New sampling theorem and multiplicative filtering in the FRFT domain

Having in consideration a fractional convolution associated with the fractional Fourier transform (FRFT), we propose a novel reconstruction formula for bandlimited signals in the FRFT domain without using the classical Shannon theorem. This may be considered the main contribution of this work, and numerical experiments are implemented to demonstrate the effectiveness of the proposed sampling theorem. As a second goal, we also look for the designing of multiplicative filters. Indeed, we also convert the multiplicative filtering in FRFT domain to the time domain, which can be realized by Fast Fourier transform. Two concrete examples are included where the use of the present results is illustrated.publishe

Challenges in diagnosing scrub typhus among hospitalized patients with undifferentiated fever at a national tertiary hospital in northern Vietnam

BACKGROUND: Scrub typhus (ST) is a leading cause of non-malarial febrile illness in Southeast Asia, but evidence of its true disease burden is limited because of difficulties of making the clinical diagnosis and lack of adequate diagnostic tests. To describe the epidemiology and clinical characteristics of ST, we conducted an observational study using multiple diagnostic assays at a national tertiary hospital in Hanoi, Vietnam. METHODOLOGY/PRINCIPAL FINDINGS: We enrolled 1,127 patients hospitalized with documented fever between June 2012 and May 2013. Overall, 33 (2.9%) patients were diagnosed with ST by PCR and/or screening of ELISA for immunoglobulin M (IgM) with confirmatory tests: 14 (42.4%) were confirmed by indirect immunoperoxidase assay (IIP), and 19 (57.6%) were by IIP and PCR. Living by farming, conjunctival injection, eschar, aspartate aminotransferase elevation, and alanine aminotransferase elevation were significantly associated with ST cases (adjusted odds ratios (aORs): 2.8, 3.07, 48.8, 3.51, and 4.13, respectively), and having a comorbidity and neutrophilia were significantly less common in ST cases (aORs: 0.29 and 0.27, respectively). The majority of the ST cases were not clinically diagnosed with rickettsiosis (72.7%). Dominant IIP reactions against a single antigen were identified in 15 ST cases, whereas indistinguishably high reactions against multiple antigens were seen in 11 ST cases. The most frequently observed dominant IIP reaction was against Karp antigen (eight cases) followed by Gilliam (four cases). The highest diagnostic accuracy of IgM ELISA in acute samples was 78%. In a phylogenetic analysis of the 56-kDa type-specific antigen gene, the majority (14 cases) were located in the Karp-related branch followed by the Gilliam-related (two cases), Kato-related (two cases), and TA763-related clades (one case). CONCLUSIONS/SIGNIFICANCE: Both the clinical and laboratory diagnoses of ST remain challenging at a tertiary hospital. Implementation of both serological and nucleic acid amplification assays covering endemic O. tsutsugamushi strains is essential

Theory of high-order harmonic generation from molecules by intense laser pulses

We show that high-order harmonics generated from molecules by intense laser pulses can be expressed as the product of a returning electron wave packet and the photo-recombination cross section (PRCS) where the electron wave packet can be obtained from simple strong-field approximation (SFA) or from a companion atomic target. Using these wave packets but replacing the PRCS obtained from SFA or from the atomic target by the accurate PRCS from molecules, the resulting HHG spectra are shown to agree well with the benchmark results from direct numerical solution of the time-dependent Schr\"odinger equation, for the case of H$_2^+$ in laser fields. The result illustrates that these powerful theoretical tools can be used for obtaining high-order harmonic spectra from molecules. More importantly, the results imply that the PRCS extracted from laser-induced HHG spectra can be used for time-resolved dynamic chemical imaging of transient molecules with temporal resolutions down to a few femtoseconds.Comment: 10 pages, 5 figure

Development of a Real-Time, Simple and High-Accuracy Fall Detection System for Elderly Using 3-DOF Accelerometers

