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.

On the relation between K-means and PLSA

Non-negative matrix factorization [5](NMF) is a well known tool for unsupervised machine learning. It can be viewed as a generalization of the K-means clustering, Expectation Maximization based clustering and aspect modeling by Probabilistic Latent Semantic Analysis (PLSA). Specifically PLSA is related to NMF with KL-divergence objective function. Further it is shown that K-means clustering is a special case of NMF with matrix L2 norm based error function. In this paper our objective is to analyze the relation between K-means clustering and PLSA by examining the KL-divergence function and matrix L2 norm based error function.

Phylogenetic analysis and molecular dating suggest that hemidactylus anamallensis is not a member of the hemidactylus radiation and has an ancient late cretaceous origin

Background of the Work: The phylogenetic position and evolution of Hemidactylus anamallensis (family Gekkonidae) has been much debated in recent times. In the past it has been variously assigned to genus Hoplodactylus (Diplodactylidae) as well as a monotypic genus `Dravidogecko' (Gekkonidae). Since 1995, this species has been assigned to Hemidactylus, but there is much disagreement between authors regarding its phylogenetic position within this genus. In a recent molecular study H. anamallensis was sister to Hemidactylus but appeared distinct from it in both mitochondrial and nuclear markers. However, this study did not include genera closely allied to Hemidactylus, thus a robust evaluation of this hypothesis was not undertaken. Methods: The objective of this study was to investigate the phylogenetic position of H. anamallensis within the gekkonid radiation. To this end, several nuclear and mitochondrial markers were sequenced from H. anamallensis, selected members of the Hemidactylus radiation and genera closely allied to Hemidactylus. These sequences in conjunction with published sequences were subjected to multiple phylogenetic analyses. Furthermore the nuclear dataset was also subjected to molecular dating analysis to ascertain the divergence between H. anamallensis and related genera. Results and Conclusion: Results showed that H. anamallensis lineage was indeed sister to Hemidactylus group but was separated from the rest of the Hemidactylus by a long branch. The divergence estimates supported a scenario wherein H. anamallensis dispersed across a marine barrier to the drifting peninsular Indian plate in the late Cretaceous whereas Hemidactylus arrived on the peninsular India after the Indian plate collided with the Eurasian plate. Based on these molecular evidence and biogeographical scenario we suggest that the genus Dravidogecko should be resurrected.

State estimation in power systems using linear model infinity norm-based trust region approach

State estimation is one of the most important functions in an energy control centre. An computationally efficient state estimator which is free from numerical instability/ill-conditioning is essential for security assessment of electric power grid. Whereas approaches to successfully overcome the numerical ill-conditioning issues have been proposed, an efficient algorithm for addressing the convergence issues in the presence of topological errors is yet to be evolved. Trust region (TR) methods have been successfully employed to overcome the divergence problem to certain extent. In this study, case studies are presented where the conventional algorithms including the existing TR methods would fail to converge. A linearised model-based TR method for successfully overcoming the convergence issues is proposed. On the computational front, unlike the existing TR methods for state estimation which employ quadratic models, the proposed linear model-based estimator is computationally efficient because the model minimiser can be computed in a single step. The model minimiser at each step is computed by minimising the linearised model in the presence of TR and measurement mismatch constraints. The infinity norm is used to define the geometry of the TR. Measurement mismatch constraints are employed to improve the accuracy. The proposed algorithm is compared with the quadratic model-based TR algorithm with case studies on the IEEE 30-bus system, 205-bus and 514-bus equivalent systems of part of Indian grid.

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.

Did southern Western Ghats of peninsular India serve as refugia for its endemic biota during the Cretaceous volcanism?

The Western Ghats (WG) of south India, a global biodiversity hotspot, has experienced complex geological history being part of Gondwana landmass and encountered extensive volcanic activity at the end of Cretaceous epoch. It also has a climatically and topographically heterogeneous landscape. Thus, the WG offer a unique setting to explore the influence of ecological and geological processes on the current diversity and distribution of its biota. To this end, three explicit biogeographical scenarios were hypothesized to evaluate the distribution and diversification of wet evergreen species of the WG - (1) southern WG was a refuge for the wet evergreen species during the Cretaceous volcanism, (2) phylogenetic breaks in the species phylogeny would correspond to geographic breaks (i.e., the Palghat gap) in the WG, and (3) species from each of the biogeographic subdivisions within the WG would form distinct clades. These hypotheses were tested on the centipede genus Digitipes from the WG which is known to be an ancient, endemic, and monophyletic group. The Digitipes molecular phylogeny was subjected to divergence date estimation using Bayesian approach, and ancestral areas were reconstructed using parsimony approach for each node in the phylogeny. Ancestral-area reconstruction suggested 13 independent dispersal events to explain the current distribution of the Digitipes species in the WG. Among these 13 dispersals, two dispersal events were at higher level in the Digitipes phylogeny and were from the southern WG to the central and northern WG independently in the Early Paleocene, after the Cretaceous Volcanism. The remaining 11 dispersal events explained the species' range expansions of which nine dispersals were from the southern WG to other biogeographic subdivisions in the Eocene-Miocene in the post-volcanic periods where species-level diversifications occurred. Taken together, these results suggest that southern WG might have served as a refuge for Digitipes species during Cretaceous volcanism.

