Hamilton's turns as visual tool-kit for designing of single-qubit unitary gates

Unitary evolutions of a qubit are traditionally represented geometrically as rotations of the Bloch sphere, but the composition of such evolutions is handled algebraically through matrix multiplication [of SU(2) or SO(3) matrices]. Hamilton's construct, called turns, provides for handling the latter pictorially through the as addition of directed great circle arcs on the unit sphere S$^2 \subset \mathbb{R}^3$, resulting in a non-Abelian version of the parallelogram law of vector addition of the Euclidean translation group. This construct is developed into a visual tool-kit for handling the design of single-qubit unitary gates. As an application, it is shown, in the concrete case wherein the qubit is realized as polarization states of light, that all unitary gates can be realized conveniently through a universal gadget consisting of just two quarter-wave plates (QWP) and one half-wave plate (HWP). The analysis and results easily transcribe to other realizations of the qubit: The case of NMR is obtained by simply substituting $\pi/2$ and $\pi$ pulses respectively for QWPs and HWPs, the phases of the pulses playing the role of the orientation of fast axes of these plates.Comment: 16 Pages, 14 Figures, Published versio

Optimizing the discrete time quantum walk using a SU(2) coin

We present a generalized version of the discrete time quantum walk, using the SU(2) operation as the quantum coin. By varying the coin parameters, the quantum walk can be optimized for maximum variance subject to the functional form $\sigma^2 \approx N^2$ and the probability distribution in the position space can be biased. We also discuss the variation in measurement entropy with the variation of the parameters in the SU(2) coin. Exploiting this we show how quantum walk can be optimized for improving mixing time in an $n$-cycle and for quantum walk search.Comment: 6 pages, 6 figure

Full-revivals in 2-D Quantum Walks

Recurrence of a random walk is described by the Polya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full-revival of its quantum state. Localization for two dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show on the example of the 2-D Grover walk that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full-revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference which has no counterpart in classical random walks

The costs of scaling up HIV prevention for high risk groups: lessons learned from the Avahan Programme in India.

OBJECTIVE: The study objective is to measure, analyse costs of scaling up HIV prevention for high-risk groups in India, in order to assist the design of future HIV prevention programmes in South Asia and beyond. DESIGN: Prospective costing study. METHODS: This study is one of the most comprehensive studies of the costs of HIV prevention for high-risk groups to date in both its scope and size. HIV prevention included outreach, sexually transmitted infections (STI) services, condom provision, expertise enhancement, community mobilisation and enabling environment activities. Economic costs were collected from 138 non-government organisations (NGOs) in 64 districts, four state level lead implementing partners (SLPs), and the national programme level (Bill and Melinda Gates Foundation (BMGF)) office over four years using a top down costing approach, presented in US$2011. RESULTS: Mean total unit costs (2004-08) per person reached at least once a year and per monthly contact were US$ 235(56-1864) and US$82(12-969) respectively. 35$ 477 per person reached in 2004 to US$145 per person reached in 2008). At the service level also unit costs decreased slightly over time from US$ 68 to US$ 64 per person reached. CONCLUSIONS: Scaling up HIV prevention for high risk groups requires significant investment in expertise enhancement and programme administration. However, unit costs decreased with programme expansion in spite of an increase in the scope of activities

Spectra of some new graph operations and some new classes of integral graphs

In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs. Keywords: Duplication corona, Duplication edge corona, Duplication neighborhood corona, Cospectral graphs, Integral graphs

Auditory Rehabilitation after Stroke: Treatment of Auditory Processing Disorders in Stroke Patients with Personal Frequency-Modulated (FM) Systems

