On the Erdos-Szekeres n-interior-point problem

The n-interior-point variant of the Erdos Szekeres problem is the following: for every n, n >= 1, does there exist a g(n) such that every point set in the plane with at least g(n) interior points has a convex polygon containing exactly n interior points. The existence of g(n) has been proved only for n <= 3. In this paper, we show that for any fixed r >= 2, and for every n >= 5, every point set having sufficiently large number of interior points and at most r convex layers contains a subset with exactly n interior points. We also consider a relaxation of the notion of convex polygons and show that for every n, n >= 1, any point set with at least n interior points has an almost convex polygon (a simple polygon with at most one concave vertex) that contains exactly n interior points. (C) 2013 Elsevier Ltd. All rights reserved.

Harmonic Analysis of DC-Link Capacitor Current in Sinusoidally Modulated Neutral-Point-Clamped Inverter

The voltage ripple and power loss in the DC-capacitor of a voltage source inverter depend on the harmonic currents flowing through the capacitor. This paper presents double Fourier series based harmonic analysis of DC capacitor current in a three-level neutral point clamped inverter, modulated with sine-triangle PWM. The analytical results are validated experimentally on a 5-kVA three-level inverter prototype. The results of the analysis are used for predicting the power loss in the DC capacitor.

Delay optimal scheduling of a discrete-time batch service queue for point-to-point channel code rate selection

We consider the problem of characterizing the minimum average delay, or equivalently the minimum average queue length, of message symbols randomly arriving to the transmitter queue of a point-to-point link which dynamically selects a (n, k) block code from a given collection. The system is modeled by a discrete time queue with an IID batch arrival process and batch service. We obtain a lower bound on the minimum average queue length, which is the optimal value for a linear program, using only the mean (λ) and variance (σ2) of the batch arrivals. For a finite collection of (n, k) codes the minimum achievable average queue length is shown to be Θ(1/ε) as ε ↓ 0 where ε is the difference between the maximum code rate and λ. We obtain a sufficient condition for code rate selection policies to achieve this optimal growth rate. A simple family of policies that use only one block code each as well as two other heuristic policies are shown to be weakly optimal in the sense of achieving the 1/ε growth rate. An appropriate selection from the family of policies that use only one block code each is also shown to achieve the optimal coefficient σ2/2 of the 1/ε growth rate. We compare the performance of the heuristic policies with the minimum achievable average queue length and the lower bound numerically. For a countable collection of (n, k) codes, the optimal average queue length is shown to be Ω(1/ε). We illustrate the selectivity among policies of the growth rate optimality criterion for both finite and countable collections of (n, k) block codes.

EESM-Based Link Adaptation in Point-to-Point and Multi-Cell OFDM Systems: Modeling and Analysis

In contemporary wideband orthogonal frequency division multiplexing (OFDM) systems, such as Long Term Evolution (LTE) and WiMAX, different subcarriers over which a codeword is transmitted may experience different signal-to-noise-ratios (SNRs). Thus, adaptive modulation and coding (AMC) in these systems is driven by a vector of subcarrier SNRs experienced by the codeword, and is more involved. Exponential effective SNR mapping (EESM) simplifies the problem by mapping this vector into a single equivalent fiat-fading SNR. Analysis of AMC using EESM is challenging owing to its non-linear nature and its dependence on the modulation and coding scheme. We first propose a novel statistical model for the EESM, which is based on the Beta distribution. It is motivated by the central limit approximation for random variables with a finite support. It is simpler and as accurate as the more involved ad hoc models proposed earlier. Using it, we develop novel expressions for the throughput of a point-to-point OFDM link with multi-antenna diversity that uses EESM for AMC. We then analyze a general, multi-cell OFDM deployment with co-channel interference for various frequency-domain schedulers. Extensive results based on LTE and WiMAX are presented to verify the model and analysis, and gain new insights.

Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics

This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a ``vortex gas'' comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via ``violent'' and ``slow'' relaxations P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a ``relative equilibrium.'' The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar ``equilibrium'' state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term ``explosive'' as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.

