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.

Haemophilus influenzae Genome Database (HIGDB): A single point web resource for Haemophilus influenzae

Background: Haemophilus influenzae (H. Influenzae) is the causative agent of pneumonia, bacteraemia and meningitis. The organism is responsible for large number of deaths in both developed and developing countries. Even-though the first bacterial genome to be sequenced was that of H. Influenzae, there is no exclusive database dedicated for H. Influenzae. This prompted us to develop the Haemophilus influenzae Genome Database (HIGDB). Methods: All data of HIGDB are stored and managed in MySQL database. The HIGDB is hosted on Solaris server and developed using PERL modules. Ajax and JavaScript are used for the interface development. Results: The HIGDB contains detailed information on 42,741 proteins, 18,077 genes including 10 whole genome sequences and also 284 three dimensional structures of proteins of H. influenzae. In addition, the database provides ``Motif search'' and ``GBrowse''. The HIGDB is freely accessible through the URL:http://bioserverl.physicslisc.ernetin/HIGDB/. Discussion: The HIGDB will be a single point access for bacteriological, clinical, genomic and proteomic information of H. influenzae. The database can also be used to identify DNA motifs within H. influenzae genomes and to compare gene or protein sequences of a particular strain with other strains of H. influenzae. (C) 2014 Elsevier Ltd. All rights reserved.

Two-point correlation function of an exclusion process with hole-dependent rates

We consider an exclusion process on a ring in which a particle hops to an empty neighboring site with a rate that depends on the number of vacancies n in front of it. In the steady state, using the well-known mapping of this model to the zero-range process, we write down an exact formula for the partition function and the particle-particle correlation function in the canonical ensemble. In the thermodynamic limit, we find a simple analytical expression for the generating function of the correlation function. This result is applied to the hop rate u(n) = 1 + (b/n) for which a phase transition between high-density laminar phase and low-density jammed phase occurs for b > 2. For these rates, we find that at the critical density, the correlation function decays algebraically with a continuously varying exponent b - 2. We also calculate the two-point correlation function above the critical density and find that the correlation length diverges with a critical exponent nu = 1/(b - 2) for b < 3 and 1 for b > 3. These results are compared with those obtained using an exact series expansion for finite systems.

Transitory second-order reciprocal connection for two surfaces in point contact

This paper investigates the instantaneous spatial higher pair to lower pair substitute-connection which is kinematically equivalent up to acceleration analysis for two smooth surfaces in point contact. The existing first-order equivalent substitute-connection consisting of a Hooke's joint (U-joint) and a spherical joint (S-joint) connected by an additional link is extended up to second-order. A two step procedure is chalked out for achieving this equivalence. First, the existing method is employed for velocity equivalence. In the second step, the two centers of substitution are obtained as a conjugate relationship involving the principal normal curvatures of the surfaces at the contact point and the screw coordinates of the instantaneous screw axis (ISA) of the first-order relative motion. Unlike the classical planar replacement, this particular substitution cannot be done by merely examining the profiles of the contacting surfaces. An illustrative example of a three-link direct-contact mechanism is presented. (C) 2014 Elsevier Ltd. All rights reserved.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

Characterization of friction at three contact pairs by photoelastic Isotropic point (IP)

Friction coefficient between a circular-disk periphery and V-block surface was determined by introducing the concept of isotropic point (IP) in isochromatic field of the disk under three-point symmetric loading. IP position on the symmetry axis depends on active coefficient of friction during experiment. We extend this work to asymmetric loading of circular disk in which case two frictional contact pairs out of three loading contacts, independently control the unconstrained IP location. Photoelastic experiment is conducted on particular case of asymmetric three-point loading of circular disk. Basics of digital image processing are used to extract few essential parameters from experimental image, particularly IP location. Analytical solution by Flamant for half plane with a concentrated load, is utilized to derive stress components for required loading configurations of the disk. IP is observed, in analytical simulations of three-point asymmetric normal loading, to move from vertical axis to the boundary along an ellipse-like curve. When friction is included in the analysis, IP approaches the center with increase in loading friction and it goes away with increase in support friction. With all these insights, using experimental IP information, friction angles at three contact pairs of circular disk under asymmetric loading, are determined.

A comparative study of failure features in aerospace grade unidirectional and bidirectional woven CFRP composite laminates under four-point bend fatigue loads

Damage mechanisms in unidirectional (UD) and bi-directional (BD) woven carbon fiber reinforced polymer (CFRP) laminates subjected to four point flexure, both in static and fatigue loadings, were studied. The damage progression in composites was monitored by observing the slopes of the load vs. deflection data that represent the stiffness of the given specimen geometry over a number of cycles. It was observed that the unidirectional composites exhibit gradual loss in stiffness whereas the bidirectional woven composites show a relatively quicker loss during stage II of fatigue damage progression. Both, the static and the fatigue failures in unidirectional carbon fiber reinforced polymer composites originates due to generation of cracks on compression face while in bidirectional woven composites the damage ensues from both the compression and the tensile faces. These observations are supported by a detailed fractographic analysis.

