Patterns in permuted binary matrices

Reorganizing a dataset so that its hidden structure can be observed is useful in any data analysis task. For example, detecting a regularity in a dataset helps us to interpret the data, compress the data, and explain the processes behind the data. We study datasets that come in the form of binary matrices (tables with 0s and 1s). Our goal is to develop automatic methods that bring out certain patterns by permuting the rows and columns. We concentrate on the following patterns in binary matrices: consecutive-ones (C1P), simultaneous consecutive-ones (SC1P), nestedness, k-nestedness, and bandedness. These patterns reflect specific types of interplay and variation between the rows and columns, such as continuity and hierarchies. Furthermore, their combinatorial properties are interlinked, which helps us to develop the theory of binary matrices and efficient algorithms. Indeed, we can detect all these patterns in a binary matrix efficiently, that is, in polynomial time in the size of the matrix. Since real-world datasets often contain noise and errors, we rarely witness perfect patterns. Therefore we also need to assess how far an input matrix is from a pattern: we count the number of flips (from 0s to 1s or vice versa) needed to bring out the perfect pattern in the matrix. Unfortunately, for most patterns it is an NP-complete problem to find the minimum distance to a matrix that has the perfect pattern, which means that the existence of a polynomial-time algorithm is unlikely. To find patterns in datasets with noise, we need methods that are noise-tolerant and work in practical time with large datasets. The theory of binary matrices gives rise to robust heuristics that have good performance with synthetic data and discover easily interpretable structures in real-world datasets: dialectical variation in the spoken Finnish language, division of European locations by the hierarchies found in mammal occurrences, and co-occuring groups in network data. In addition to determining the distance from a dataset to a pattern, we need to determine whether the pattern is significant or a mere occurrence of a random chance. To this end, we use significance testing: we deem a dataset significant if it appears exceptional when compared to datasets generated from a certain null hypothesis. After detecting a significant pattern in a dataset, it is up to domain experts to interpret the results in the terms of the application.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Optimum weighting function in bispectral analysis in speckle interferometry - Binary star parity detection

In order to describe the atmospheric turbulence which limits the resolution of long-exposure images obtained using ground-based large telescopes, a simplified model of a speckle pattern, reducing the complexity of calculating field-correlations of very high order, is presented. Focal plane correlations are used instead of correlations in the spatial frequency domain. General tripple correlations for a point source and for a binary are calculated and it is shown that they are not a strong function of the binary separation. For binary separations close to the diffraction limit of the telescope, the genuine triple correlation technique ensures a better SNR than the near-axis Knox-Thompson technique. The simplifications allow a complete analysis of the noise properties at all levels of light.

A modified sulphide capacity function

The sulphide capacity as originally defined by Fincham and Richardson is a strong function of composition in pseudobinary oxide melts of interest in extractive metallurgy. From an analysis of data available in the literature, it is shown that sulphide capacity is directly proportional to the activity of the basic oxide in the melt, within the uncertainty of experimental data. A single parameter is sufficient to describe the sulphide capacity of a binary slag system under isothermal and isobaric conditions. The correlation indicates that the activity coefficient of the sulphide ion or the neutral base metal sulphide dissolved in the melt is independent of composition in pseudobinary melts within experimental uncertainty. Structural variations in the melt with composition do not seem to affect the activity coefficient of the sulphide. A modified sulphide capacity function is defined which makes the treatment more elegant and greatly simplifies data storage and retrieval. The modified function is not based on any model for the melt.

Nestedness pattern in stream diatom assemblages of central Western Ghats

Community diversity and the population abundance of a particular group of species are controlled by immediate environment, inter-and intra-species interactions, landscape conditions, historical events and evolutionary processes. Nestedness is a measure of order in an ecological system, referring to the order in which the number of species is related to area or other factors. In this study we have studied the nestedness pattern in stream diatom assemblages in 24 stream sites of central Western Ghats, and report 98 taxa from the streams of central Western Ghats region. The communities show highly significant nested pattern. The Mantel test of matrix revealed a strong relationship between species assemblages and environmental conditions at the sites. A significant relationship between species assemblage and environmental condition was observed. Principal component analysis (PCA) indicated that environmental conditions differed markedly across the sampling sites, with the first three components explaining 78% of variance. Species composition of diatoms is significantly correlated with environmental distance across geographical extent. The current pattern suggests that micro-environment at regional levels influences the species composition of epilithic diatoms in streams. The nestedness shown by the diatom community was highly significant, even though it had a high proportion of idiosyncratic species, characterized with high numbers of cosmopolitan species, whereas the nested species were dominated by endemic species. PCA identifies ionic parameters and nutrients as the major features which determine the characteristics of the sampling sites. Hence the local water quality parameters are the major factors in deciding the diatom species assemblages.

