Online Handwriting Recognition of Tamil Script Using Fractal Geometry

We present a fractal coding method to recognize online handwritten Tamil characters and propose a novel technique to increase the efficiency in terms of time while coding and decoding. This technique exploits the redundancy in data, thereby achieving better compression and usage of lesser memory. It also reduces the encoding time and causes little distortion during reconstruction. Experiments have been conducted to use these fractal codes to classify the online handwritten Tamil characters from the IWFHR 2006 competition dataset. In one approach, we use fractal coding and decoding process. A recognition accuracy of 90% has been achieved by using DTW for distortion evaluation during classification and encoding processes as compared to 78% using nearest neighbor classifier. In other experiments, we use the fractal code, fractal dimensions and features derived from fractal codes as features in separate classifiers. While the fractal code is successful as a feature, the other two features are not able to capture the wide within-class variations.

Study of liquid crystalline order by NMR

The liquid crystalline phase represents a unique state of matter where partial order exists on molecular and supra-molecular levels and is responsible for several interesting properties observed in this phase. Hence a detailed study of ordering in liquid crystals is of significant scientific and technological interest. NMR provides several parameters that can be used to obtain information about the liquid crystalline phase. Of these, the measurement of dipolar couplings between nuclei has proved to be a convenient way of obtaining liquid crystalline ordering since the coupling is dependent on the average orientation of the dipolar vector in the magnetic field which also aligns the liquid crystal.However, measurement of the dipolar coupling between a pair of selected nuclei is beset with problems that require special solutions. In this article the use of cross polarization for measuring dipolar couplings in liquid crystals is illustrated. Transient oscillations observed during cross polarization provide the dipolar couplings between essentially isolated nearest neighbor spins which can be extracted for several sites simultaneously by employing two-dimensional NMR techniques. The use of the method for obtaining heteronuclear dipolar couplings and hence the order parameters of liquid crystals is presented. Several modifications to the basic experiment are considered and their utility illustrated. A method for obtaining proton–proton dipolar couplings, by utilizing cross polarization from the dipolar reservoir, is presented. Some applications are also highlighted.

Effect of dimerization on dynamics of spin-charge separation in Pariser-Parr-Pople model: A time-dependent density matrix renormalization group study

We investigate the effect of static electron-phonon coupling on real-time dynamics of spin and charge transport in pi-conjugated polyene chains. The polyene chain is modeled by the Pariser-Parr-Pople Hamiltonian with dimerized nearest-neighbor parameter t(0)(1 + delta) for short bonds and t(0)(1 - delta) for long bonds, and long-range electron-electron interactions. We follow the time evolution of the spin and charge using time-dependent density matrix renormalization group technique when a hole is injected at one end of the chain in its ground state. We find that spin and charge dynamics followed through spin and charge velocities depend both on chain length and extent of dimerization delta. Analysis of the results requires focusing on physical quantities such as average spin and charge polarizations, particularly in the large dimerization limit. In the dimerization range 0.0 <= delta <= 0.15, spin-charge dynamics is found to have a well-defined behavior, with spin-charge separation (measured as the ratio of charge velocity to spin velocity) as well as the total amount of charge and spin transported in a given time along the chain decreasing as dimerization increases. However, in the range 0.3 <= delta <= 0.5, it is observed that the dynamics of spin and charge transport becomes complicated. It is observed that, for large delta values, spin-charge separation is suppressed and the injected hole fails to travel the entire length of the chain.

