Quantum Algorithms with Fixed Points: The Case of Database Search

The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which get around this limitation. The first replaces selective inversions in the algorithm by selective phase shifts of $\frac{\pi}{3}$. The second controls the selective inversion operations using two ancilla qubits, and irreversible measurement operations on the ancilla qubits drive the starting state towards the target state. Using $q$ oracle queries, these variations reduce the probability of finding a non-target state from $\epsilon$ to $\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead to robust quantum algorithms, and provide conceptually new schemes for error correction.

Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal order error estimates are derived in both the energy norm and the L 2 norm, and we establish the uniform convergence of V-cycle, F-cycle and W-cycle multigrid algorithms for the resulting discrete problems. Numerical results that confirm the theoretical results are also presented.

Swarm intelligence algorithms for integrated optimization of piezoelectric actuator and sensor placement and feedback gains

Swarm intelligence algorithms are applied for optimal control of flexible smart structures bonded with piezoelectric actuators and sensors. The optimal locations of actuators/sensors and feedback gain are obtained by maximizing the energy dissipated by the feedback control system. We provide a mathematical proof that this system is uncontrollable if the actuators and sensors are placed at the nodal points of the mode shapes. The optimal locations of actuators/sensors and feedback gain represent a constrained non-linear optimization problem. This problem is converted to an unconstrained optimization problem by using penalty functions. Two swarm intelligence algorithms, namely, Artificial bee colony (ABC) and glowworm swarm optimization (GSO) algorithms, are considered to obtain the optimal solution. In earlier published research, a cantilever beam with one and two collocated actuator(s)/sensor(s) was considered and the numerical results were obtained by using genetic algorithm and gradient based optimization methods. We consider the same problem and present the results obtained by using the swarm intelligence algorithms ABC and GSO. An extension of this cantilever beam problem with five collocated actuators/sensors is considered and the numerical results obtained by using the ABC and GSO algorithms are presented. The effect of increasing the number of design variables (locations of actuators and sensors and gain) on the optimization process is investigated. It is shown that the ABC and GSO algorithms are robust and are good choices for the optimization of smart structures.

Interference Alignment Algorithms for the K User Constant MIMO Interference Channel

This paper considers the degrees of freedom (DOF) for a K user multiple-input multiple-output (MIMO) M x N interference channel using interference alignment (IA). A new performance metric for evaluating the efficacy of IA algorithms is proposed, which measures the extent to which the desired signal dimensionality is preserved after zero-forcing the interference at the receiver. Inspired by the metric, two algorithms are proposed for designing the linear precoders and receive filters for IA in the constant MIMO interference channel with a finite number of symbol extensions. The first algorithm uses an eigenbeamforming method to align sub-streams of the interference to reduce the dimensionality of the interference at all the receivers. The second algorithm is iterative, and is based on minimizing the interference leakage power while preserving the dimensionality of the desired signal space at the intended receivers. The improved performance of the algorithms is illustrated by comparing them with existing algorithms for IA using Monte Carlo simulations.

Discrete control algorithms for a tubular ammonia reactor

The specific objective of this paper is to develop direct digital control strategies for an ammonia reactor using quadratic regulator theory and compare the performance of the resultant control system with that under conventional PID regulators. The controller design studies are based on a ninth order state-space model obtained from the exact nonlinear distributed model using linearization and lumping approximations. The evaluation of these controllers with reference to their disturbance rejection capabilities and transient response characteristics, is carried out using hybrid computer simulation.

Fast Robust Pattern Classification Algorithms for Real Time Neuro-Motor Prosthetic Applications

In this paper, we give a brief review of pattern classification algorithms based on discriminant analysis. We then apply these algorithms to classify movement direction based on multivariate local field potentials recorded from a microelectrode array in the primary motor cortex of a monkey performing a reaching task. We obtain prediction accuracies between 55% and 90% using different methods which are significantly above the chance level of 12.5%.

