arXiv subjects

Abhishek Kumar

Publications and source records attributed to Abhishek Kumar.

At least 217 records · Page 12Linked to original sources

arXiv2016

Phenomenology of buoyancy-driven turbulence: recent results

In this paper, we review the recent developments in the field of buoyancy-driven turbulence. Scaling and numerical arguments show that the stably-stratified turbulence with moderate stratification has kinetic energy spectrum $E_u(k) \sim k^{-11/5}$ and the kinetic energy flux $Π_u(k) \sim k^{-4/5}$, which is called Bolgiano-Obukhov scaling. The energy flux for the Rayleigh-Bénard convection (RBC) however is approximately constant in the inertial range that results in Kolmorogorv's spectrum ($E_u(k) \sim k^{-5/3}$) for the kinetic energy. The phenomenology of RBC should apply to other flows where the buoyancy feeds the kinetic energy, e.g. bubbly turbulence and fully-developed Rayleigh Taylor instability. This paper also covers several models that predict the Reynolds and Nusselt numbers of RBC. Recent works show that the viscous dissipation rate of RBC scales as $\sim \mathrm{Ra}^{1.3}$, where $\mathrm{Ra}$ is the Rayleigh number.

physics.flu-dyn↗

arXiv2016

Dynamics of large-scale quantities in Rayleigh-Bénard convection

In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity, $U$, or the Péclet number that is applicable for arbitrary Rayleigh number $\mathrm{Ra}$ and Prandtl number $\mathrm{Pr}$. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of $\mathrm{Ra}^{1/2}$ to the experimentally observed scaling of nearly $\mathrm{Ra}^{0.3}$.

physics.flu-dyn↗

arXiv2016

Near isotropic behaviour of turbulent thermal convection

We investigate the anisotropy in turbulent convection in a 3D box using direct numerical simulation. We compute the anisotropic parameter $A = u_\perp^{2}/(2u_{\parallel}^{2})$, where $u_{\perp}$ and $u_{\parallel}$ are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number $\mathrm{Pr} \approx 1$, but the anisotropy increases with the Prandtl number. For $\mathrm{Pr}=\infty$, $A \approx 0.3$, thus anisotropy is not very significant even in extreme cases. We also observe that $u_{\parallel}$ feeds energy to $u_{\perp}$ via pressure. The computation of shell-to-shell energy transfers reveals that the energy transfer in turbulent convection is local and forward, similar to hydrodynamic turbulence. These results are consistent with the Kolmogorov's spectrum observed by Kumar et al.~[Phys. Rev. E {\bf 90}, 023016 (2014)] for turbulent convection.

physics.flu-dyn↗

arXiv2016

S3Pool: Pooling with Stochastic Spatial Sampling

Feature pooling layers (e.g., max pooling) in convolutional neural networks (CNNs) serve the dual purpose of providing increasingly abstract representations as well as yielding computational savings in subsequent convolutional layers. We view the pooling operation in CNNs as a two-step procedure: first, a pooling window (e.g., $2\times 2$) slides over the feature map with stride one which leaves the spatial resolution intact, and second, downsampling is performed by selecting one pixel from each non-overlapping pooling window in an often uniform and deterministic (e.g., top-left) manner. Our starting point in this work is the observation that this regularly spaced downsampling arising from non-overlapping windows, although intuitive from a signal processing perspective (which has the goal of signal reconstruction), is not necessarily optimal for \emph{learning} (where the goal is to generalize). We study this aspect and propose a novel pooling strategy with stochastic spatial sampling (S3Pool), where the regular downsampling is replaced by a more general stochastic version. We observe that this general stochasticity acts as a strong regularizer, and can also be seen as doing implicit data augmentation by introducing distortions in the feature maps. We further introduce a mechanism to control the amount of distortion to suit different datasets and architectures. To demonstrate the effectiveness of the proposed approach, we perform extensive experiments on several popular image classification benchmarks, observing excellent improvements over baseline models. Experimental code is available at https://github.com/Shuangfei/s3pool.

cs.LG↗

arXiv2016

Fully-adaptive Feature Sharing in Multi-Task Networks with Applications in Person Attribute Classification