Effect of dynamical asymmetry on the viscosity of a random copolymer melt

The variation of the viscosity as a function of the sequence distribution in an A-B random copolymer melt is determined. The parameters that characterize the random copolymer are the fraction of A monomers f, the parameter lambda which determines the correlation in the monomer identities along a chain and the Flory chi parameter chi(F) which determines the strength of the enthalpic repulsion between monomers of type A and B. For lambda>0, there is a greater probability of finding like monomers at adjacent positions along the chain, and for lambda<0 unlike monomers are more likely to be adjacent to each other. The traditional Markov model for the random copolymer melt is altered to remove ultraviolet divergences in the equations for the renormalized viscosity, and the phase diagram for the modified model has a binary fluid type transition for lambda>0 and does not exhibit a phase transition for lambda<0. A mode coupling analysis is used to determine the renormalization of the viscosity due to the dependence of the bare viscosity on the local concentration field. Due to the dissipative nature of the coupling. there are nonlinearities both in the transport equation and in the noise correlation. The concentration dependence of the transport coefficient presents additional difficulties in the formulation due to the Ito-Stratonovich dilemma, and there is some ambiguity about the choice of the concentration to be used while calculating the noise correlation. In the Appendix, it is shown using a diagrammatic perturbation analysis that the Ito prescription for the calculation of the transport coefficient, when coupled with a causal discretization scheme, provides a consistent formulation that satisfies stationarity and the fluctuation dissipation theorem. This functional integral formalism is used in the present analysis, and consistency is verified for the present problem as well. The upper critical dimension for this type of renormaliaation is 2, and so there is no divergence in the viscosity in the vicinity of a critical point. The results indicate that there is a systematic dependence of the viscosity on lambda and chi(F). The fluctuations tend to increase the viscosity for lambda<0, and decrease the viscosity for lambda>0, and an increase in chi(F) tends to decrease the viscosity. (C) 1996 American Institute of Physics.

Wet chemical formation of nanoparticles of binary perovskites through isothermal gel to crystallite conversion

Coarse BO2·xH2O (2 < x < 80) gels, free of anion contaminants react with A(OH)2 under refluxing conditions at 70�100°C giving rise to crystallites of single phased, nanometer size powders of ABO3 perovskites (A = Ba, Sr, Ca, Mg, Pb; B = Zr, Ti, Sn). Solid solutions of perovskites could be prepared from compositionally modified gels or mixtures of A(OH)2. Donor doped perovskites could also be prepared from the same method so that the products after processing are often semiconducting. Faster interfacial diffusion of A2+ ions into the gel generates the crystalline regions whose composition is controllable by the A/B ratio as well as the A(OH)2 concentration.

Total peroxidase activity and peroxidase isoforms as modified by salt stress in two cultivars of fox-tail millet with differential salt tolerance

The effect of NaCl on total peroxidase activity, induction of isoperoxidases and lipid peroxidation in 5-day-old seedlings of two contrasting genotypes of Setaria italica L. (Prasad, a salt tolerant cultivar and Lepakshi, a salt susceptible cultivar), was studied. Total peroxidase activity increased under NaCl salinity and the degree of elevation in the activity was salt concentration dependent. Nevertheless, a greater activity was recorded in the tolerant cultivar (cv Prasad) compared to the susceptible (cv Lepakshi) one in all days of sampling. Further, the pattern of isoperoxidases was modified during stress conditions as evident from the electrophoregrams. Although, five acidic isoforms were detected in both cultivars, differences were found between the cultivars. Furthermore, it was observed that acidic isoperoxidases were strongly expressed and an acidic isoperoxidase, A(3p) (27 kDa) is specifically found in the tolerant cultivar (cv Prasad) under NaCl stress. This isoform was partially purified and found to be thermostable with pr 5.5 and the optimum pH 7.4. A close correlation exists between the rate of lipid peroxidation in terms of malonaldehyde (MDA) content and total peroxidase activity per gram fresh weight with salt tolerance of the two cultivars. The tolerant cultivar (cv Prasad) had low MDA content and high total peroxidase activity than the susceptible variety (cv Lepakshi) during salinity stress. (C) 1999 Published by Elsevier Science Ireland Ltd. All rights reserved.

