In a sensor network governed by a linear dynamical system, often due to practical constraints such as computational and power limitations, it is desired to select a small subset to perform the state estimation task. In this paper, we formulate this task as the combinatorial problem of maximizing a monotone set function under a uniform matroid constraint. By introducing the notion of curvature we show that the proposed objective function is weak submodular under certain conditions by establishing an upperbound on its maximum element-wise curvature. To efficiently solve the proposed combinatorial problem, we develop a randomized greedy algorithm that is significantly faster than state-of-the-art methods. we analyze the performance of the proposed algorithm and establish performance guarantees on the mean square error (MSE) of the linear estimator that uses the selected sensors in terms of the optimal MSE. Extensive simulation results demonstrate efficacy of the randomized greedy algorithm in a comparison with greedy and semidefinite programming relaxation methods.
Inflammation has been linked to various steps in tumorigenesis. Interleukin (IL)-6 and IL-18 are two inflammatory cytokines whose serum concentrations are elevated in several types of cancer, including head and neck squamous cell carcinoma (HNSCC) in some studies. This study was designed to analyze the serum concentrations of these cytokines in Iranian HNSCC patients. Serum IL-6 and IL-18 concentrations were assayed by ELISA commercial kits in 65 untreated patients and 20 healthy volunteers. Serum IL-6 concentration was significantly increased in patients compared to healthy individuals (p < 0.000). IL-6 concentration increased as the tumor stage progressed, and a significant difference appeared between stage IV vs. stage I/II/III (p = 0.03) disease. Although serum IL-18 concentration was higher in patients than in healthy individuals, the difference was not statistically significant (p = 0.06). Moreover, there was no association between serum IL-18 concentration and tumor stage (p = 0.47). A significant difference was observed in serum IL-18 concentration according to the gender with higher IL-18 concentration in male patients (p = 0.01). In conclusion, serum concentration of IL-6 might correlate with the stage of tumor progression in Iranian HNSCC patients. Further studies with larger numbers of patients are required to exclude the possible minor correlation of serum IL-18 concentration with tumor stage.
We study the problem of estimating a random process from the observations collected by a network of sensors that operate under resource constraints. When the dynamics of the process and sensor observations are described by a state-space model and the resource are unlimited, the conventional Kalman filter provides the minimum mean-square error (MMSE) estimates. However, at any given time, restrictions on the available communications bandwidth and computational capabilities and/or power impose a limitation on the number of network nodes whose observations can be used to compute the estimates. We formulate the problem of selecting the most informative subset of the sensors as a combinatorial problem of maximizing a monotone set function under a uniform matroid constraint. For the MMSE estimation criterion we show that the maximum element-wise curvature of the objective function satisfies a certain upper-bound constraint and is, therefore, weak submodular. We develop an efficient randomized greedy algorithm for sensor selection and establish guarantees on the estimator's performance in this setting. Extensive simulation results demonstrate the efficacy of the randomized greedy algorithm compared to state-of-the-art greedy and semidefinite programming relaxation methods. Index Terms sensor selection, sensor networks, Kalman filtering, weak submodularity I. INTRODUCTION M ODERN sensor networks deploy a large number of nodes that either exchange their noisy and possibly processed observations of a random process or forward those observations to a data fusion center. Due to constraints on computation, power and communication resources, instead of estimating the process using information collected by the entire network, the fusion center typically queries a relatively small subset of the available sensors. The problem of selecting the sensors that would acquire the most informative observations arises in a number of applications in control and signal processing systems including sensor selection for Kalman filtering [2]-[4], batch state and stochastic process estimation [5], [6], minimal actuator placement [7], [8], voltage control and meter Abolfazl Hashemi and Haris Vikalo are with the
Automatic synthesis from linear temporal logic (LTL) specifications is widely used in robotic motion planning, control of autonomous systems, and load distribution in power networks. A common specification pattern in such applications consists of an LTL formula describing the requirements on the behaviour of the system, together with a set of additional desirable properties. We study the synthesis problem in settings where the overall specification is unrealizable, more precisely, when some of the desirable properties have to be (temporarily) violated in order to satisfy the system's objective. We provide a quantitative semantics of sets of safety specifications, and use it to formalize the "besteffort" satisfaction of such soft specifications while satisfying the hard LTL specification. We propose an algorithm for synthesizing implementations that are optimal with respect to this quantitative semantics. Our method builds upon the idea of the bounded synthesis approach, and we develop a MaxSAT encoding which allows for maximizing the quantitative satisfaction of the safety specifications. We evaluate our algorithm on scenarios from robotics and power distribution networks.
We study the problem of selecting most informative subset of a large observation set to enable accurate estimation of unknown parameters. This problem arises in a variety of settings in machine learning and signal processing including feature selection, phase retrieval, and target localization. Since for quadratic measurement models the moment matrix of the optimal estimator is generally unknown, majority of prior work resorts to approximation techniques such as linearization of the observation model to optimize the alphabetical optimality criteria of an approximate moment matrix. Conversely, by exploiting a connection to the classical Van Trees' inequality, we derive new alphabetical optimality criteria without distorting the relational structure of the observation model. We further show that under certain conditions on parameters of the problem these optimality criteria are monotone and (weak) submodular set functions. These results enable us to develop an efficient greedy observation selection algorithm uniquely tailored for quadratic models, and provide theoretical bounds on its achievable utility.
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