Prototype learning methods for online handwriting recognition

In this paper, we study different methods for prototype selection for recognizing handwritten characters of Tamil script. In the first method, cumulative pairwise- distances of the training samples of a given class are used to select prototypes. In the second method, cumulative distance to allographs of different orientation is used as a criterion to decide if the sample is representative of the group. The latter method is presumed to offset the possible orientation effect. This method still uses fixed number of prototypes for each of the classes. Finally, a prototype set growing algorithm is proposed, with a view to better model the differences in complexity of different character classes. The proposed algorithms are tested and compared for both writer independent and writer adaptation scenarios.

Determinant: Old algorithms, new insights (Extended Abstract)

In this paper we approach the problem of computing the characteristic polynomial of a matrix from the combinatorial viewpoint. We present several combinatorial characterizations of the coefficients of the characteristic polynomial, in terms of walks and closed walks of different kinds in the underlying graph. We develop algorithms based on these characterizations, and show that they tally with well-known algorithms arrived at independently from considerations in linear algebra.

Synthesis of configurable architectures for DSP algorithms

ASICs offer the best realization of DSP algorithms in terms of performance, but the cost is prohibitive, especially when the volumes involved are low. However, if the architecture synthesis trajectory for such algorithms is such that the target architecture can be identified as an interconnection of elementary parameterized computational structures, then it is possible to attain a close match, both in terms of performance and power with respect to an ASIC, for any algorithmic parameters of the given algorithm. Such an architecture is weakly programmable (configurable) and can be viewed as an application specific instruction-set processor (ASIP). In this work, we present a methodology to synthesize ASIPs for DSP algorithms.

Space vector based bus clamped PWM algorithms for three level inverters: implementation, performance analysis and application considerations

This paper describes the different types of space vector based bus clamped PWM algorithms for three level inverters. A novel bus clamp PWM algorithm for low modulation indices region is also presented. The principles and switching sequences of all the types of bus clamped algorithms for high switching frequency are presented. Synchronized version of the PWM sequences for high power applications where switching frequency is low is also presented. The implementation details on DSP based digital controller and experimental results are presented. The THD of the output waveforms is studied for the entire operating region and is compared with the conventional space vector PWM technique. The bus clamped techniques can be used to reduce the switching losses or to improve the output voltage quality or both.. Different issues dominate depending on the type of application and power rating of the inverters. The results presented in this paper can be used for judicious use of the PWM techniques, which result in improved system efficiency and performance.

A unified view of the Apriori-based algorithms for frequent episode discovery

Frequent episode discovery framework is a popular framework in temporal data mining with many applications. Over the years, many different notions of frequencies of episodes have been proposed along with different algorithms for episode discovery. In this paper, we present a unified view of all the apriori-based discoverymethods for serial episodes under these different notions of frequencies. Specifically, we present a unified view of the various frequency counting algorithms. We propose a generic counting algorithm such that all current algorithms are special cases of it. This unified view allows one to gain insights into different frequencies, and we present quantitative relationships among different frequencies.Our unified view also helps in obtaining correctness proofs for various counting algorithms as we show here. It also aids in understanding and obtaining the anti-monotonicity properties satisfied by the various frequencies, the properties exploited by the candidate generation step of any apriori-based method. We also point out how our unified view of counting helps to consider generalization of the algorithm to count episodes with general partial orders.

Fast algorithms for frequent episode discovery in event sequences

In this paper we consider the process of discovering frequent episodes in event sequences. The most computationally intensive part of this process is that of counting the frequencies of a set of candidate episodes. We present two new frequency counting algorithms for speeding up this part. These, referred to as non-overlapping and non-inteleaved frequency counts, are based on directly counting suitable subsets of the occurrences of an episode. Hence they are different from the frequency counts of Mannila et al [1], where they count the number of windows in which the episode occurs. Our new frequency counts offer a speed-up factor of 7 or more on real and synthetic datasets. We also show how the new frequency counts can be used when the events in episodes have time-durations as well.