Spectral Clustering with Jensen-type kernels and their multi-point extensions

Motivated by multi-distribution divergences, which originate in information theory, we propose a notion of `multipoint' kernels, and study their applications. We study a class of kernels based on Jensen type divergences and show that these can be extended to measure similarity among multiple points. We study tensor flattening methods and develop a multi-point (kernel) spectral clustering (MSC) method. We further emphasize on a special case of the proposed kernels, which is a multi-point extension of the linear (dot-product) kernel and show the existence of cubic time tensor flattening algorithm in this case. Finally, we illustrate the usefulness of our contributions using standard data sets and image segmentation tasks.

Asymptotic Bounds on the Power-Delay Tradeoff for Fading Point-to-Point Links From Geometric Bounds on the Stationary Distribution of the Queue Length

The optimal power-delay tradeoff is studied for a time-slotted independently and identically distributed fading point-to-point link, with perfect channel state information at both transmitter and receiver, and with random packet arrivals to the transmitter queue. It is assumed that the transmitter can control the number of packets served by controlling the transmit power in the slot. The optimal tradeoff between average power and average delay is analyzed for stationary and monotone transmitter policies. For such policies, an asymptotic lower bound on the minimum average delay of the packets is obtained, when average transmitter power approaches the minimum average power required for transmitter queue stability. The asymptotic lower bound on the minimum average delay is obtained from geometric upper bounds on the stationary distribution of the queue length. This approach, which uses geometric upper bounds, also leads to an intuitive explanation of the asymptotic behavior of average delay. The asymptotic lower bounds, along with previously known asymptotic upper bounds, are used to identify three new cases where the order of the asymptotic behavior differs from that obtained from a previously considered approximate model, in which the transmit power is a strictly convex function of real valued service batch size for every fade state.

Harmonic analysis of DC capacitor current in sinusoidal and space-vector modulated neutral-point-clamped inverters

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 a double Fourier series based analysis of the harmonic contents of the DC capacitor current in a three-level neutral-point clamped (NPC) inverter, modulated with sine-triangle pulse-width modulation (SPWM) or conventional space vector pulse-width modulation (CSVPWM) schemes. The analytical results are validated experimentally on a 3-kVA three-level inverter prototype. The capacitor current in an NPC inverter has a periodicity of 120(a similar to) at the fundamental or modulation frequency. Hence, this current contains third-harmonic and triplen-frequency components, apart from switching frequency components. The harmonic components vary with modulation index and power factor for both PWM schemes. The third harmonic current decreases with increase in modulation index and also decreases with increase in power factor in case of both PWM methods. In general, the third harmonic content is higher with SPWM than with CSVPWM at a given operating condition. Also, power loss and voltage ripple in the DC capacitor are estimated for both the schemes using the current harmonic spectrum and equivalent series resistance (ESR) of the capacitor.

Determinantal point processes in the plane from products of random matrices

We show that the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of k independent n x n matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.

Position-dependent velocity of an effective temperature point for the estimation of the thermal diffusivity of solids

A new approach is proposed to estimate the thermal diffusivity of optically transparent solids at ambient temperature based on the velocity of an effective temperature point (ETP), and by using a two-beam interferometer the proposed concept is corroborated. 1D unsteady heat flow via step-temperature excitation is interpreted as a `micro-scale rectilinear translatory motion' of an ETP. The velocity dependent function is extracted by revisiting the Fourier heat diffusion equation. The relationship between the velocity of the ETP with thermal diffusivity is modeled using a standard solution. Under optimized thermal excitation, the product of the `velocity of the ETP' and the distance is a new constitutive equation for the thermal diffusivity of the solid. The experimental approach involves the establishment of a 1D unsteady heat flow inside the sample through step-temperature excitation. In the moving isothermal surfaces, the ETP is identified using a two-beam interferometer. The arrival-time of the ETP to reach a fixed distance away from heat source is measured, and its velocity is calculated. The velocity of the ETP and a given distance is sufficient to estimate the thermal diffusivity of a solid. The proposed method is experimentally verified for BK7 glass samples and the measured results are found to match closely with the reported value.

Two-Point Closure Strategy in the Mapping Closure Approximation Approach

A two-point closure strategy in mapping closure approximation (MCA) approach is developed for the evolution of the probability density function (PDF) of a scalar advected by stochastic velocity fields. The MCA approach is based on multipoint statistics. We formulate a MCA modeled system using the one-point PDFs and two-point correlations. The MCA models can describe both the evolution of the PDF shape and the rate at which the PDF evolves.