Dynamics of edge dislocations in a sheared lamellar mesophase

The dynamics and interactions of edge dislocations in a nearly aligned sheared lamellar mesophase is analysed to provide insights into the relationship between disorder and rheology. First, the mesoscale permeation and momentum equations for the displacement field in the presence of external forces are derived from the model H equations for the concentration and momentum field. The secondary flow generated due to the mean shear around an isolated defect is calculated, and the excess viscosity due to the presence of the defect is determined from the excess energy dissipation due to the secondary flow. The excess viscosity for an isolated defect is found to increase with system size in the cross-stream direction as L-3/2 for an isolated defect, though this divergence is cut-off due to interactions in a defect suspension. As the defects are sheared past each other due to the mean flow, the Peach-Koehler force due to elastic interaction between pairs of defects is found to cause no net displacement relative to each other as they approach from large separation to the distance of closest approach. The equivalent force due to viscous interactions is found to increase the separation for defects of opposite sign, and decrease the separation for defects of same sign. During defect interactions, we find that there is no buckling instability due to dilation of layers for systems of realistic size. However, there is another mechanism, which is the velocity difference generated across a slightly deformed bilayer due to the mean shear, which could result in the creation of new defects. (C) 2013 AIP Publishing LLC.

Filling-in Void and Sparse Regions in Protein Sequence Space by Protein-Like Artificial Sequences Enables Remarkable Enhancement in Remote Homology Detection Capability

Protein functional annotation relies on the identification of accurate relationships, sequence divergence being a key factor. This is especially evident when distant protein relationships are demonstrated only with three-dimensional structures. To address this challenge, we describe a computational approach to purposefully bridge gaps between related protein families through directed design of protein-like ``linker'' sequences. For this, we represented SCOP domain families, integrated with sequence homologues, as multiple profiles and performed HMM-HMM alignments between related domain families. Where convincing alignments were achieved, we applied a roulette wheel-based method to design 3,611,010 protein-like sequences corresponding to 374 SCOP folds. To analyze their ability to link proteins in homology searches, we used 3024 queries to search two databases, one containing only natural sequences and another one additionally containing designed sequences. Our results showed that augmented database searches showed up to 30% improvement in fold coverage for over 74% of the folds, with 52 folds achieving all theoretically possible connections. Although sequences could not be designed between some families, the availability of designed sequences between other families within the fold established the sequence continuum to demonstrate 373 difficult relationships. Ultimately, as a practical and realistic extension, we demonstrate that such protein-like sequences can be ``plugged-into'' routine and generic sequence database searches to empower not only remote homology detection but also fold recognition. Our richly statistically supported findings show that complementary searches in both databases will increase the effectiveness of sequence-based searches in recognizing all homologues sharing a common fold. (C) 2013 Elsevier Ltd. All rights reserved.

Generative Maximum Entropy Learning for Multiclass Classification

Maximum entropy approach to classification is very well studied in applied statistics and machine learning and almost all the methods that exists in literature are discriminative in nature. In this paper, we introduce a maximum entropy classification method with feature selection for large dimensional data such as text datasets that is generative in nature. To tackle the curse of dimensionality of large data sets, we employ conditional independence assumption (Naive Bayes) and we perform feature selection simultaneously, by enforcing a `maximum discrimination' between estimated class conditional densities. For two class problems, in the proposed method, we use Jeffreys (J) divergence to discriminate the class conditional densities. To extend our method to the multi-class case, we propose a completely new approach by considering a multi-distribution divergence: we replace Jeffreys divergence by Jensen-Shannon (JS) divergence to discriminate conditional densities of multiple classes. In order to reduce computational complexity, we employ a modified Jensen-Shannon divergence (JS(GM)), based on AM-GM inequality. We show that the resulting divergence is a natural generalization of Jeffreys divergence to a multiple distributions case. As far as the theoretical justifications are concerned we show that when one intends to select the best features in a generative maximum entropy approach, maximum discrimination using J-divergence emerges naturally in binary classification. Performance and comparative study of the proposed algorithms have been demonstrated on large dimensional text and gene expression datasets that show our methods scale up very well with large dimensional datasets.

