A Split-and-Merge Dictionary Learning Algorithm for Sparse Representation: Application to Image Denoising

In big data image/video analytics, we encounter the problem of learning an over-complete dictionary for sparse representation from a large training dataset, which cannot be processed at once because of storage and computational constraints. To tackle the problem of dictionary learning in such scenarios, we propose an algorithm that exploits the inherent clustered structure of the training data and make use of a divide-and-conquer approach. The fundamental idea behind the algorithm is to partition the training dataset into smaller clusters, and learn local dictionaries for each cluster. Subsequently, the local dictionaries are merged to form a global dictionary. Merging is done by solving another dictionary learning problem on the atoms of the locally trained dictionaries. This algorithm is referred to as the split-and-merge algorithm. We show that the proposed algorithm is efficient in its usage of memory and computational complexity, and performs on par with the standard learning strategy, which operates on the entire data at a time. As an application, we consider the problem of image denoising. We present a comparative analysis of our algorithm with the standard learning techniques that use the entire database at a time, in terms of training and denoising performance. We observe that the split-and-merge algorithm results in a remarkable reduction of training time, without significantly affecting the denoising performance.

Time Dependent Operator-split and Unsplit Schemes for One Dimensional Premixed Flames

This paper is concerned with a study of an operator split scheme and unsplit scheme for the computation of adiabatic freely propagating one-dimensional premixed flames. The study uses unsteady method for both split and unsplit schemes employing implicit chemistry and explicit diffusion, a combination which is stable and convergent. Solution scheme is not sensitive to the initial starting estimate and provides steady state even with straight line profiles (far from steady state) in small number of time steps. Two systems H2-Air and H2-NO (involving complex nitrogen chemistry) are considered in presentinvestigation. Careful comparison shows that the operator split approach is slightly superior than the unsplit when chemistry becomes complex. Comparison of computational times with those of existing steady and unsteady methods seems to suggest that the method employing implicit-explicit algorithm is very efficient and robust.

Rainbow colouring of split and threshold Graphs

A rainbow colouring of a connected graph is a colouring of the edges of the graph, such that every pair of vertices is connected by at least one path in which no two edges are coloured the same. Such a colouring using minimum possible number of colours is called an optimal rainbow colouring, and the minimum number of colours required is called the rainbow connection number of the graph. A Chordal Graph is a graph in which every cycle of length more than 3 has a chord. A Split Graph is a chordal graph whose vertices can be partitioned into a clique and an independent set. A threshold graph is a split graph in which the neighbourhoods of the independent set vertices form a linear order under set inclusion. In this article, we show the following: 1. The problem of deciding whether a graph can be rainbow coloured using 3 colours remains NP-complete even when restricted to the class of split graphs. However, any split graph can be rainbow coloured in linear time using at most one more colour than the optimum. 2. For every integer k ≥ 3, the problem of deciding whether a graph can be rainbow coloured using k colours remains NP-complete even when restricted to the class of chordal graphs. 3. For every positive integer k, threshold graphs with rainbow connection number k can be characterised based on their degree sequence alone. Further, we can optimally rainbow colour a threshold graph in linear time.

MAST: multi-script annotation toolkit for scenic text

This paper describes a semi-automatic tool for annotation of multi-script text from natural scene images. To our knowledge, this is the maiden tool that deals with multi-script text or arbitrary orientation. The procedure involves manual seed selection followed by a region growing process to segment each word present in the image. The threshold for region growing can be varied by the user so as to ensure pixel-accurate character segmentation. The text present in the image is tagged word-by-word. A virtual keyboard interface has also been designed for entering the ground truth in ten Indic scripts, besides English. The keyboard interface can easily be generated for any script, thereby expanding the scope of the toolkit. Optionally, each segmented word can further be labeled into its constituent characters/symbols. Polygonal masks are used to split or merge the segmented words into valid characters/symbols. The ground truth is represented by a pixel-level segmented image and a '.txt' file that contains information about the number of words in the image, word bounding boxes, script and ground truth Unicode. The toolkit, developed using MATLAB, can be used to generate ground truth and annotation for any generic document image. Thus, it is useful for researchers in the document image processing community for evaluating the performance of document analysis and recognition techniques. The multi-script annotation toolokit (MAST) is available for free download.

Optimality of orthogonal sequences with multi-dimensional signaling

The sum capacity on a symbol-synchronous CDMA system having processing gain N and supporting K power constrained users is achieved by employing any set of N orthogonal sequences if a few users are allowed to signal along multiple dimensions. Analogously, the minimum received power (energy-per-chip) on the symbolsynchronous CDMA system supporting K users that demand specified data rates is attained by employing any set of N orthogonal sequences. At most (N - 1) users need to be split and if there are no oversized users, these split users need to signal only in two dimensions each. These results show that sum capacity or minimum sum power can be achieved with minimal downlink signaling.

