Electrical Engineering

In this paper, we re-examine the recently proposed distributed state estimators based on quantized innovations. It is widely believed that the error covariance of the Quantized Innovation Kalman filter [1,2] follows a modified Riccati recursion. We present stable linear dynamical systems for which this is violated and the filter diverges. We propose a Particle Filter that approximates the optimal nonlinear filter and observe that the error covariance of the Particle Filter follows the modified Riccati recursion of [1,2]. We also simulate a Posterior Cramer-Rao bound (PCRB) for this filtering problem.

We study the problem of optimal estimation using quantized innovations, with application to distributed estimation over sensor networks. We show that the state probability density conditioned on the quantized innovations can be expressed as the sum of a Gaussian random vector and a certain truncated Gaussian vector. This structure bears close resemblance to the full information Kalman filter and so allows us to effectively combine the Kalman structure with a particle filter to recursively compute the state estimate. We call the resuting filter the Kalman like particle filter (KLPF) and observe that it delivers close to optimal performance using far fewer particles than that of a particle filter directly applied to the original problem. We also note that the conditional state density follows a, so called, generalized closed skew-normal (GCSN) distribution.

This paper describes an extension to stochastic Kronecker graphs that provides the special structure required for searchability, by defining a ``distance''-dependent Kronecker operator. We show how this extension of Kronecker graphs can generate several existing social network models, such as the Watts-Strogatz small-world model and Kleinberg's lattice-based model. We focus on a specific example of an expanding hypercube, reminiscent of recently proposed social network models based on a hidden hyperbolic metric space, and prove that a greedy forwarding algorithm can find very short paths of length O((loglog(n))^2) for graphs with n nodes.

A state-feedback controller was designed to mimic the Starling response of the heart in a mock circulatory system (MCS). Reference volume trajectory of the mock ventricle was determined by the maximum ventricular elastance (Emax), end-systolic ventricular pressure, and left atrial pressure. The controller drives a voice coil actuator (VCA) to follow the reference volume, and thus generate the desired chamber pressure, by using position and speed feedbacks. The nonlinear load applied to the VCA was compensated for by using the chamber pressure measurement to improve the controller response. The controller was tested in computer simulation by changing the load conditions and Emax of the MCS. The MCS along with the controller was able to reproduce human heart function from healthy to sick conditions. This control algorithm will be implemented in digital signal processor to control the MCS for left ventricular assist device testing.

In this paper, we study DFT bank transceivers with filter
length longer than the block size. Given a fixed transmit (or
receive) prototype filter, it has been shown recently that we
are able to design the receive (or correspondingly transmit)
prototype filter so that the signal to interference ratio (SIR)
is maximized for multipath fading channels. However only
the transmit (or receive) filters are guaranteed to have good
stopband attenuation. In this paper, we propose an iterative
method that allow us to design channel-resilient DFT bank
transceivers where both the transmit and receive filters can
have good stopband attenuation. Moreover the proposed iterative
procedure can increase the SIR significantly.

Performing distributed consensus in a network has been an important research problem for several years, and is directly applicable to sensor networks, autonomous vehicle formation, etc. While there exists a wide variety of algorithms that can be proven to asymptotically reach consensus, in applications involving time-varying parameters and tracking, it is often crucial to reach consensus “as quickly as possible”. In [1] it has been shown that, with global knowledge of the network topology, it is possible to optimize the convergence time in distributed averaging algorithms via solving a semi-definite pro- gram (SDP) to obtain the optimal averaging weights. Unfortunately, in most applications, nodes do not have knowledge of the full network topology and cannot implement the required SDP in a distributed fashion. In this paper, we present a symmetric adaptive weight algorithm for distributed consensus averaging on bi-directional noiseless networks. The algorithm uses an LMS (Least Mean Squares) approach to adaptively update the edge weights used to calculate each node’s values. The derivation shows that global error can be minimized in a distributed fashion and that the resulting adaptive weights are symmetric—symmetry being critical for convergence to the true average. Simulations show that convergence time is nearly equal to that of a non-symmetric adaptive algorithm developed in [2], and significantly better than that of the non-adaptive Metropolis-Hastings algorithm. Most importantly, our symmetric adaptive algorithm converges to the sample mean, whereas the method of [2] converges to an arbitrary value and results in significant error.

