Distributed Local Linear Parameter Estimation using Gaussian SPAWN

We consider the problem of estimating local sensor parameters, where the local parameters and sensor observations are related through linear stochastic models. Sensors exchange messages and cooperate with each other to estimate their own local parameters iteratively. We study the Gaussian Sum-Product Algorithm over a Wireless Network (gSPAWN) procedure, which is based on belief propagation, but uses fixed size broadcast messages at each sensor instead. Compared with the popular diffusion strategies for performing network parameter estimation, whose communication cost at each sensor increases with increasing network density, the gSPAWN algorithm allows sensors to broadcast a message whose size does not depend on the network size or density, making it more suitable for applications in wireless sensor networks. We show that the gSPAWN algorithm converges in mean and has mean-square stability under some technical sufficient conditions, and we describe an application of the gSPAWN algorithm to a network localization problem in non-line-of-sight environments. Numerical results suggest that gSPAWN converges much faster in general than the diffusion method, and has lower communication costs, with comparable root mean square errors

The quantum speed up as advanced knowledge of the solution

With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple two line argument for this without having to describe the details of the search algorithm". The answer provided in this work is: "because any quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem". This empirical fact, unnoticed so far, holds for both quadratic and exponential speed ups and is theoretically justified in three steps: (i) once the physical representation is extended to the production of the problem on the part of the oracle and to the final measurement of the computer register, quantum computation is reduction on the solution of the problem under a relation representing problem-solution interdependence, (ii) the speed up is explained by a simple consideration of time symmetry, it is the gain of information about the solution due to backdating, to before running the algorithm, a time-symmetric part of the reduction on the solution; this advanced knowledge of the solution reduces the size of the solution space to be explored by the algorithm, (iii) if I is the information acquired by measuring the content of the computer register at the end of the algorithm, the quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of I, which brings us to the initial statement.Comment: 23 pages, to be published in IJT

Explicit formulae for the eigenfunctions of the N-body Calogero model

We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the inter-particle distance. We elaborate a novel solution algorithm which allows us to obtain fully explicit formulae for its eigenfunctions, arbitrary coupling parameter and particle number. We also show that our method applies, with minor changes, to all Calogero models associated with classical root systems

The Effect of Data Density on the Accuracy of Foot-Line Determination Through Maximum Curvature Surface by Automatic Ridge-Tracing Algorithm

The influence of data density on the accuracy of foot-line determination by the automatic ridge-tracing algorithm is investigated through a set of simulated bathymetric surfaces. The results show that no obvious differences exist for different sea bottom morphology, different depths and gradients of continental slope when data are dense enough, i.e., when the data interval is smaller than some 12.5 km. When the data are very sparse, the accuracy of the foot-line determination becomes worse as the surfaces become more complicated or the gradients become steep. Approximately, the root mean square error of foot-line determination is equal to one third of the data interval and the areal error is 23km2/100km foot-line length per one kilometre of the data interval

Using a causal smoothing to improve the performance of an on-line neural network glucose prediction algorithm

This work evaluates a spline-based smoothing method applied to the output of a glucose predictor. Methods:Our on-line prediction algorithm is based on a neural network model (NNM). We trained/validated the NNM with a prediction horizon of 30 minutes using 39/54 profiles of patients monitored with the Guardian® Real-Time continuous glucose monitoring system The NNM output is smoothed by fitting a causal cubic spline. The assessment parameters are the error (RMSE), mean delay (MD) and the high-frequency noise (HFCrms). The HFCrms is the root-mean-square values of the high-frequency components isolated with a zero-delay non-causal filter. HFCrms is 2.90±1.37 (mg/dl) for the original profiles

O(log log Rank) competitive ratio for the Matroid Secretary Problem

In the Matroid Secretary Problem (MSP), the elements of the ground set of a Matroid are revealed on-line one by one, each together with its value. An algorithm for the MSP is called Matroid-Unknown if, at every stage of its execution, it only knows (i) the elements that have been revealed so far and their values and (ii) an oracle for testing whether or not a subset the elements that have been revealed so far forms an independent set. An algorithm is called Known-Cardinality if it knows (i), (ii) and also knows from the start the cardinality n of the ground set of the Matroid. We present here a Known-Cardinality algorithm with a competitive-ratio of order log log the rank of the Matroid. The prior known results for a OC algorithm are a competitive-ratio of log the rank of the Matroid, by Babaioff et al. (2007), and a competitive-ratio of square root of log the rank of the Matroid, by Chakraborty and Lachish (2012)

Accurate Range-based Indoor Localization Using PSO-Kalman Filter Fusion

Accurate indoor localization often depends on infrastructure support for distance estimation in range-based techniques. One can also trade off accuracy to reduce infrastructure investment by using relative positions of other nodes, as in range-free localization. Even for range-based methods where accurate Ultra-WideBand (UWB) signals are used, non line-of-sight (NLOS) conditions pose significant difficulty in accurate indoor localization. Existing solutions rely on additional measurements from sensors and typically correct the noise using a Kalman filter (KF). Solutions can also be customized to specific environments through extensive profiling. In this work, a range-based indoor localization algorithm called PSO - Kalman Filter Fusion (PKFF) is proposed that minimizes the effects of NLOS on localization error without using additional sensors or profiling. Location estimates from a windowed Particle Swarm Optimization (PSO) and a dynamically adjusted KF are fused based on a weighted variance factor. PKFF achieved a 40% lower 90-percentile root-mean-square localization error (RMSE) over the standard least squares trilateration algorithm at 61 cm compared to 102 cm