper study performance subclass distributed averaging algorithms where information exchange between neighboring (agents) subject deterministic uniform quantization. With such quantization, precise cannot be...

Starcraft II (SC2) is widely considered as the most challenging Real Time Strategy (RTS) game. The underlying challenges include a large observation space, huge (continuous and infinite) action partial observations, simultaneous move for all players, long horizon delayed rewards local decisions. To push frontier of AI research, Deepmind Blizzard jointly developed StarCraft Learning Environment (SC2LE) testbench complex decision making systems. SC2LE provides few mini games such MoveToBeacon,...

Initializing an effective dictionary is indispensable step for sparse representation. In this paper, we focus on the selection problem with objective to select a compact subset of basis from original training data instead learning new matrix as models do. We first design model via l2,0 norm. For optimization, propose two methods: one standard forward-backward greedy algorithm, which not suitable large-scale problems; other based gradient cues at each forward iteration and speeds up process...