This paper focuses on a generalization of stochastic Kronecker graphs, introducing a Kronecker-like operator and defining a family of generator matrices H dependent on distances between nodes in a specified graph embedding. We prove that any lattice-based network model with sufficiently small distance-dependent connection prob- ability will have a Poisson degree distribution and provide a general framework to prove searchability for such a net- work. Using this framework, we focus on a specific example of an expanding hypercube and discuss the similarities and differences of such a model with recently proposed network models based on a hidden metric space. We also prove that a greedy forwarding algorithm can find very short paths of length O((loglog n)^2) on the hypercube with n nodes, demonstrating that distance-dependent Kronecker graphs can generate searchable network models. EDICS: OTH- EMRG, SEN-APPL, SPC-APPL

In this paper we quantify the total cost of an epidemic spreading through a social network, accounting for both the immunization and disease costs. Previous research has typically focused on determining the optimal strategy to limit the lifetime of a disease, without considering the cost of such strategies. In the large graph limit, we calculate the exact expected disease cost for a general random graph, and we illustrate it for the specific example of an Erdos-Renyi network. We also give an upper bound on the expected disease cost for finite-size graphs. Finally, we study how to optimally perform a one-shot immunization to minimize the social cost of a disease, including both the cost of the disease and the cost of immunization.

Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In the these markets, externalities such as complementarities and peer effects severely complicate the preference ordering of each agent. Further, research has shown that externalities lead to serious problems for market stability and for developing efficient algorithms to find stable matchings.
In this paper we make the observation that peer effects are often the result of underlying social connections, and we explore a formulation of the many-to-one matching market where peer effects are derived from an underlying social net- work. Our model captures peer effects and complementarities using utility functions rather than traditional preference ordering. With this model and considering pairwise stability, we prove that stable matchings always exist and characterize the set of stable matchings in terms of social welfare. We also give distributed algorithms that are guaranteed to converge to a stable matching. To assess the competitive ratio of these algorithms and to more generally characterize the efficiency of matching markets with externalities, we prove general bounds on how far the welfare of the worst-case stable matching can be from the welfare of the optimal matching, and find that the structure of the social network (e.g. how well clustered the network is) plays a large role.

How the brain integrates signals from specific areas has been a longstanding critical question for neurobiologists. Two recent observations suggest a new approach to fMRI data analysis of this question. First, in many instances, the brain analyzes inputs by decomposing the information along several salient dimensions. For example, earlier work demonstrated that the brain splits a monetary gamble in terms of expected reward (ER) and variance of the reward (risk) [Preuschoff, K., Bossaerts, P., Quartz, S., 2006. Neural differentiation of expected reward and risk in human subcortical structures. Neuron 51, 381-390]. However, since ER and risk activate separate brain regions, the brain needs to integrate these activations to obtain an overall evaluation of the gamble. Second, recent evidence suggests that the correlation of the activity between neurons may serve a specific organizational purpose [Romo, R., Hernandez, A., Zainos, A., Salinas, E., 2003. Correlated neuronal discharges that increase coding efficiency during perceptual discrimination. Neuron 38, 649-657; Salinas, E., Sejnowski, T.J., 2001. Correlated neuronal activity and the flow of neural information. Nat. Rev. Neurosci. 2, 539]. Specifically, it is hypothesized that correlations allow brain regions to integrate several signals in a way that minimizes noise. Under this hypothesis, we show here that canonical correlation analysis of fMRI data identifies how the signals from several regions are combined. A general linear model then verifies whether the identified combination indeed activates a projection area in the brain. We illustrate the proposed procedure on data recorded while human subjects played a simple card game. We show that the brain adds the signals of ER and risk to form a measure that activates the medial prefrontal cortex, consistent with the role of this brain structure in the evaluation of monetary gambles.

Experimental evidence has consistently confirmed the ability of uninformed traders, even novices, to infer information from the trading process. After contrasting brain activation in subjects watching markets with and without insiders, we hypothesize that Theory of Mind (ToM) helps explain this pattern, where ToM refers to the human capacity to discern malicious or benevolent intent. We find that skill in predicting price changes in markets with insiders correlates with scores on two ToM tests. We document GARCH-like persistence in transaction price changes that may help investors read markets when there are insiders.