Lower Bounds for Sums of Powers of Low Degree Univariates

We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degree polynomials. We prove a lower bound of Omega(root d/t) for writing an explicit univariate degree-d polynomial f(x) as a sum of powers of degree-t polynomials.

A Bacterial Foraging Optimization and Learning Automata Based Feature Selection for Motor Imagery EEG Classification

Selection of relevant features is an open problem in Brain-computer interfacing (BCI) research. Sometimes, features extracted from brain signals are high dimensional which in turn affects the accuracy of the classifier. Selection of the most relevant features improves the performance of the classifier and reduces the computational cost of the system. In this study, we have used a combination of Bacterial Foraging Optimization and Learning Automata to determine the best subset of features from a given motor imagery electroencephalography (EEG) based BCI dataset. Here, we have employed Discrete Wavelet Transform to obtain a high dimensional feature set and classified it by Distance Likelihood Ratio Test. Our proposed feature selector produced an accuracy of 80.291% in 216 seconds.

Power Allocation in MIMO Wiretap Channel with Statistical CSI and Finite-Alphabet Input

In this paper, we consider the problem of power allocation in MIMO wiretap channel for secrecy in the presence of multiple eavesdroppers. Perfect knowledge of the destination channel state information (CSI) and only the statistical knowledge of the eavesdroppers CSI are assumed. We first consider the MIMO wiretap channel with Gaussian input. Using Jensen's inequality, we transform the secrecy rate max-min optimization problem to a single maximization problem. We use generalized singular value decomposition and transform the problem to a concave maximization problem which maximizes the sum secrecy rate of scalar wiretap channels subject to linear constraints on the transmit covariance matrix. We then consider the MIMO wiretap channel with finite-alphabet input. We show that the transmit covariance matrix obtained for the case of Gaussian input, when used in the MIMO wiretap channel with finite-alphabet input, can lead to zero secrecy rate at high transmit powers. We then propose a power allocation scheme with an additional power constraint which alleviates this secrecy rate loss problem, and gives non-zero secrecy rates at high transmit powers.

DETERMINISTIC ALGORITHMS FOR MATCHING AND PACKING PROBLEMS BASED ON REPRESENTATIVE SETS

In this work, we study the well-known r-DIMENSIONAL k-MATCHING ((r, k)-DM), and r-SET k-PACKING ((r, k)-SP) problems. Given a universe U := U-1 ... U-r and an r-uniform family F subset of U-1 x ... x U-r, the (r, k)-DM problem asks if F admits a collection of k mutually disjoint sets. Given a universe U and an r-uniform family F subset of 2(U), the (r, k)-SP problem asks if F admits a collection of k mutually disjoint sets. We employ techniques based on dynamic programming and representative families. This leads to a deterministic algorithm with running time O(2.851((r-1)k) .vertical bar F vertical bar. n log(2)n . logW) for the weighted version of (r, k)-DM, where W is the maximum weight in the input, and a deterministic algorithm with running time O(2.851((r-0.5501)k).vertical bar F vertical bar.n log(2) n . logW) for the weighted version of (r, k)-SP. Thus, we significantly improve the previous best known deterministic running times for (r, k)-DM and (r, k)-SP and the previous best known running times for their weighted versions. We rely on structural properties of (r, k)-DM and (r, k)-SP to develop algorithms that are faster than those that can be obtained by a standard use of representative sets. Incorporating the principles of iterative expansion, we obtain a better algorithm for (3, k)-DM, running in time O(2.004(3k).vertical bar F vertical bar . n log(2)n). We believe that this algorithm demonstrates an interesting application of representative families in conjunction with more traditional techniques. Furthermore, we present kernels of size O(e(r)r(k-1)(r) logW) for the weighted versions of (r, k)-DM and (r, k)-SP, improving the previous best known kernels of size O(r!r(k-1)(r) logW) for these problems.

On the Gaussian Many-to-One X Channel

In this paper, the Gaussian many-to-one X channel (XC), which is a special case of general multiuser XC, is studied. In the Gaussian many-to-one XC, communication links exist between all transmitters and one of the receivers, along with a communication link between each transmitter and its corresponding receiver. As per the XC assumption, transmission of messages is allowed on all the links of the channel. This communication model is different from the corresponding manyto- one interference channel (IC). Transmission strategies, which involve using Gaussian codebooks and treating interference from a subset of transmitters as noise, are formulated for the above channel. Sum-rate is used as the criterion of optimality for evaluating the strategies. Initially, a 3 x 3 many-to-one XC is considered and three transmission strategies are analyzed. The first two strategies are shown to achieve sum-rate capacity under certain channel conditions. For the third strategy, a sum-rate outer bound is derived and the gap between the outer bound and the achieved rate is characterized. These results are later extended to the K x K case. Next, a region in which the many-to-one XC can be operated as a many-to-one IC without the loss of sum-rate is identified. Furthermore, in the above region, it is shown that using Gaussian codebooks and treating interference as noise achieve a rate point that is within K/2 -1 bits from the sum-rate capacity. Subsequently, some implications of the above results to the Gaussian many-to-one IC are discussed. Transmission strategies for the many-to-one IC are formulated, and channel conditions under which the strategies achieve sum-rate capacity are obtained. A region where the sum-rate capacity can be characterized to within K/2 -1 bits is also identified. Finally, the regions where the derived channel conditions are satisfied for each strategy are illustrated for a 3 x 3 many-to-one XC and the corresponding many-to-one IC.

Social optimum in social groups with give-and-take criterion

We consider a Social Group' of networked nodes, seeking a universe' of segments. Each node has a subset of the universe and access to an expensive resource for downloading data. Nodes can also acquire the universe by exchanging copies of segments among themselves, at low cost, using inter-node links. While exchanges over inter-node links ensure minimum cost, some nodes in the group try to exploit the system. We term such nodes as non-reciprocating nodes' and prohibit such behavior by proposing the give-and-take' criterion, where exchange is allowed if each node has segments unavailable with the other. Under this criterion, we consider the problem of maximizing the number of nodes with the universe at the end of local exchanges. First, we present a randomized algorithm that is shown to be optimal in the asymptotic regime. Then, we present greedy links algorithm, which performs well for most of the scenarios and yields an optimal result when the number of nodes is four. The polygon algorithm is proposed, which yields an optimal result when each of the nodes has a unique segment. After presenting some intuitive algorithms (e.g., greedy incremental algorithm and rarest first algorithm), we compare the performances of all proposed algorithms with the optimal. Copyright (c) 2015 John Wiley & Sons, Ltd.

Discovering compressing serial episodes from event sequences

Most pattern mining methods yield a large number of frequent patterns, and isolating a small relevant subset of patterns is a challenging problem of current interest. In this paper, we address this problem in the context of discovering frequent episodes from symbolic time-series data. Motivated by the Minimum Description Length principle, we formulate the problem of selecting relevant subset of patterns as one of searching for a subset of patterns that achieves best data compression. We present algorithms for discovering small sets of relevant non-redundant episodes that achieve good data compression. The algorithms employ a novel encoding scheme and use serial episodes with inter-event constraints as the patterns. We present extensive simulation studies with both synthetic and real data, comparing our method with the existing schemes such as GoKrimp and SQS. We also demonstrate the effectiveness of these algorithms on event sequences from a composable conveyor system; this system represents a new application area where use of frequent patterns for compressing the event sequence is likely to be important for decision support and control.