Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Search on a hypercubic lattice using a quantum random walk. II. d = 2

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d = 2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article A. Patel and M. A. Rahaman, Phys. Rev. A 82, 032330 (2010)] provides an O(root N ln N) algorithm, which is not optimal. The scaling behavior can be improved to O(root N ln N) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78, 012310 (2008)]. We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.

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A New Definition of A Priori Knowledge: In Search of a Modal Basis

In this paper I will offer a novel understanding of a priori knowledge. My claim is that the sharp distinction that is usually made between a priori and a posteriori knowledge is groundless. It will be argued that a plausible understanding of a priori and a posteriori knowledge has to acknowledge that they are in a constant bootstrapping relationship. It is also crucial that we distinguish between a priori propositions that hold in the actual world and merely possible, non-actual a priori propositions, as we will see when considering cases like Euclidean geometry. Furthermore, contrary to what Kripke seems to suggest, a priori knowledge is intimately connected with metaphysical modality, indeed, grounded in it. The task of a priori reasoning, according to this account, is to delimit the space of metaphysically possible worlds in order for us to be able to determine what is actual.

Energy efficient asymmetric binary search switching technique for SAR ADC

An asymmetric binary search switching technique for a successive approximation register (SAR) ADC is presented, and trade-off between switching energy and conversion cycles is discussed. Without using any additional switches, the proposed technique consumes 46% less switching energy, for a small input swing (0.5 V-ref (P-P)), as compared to the last reported efficient switching technique in literature for an 8-bit SAR ADC. For a full input swing (2 V-ref (P-P)), the proposed technique consumes 16.5% less switching energy.

Search for the Higgs boson in the all-hadronic final state using the CDF II detector

We report on a search for the production of the Higgs boson decaying to two bottom quarks accompanied by two additional quarks. The data sample used corresponds to an integrated luminosity of approximately 4  fb-1 of pp̅ collisions at √s=1.96  TeV recorded by the CDF II experiment. This search includes twice the integrated luminosity of the previous published result, uses analysis techniques to distinguish jets originating from light flavor quarks and those from gluon radiation, and adds sensitivity to a Higgs boson produced by vector boson fusion. We find no evidence of the Higgs boson and place limits on the Higgs boson production cross section for Higgs boson masses between 100  GeV/c2 and 150  GeV/c2 at the 95% confidence level. For a Higgs boson mass of 120  GeV/c2, the observed (expected) limit is 10.5 (20.0) times the predicted standard model cross section.

Random-Restart Reactive Tabu Search Algorithm for Detection in Large-MIMO Systems

We present a low-complexity algorithm based on reactive tabu search (RTS) for near maximum likelihood (ML) detection in large-MIMO systems. The conventional RTS algorithm achieves near-ML performance for 4-QAM in large-MIMO systems. But its performance for higher-order QAM is far from ML performance. Here, we propose a random-restart RTS (R3TS) algorithm which achieves significantly better bit error rate (BER) performance compared to that of the conventional RTS algorithm in higher-order QAM. The key idea is to run multiple tabu searches, each search starting with a random initial vector and choosing the best among the resulting solution vectors. A criterion to limit the number of searches is also proposed. Computer simulations show that the R3TS algorithm achieves almost the ML performance in 16 x 16 V-BLAST MIMO system with 16-QAM and 64-QAM at significantly less complexities than the sphere decoder. Also, in a 32 x 32 V-BLAST MIMO system, the R3TS performs close to ML lower bound within 1.6 dB for 16-QAM (128 bps/Hz), and within 2.4 dB for 64-QAM (192 bps/Hz) at 10(-3) BER.

Search Strategies for Multiple UAV Search and Destroy Missions

Multiple UAVs are deployed to carry out a search and destroy mission in a bounded region. The UAVs have limited sensor range and can carry limited resources which reduce with use. The UAVs perform a search task to detect targets. When a target is detected which requires different type and quantities of resources to completely destroy, then a team of UAVs called as a coalition is formed to attack the target. The coalition members have to modify their route to attack the target, in the process, the search task is affected, as search and destroy tasks are coupled. The performance of the mission is a function of the search and the task allocation strategies. Therefore, for a given task allocation strategy, we need to devise search strategies that are efficient. In this paper, we propose three different search strategies namely; random search strategy, lanes based search strategy and grid based search strategy and analyze their performance through Monte-Carlo simulations. The results show that the grid based search strategy performs the best but with high information overhead.

Frontier Based Multiple Goal Search in Unknown Environments

We present a frontier based algorithm for searching multiple goals in a fully unknown environment, with only information about the regions where the goals are most likely to be located. Our algorithm chooses an ``active goal'' from the ``active goal list'' generated by running a Traveling Salesman Problem (Tsp) routine with the given centroid locations of the goal regions. We use the concept of ``goal switching'' which helps not only in reaching more number of goals in given time, but also prevents unnecessary search around the goals that are not accessible (surrounded by walls). The simulation study shows that our algorithm outperforms Multi-Heuristic LRTA* (MELRTA*) which is a significant representative of multiple goal search approaches in an unknown environment, especially in environments with wall like obstacles.

