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.

Investigations on Optimal Pulse-Width Modulation to Minimize Total Harmonic Distortion in the Line Current

PWM waveforms with positive voltage transition at the positive zero crossing of the fundamental voltage (type-A) are generally considered for PWM waveform with even number of switching angles per quarter whereas, waveforms with negative voltage transition at the positive zero crossing (type-B) are considered for odd number of switching angles per quarter. Optimal PWM, for minimization of total harmonic distortion of line to line (VWTHD), is generally solved with the aforementioned criteria. This paper establishes that a combination of both types of waveforms gives better performance than any individual type in terms of minimum VWTHD for complete range of modulation index (M). Optimal PWM for minimum VWTHD is solved for PWM waveforms with pulse numbers (P) of 5 and 7. Both type-A and type-B waveforms are found to be better in different ranges of M. The theoretical findings are confirmed through simulation and experimental results on a 3.7 kW squirrel cage induction motor in an open-loop V/f drive. Further, the optimal PWM is analysed from a space vector point of view.

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.

Investigation of schemes for incorporating generator Q limits in the fast decoupled load flow method

Fast Decoupled Load Flow (FDLF) is a very popular and widely used power flow analysis method because of its simplicity and efficiency. Even though the basic FDLF algorithm is well investigated, the same is not true in the case of additional schemes/modifications required to obtain adjusted load flow solutions using the FDLF method. Handling generator Q limits is one such important feature needed in any practical load flow method. This paper presents a comprehensive investigation of two classes of schemes intended to handle this aspect i.e. the bus type switching scheme and the sensitivity scheme. We propose two new sensitivity based schemes and assess their performance in comparison with the existing schemes. In addition, a new scheme to avoid the possibility of anomalous solutions encountered while using the conventional schemes is also proposed and evaluated. Results from extensive simulation studies are provided to highlight the strengths and weaknesses of these existing and proposed schemes, especially from the point of view of reliability.

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.

Phase Inversion of Agitated Liquid-Liquid Dispersions in the Presence of Micrometer-Sized Particles

We have investigated the impact of partially wetting particles of tens of micrometers on inversion instability of agitated liquid liquid dispersions. Particles of this size can be easily separated from the exit streams to avoid downstream processing-related issues. The results show that the presence of hydrophilic particles in small quantities (volume fraction range of 2 X 10(-4) to 1.25 x 10(-2)) significantly decreases the dispersed phase fraction at which water-in-oil (w/o) dispersions invert but leaves the inversion of oil-in-water (o/w) dispersions nearly unaffected. The addition of the same particles after they are hydrophobized decreases the dispersed phase fraction at which o/w dispersions invert but leaves the inversion of w/o dispersions unaffected. These findings suggest an increased rate of coalescence of drops when particles wet drops preferentially and a marginal decrease when they wet the continuous phase preferentially. High-speed conductivity measurements on w/o dispersion show transient conduction of a few hundred milliseconds duration through voltage pulses. Close to the inversion point, voltage pulses appear at high frequency for even 7 cm separation between the electrodes. The presence of hydrophilic particles produces a nearly identical signal at a significantly lower dispersed phase fraction itself, close to the new lowered inversion point in the presence of particles. We propose formation of elongated domains of the conducting dispersed phase through a rapid coalescence-deformation-breakup process to explain the new observations. The voltage signal appears as a forerunner of inversion instability.

Isolated singularities of polyharmonic operator in even dimension

We consider the equation Delta(2)u = g(x, u) >= 0 in the sense of distribution in Omega' = Omega\textbackslash {0} where u and -Delta u >= 0. Then it is known that u solves Delta(2)u = g(x, u) + alpha delta(0) - beta Delta delta(0), for some nonnegative constants alpha and beta. In this paper, we study the existence of singular solutions to Delta(2)u = a(x) f (u) + alpha delta(0) - beta Delta delta(0) in a domain Omega subset of R-4, a is a nonnegative measurable function in some Lebesgue space. If Delta(2)u = a(x) f (u) in Omega', then we find the growth of the nonlinearity f that determines alpha and beta to be 0. In case when alpha = beta = 0, we will establish regularity results when f (t) <= Ce-gamma t, for some C, gamma > 0. This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (N >= 5) with a specific weight function a(x) = |x|(sigma). Later, we discuss its analogous generalization for the polyharmonic operator.

Speaker verification based on the fusion of speech acoustics and inverted articulatory signals

We propose apractical, feature-level and score-level fusion approach by combining acoustic and estimated articulatory information for both text independent and text dependent speaker verification. From a practical point of view, we study how to improve speaker verification performance by combining dynamic articulatory information with the conventional acoustic features. On text independent speaker verification, we find that concatenating articulatory features obtained from measured speech production data with conventional Mel-frequency cepstral coefficients (MFCCs) improves the performance dramatically. However, since directly measuring articulatory data is not feasible in many real world applications, we also experiment with estimated articulatory features obtained through acoustic-to-articulatory inversion. We explore both feature level and score level fusion methods and find that the overall system performance is significantly enhanced even with estimated articulatory features. Such a performance boost could be due to the inter-speaker variation information embedded in the estimated articulatory features. Since the dynamics of articulation contain important information, we included inverted articulatory trajectories in text dependent speaker verification. We demonstrate that the articulatory constraints introduced by inverted articulatory features help to reject wrong password trials and improve the performance after score level fusion. We evaluate the proposed methods on the X-ray Microbeam database and the RSR 2015 database, respectively, for the aforementioned two tasks. Experimental results show that we achieve more than 15% relative equal error rate reduction for both speaker verification tasks. (C) 2015 Elsevier Ltd. All rights reserved.

Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.

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.

High-throughput miniaturized microfluidic microscopy with radially parallelized channel geometry

In this article, we present a novel approach to throughput enhancement in miniaturized microfluidic microscopy systems. Using the presented approach, we demonstrate an inexpensive yet high-throughput analytical instrument. Using the high-throughput analytical instrument, we have been able to achieve about 125,880 cells per minute (more than one hundred and twenty five thousand cells per minute), even while employing cost-effective low frame rate cameras (120 fps). The throughput achieved here is a notable progression in the field of diagnostics as it enables rapid quantitative testing and analysis. We demonstrate the applicability of the instrument to point-of-care diagnostics, by performing blood cell counting. We report a comparative analysis between the counts (in cells per mu l) obtained from our instrument, with that of a commercially available hematology analyzer.

Cost effective campaigning in social networks

Campaigners are increasingly using online social networking platforms for promoting products, ideas and information. A popular method of promoting a product or even an idea is incentivizing individuals to evangelize the idea vigorously by providing them with referral rewards in the form of discounts, cash backs, or social recognition. Due to budget constraints on scarce resources such as money and manpower, it may not be possible to provide incentives for the entire population, and hence incentives need to be allocated judiciously to appropriate individuals for ensuring the highest possible outreach size. We aim to do the same by formulating and solving an optimization problem using percolation theory. In particular, we compute the set of individuals that are provided incentives for minimizing the expected cost while ensuring a given outreach size. We also solve the problem of computing the set of individuals to be incentivized for maximizing the outreach size for given cost budget. The optimization problem turns out to be non trivial; it involves quantities that need to be computed by numerically solving a fixed point equation. Our primary contribution is, that for a fairly general cost structure, we show that the optimization problems can be solved by solving a simple linear program. We believe that our approach of using percolation theory to formulate an optimization problem is the first of its kind. (C) 2016 Elsevier B.V. All rights reserved.