Modified kinetic flux vector splitting (m-KFVS) method for compressible flows

To resolve many flow features accurately, like accurate capture of suction peak in subsonic flows and crisp shocks in flows with discontinuities, to minimise the loss in stagnation pressure in isentropic flows or even flow separation in viscous flows require an accurate and low dissipative numerical scheme. The first order kinetic flux vector splitting (KFVS) method has been found to be very robust but suffers from the problem of having much more numerical diffusion than required, resulting in inaccurate computation of the above flow features. However, numerical dissipation can be reduced by refining the grid or by using higher order kinetic schemes. In flows with strong shock waves, the higher order schemes require limiters, which reduce the local order of accuracy to first order, resulting in degradation of flow features in many cases. Further, these schemes require more points in the stencil and hence consume more computational time and memory. In this paper, we present a low dissipative modified KFVS (m-KFVS) method which leads to improved splitting of inviscid fluxes. The m-KFVS method captures the above flow features more accurately compared to first order KFVS and the results are comparable to second order accurate KFVS method, by still using the first order stencil. (C) 2011 Elsevier Ltd. All rights reserved.

Geoinformatics for Urbanisation and Urban Sprawl Pattern Analysis

Urbanisation is the increase in the population of cities in proportion to the region's rural population. Urbanisation in India is very rapid with urban population growing at around 2.3 percent per annum. Urban sprawl refers to the dispersed development along highways or surrounding the city and in rural countryside with implications such as loss of agricultural land, open space and ecologically sensitive habitats. Sprawl is thus a pattern and pace of land use in which the rate of land consumed for urban purposes exceeds the rate of population growth resulting in an inefficient and consumptive use of land and its associated resources. This unprecedented urbanisation trend due to burgeoning population has posed serious challenges to the decision makers in the city planning and management process involving plethora of issues like infrastructure development, traffic congestion, and basic amenities (electricity, water, and sanitation), etc. In this context, to aid the decision makers in following the holistic approaches in the city and urban planning, the pattern, analysis, visualization of urban growth and its impact on natural resources has gained importance. This communication, analyses the urbanisation pattern and trends using temporal remote sensing data based on supervised learning using maximum likelihood estimation of multivariate normal density parameters and Bayesian classification approach. The technique is implemented for Greater Bangalore – one of the fastest growing city in the World, with Landsat data of 1973, 1992 and 2000, IRS LISS-3 data of 1999, 2006 and MODIS data of 2002 and 2007. The study shows that there has been a growth of 466% in urban areas of Greater Bangalore across 35 years (1973 to 2007). The study unravels the pattern of growth in Greater Bangalore and its implication on local climate and also on the natural resources, necessitating appropriate strategies for the sustainable management.

Effect of Electromagnetic Stirring on Macrosegregation during Solidification of a Binary Alloy

The effect of electromagnetic stirring of melt on the final macrosegregation in the continuous casting of an aluminium alloy billet is studied numerically. A continuum mixture model for solidification in presence of electromagnetic stirring is presented. As a case study, simulations are performed for direct chill (DC) casting of an Al-Cu alloy and the effect of electromagnetic stirring on macrosegregation is analysed. The model predicts the temperature, velocity, and species distribution in the mold. As a special case, we have also studied the case in which dendritic particles are fragmented at the interface due to vigorous electromagnetic stirring. For this case, an additional conservation equation for the transport of solid fraction is solved. For modeling the resistance offered by moving solid crystals, a switching function in the momentum equations is used for variation of viscosity. The fragmentation and transport of dendritic particles has a profound effect on the final macrosegregation and microstructure of the solidified billet. It is found that the application of electromagnetic stirring in continuous casting of billets results in better temperature uniformity and macrosegregation pattern.

Fast Robust Pattern Classification Algorithms for Real Time Neuro-Motor Prosthetic Applications

In this paper, we give a brief review of pattern classification algorithms based on discriminant analysis. We then apply these algorithms to classify movement direction based on multivariate local field potentials recorded from a microelectrode array in the primary motor cortex of a monkey performing a reaching task. We obtain prediction accuracies between 55% and 90% using different methods which are significantly above the chance level of 12.5%.