Fermi-Edge Transmission Resonance in Graphene Driven by a Single Coulomb Impurity

The interaction between the Fermi sea of conduction electrons and a nonadiabatic attractive impurity potential can lead to a power-law divergence in the tunneling probability of charge through the impurity. The resulting effect, known as the Fermi edge singularity (FES), constitutes one of the most fundamental many-body phenomena in quantum solid state physics. Here we report the first observation of FES for Dirac fermions in graphene driven by isolated Coulomb impurities in the conduction channel. In high-mobility graphene devices on hexagonal boron nitride substrates, the FES manifests in abrupt changes in conductance with a large magnitude approximate to e(2)/h at resonance, indicating total many-body screening of a local Coulomb impurity with fluctuating charge occupancy. Furthermore, we exploit the extreme sensitivity of graphene to individual Coulomb impurities and demonstrate a new defect-spectroscopy tool to investigate strongly correlated phases in graphene in the quantum Hall regime.

Current kinematics and dynamics of Africa and the East African Rift System

Although the East African Rift System (EARS) is an archetype continental rift, the forces driving its evolution remain debated. Some contend buoyancy forces arising from gravitational potential energy (GPE) gradients within the lithosphere drive rifting. Others argue for a major role of the diverging mantle flow associated with the African Superplume. Here we quantify the forces driving present-day continental rifting in East Africa by (1) solving the depth averaged 3-D force balance equations for 3-D deviatoric stress associated with GPE, (2) inverting for a stress field boundary condition that we interpret as originating from large-scale mantle tractions, (3) calculating dynamic velocities due to lithospheric buoyancy forces, lateral viscosity variations, and velocity boundary conditions, and (4) calculating dynamic velocities that result from the stress response of horizontal mantle tractions acting on a viscous lithosphere in Africa and surroundings. We find deviatoric stress associated with lithospheric GPE gradients are similar to 8-20 MPa in EARS, and the minimum deviatoric stress resulting from basal shear is similar to 1.6 MPa along the EARS. Our dynamic velocity calculations confirm that a force contribution from GPE gradients alone is sufficient to drive Nubia-Somalia divergence and that additional forcing from horizontal mantle tractions overestimates surface kinematics. Stresses from GPE gradients appear sufficient to sustain present-day rifting in East Africa; however, they are lower than the vertically integrated strength of the lithosphere along most of the EARS. This indicates additional processes are required to initiate rupture of continental lithosphere, but once it is initiated, lithospheric buoyancy forces are enough to maintain rifting.

Wrinkling of Atomic Planes in Ultrathin Au Nanowires

A detailed understanding of structure and stability of nanowires is critical for applications. Atomic resolution imaging of ultrathin single crystalline Au nanowires using aberration-corrected microscopy reveals an intriguing relaxation whereby the atoms in the close-packed atomic planes normal to the growth direction are displaced in the axial direction leading to wrinkling of the (111) atomic plane normal to the wire axis. First-principles calculations of the structure of such nanowires confirm this wrinkling phenomenon, whereby the close-packed planes relax to form saddle-like surfaces. Molecular dynamics studies of wires with varying diameters and different bounding surfaces point to the key role of surface stress on the relaxation process. Using continuum mechanics arguments, we show that the wrinkling arises due to anisotropy in the surface stresses and in the elastic response, along with the divergence of surface-induced bulk stress near the edges of a faceted structure. The observations provide new understanding on the equilibrium structure of nanoscale systems and could have important implications for applications in sensing and actuation.

