Optimization for efficient structure-control systems

The efficiency of a structure-control system is a nondimensional parameter which indicates the fraction of the total control power expended usefully in controlling a finite-dimensional system. The balance of control power is wasted on the truncated dynamics serving no useful purpose towards the control objectives. Recently, it has been demonstrated that the concept of efficiency can be used to address a number of control issues encountered in the control of dynamic systems such as the spillover effects, selection of a good input configuration and obtaining reduced order control models. Reference (1) introduced the concept and presented analyses of several Linear Quadratic Regulator designs on the basis of their efficiencies. Encouraged by the results of Ref. (1), Ref. (2) introduces an efficiency modal analysis of a structure-control system which gives an internal characterization of the controller design and establishes the link between the control design and the initial disturbances to affect efficient structure-control system designs. The efficiency modal analysis leads to identification of principal controller directions (or controller modes) distinct from the structural natural modes. Thus ultimately, many issues of the structure-control system revolve around the idea of insuring compatibility of the structural modes and the controller modes with each other, the better the match the higher the efficiency. A key feature in controlling a reduced order model of a high dimensional (or infinity-dimensional distributed parameter system) structural dynamic system must be to achieve high efficiency of the control system while satisfying the control objectives and/or constraints. Formally, this can be achieved by designing the control system and structural parameters simultaneously within an optimization framework. The subject of this paper is to present such a design procedure

Super-activation of quantum non-locality

In this paper we show that quantum non-locality can be super-activated. That is, one can obtain violations of Bell inequalities by tensorizing a local state with itself. Moreover, previous results suggest that such Bell violations can be very large.Comment: v2: Refs added. Same results, v3: Minor corrections. Close to the published versio

All quantum states useful for teleportation are nonlocal resources

Understanding the relation between the different forms of inseparability in quantum mechanics is a longstanding problem in the foundations of quantum theory and has implications for quantum information processing. Here we make progress in this direction by establishing a direct link between quantum teleportation and Bell nonlocality. In particular, we show that all entangled states which are useful for teleportation are nonlocal resources, i.e. lead to deterministic violation of Bell's inequality. Our result exploits the phenomenon of super-activation of quantum nonlocality, recently proved by Palazuelos, and suggests that the latter might in fact be generic.Comment: 4 pages. v2: Title and abstract changed, presentation improved, references updated, same result

Speaker Recognition Based Home Automation Using Matlab

Due to decline in both physical and mental abilities, some elderly are not allowed to leave the bed without assistance. Some time they are unable to make the desirable bodily movements and repositioning. In this paper the home automation is obtained using MATLAB based speaker recognition. The feature extraction of speech signal is done by using MFCC and for selection of features of speech signal vector quantization is used. By using above two steps the speaker is recognized and then this is given to the microcontroller by using serial communication .Then the particular home appliance get operated

Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum computation. In this paper we completely characterize the class of boolean functions computable by unitary two-qubit matchgate circuits with some probability of success. We show that this class precisely coincides with that of the linear threshold gates. The latter is a fundamental family which appears in several fields, such as the study of neural networks. Using the above characterization, we further show that the power of matchgate circuits is surprisingly trivial in those cases where the computation is to succeed with high probability. In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions depending on only a single bit of the input

On the Approximability of Digraph Ordering

Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute a labeling $\ell : V \to [k]$ maximizing the number of forward edges, i.e. edges (u,v) such that $\ell$(u) < $\ell$(v). For different values of k, this reduces to Maximum Acyclic Subgraph (k=n), and Max-Dicut (k=2). This work studies the approximability of Max-k-Ordering and its generalizations, motivated by their applications to job scheduling with soft precedence constraints. We give an LP rounding based 2-approximation algorithm for Max-k-Ordering for any k={2,..., n}, improving on the known 2k/(k-1)-approximation obtained via random assignment. The tightness of this rounding is shown by proving that for any k={2,..., n} and constant $\varepsilon > 0$, Max-k-Ordering has an LP integrality gap of 2 - $\varepsilon$ for $n^{\Omega\left(1/\log\log k\right)}$ rounds of the Sherali-Adams hierarchy. A further generalization of Max-k-Ordering is the restricted maximum acyclic subgraph problem or RMAS, where each vertex v has a finite set of allowable labels $S_v \subseteq \mathbb{Z}^+$. We prove an LP rounding based $4\sqrt{2}/(\sqrt{2}+1) \approx 2.344$ approximation for it, improving on the $2\sqrt{2} \approx 2.828$ approximation recently given by Grandoni et al. (Information Processing Letters, Vol. 115(2), Pages 182-185, 2015). In fact, our approximation algorithm also works for a general version where the objective counts the edges which go forward by at least a positive offset specific to each edge. The minimization formulation of digraph ordering is DAG edge deletion or DED(k), which requires deleting the minimum number of edges from an n-vertex directed acyclic graph (DAG) to remove all paths of length k. We show that both, the LP relaxation and a local ratio approach for DED(k) yield k-approximation for any $k\in [n]$.Comment: 21 pages, Conference version to appear in ESA 201

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction

Approximation Algorithms for Connected Maximum Cut and Related Problems

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph G[S] is connected. We present the first non-trivial \Omega(1/log n) approximation algorithm for the connected maximum cut problem in general graphs using novel techniques. We then extend our algorithm to an edge weighted case and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark contrast to the classical max-cut problem, we show that the connected maximum cut problem remains NP-hard even on unweighted, planar graphs. On the positive side, we obtain a polynomial time approximation scheme for the connected maximum cut problem on planar graphs and more generally on graphs with bounded genus.Comment: 17 pages, Conference version to appear in ESA 201

Hitting Diamonds and Growing Cacti

We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primal-dual method. Moreover, we show that the integrality gap of the natural LP relaxation of the problem is \Theta(\log n), where n denotes the number of vertices in the graph.Comment: v2: several minor changes