In-situ measurements of concentration and temperature during transient solidification of aqueous solution of ammonium chloride using laser interferometry

The variation in temperature and concentration plays a crucial role in predicting the final microstructure during solidification of a binary alloy. Most of the experimental techniques used to measure concentration and temperature are intrusive in nature and affect the flow field. In this paper, the main focus is laid on in-situ, non-intrusive, transient measurement of concentration and temperature during the solidification of a binary mixture of aqueous ammonium chloride solution (a metal-analog system) in a top cooled cavity using laser based Mach-Zehnder Interferometric technique. It was found from the interferogram, that the angular deviation of fringe pattern and the total number of fringes exhibit significant sensitivity to refractive index and hence are functions of the local temperature and concentration of the NH4Cl solution inside the cavity. Using the fringe characteristics, calibration curves were established for the range of temperature and concentration levels expected during the solidification process. In the actual solidification experiment, two hypoeutectic solutions (5% and 15% NH4Cl) were chosen. The calibration curves were used to determine the temperature and concentration of the solution inside the cavity during solidification of 5% and 15% NH4Cl solution at different instants of time. The measurement was carried out at a fixed point in the cavity, and the concentration variation with time was recorded as the solid-liquid interface approached the measurement point. The measurement exhibited distinct zones of concentration distribution caused by solute rejection and Rayleigh Benard convection. Further studies involving flow visualization with laser scattering confirmed the Rayleigh Benard convection. Computational modeling was also performed, which corroborated the experimental findings. (C) 2011 Elsevier Ltd. All rights reserved.

Insights to urban dynamics through landscape spatial pattern analysis

Urbanisation is a dynamic complex phenomenon involving large scale changes in the land uses at local levels. Analyses of changes in land uses in urban environments provide a historical perspective of land use and give an opportunity to assess the spatial patterns, correlation, trends, rate and impacts of the change, which would help in better regional planning and good governance of the region. Main objective of this research is to quantify the urban dynamics using temporal remote sensing data with the help of well-established landscape metrics. Bangalore being one of the rapidly urbanising landscapes in India has been chosen for this investigation. Complex process of urban sprawl was modelled using spatio temporal analysis. Land use analyses show 584% growth in built-up area during the last four decades with the decline of vegetation by 66% and water bodies by 74%. Analyses of the temporal data reveals an increase in urban built up area of 342.83% (during 1973-1992), 129.56% (during 1992-1999), 106.7% (1999-2002), 114.51% (2002-2006) and 126.19% from 2006 to 2010. The Study area was divided into four zones and each zone is further divided into 17 concentric circles of 1 km incrementing radius to understand the patterns and extent of the urbanisation at local levels. The urban density gradient illustrates radial pattern of urbanisation for the period 1973-2010. Bangalore grew radially from 1973 to 2010 indicating that the urbanisation is intensifying from the central core and has reached the periphery of the Greater Bangalore. Shannon's entropy, alpha and beta population densities were computed to understand the level of urbanisation at local levels. Shannon's entropy values of recent time confirms dispersed haphazard urban growth in the city, particularly in the outskirts of the city. This also illustrates the extent of influence of drivers of urbanisation in various directions. Landscape metrics provided in depth knowledge about the sprawl. Principal component analysis helped in prioritizing the metrics for detailed analyses. The results clearly indicates that whole landscape is aggregating to a large patch in 2010 as compared to earlier years which was dominated by several small patches. The large scale conversion of small patches to large single patch can be seen from 2006 to 2010. In the year 2010 patches are maximally aggregated indicating that the city is becoming more compact and more urbanised in recent years. Bangalore was the most sought after destination for its climatic condition and the availability of various facilities (land availability, economy, political factors) compared to other cities. The growth into a single urban patch can be attributed to rapid urbanisation coupled with the industrialisation. Monitoring of growth through landscape metrics helps to maintain and manage the natural resources. (C) 2012 Elsevier B.V. All rights reserved.

Complex structural phase transitions in slightly Ca modified Na0.5Bi0.5TiO3

A temperature dependent neutron powder diffraction study, in conjunction with dielectric and ferroelectric characterization, of slightly Ca modified Na0.5Bi0.5TiO3 (NBT) revealed an instability with regard to a non-polar orthorhombic (Pbnm) distortion above room temperature. This intermediate orthorhombic phase has earlier been reported for unmodified NBT by electron diffraction studies, but has never been captured by global (x-ray/neutron) diffraction techniques. Calcium substitution seems to amplify the magnitude of this intermediate orthorhombic distortion thereby making the corresponding superlattice reflections become visible in the neutron diffraction pattern. The study revealed the following sequence of very complex structural evolution with temperature: Cc -> Cc + Pbnm -> Pbnm + P4/mbm -> P4/mbm -> Pm (3) over barm.