Parameterized Algorithms for MAX COLORABLE INDUCED SUBGRAPH Problem on Perfect Graphs

We address the parameterized complexity ofMaxColorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis and Gavril IPL 1987] showed that this problem is NP-complete even on split graphs if q is part of input, but gave a n(O(q)) algorithm on chordal graphs. We first observe that the problem is W2]-hard parameterized by q, even on split graphs. However, when parameterized by l, the number of vertices in the solution, we give two fixed-parameter tractable algorithms. The first algorithm runs in time 5.44(l) (n+#alpha(G))(O(1)) where #alpha(G) is the number of maximal independent sets of the input graph. The second algorithm runs in time q(l+o()l())n(O(1))T(alpha) where T-alpha is the time required to find a maximum independent set in any induced subgraph of G. The first algorithm is efficient when the input graph contains only polynomially many maximal independent sets; for example split graphs and co-chordal graphs. The running time of the second algorithm is FPT in l alone (whenever T-alpha is a polynomial in n), since q <= l for all non-trivial situations. Finally, we show that (under standard complexitytheoretic assumptions) the problem does not admit a polynomial kernel on split and perfect graphs in the following sense: (a) On split graphs, we do not expect a polynomial kernel if q is a part of the input. (b) On perfect graphs, we do not expect a polynomial kernel even for fixed values of q >= 2.

A Multi-phase Approach for Improving Information Diffusion in Social Networks

For maximizing influence spread in a social network, given a certain budget on the number of seed nodes, we investigate the effects of selecting and activating the seed nodes in multiple phases. In particular, we formulate an appropriate objective function for two-phase influence maximization under the independent cascade model, investigate its properties, and propose algorithms for determining the seed nodes in the two phases. We also study the problem of determining an optimal budget-split and delay between the two phases.

Split-Freedom And Mvd-Intersection - A New Characterization Of Multivalued Dependencies Having Conflict-Free Covers

Sets of multivalued dependencies (MVDs) having conflict-free covers are important to the theory and design of relational databases [2,12,15,16]. Their desirable properties motivate the problem of testing a set M of MVDs for the existence of a confiict-free cover. In [8] Goodman and Tay have proposed an approach based on the possible equivalence of M to a single (acyclic) join dependency (JD). We remark that their characterization does not lend an insight into the nature of such sets of MVDs. Here, we use notions that are intrinsic to MVDs to develop a new characterization. Our approach proceeds in two stages. In the first stage, we use the notion of “split-free” sets of MVDs and obtain a characterization of sets M of MVDs having split-free covers. In the second, we use the notion of “intersection” of MVDs to arrive at a necessary and sufficient condition for a split-free set of MVDs to be conflict-free. Based on our characterizations, we also give polynomial-time algorithms for testing whether M has split-free and conflict-free covers. The highlight of our approach is the clear insight it provides into the nature of sets of MVDs having conflict-free covers. Less emphasis is given in this paper to the actual efficiency of the algorthms. Finally, as a bonus, we derive a desirable property of split-free sets of MVDs,thereby showing that they are interesting in their own right.

Multiple imaging and multichannel optical processing with split lenses

The use of split lenses for multiple imaging and multichannel optical processing is demonstrated. Conditions are obtained for nonoverlapping of multipled images and avoiding crosstalk in the multichannel processing. Almost uniform intensity across the multipled images is an advantage here, while the low ƒ/No. of the split lens segments puts a limit in the resolution in image processing. Experimental results of multiple imaging and of a few multichannel processing are presented.

A note on the damping and oscillations of a fluid drop moving in another fluid

The oscillations of a drop moving in another fluid medium have been studied at low values of Reynolds number and Weber number by taking into consideration the shape of the drop and the viscosities of the two phases in addition to the interfacial tension. The deformation of the drop modifies the Lamb's expression for frequency by including a correction term while the viscous effects split the frequency into a pair of frequencies—one lower and the other higher than Lamb's. The lower frequency mode has ample experimental support while the higher frequency mode has also been observed. The two modes almost merge with Lamb's frequency for the asymptotic cases of a drop in free space or a bubble in a dense viscous fluid but the splitting becomes large when the two fluids have similar properties. Instead of oscillations, aperiodic damping modes are found to occur in drops with sizes smaller than a critical size ($\sim\hat{\rho}\hat{\nu}^2/T $). With the help of these calculations, many of the available experimental results are analyzed and discussed.