Purpose: Auditory disability due to impaired auditory processing (AP) despite normal pure-tone thresholds is common after stroke, and it leads to isolation, reduced quality of life and physical decline. There are currently no proven remedial interventions for AP deficits in stroke patients. This is the first study to investigate the benefits of personal frequency-modulated (FM) systems in stroke patients with disordered AP. Methods: Fifty stroke patients had baseline audiological assessments, AP tests and completed the (modified) Amsterdam Inventory for Auditory Disability (AIAD) and Hearing Handicap Inventory for Elderly (HHIE) questionnaires. Nine out of these fifty patients were diagnosed with disordered AP based on severe deficits in understanding speech in background noise but with normal pure-tone thresholds. These nine patients underwent spatial speech-in-noise testing in a sound-attenuating chamber (the “crescent of sound”) with and without FM systems. Results: The signal-to-noise-ratio (SNR) for 50% correct speech recognition performance was measured with speech presented from 0° azimuth and competing babble from ±90° azimuth. Spatial release from masking (SRM) was defined as the difference between SNRs measured with co-located speech and babble and SNRs measured with spatially separated speech and babble. The SRM significantly improved when babble was spatially separated from target speech, while the patients had the FM systems in their ears compared to without the FM systems. Conclusions: Personal FM systems may substantially improve speech-in-noise deficits in stroke patients who are not eligible for conventional hearing aids. FMs are feasible in stroke patients and show promise to address impaired AP after stroke

Lagrangian perfect fluids and black hole mechanics

The first law of black hole mechanics (in the form derived by Wald), is expressed in terms of integrals over surfaces, at the horizon and spatial infinity, of a stationary, axisymmetric black hole, in a diffeomorphism invariant Lagrangian theory of gravity. The original statement of the first law given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system contained, in addition, volume integrals of the fluid fields, over a spacelike slice stretching between these two surfaces. When applied to the Einstein-perfect fluid system, however, Wald's methods yield restricted results. The reason is that the fluid fields in the Lagrangian of a gravitating perfect fluid are typically nonstationary. We therefore first derive a first law-like relation for an arbitrary Lagrangian metric theory of gravity coupled to arbitrary Lagrangian matter fields, requiring only that the metric field be stationary. This relation includes a volume integral of matter fields over a spacelike slice between the black hole horizon and spatial infinity, and reduces to the first law originally derived by Bardeen, Carter and Hawking when the theory is general relativity coupled to a perfect fluid. We also consider a specific Lagrangian formulation for an isentropic perfect fluid given by Carter, and directly apply Wald's analysis. The resulting first law contains only surface integrals at the black hole horizon and spatial infinity, but this relation is much more restrictive in its allowed fluid configurations and perturbations than that given by Bardeen, Carter and Hawking. In the Appendix, we use the symplectic structure of the Einstein-perfect fluid system to derive a conserved current for perturbations of this system: this current reduces to one derived ab initio for this system by Chandrasekhar and Ferrari.Comment: 26 pages LaTeX-2

Fractional recurrence in discrete-time quantum walk

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude corresponding to different paths fail to satisfy the complete quantum recurrence theorem. Due to the revival of the fractional wave packet, a fractional recurrence characterized using quantum P\'olya number can be seen.Comment: 10 pages, 11 figure : Accepted to appear in Central European Journal of Physic

Reduction of the size of datasets by using evolutionary feature selection: the case of noise in a modern city

Smart city initiatives have emerged to mitigate the negative effects of a very fast growth of urban areas. Most of the population in our cities are exposed to high levels of noise that generate discomfort and different health problems. These issues may be mitigated by applying different smart cities solutions, some of them require high accurate noise information to provide the best quality of serve possible. In this study, we have designed a machine learning approach based on genetic algorithms to analyze noise data captured in the university campus. This method reduces the amount of data required to classify the noise by addressing a feature selection optimization problem. The experimental results have shown that our approach improved the accuracy in 20% (achieving an accuracy of 87% with a reduction of up to 85% on the original dataset).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. This research has been partially funded by the Spanish MINECO and FEDER projects TIN2016-81766-REDT (http://cirti.es), and TIN2017-88213-R (http://6city.lcc.uma.es)