We address the consensus-based distributed linear filtering problem, where a discrete time, linear stochastic process is observed by a network of sensors. We assume that the consensus weights are known and we first provide sufficient conditions under which the stochastic process is detectable, i.e. for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors (without noise) is asymptotically stable. Next, we develop a distributed, sub-optimal filtering scheme based on minimizing an upper bound on a quadratic filtering cost. In the stationary case, we provide sufficient conditions under which this scheme converges; conditions expressed in terms of the convergence properties of a set of coupled Riccati equations.

Abstract-We investigate collaborative optimization of an objective function expressed as a sum of local convex functions, when the agents make decisions in a distributed manner using local information, while the communication topology used to exchange messages and information is modeled by a graph-valued random process, assumed independent and identically distributed. Specifically, we study the performance of the consensus-based multi-agent distributed subgradient method and show how it depends on the probability distribution of the random graph. For the case of a constant stepsize, we first give an upper bound on the difference between the objective function, evaluated at the agents' estimates of the optimal decision vector, and the optimal value. Second, for a particular class of convex functions, we give an upper bound on the distances between the agents' estimates of the optimal decision vector and the minimizer. In addition, we provide the rate of convergence to zero of the time varying component of the aforementioned upper bound. The addressed metrics are evaluated via their expected values. As an application, we show how the distributed optimization algorithm can be used to perform collaborative system identification and provide numerical experiments under the randomized and broadcast gossip protocols.

The authors investigate the ion conduction of molecular beam epitaxy grown CaF2∕BaF2 multilayers perpendicular to the interfaces. Unlike previous measurements along the heterostructure boundaries, the more resistive contributions dominate here; the detailed analysis allows for a complementary insight into the charge carrier distribution. The features of perpendicular conductivites in both semi-infinite and mesoscopic situations can be qualitatively as well as quantitatively explained by the same defect chemical model used for parallel ion conduction. The authors can distinguish three different size regimes. For large interfacial spacings (ℓ>50nm), the conduction is dominated by bulk parts of the CaF2 layers, showing only a slight increase with decreasing layer thickness. For very small spacings, i.e., ℓ<30nm, the conductivity increases steeply and tends toward a saturation value, corresponding to the space charge overlap situation with the overall value that can be attributed to Fi′ accumulated in CaF2. The intermediate range (30nm<ℓ<50nm) is characterized by markedly lower activation energies in which the transition from Fi′ (depleted near the interface) to VF• (enriched near the interface) in BaF2 plays a significant role.

We describe the development of an algorithm for the automatic classification of heart sound phonocardiogram waveforms as normal, abnormal or uncertain. Our approach consists of three major components: 1) Heart sound segmentation, 2) Transformation of one-dimensional waveforms into two-dimensional timefrequency heat map representations using Mel-frequency cepstral coefficients and 3) Classification of MFCC heat maps using deep convolutional neural networks. We applied the above approach to produce submissions for the 2016 PhysioNet Computing in Cardiology Challenge. We present results from the challenge, as well as describe in detail the resulting neural network architecture produced and design decisions made. IntroductionThe goal of the 2016 PhysioNet Computing in Cardiology Challenge was to accurately classify normal and abnormal heart sounds from phonocardiogram (PCG) waveforms. A particular aim was to identify from a single short recording whether a subject should be referred on for expert diagnosis. Accurate and robust algorithms were required that could deal with heart sounds that exhibit very poor signal quality.The challenge training set consisted of 3,240 heart sound recordings, lasting from 5 seconds to just over 120 seconds. Recordings were collected from nine different locations on the body (including aortic area, pulmonic area, tricuspid area and mitral area, among others). Recordings from healthy subjects were labeled as normal. Recordings from subjects with a confirmed cardiac diagnosis were labeled as abnormal. Abnormal recordings were collected from patients who suffered from a variety of illnesses, including heart valve defects (mitral valve prolapse, mitral regurgitation, aortic stenosis, valvular surgery) and coronary artery disease. An in depth description of the challenge and the dataset is provided in [1], as well as a thorough review of the field of cardiac auscultation.We present an algorithm that computes heat maps of the time-frequency distribution of signal energy and uses a deep convolutional neural network to automatically classify normal versus abnormal heart sound recordings. Logistic regression hidden semi-Markov model-based heart sound segmentation is first performed on the PCG waveform. Spectrograms (energy maps) consisting of 6 cepstral coefficients that capture Mel-frequencies varying over time are derived for overlapping sliding windows of threesecond duration, beginning at the first heart sound, S 1 . A deep convolutional neural network consisting of two alternating convolution and max pooling layers is trained to perform automatic feature extraction. A final multilayer perceptron, consisting of two fully connected layers, distinguishes between normal and abnormal spectrograms. Heart sound recordings of variable length are dealt with by computing an ensemble of logit scores for all overlapping three-second segments contained within a recording and maximizing the average scores computed for all classes. ApproachOur approach consists of three major components: 1. Segme...

Abstract. This paper discusses the linear asymptotic consensus problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. The switching is determined by a finite state Markov process, each topology corresponding to a state of the process. We address the cases where the dynamics of the agents is expressed both in continuous time and in discrete time. We show that, if the consensus matrices are doubly stochastic, average consensus is achieved in the mean square sense and the almost sure sense if and only if the graph resulting from the union of graphs corresponding to the states of the Markov process is strongly connected. The aim of this paper is to show how techniques from the theory of Markovian jump linear systems, in conjunction with results inspired by matrix and graph theory, can be used to prove convergence results for stochastic consensus problems. 1. Introduction. A consensus problem consists of a group of dynamic agents that seek to agree upon certain quantities of interest by exchanging information according to a set of rules. This problem can model many phenomena involving information exchange between agents such as cooperative control of vehicles, formation control, flocking, synchronization, and parallel computing. Distributed computation over networks has a long history in control theory starting with the work of Borkar and Varaiya [1] and Tsitsiklis, Bertsekas, and Athans (see [22,23]) on asynchronous agreement problems and parallel computing. A theoretical framework for solving consensus problems was introduced by Olfati-Saber and Murray [16,17], while Jadbabaie, Lin, and Morse studied alignment problems [7] for reaching an agreement. Relevant extensions of the consensus problem were done by Ren and Beard [19], by Moreau [11], and, more recently, by Nedic and Ozdaglar (see [12,14]).Typically agents are connected via a network that changes with time due to link failures, packet drops, node failure, etc. Such variations in topology can happen randomly, which motivates the investigation of consensus problems under a stochastic framework. Hatano and Mesbahi consider in [6] an agreement problem over random information networks, where the existence of an information channel between a pair of elements at each time instance is probabilistic and independent of other channels. In [18], Porfiri and Stilwell provide sufficient conditions for reaching consensus almost surely in the case of a discrete linear system, where the communication flow is given by a directed graph derived from a random graph process, independent of other time instances. Under a similar communication topology model, Tahbaz-Salehi and Jadbabaie give necessary and sufficient conditions for almost sure convergence to

Abstract-In this paper we discuss the consensus problem for a network of dynamic agents with undirected information flow and random switching topologies. The switching is determined by a Markov chain, each topology corresponding to a state of the Markov chain. We show that in order to achieve consensus almost surely and from any initial state the sets of graphs corresponding to the closed positive recurrent sets of the Markov chain must be jointly connected. The analysis relies on tools from matrix theory, Markovian jump linear systems theory and random processes theory. The distinctive feature of this work is addressing the consensus problem with "Markovian switching" topologies.

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