Analysis and design of split-capacitor resistive-inductive passive damping for LCL filters in grid-connected inverters

Grid-connected inverters require a third-order LCL filter to meet standards such as the IEEE Std. 519-1992 while being compact and cost-effective. LCL filter introduces resonance, which needs to be damped through active or passive methods. Passive damping schemes have less control complexity and are more reliable. This study explores the split-capacitor resistive-inductive (SC-RL) passive damping scheme. The SC-RL damped LCL filter is modelled using state space approach. Using this model, the power loss and damping are analysed. Based on the analysis, the SC-RL scheme is shown to have lower losses than other simpler passive damping methods. This makes the SC-RL scheme suitable for high power applications. A method for component selection that minimises the power loss in the damping resistors while keeping the system well damped is proposed. The design selection takes into account the influence of switching frequency, resonance frequency and the choice of inductance and capacitance values of the filter on the damping component selection. The use of normalised parameters makes it suitable for a wide range of design applications. Analytical results show the losses and quality factor to be in the range of 0.05-0.1% and 2.0-2.5, respectively, which are validated experimentally.

Analysis of sine-triangle and zero-sequence injection modulation schemes for split-phase induction motor drive

A split-phase induction motor is fed from two three-phase voltage source inverters for speed control. This study analyses carrier-comparison based pulse width modulation (PWM) schemes for a split-phase motor drive, from a space-vector perspective. Sine-triangle PWM, one zero-sequence injection PWM where the same zero-sequence signal is used for both the inverters, and another zero-sequence injection PWM where different zero-sequence signals are employed for the two inverters are considered. The set of voltage vectors applied, the sequence in which the voltage vectors are applied, and the resulting current ripple vector are analysed for all the PWM methods. Besides all the PWM methods are compared in terms of dc bus utilisation. For the same three-phase sine reference, the PWM method with different zero-sequence signals for the two inverters is found to employ a set of vectors different from the other methods. Both analysis and experimental results show that this method results in lower total harmonic distortion and higher dc bus utilisation than the other two PWM methods.

Effect Of Administration Of Luteinizing-Hormone (Lh) And Deprivation Of Lh On The Proteins Of Smooth Endoplasmic-Reticulum Of Immature And Adult-Rat Leydig-Cells

Analysis of proteins of smooth endoplasmic reticulum (SER) of Leydig cells from immature and admit rats by two-dimensional polyacrylamide gel electrophoresis (SDS-PAGE) revealed the presence of several new proteins in the adult rats. Administration of human chorionic gonadotropin to immature rats for ten days also resulted in a significant increase as well as the appearance of several new proteins. The general pattern of SDS-PAGE analysis of the SER proteins of Leydig cells resembled that of the adult rat. SDS-PAGE analysis of the SER proteins of Leydig cells from adult rats following deprivation of endogenous luteinizing hormone by administration of antiserum to ovine luteinizing hormone resulted in a pattern which to certain extent resembled that of an immature I at. Western Blot analysis of luteinizing hormone antiserum treated rat Leydig cell proteins revealed a decrease in the 17-alpha-hydroxylase compared to the control. These results provide biochemical evidence for the suggestion that one of the main functions of luteinizing hormone is the control of biogenesis and/or turnover SER of Leydig cells in the rat.

Integral Formulation of the Problem of Current Distribution in Compulsator Wires of Electromagnetic Launchers and Railguns

Compulsators are power sources of choice for use in electromagnetic launchers and railguns. These devices hold the promise of reducing unit costs of payload to orbit. In an earlier work, the author had calculated the current distribution in compulsator wires by considering the wire to be split into a finite number of separate wires. The present work develops an integral formulation of the problem of current distribution in compulsator wires which leads to an integrodifferential equation. Analytical solutions, including those for the integration constants, are obtained in closed form. The analytical solutions present a much clearer picture of the effect of various input parameters on the cross-sectional current distribution and point to ways in which the desired current density distribution can be achieved. Results are graphically presented and discussed, with particular reference to a 50-kJ compulsator in Bangalore. Finite-element analysis supports the results.

Non-bonded interactions in 2,2,4,4-tetramethyl-1,3-cyclobutanedithione and 2,2,4,4-tetramethyl-3-thio-1,3-cyclobutanedione

Electronic absorption and emission spectra as well as He(I) photoelectron spectra of 2,2,4,4-tetramethyl-,3-cyclobutanedithione and 2,2,4,4-tetramethyl-1-3-thio-1,3-cyclobutanedione have been interpreted on the basis of molecular orbital calculations. The results show that the non-bonded orbital of the dithione is split owing to through-bond interaction, the magnitude of splitting being 0.4 eV. The π* orbital of the dithione appears to be split by about 0.2 eV. Electronic absorption spectra show evidence for the existence of four n—π* transitions, arising out of the splitting of the orbitals referred to above, just as in the case of 2,2,4,4-tetramethyl-1,3-cyclobutanedione. Electronic and photoelectron spectra of the thio-dione show evidence for weak interaction between the C=S and C&.zdbnd;O groups, probably via π* orbitals. Infrared spectra of both the dithione and the thio-dione are consistent with the planar cyclobutane ring; the ring-puckering frequency responsible for non-bonded interactions is around 67 cm−1 in both the dithione and the thio-dione, the value not being very different from that in the dione. The 1,3-transannular distance is also similar in the three molecules.