© 2018, King Fahd University of Petroleum & Minerals. Falls represent a major problem for the elderly people aged 60 or above. There are many monitoring systems which are currently available to detect the fall. However, there is a great need to propose a system which is of optimal effectiveness. In this paper, we propose to develop a low-cost fall detection system to precisely detect an event when an elderly person accidentally falls. The fall detection algorithm compares the acceleration with lower fall threshold and upper fall threshold values to accurately detect a fall event. The post-fall recognition module is the combination of posture recognition and vertical velocity estimation that has been added to our proposed method to enhance the performance and accuracy. In case of a fall, our device will transmit the location information to the contacts instantly via SMS and voice call. A smartphone application will ensure that the notifications are delivered to the elderly person’s relatives so that medical attention can be provided with minimal delay. The system was tested by volunteers and achieved 100% sensitivity and accuracy. This was confirmed by testing with public datasets and it also achieved the same percentage in sensitivity and accuracy as in our recorded datasets

Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights

This paper presents new convolutions for the fractional Fourier transform which are somehow associated with the Hermite functions. Consequent inequalities and properties are derived for these convolutions, among which we emphasize two new types of Young's convolution inequalities. The results guarantee a general framework where the present convolutions are well-defined, allowing larger possibilities than the known ones for other convolutions. Furthermore, we exemplify the use of our convolutions by providing explicit solutions of some classes of integral equations which appear in engineering problems

The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue of DCDS-

Spin transfer torque generated magnetic droplet solitons (invited)

We present recent experimental and numerical advancements in the understanding of spin transfer torque generated magnetic droplet solitons. The experimental work focuses on nano-contact spin torque oscillators (NC-STOs) based on orthogonal (pseudo) spin valves where the Co fixed layer has an easy-plane anisotropy, and the [Co/Ni] free layer has a strong perpendicular magnetic anisotropy. The NC-STO resistance and microwave signal generation are measured simultaneously as a function of drive current and applied perpendicular magnetic field. Both exhibit dramatic transitions at a certain current dependent critical field value, where the microwave frequency drops 10 GHz, modulation sidebands appear, and the resistance exhibits a jump, while the magnetoresistance changes sign. We interpret these observations as the nucleation of a magnetic droplet soliton with a large fraction of its magnetization processing with an angle greater than 90°, i.e., around a direction opposite that of the applied field. This interpretation is corroborated by numerical simulations. When the field is further increased, we find that the droplet eventually collapses under the pressure from the Zeeman energy

Компактные разностные схемы для уравнения Клейна-Гордона

In this paper, we consider compact difference approximation of the fourth-order schemes for linear, semi-linear, and quasilinear Klein-Gordon equations. with respect to a small perturbation of initial conditions, right-hand side, and coefficients of the linear equations the strong stability of difference schemes is proved. The conducted numerical experiment shows how Runge rule is used to determine the orders of convergence of the difference scheme in the case of two independent variables.В настоящей работе рассматриваются компактные разностные схемы четвертого порядка аппроксимации для линейных, полулинейных и квазилинейных уравнений Клейна-Гордона. Для линейных уравнений доказывается сильная устойчивость разностного решения по отношению к малому возмущению начальных условий, правой части и коэффициентов уравнений. На примере вычислительного эксперимента показывается, как использовать правило Рунге для определения разных порядков скорости сходимости разностной схемы в случае наличия двух независимых переменных

Multifractal analysis of complex networks

Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions $D_{q}$ of some theoretical networks, namely scale-free networks, small world networks and random networks, and one kind of real networks, namely protein-protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein-protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of $D_{q}$ due to changes in the parameters of the theoretical network models is also discussed.Comment: 18 pages, 7 figures, 4 table

Representations of U_q(sl(N)) at Roots of Unity

The Gelfand--Zetlin basis for representations of $U_q(sl(N))$ is improved to fit better the case when $q$ is a root of unity. The usual $q$-deformed representations, as well as the nilpotent, periodic (cyclic), semi-periodic (semi-cyclic) and also some atypical representations are now described with the same formalism.Comment: 18 pages, Plain TeX, Macros harvmac.tex and epsf needed 3 figures in a uuencoded tar separate file. Some references are added. Also available at http://lapphp0.in2p3.fr/preplapp/psth/uqsln.ps.g