Layered Tabu Search Algorithm for Large-MIMO Detection and a Lower Bound on ML Performance

In this paper, we are concerned with low-complexity detection in large multiple-input multiple-output (MIMO) systems with tens of transmit/receive antennas. Our new contributions in this paper are two-fold. First, we propose a low-complexity algorithm for large-MIMO detection based on a layered low-complexity local neighborhood search. Second, we obtain a lower bound on the maximum-likelihood (ML) bit error performance using the local neighborhood search. The advantages of the proposed ML lower bound are i) it is easily obtained for MIMO systems with large number of antennas because of the inherent low complexity of the search algorithm, ii) it is tight at moderate-to-high SNRs, and iii) it can be tightened at low SNRs by increasing the number of symbols in the neighborhood definition. Interestingly, the proposed detection algorithm based on the layered local search achieves bit error performances which are quite close to this lower bound for large number of antennas and higher-order QAM. For e. g., in a 32 x 32 V-BLAST MIMO system, the proposed detection algorithm performs close to within 1.7 dB of the proposed ML lower bound at 10(-3) BER for 16-QAM (128 bps/Hz), and close to within 4.5 dB of the bound for 64-QAM (192 bps/Hz).

Multiple UAV Coalitions for a Search and Prosecute Mission

Unmanned aerial vehicles (UAVs) have the potential to carry resources in support of search and prosecute operations. Often to completely prosecute a target, UAVs may have to simultaneously attack the target with various resources with different capacities. However, the UAVs are capable of carrying only limited resources in small quantities, hence, a group of UAVs (coalition) needs to be assigned that satisfies the target resource requirement. The assigned coalition must be such that it minimizes the target prosecution delay and the size of the coalition. The problem of forming coalitions is computationally intensive due to the combinatorial nature of the problem, but for real-time applications computationally cheap solutions are required. In this paper, we propose decentralized sub-optimal (polynomial time) and decentralized optimal coalition formation algorithms that generate coalitions for a single target with low computational complexity. We compare the performance of the proposed algorithms to that of a global optimal solution for which we need to solve a centralized combinatorial optimization problem. This problem is computationally intensive because the solution has to (a) provide a coalition for each target, (b) design a sequence in which targets need to be prosecuted, and (c) take into account reduction of UAV resources with usage. To solve this problem we use the Particle Swarm Optimization (PSO) technique. Through simulations, we study the performance of the proposed algorithms in terms of mission performance, complexity of the algorithms and the time taken to form the coalition. The simulation results show that the solution provided by the proposed algorithms is close to the global optimal solution and requires far less computational resources.

Automated Multi-Agent Search Using Centroidal Voronoi Configuration

This paper addresses the problem of automated multiagent search in an unknown environment. Autonomous agents equipped with sensors carry out a search operation in a search space, where the uncertainty, or lack of information about the environment, is known a priori as an uncertainty density distribution function. The agents are deployed in the search space to maximize single step search effectiveness. The centroidal Voronoi configuration, which achieves a locally optimal deployment, forms the basis for the proposed sequential deploy and search strategy. It is shown that with the proposed control law the agent trajectories converge in a globally asymptotic manner to the centroidal Voronoi configuration. Simulation experiments are provided to validate the strategy. Note to Practitioners-In this paper, searching an unknown region to gather information about it is modeled as a problem of using search as a means of reducing information uncertainty about the region. Moreover, multiple automated searchers or agents are used to carry out this operation optimally. This problem has many applications in search and surveillance operations using several autonomous UAVs or mobile robots. The concept of agents converging to the centroid of their Voronoi cells, weighted with the uncertainty density, is used to design a search strategy named as sequential deploy and search. Finally, the performance of the strategy is validated using simulations.

Genetic search: Analysis using fitness moments

Genetic Algorithms are efficient and robust search methods that are being employed in a plethora of applications with extremely large search spaces. The directed search mechanism employed in Genetic Algorithms performs a simultaneous and balanced, exploration of new regions in the search space and exploitation of already discovered regions.This paper introduces the notion of fitness moments for analyzing the working of Genetic Algorithms (GAs). We show that the fitness moments in any generation may be predicted from those of the initial population. Since a knowledge of the fitness moments allows us to estimate the fitness distribution of strings, this approach provides for a method of characterizing the dynamics of GAs. In particular the average fitness and fitness variance of the population in any generation may be predicted. We introduce the technique of fitness-based disruption of solutions for improving the performance of GAs. Using fitness moments, we demonstrate the advantages of using fitness-based disruption. We also present experimental results comparing the performance of a standard GA and GAs (CDGA and AGA) that incorporate the principle of fitness-based disruption. The experimental evidence clearly demonstrates the power of fitness based disruption.