Singlet-state creation and universal quantum computation in NMR using a genetic algorithm

The experimental implementation of a quantum algorithm requires the decomposition of unitary operators. Here we treat unitary-operator decomposition as an optimization problem, and use a genetic algorithm-a global-optimization method inspired by nature's evolutionary process-for operator decomposition. We apply this method to NMR quantum information processing, and find a probabilistic way of performing universal quantum computation using global hard pulses. We also demonstrate the efficient creation of the singlet state (a special type of Bell state) directly from thermal equilibrium, using an optimum sequence of pulses.

Algorithmic aspects of k-tuple total domination in graphs

For a fixed positive integer k, a k-tuple total dominating set of a graph G = (V. E) is a subset T D-k of V such that every vertex in V is adjacent to at least k vertices of T Dk. In minimum k-tuple total dominating set problem (MIN k-TUPLE TOTAL DOM SET), it is required to find a k-tuple total dominating set of minimum cardinality and DECIDE MIN k-TUPLE TOTAL DOM SET is the decision version of MIN k-TUPLE TOTAL DOM SET problem. In this paper, we show that DECIDE MIN k-TUPLE TOTAL DOM SET is NP-complete for split graphs, doubly chordal graphs and bipartite graphs. For chordal bipartite graphs, we show that MIN k-TUPLE TOTAL DOM SET can be solved in polynomial time. We also propose some hardness results and approximation algorithms for MIN k-TUPLE TOTAL DOM SET problem. (c) 2012 Elsevier B.V. All rights reserved.

Functional maps within a single neuron

Narayanan R, Johnston D. Functional maps within a single neuron. J Neurophysiol 108: 2343-2351, 2012. First published August 29, 2012; doi:10.1152/jn.00530.2012.-The presence and plasticity of dendritic ion channels are well established. However, the literature is divided on what specific roles these dendritic ion channels play in neuronal information processing, and there is no consensus on why neuronal dendrites should express diverse ion channels with different expression profiles. In this review, we present a case for viewing dendritic information processing through the lens of the sensory map literature, where functional gradients within neurons are considered as maps on the neuronal topograph. Under such a framework, drawing analogies from the sensory map literature, we postulate that the formation of intraneuronal functional maps is driven by the twin objectives of efficiently encoding inputs that impinge along different dendritic locations and of retaining homeostasis in the face of changes that are required in the coding process. In arriving at this postulate, we relate intraneuronal map physiology to the vast literature on sensory maps and argue that such a metaphorical association provides a fresh conceptual framework for analyzing and understanding single-neuron information encoding. We also describe instances where the metaphor presents specific directions for research on intraneuronal maps, derived from analogous pursuits in the sensory map literature. We suggest that this perspective offers a thesis for why neurons should express and alter ion channels in their dendrites and provides a framework under which active dendrites could be related to neural coding, learning theory, and homeostasis.

On improving the generalization of SVM classifier

The generalization performance of the SVM classifier depends mainly on the VC dimension and the dimensionality of the data. By reducing the VC dimension of the SVM classifier, its generalization performance is expected to increase. In the present paper, we argue that the VC dimension of SVM classifier can be reduced by applying bootstrapping and dimensionality reduction techniques. Experimental results showed that bootstrapping the original data and bootstrapping the projected (dimensionally reduced) data improved the performance of the SVM classifier.

Loss ratio of the EDF scheduling policy with early discarding technique

This paper considers a firm real-time M/M/1 system, where jobs have stochastic deadlines till the end of service. A method for approximately specifying the loss ratio of the earliest-deadline-first scheduling policy along with exit control through the early discarding technique is presented. This approximation uses the arrival rate and the mean relative deadline, normalized with respect to the mean service time, for exponential and uniform distributions of relative deadlines. Simulations show that the maximum approximation error is less than 4% and 2% for the two distributions, respectively, for a wide range of arrival rates and mean relative deadlines. (C) 2013 Elsevier B.V. All rights reserved.

Classification calibration dimension for general multiclass losses

We study consistency properties of surrogate loss functions for general multiclass classification problems, defined by a general loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be classification calibrated with respect to a loss matrix in this setting. We then introduce the notion of \emph{classification calibration dimension} of a multiclass loss matrix, which measures the smallest `size' of a prediction space for which it is possible to design a convex surrogate that is classification calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, as one application, we provide a different route from the recent result of Duchi et al.\ (2010) for analyzing the difficulty of designing `low-dimensional' convex surrogates that are consistent with respect to pairwise subset ranking losses. We anticipate the classification calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems.

The Lovasz θ function, SVMs and finding large dense subgraphs

The Lovasz θ function of a graph, is a fundamental tool in combinatorial optimization and approximation algorithms. Computing θ involves solving a SDP and is extremely expensive even for moderately sized graphs. In this paper we establish that the Lovasz θ function is equivalent to a kernel learning problem related to one class SVM. This interesting connection opens up many opportunities bridging graph theoretic algorithms and machine learning. We show that there exist graphs, which we call SVM−θ graphs, on which the Lovasz θ function can be approximated well by a one-class SVM. This leads to a novel use of SVM techniques to solve algorithmic problems in large graphs e.g. identifying a planted clique of size Θ(n√) in a random graph G(n,12). A classic approach for this problem involves computing the θ function, however it is not scalable due to SDP computation. We show that the random graph with a planted clique is an example of SVM−θ graph, and as a consequence a SVM based approach easily identifies the clique in large graphs and is competitive with the state-of-the-art. Further, we introduce the notion of a ''common orthogonal labeling'' which extends the notion of a ''orthogonal labelling of a single graph (used in defining the θ function) to multiple graphs. The problem of finding the optimal common orthogonal labelling is cast as a Multiple Kernel Learning problem and is used to identify a large common dense region in multiple graphs. The proposed algorithm achieves an order of magnitude scalability compared to the state of the art.

Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.

Efficient simulation of unitary operators by combining two numerical algorithms: An NMR simulation of the mirror-inversion propagator of an XY spin chain

Precise experimental implementation of unitary operators is one of the most important tasks for quantum information processing. Numerical optimization techniques are widely used to find optimized control fields to realize a desired unitary operator. However, finding high-fidelity control pulses to realize an arbitrary unitary operator in larger spin systems is still a difficult task. In this work, we demonstrate that a combination of the GRAPE algorithm, which is a numerical pulse optimization technique, and a unitary operator decomposition algorithm Ajoy et al., Phys. Rev. A 85, 030303 (2012)] can realize unitary operators with high experimental fidelity. This is illustrated by simulating the mirror-inversion propagator of an XY spin chain in a five-spin dipolar coupled nuclear spin system. Further, this simulation has been used to demonstrate the transfer of entangled states from one end of the spin chain to the other end.

Optical properties of an inhomogeneously broadened Lambda V-system with multiple excited states

We present a theoretical model using a density matrix approach to show the influence of multiple excited states on the optical properties of an inhomogeneously broadened Lambda V-system of the Rb-87 D2 line. These closely spaced multiple excited states cause asymmetry in absorption and dispersion profiles. We observe the reduced absorption profiles, due to dressed state interactions of the applied electromagnetic fields, which results the Mollow sideband-like transparency windows. In a room temperature vapor, we obtain a narrow enhanced absorption and steep positive dispersion at the line center when the strengths of control and pump fields are equal. Here, we show how the probe transmittance varies when it passes through the atomic medium. We also discuss the transient behavior of our system which agrees well with the corresponding absorption and dispersion profiles. This study has potential applications in controllability of group velocity, and for optical and quantum information processing.

Energy Efficient GPS Acquisition with Sparse-GPS

Following rising demands in positioning with GPS, low-cost receivers are becoming widely available; but their energy demands are still too high. For energy efficient GPS sensing in delay-tolerant applications, the possibility of offloading a few milliseconds of raw signal samples and leveraging the greater processing power of the cloud for obtaining a position fix is being actively investigated. In an attempt to reduce the energy cost of this data offloading operation, we propose Sparse-GPS(1): a new computing framework for GPS acquisition via sparse approximation. Within the framework, GPS signals can be efficiently compressed by random ensembles. The sparse acquisition information, pertaining to the visible satellites that are embedded within these limited measurements, can subsequently be recovered by our proposed representation dictionary. By extensive empirical evaluations, we demonstrate the acquisition quality and energy gains of Sparse-GPS. We show that it is twice as energy efficient than offloading uncompressed data, and has 5-10 times lower energy costs than standalone GPS; with a median positioning accuracy of 40 m.

Sparse Representation Based Acoustic Rangefinders: From Sensor Platforms to Mobile Devices

Acoustic rangerfinders are a promising technology for accurate proximity detection, a critical requirement for many emerging mobile computing applications. While state-of-the-art systems deliver robust ranging performance, the computational intensiveness of their detection mechanism expedites the energy depletion of the associated devices that are typically powered by batteries. The contribution of this article is fourfold. First, it outlines the common factors that are important for ranging. Second, it presents a review of acoustic rangers and identifies their potential problems. Third, it explores the design of an information processing framework based on sparse representation that could potentially address existing challenges, especially for mobile devices. Finally, it presents mu-BeepBeep: a low energy acoustic ranging service for mobile devices, and empirically evaluates its benefits.

On strong centerpoints

Let P be a set of n points in R-d and F be a family of geometric objects. We call a point x is an element of P a strong centerpoint of P w.r.t..F if x is contained in all F is an element of F that contains more than cn points of P, where c is a fixed constant. A strong centerpoint does not exist even when F is the family of halfspaces in the plane. We prove the existence of strong centerpoints with exact constants for convex polytopes defined by a fixed set of orientations. We also prove the existence of strong centerpoints for abstract set systems with bounded intersection. (C) 2014 Elsevier B.V. All rights reserved.

Do gamma oscillations play a role in cerebral cortex?

Gamma rhythm (which has a center frequency between 30 and 80 Hz) is modulated by cognitive mechanisms such as attention and memory, and has been hypothesized to play a role in mediating these processes by supporting communication channels between cortical areas or encoding information in its phase. We highlight several issues related to gamma rhythms, such as low and inconsistent power, its dependence on low-level stimulus features, problems due to conduction delays, and contamination due to spike-related activity that makes accurate estimation of gamma phase difficult. Gamma rhythm could be a potentially useful signature of excitation-inhibition interactions in the brain, but whether it also provides a mechanism for information processing or coding remains an open question.

Non-deterministic transducer models of retransmission protocols over noisy channels

Retransmission protocols such as HDLC and TCP are designed to ensure reliable communication over noisy channels (i.e., channels that can corrupt messages). Thakkar et al. 15] have recently presented an algorithmic verification technique for deterministic streaming string transducer (DSST) models of such protocols. The verification problem is posed as equivalence checking between the specification and protocol DSSTs. In this paper, we argue that more general models need to be obtained using non-deterministic streaming string transducers (NSSTs). However, equivalence checking is undecidable for NSSTs. We present two classes where the models belong to a sub-class of NSSTs for which it is decidable. (C) 2015 Elsevier B.V. All rights reserved.