Repulsive fermions in optical lattices: Phase separation versus coexistence of antiferromagnetism and d-wave superfluidity

We investigate a system of fermions on a two-dimensional optical square lattice in the strongly repulsive coupling regime. In this case, the interactions can be controlled by laser intensity as well as by Feshbach resonance. We compare the energetics of states with resonating valence bond d-wave superfluidity, antiferromagnetic long-range order, and a homogeneous state with coexistence of superfluidity and antiferromagnetism. Using a variational formalism, we show that the energy density of a hole e(hole)(x) has a minimum at doping x = x(c) that signals phase separation between the antiferromagnetic and d-wave paired superfluid phases. The energy of the phase-separated ground state is, however, found to be very close to that of a homogeneous state with coexisting antiferromagnetic and superfluid orders. We explore the dependence of the energy on the interaction strength and on the three-site hopping terms and compare with the nearest-neighbor hopping t-J model.

The inhomogeneous extended Bose-Hubbard model: A mean-field theory

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential mu and on-site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential.

Density matrix renormalization group algorithm for Bethe lattices of spin-1/2 or spin-1 sites with Heisenberg antiferromagnetic exchange

A density matrix renormalization group (DMRG) algorithm is presented for the Bethe lattice with connectivity Z = 3 and antiferromagnetic exchange between nearest-neighbor spins s = 1/2 or 1 sites in successive generations g. The algorithm is accurate for s = 1 sites. The ground states are magnetic with spin S(g) = 2(g)s, staggered magnetization that persists for large g > 20, and short-range spin correlation functions that decrease exponentially. A finite energy gap to S > S(g) leads to a magnetization plateau in the extended lattice. Closely similar DMRG results for s = 1/2 and 1 are interpreted in terms of an analytical three-site model.

GINZBURG-LANDAU LIKE THEORY OF HIGH TEMPERATURE SUPERCONDUCTIVITY IN THE CUPRATES: EMERGENT d-WAVE ORDER

High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the celebrated description of superconductivity due to Ginzburg and Landau and believed to describe its essence. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. We propose that there is, for superconducting cuprates, a similar functional of the complex, in plane, nearest neighbor spin singlet bond (or Cooper) pair amplitude psi(ij). Further, we suggest that a crucial part of it is a (short range) positive interaction between nearest neighbor bond pairs, of strength J'. Such an interaction leads to nonzero long wavelength phase stiffness or superconductive long range order, with the observed d-wave symmetry, below a temperature T-c similar to zJ' where z is the number of nearest neighbors; d-wave superconductivity is thus an emergent, collective consequence. Using the functional, we calculate a large range of properties, e. g., the pseudogap transition temperature T* as a function of hole doping x, the transition curve T-c(x), the superfluid stiffness rho(s)(x, T), the specific heat (without and with a magnetic field) due to the fluctuating pair degrees of freedom and the zero temperature vortex structure. We find remarkable agreement with experiment. We also calculate the self-energy of electrons hopping on the square cuprate lattice and coupled to electrons of nearly opposite momenta via inevitable long wavelength Cooper pair fluctuations formed of these electrons. The ensuing results for electron spectral density are successfully compared with recent experimental results for angle resolved photo emission spectroscopy (ARPES), and comprehensively explain strange features such as temperature dependent Fermi arcs above T-c and the ``bending'' of the superconducting gap below T-c.

Ferrimagnetism, antiferromagnetism, and magnetic frustration in La2-xSrxCuRuO6 (0 <= x <= 1)

We studied structural and magnetic properties of a series of insulating double perovskite compounds, La2-xSrxCuRuO6 (0 <= x <= 1), representing doping via A-site substitution. The end members La2CuRuO6 and LaSrCuRuO6 form in monoclinic structure while the intermediate Sr doped compounds stabilize in triclinic structure. The Cu and Ru ions sit on alternate B sites of the perovskite lattice with similar to 15% antisite defects in the undoped sample while the Sr-doped samples show a tendency to higher ordering at B sites. The undoped (x = 0) compound shows a ferrimagnetic-like behavior at low temperatures. In surprising contrast to the usual expectation of an enhancement of ferromagnetic interaction on doping, an antiferromagnetic-like ground state is realized for all doped samples (x > 0). Heat capacity measurements indicate the absence of any long-range magnetic order in any of these compounds. The magnetic relaxation and memory effects observed in all compounds suggest glassy dynamical properties associated with magnetic disorder and frustration. We show that the observed magnetic properties are dominated by the competition between the nearest-neighbor Ru-O-Cu 180 degrees superexchange interaction and the next-nearest-neighbor Ru-O-O-Ru 90 degrees superexchange interaction as well as by the formation of antisite defects with interchanged Cu and Ru positions. Our calculated exchange interaction parameters from first principles calculations for x = 0 and x = 1 support this interpretation.