Dense shallow granular flows

Simplified equations are derived for a granular flow in the `dense' limit where the volume fraction is close to that for dynamical arrest, and the `shallow' limit where the stream-wise length for flow development (L) is large compared with the cross-stream height (h). The mass and diameter of the particles are set equal to 1 in the analysis without loss of generality. In the dense limit, the equations are simplified by taking advantage of the power-law divergence of the pair distribution function chi proportional to (phi(ad) - phi)(-alpha), and a faster divergence of the derivativ rho(d chi/d rho) similar to (d chi/d phi), where rho and phi are the density and volume fraction, and phi(ad) is the volume fraction for arrested dynamics. When the height h is much larger than the conduction length, the energy equation reduces to an algebraic balance between the rates of production and dissipation of energy, and the stress is proportional to the square of the strain rate (Bagnold law). In the shallow limit, the stress reduces to a simplified Bagnold stress, where all components of the stress are proportional to (partial derivative u(x)/partial derivative y)(2), which is the cross-stream (y) derivative of the stream-wise (x) velocity. In the simplified equations for dense shallow flows, the inertial terms are neglected in the y momentum equation in the shallow limit because the are O(h/L) smaller than the divergence of the stress. The resulting model contains two equations, a mass conservation equations which reduces to a solenoidal condition on the velocity in the incompressible limit, and a stream-wise momentum equation which contains just one parameter B which is a combination of the Bagnold coefficients and their derivatives with respect to volume fraction. The leading-order dense shallow flow equations, as well as the first correction due to density variations, are analysed for two representative flows. The first is the development from a plug flow to a fully developed Bagnold profile for the flow down an inclined plane. The analysis shows that the flow development length is ((rho) over barh(3)/B) , where (rho) over bar is the mean density, and this length is numerically estimated from previous simulation results. The second example is the development of the boundary layer at the base of the flow when a plug flow (with a slip condition at the base) encounters a rough base, in the limit where the momentum boundary layer thickness is small compared with the flow height. Analytical solutions can be found only when the stream-wise velocity far from the surface varies as x(F), where x is the stream-wise distance from the start of the rough base and F is an exponent. The boundary layer thickness increases as (l(2)x)(1/3) for all values of F, where the length scale l = root 2B/(rho) over bar. The analysis reveals important differences between granular flows and the flows of Newtonian fluids. The Reynolds number (ratio of inertial and viscous terms) turns out to depend only on the layer height and Bagnold coefficients, and is independent of the flow velocity, because both the inertial terms in the conservation equations and the divergence of the stress depend on the square of the velocity/velocity gradients. The compressibility number (ratio of the variation in volume fraction and mean volume fraction) is independent of the flow velocity and layer height, and depends only on the volume fraction and Bagnold coefficients.

An improved free surface modeling for incompressible SPH

In Incompressible Smooth Particle Hydrodynamics (ISPH), a pressure Poisson equation (PPE) is solved to obtain a divergence free velocity field. When free surfaces are simulated using this method a Dirichlet boundary condition for pressure at the free surface has to be applied. In existing ISPH methods this is achieved by identifying free surface particles using heuristically chosen threshold of a parameter such as kernel sum, density or divergence of the position, and explicitly setting their pressure values. This often leads to clumping of particles near the free surface and spraying off of surface particles during splashes. Moreover, surface pressure gradients in flows where surface tension is important are not captured well using this approach. We propose a more accurate semi-analytical approach to impose Dirichlet boundary conditions on the free surface. We show the efficacy of the proposed algorithm by using test cases of elongation of a droplet and dam break. We perform two dimensional simulations of water entry and validate the proposed algorithm with experimental results. Further, a three dimensional simulation of droplet splash is shown to compare well with the Volume-of-Fluid simulations. (C) 2014 Elsevier Ltd. All rights reserved.

Spinning strings and minimal surfaces in AdS(3) with mixed 3-form fluxes

Motivated by the recent proposal for the S-matrix in AdS(3) x S-3 with mixed three form fluxes, we study classical folded string spinning in AdS(3) with both Ramond and Neveu-Schwarz three form fluxes. We solve the equations of motion of these strings and obtain their dispersion relation to the leading order in the Neveu-Schwarz flux b. We show that dispersion relation for the spinning strings with large spin S acquires a term given by -root lambda/2 pi b(2) log(2) S in addition to the usual root lambda/pi log S term where root lambda is proportional to the square of the radius of AdS(3). Using SO(2, 2) transformations and re-parmetrizations we show that these spinning strings can be related to light like Wilson loops in AdS(3) with Neveu-Schwarz flux b. We observe that the logarithmic divergence in the area of the light like Wilson loop is also deformed by precisely the same coefficient of the b(2) log(2) S term in the dispersion relation of the spinning string. This result indicates that the coefficient of b(2) log(2) S has a property similar to the coefficient of the log S term, known as cusp-anomalous dimension, and can possibly be determined to all orders in the coupling lambda using the recent proposal for the S-matrix.