Analytical Closed-Form Expressions for Harmonic Distortion Corresponding to Novel Switching Sequences for Neutral-Point-Clamped Inverters

Analytical closed-form expressions for harmonic distortion factors corresponding to various pulsewidth modulation (PWM) techniques for a two-level inverter have been reported in the literature. This paper derives such analytical closed-form expressions, pertaining to centered space-vector PWM (CSVPWM) and eight different advanced bus-clamping PWM (ABCPWM) schemes, for a three-level neutral-point-clamped (NPC) inverter. These ABCPWM schemes switch each phase at twice the nominal switching frequency in certain intervals of the line cycle while clamping each phase to one of the dc terminals over certain other intervals. The harmonic spectra of the output voltages, corresponding to the eight ABCPWM schemes, are studied and compared experimentally with that of CSVPWM over the entire modulation range. The measured values of weighted total harmonic distortion (WTHD) of the line voltage V-WTHD are used to validate the analytical closed-form expressions derived. The analytical expressions, pertaining to two of the ABCPWM methods, are also validated by measuring the total harmonic distortion (THD) in the line current I-THD on a 2.2-kW constant volts-per-hertz induction motor drive.

Design of a Low Power 64 Point FFT Architecture for WLAN Applications

This paper presents a Radix-4(3) based FFT architecture suitable for OFDM based WLAN applications. The radix-4(3) parallel unrolled architecture presented here, uses a radix-4 butterfly unit which takes all four inputs in parallel and can selectively produce one out of the four outputs. A 64 point FFT processor based on the proposed architecture has been implemented in UMC 130nm 1P8M CMOS process with a maximum clock frequency of 100 MHz and area of 0.83mm(2). The proposed processor provides a throughput of four times the clock rate and can finish one 64 point FFT computation in 16 clock cycles. For IEEE 802.11a/g WLAN, the processor needs to be operated at a clock rate of 5 MHz with a power consumption of 2.27 mW which is 27% less than the previously reported low power implementations.

High Throughput, Low Latency, Memory Optimized 64K Point FFT Architecture using Novel Radix-4 Butterfly Unit

In this paper we propose a fully parallel 64K point radix-4(4) FFT processor. The radix-4(4) parallel unrolled architecture uses a novel radix-4 butterfly unit which takes all four inputs in parallel and can selectively produce one out of the four outputs. The radix-4(4) block can take all 256 inputs in parallel and can use the select control signals to generate one out of the 256 outputs. The resultant 64K point FFT processor shows significant reduction in intermediate memory but with increased hardware complexity. Compared to the state-of-art implementation 5], our architecture shows reduced latency with comparable throughput and area. The 64K point FFT architecture was synthesized using a 130nm CMOS technology which resulted in a throughput of 1.4 GSPS and latency of 47.7 mu s with a maximum clock frequency of 350MHz. When compared to 5], the latency is reduced by 303 mu s with 50.8% reduction in area.

End point estimates for Radon transform of radial functions on non-Euclidean spaces

We prove end point estimate for Radon transform of radial functions on affine Grasamannian and real hyperbolic space. We also discuss analogs of these results on the sphere.

Accurate point matching based on multi-objective Genetic Algorithm for multi-sensor satellite imagery

This paper investigates a novel approach for point matching of multi-sensor satellite imagery. The feature (corner) points extracted using an improved version of the Harris Corner Detector (HCD) is matched using multi-objective optimization based on a Genetic Algorithm (GA). An objective switching approach to optimization that incorporates an angle criterion, distance condition and point matching condition in the multi-objective fitness function is applied to match corresponding corner-points between the reference image and the sensed image. The matched points obtained in this way are used to align the sensed image with a reference image by applying an affine transformation. From the results obtained, the performance of the image registration is evaluated and compared with existing methods, namely Nearest Neighbor-Random SAmple Consensus (NN-Ran-SAC) and multi-objective Discrete Particle Swarm Optimization (DPSO). From the performed experiments it can be concluded that the proposed approach is an accurate method for registration of multi-sensor satellite imagery. (C) 2014 Elsevier Inc. All rights reserved.