Quantum phases of dimerized and frustrated Heisenberg spin chains with s=1/2, 1 and 3/2: an entanglement entropy and fidelity study

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J(2)) and dimerization (delta). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J(2)-delta plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

Predictability and chaotic nature of daily streamflow

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system in many approaches. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation dimension method (Grassberger-Procaccia algorithm) and false nearest neighbor method. Embedding dimensions of 6-7 obtained indicates the possible presence of low-dimensional chaotic behavior. The predictability of the system is estimated by calculating the system’s Lyapunov exponent. A positive maximum Lyapunov exponent of 0.167 indicates that the system is chaotic and unstable with a maximum predictability of only 6 days. These results give a positive indication towards considering streamflow as a low dimensional chaotic system than as a stochastic system.

Recognition of Kannada characters extracted from scene images

In this paper, we describe a method for feature extraction and classification of characters manually isolated from scene or natural images. Characters in a scene image may be affected by low resolution, uneven illumination or occlusion. We propose a novel method to perform binarization on gray scale images by minimizing energy functional. Discrete Cosine Transform and Angular Radial Transform are used to extract the features from characters after normalization for scale and translation. We have evaluated our method on the complete test set of Chars74k dataset for English and Kannada scripts consisting of handwritten and synthesized characters, as well as characters extracted from camera captured images. We utilize only synthesized and handwritten characters from this dataset as training set. Nearest neighbor classification is used in our experiments.

Feature selection for unsupervised learning

In this paper, we present a methodology for identifying best features from a large feature space. In high dimensional feature space nearest neighbor search is meaningless. In this feature space we see quality and performance issue with nearest neighbor search. Many data mining algorithms use nearest neighbor search. So instead of doing nearest neighbor search using all the features we need to select relevant features. We propose feature selection using Non-negative Matrix Factorization(NMF) and its application to nearest neighbor search. Recent clustering algorithm based on Locally Consistent Concept Factorization(LCCF) shows better quality of document clustering by using local geometrical and discriminating structure of the data. By using our feature selection method we have shown further improvement of performance in the clustering.

Efficient classification using phrases generated by topic models

There are many popular models available for classification of documents like Naïve Bayes Classifier, k-Nearest Neighbors and Support Vector Machine. In all these cases, the representation is based on the “Bag of words” model. This model doesn't capture the actual semantic meaning of a word in a particular document. Semantics are better captured by proximity of words and their occurrence in the document. We propose a new “Bag of Phrases” model to capture this discriminative power of phrases for text classification. We present a novel algorithm to extract phrases from the corpus using the well known topic model, Latent Dirichlet Allocation(LDA), and to integrate them in vector space model for classification. Experiments show a better performance of classifiers with the new Bag of Phrases model against related representation models.

Quantum phases and phase transitions of frustrated hard-core bosons on a triangular ladder

Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.

Predictability and chaotic nature of daily streamflow

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system in many approaches. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation dimension method (Grassberger-Procaccia algorithm) and false nearest neighbor method. Embedding dimensions of 6-7 obtained indicates the possible presence of low-dimensional chaotic behavior. The predictability of the system is estimated by calculating the system's Lyapunov exponent. A positive maximum Lyapunov exponent of 0.167 indicates that the system is chaotic and unstable with a maximum predictability of only 6 days. These results give a positive indication towards considering streamflow as a low dimensional chaotic system than as a stochastic system.