Overview of nano-drugs characteristics for clinical application: the journey from the entry to the exit point

The ever-increasing number of diseases worldwide requires comprehensive, efficient, and cost-effective modes of treatments. Among various strategies, nanomaterials fulfill most of these criteria. The unique physicochemical properties of nanoparticles have made them a premier choice as a drug or a drug delivery system for the purpose of treatment, and as bio-detectors for disease prognosis. However, the main challenge is the proper consideration of the physical properties of these nanomaterials, while developing them as potential tools for therapeutics and/or diagnostics. In this review, we focus mainly on the characteristics of nanoparticles to develop an effective and sensitive system for clinical purposes. This review will present an overview of the important properties of nanoparticles, through their journey from its route of administration until disposal from the human body after accomplishing targeted functionality. We have chosen cancer as our model disease to explain the potentiality of nano-systems for therapeutics and diagnostics in relation to several organs (intestine, lung, brain, etc.). Furthermore, we have discussed their biodegradability and accumulation probability which can cause unfavorable side effects in healthy human subjects.

Substituent effect on fluorescence signaling of the cell permeable HSO4- receptors through single point to ratiometric response in green solvent

Two new 2-(2-aminophenyl)benzimidazole-based HSO4- ion selective receptors, 6-(4-nitrophenyl)-5,6-dihydrobenzo4,5]imidazo1,2-c]quinazoline (L1H) and 6-(4-methoxyphenyl)-5,6-dihydrobenzo4,5]imidazo1,2-c] quinazoline (L2H), and their 1 : 1 molecular complexes with HSO4- were prepared in a facile synthetic method and characterized by physicochemical and spectroscopic techniques along with the detailed structural analysis of L1H by single crystal X-ray crystallography. Both receptors (L1H and L2H) behave as highly selective chemosensor for HSO4- ions at biological pH in ethanol-water HEPES buffer (1/5) (v/v) medium over other anions such as F-, Cl-, Br-, I-, AcO-, H2PO4-, N-3(-) and ClO4-. Theoretical and experimental studies showed that the emission efficiency of the receptors (L1H and L2H) was tuned successfully through single point to ratiometric detection by employing the substituent effects. Using 3 sigma method the LOD for HSO4- ions were found to be 18.08 nM and 14.11 nM for L1H and L2H, respectively, within a very short responsive time (15-20 s) in 100 mM HEPES buffer (ethanol-water: 1/5, v/v). Comparison of the utility of the probes (L1H and L2H) as biomarkers for the detection of intracellular HSO4- ions concentrations under a fluorescence microscope has also been included and both probes showed no cytotoxic effect.

Fixed-orientation equilateral triangle matching of point sets

Given a point set P and a class C of geometric objects, G(C)(P) is a geometric graph with vertex set P such that any two vertices p and q are adjacent if and only if there is some C is an element of C containing both p and q but no other points from P. We study G(del)(P) graphs where del is the class of downward equilateral triangles (i.e., equilateral triangles with one of their sides parallel to the x-axis and the corner opposite to this side below that side). For point sets in general position, these graphs have been shown to be equivalent to half-Theta(6) graphs and TD-Delaunay graphs. The main result in our paper is that for point sets P in general position, G(del)(P) always contains a matching of size at least vertical bar P vertical bar-1/3] and this bound is tight. We also give some structural properties of G(star)(P) graphs, where is the class which contains both upward and downward equilateral triangles. We show that for point sets in general position, the block cut point graph of G(star)(P) is simply a path. Through the equivalence of G(star)(P) graphs with Theta(6) graphs, we also derive that any Theta(6) graph can have at most 5n-11 edges, for point sets in general position. (C) 2013 Elsevier B.V. All rights reserved.