Multi-task learning aims to improve generalization performance of multiple prediction tasks by appropriately sharing relevant information across them. In the context of deep neural networks, this idea is often realized by hand-designed network architectures with layers that are shared across tasks and branches that encode task-specific features. However, the space of possible multi-task deep architectures is combinatorially large and often the final architecture is arrived at by manual exploration of this space subject to designer's bias, which can be both error-prone and tedious. In this work, we propose a principled approach for designing compact multi-task deep learning architectures. Our approach starts with a thin network and dynamically widens it in a greedy manner during training using a novel criterion that promotes grouping of similar tasks together. Our Extensive evaluation on person attributes classification tasks involving facial and clothing attributes suggests that the models produced by the proposed method are fast, compact and can closely match or exceed the state-of-the-art accuracy from strong baselines by much more expensive models.

cs.CV↗

arXiv2016

Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

In this paper we characterize the scaling of energy spectra, and the interscale transfer of energy and enstrophy, for strongly, moderately and weakly stably stratified two-dimensional (2D) turbulence under large-scale random forcing. In the strongly stratified case, a large-scale vertically sheared horizontal flow (VSHF) co-exists with small scale turbulence. The VSHF consists of internal gravity waves and the turbulent flow has a kinetic energy (KE) spectrum that follows an approximate $k^{-3}$ scaling with zero KE flux and a robust positive enstrophy flux. The spectrum of the turbulent potential energy (PE) also approximately follows a $k^{-3}$ power-law and its flux is directed to small scales. For moderate stratification, there is no VSHF and the KE of the turbulent flow exhibits Bolgiano-Obukhov scaling that transitions from a shallow $k^{-11/5}$ form at large scales, to a steeper approximate $k^{-3}$ scaling at small scales. The entire range of scales shows a strong forward enstrophy flux, and interestingly, large (small) scales show an inverse (forward) KE flux. The PE flux in this regime is directed to small scales, and the PE spectrum is characterized by an approximate $k^{-1.64}$ scaling. Finally, for weak stratification, KE is transferred upscale and its spectrum closely follows a $k^{-2.5}$ scaling, while PE exhibits a forward transfer and its spectrum shows an approximate $k^{-1.6}$ power-law. For all stratification strengths, the total energy always flows from large to small scales and almost all the spectral indices are well explained by accounting for the scale dependent nature of the corresponding flux.

physics.flu-dyn↗

arXiv2016

Improving the detection accuracy of unknown malware by partitioning the executables in groups

Detection of unknown malware with high accuracy is always a challenging task. Therefore, in this paper, we study the classification of unknown malware by two methods. In the first/regular method, similar to other authors [17][16][20] approaches we select the features by taking all dataset in one group and in the second method, we select the features by partitioning the dataset in the range of file 5 KB size. We find that the second method to detect the malware with ~8.7% more accurate than the first/regular method.

cs.CR↗

arXiv2015

A new Initial Centroid finding Method based on Dissimilarity Tree for K-means Algorithm

Cluster analysis is one of the primary data analysis technique in data mining and K-means is one of the commonly used partitioning clustering algorithm. In K-means algorithm, resulting set of clusters depend on the choice of initial centroids. If we can find initial centroids which are coherent with the arrangement of data, the better set of clusters can be obtained. This paper proposes a method based on the Dissimilarity Tree to find, the better initial centroid as well as every bit more accurate cluster with less computational time. Theory analysis and experimental results indicate that the proposed method can effectively improve the accuracy of clusters and reduce the computational complexity of the K-means algorithm.

cs.LG↗

arXiv2015

Exact and Heuristic Algorithms for Semi-Nonnegative Matrix Factorization

Given a matrix $M$ (not necessarily nonnegative) and a factorization rank $r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$ with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that $UV$ is the best possible approximation of $M$ according to some metric. In this paper, we study the properties of semi-NMF from which we develop exact and heuristic algorithms. Our contribution is threefold. First, we prove that the error of a semi-NMF of rank $r$ has to be smaller than the best unconstrained approximation of rank $r-1$. This leads us to a new initialization procedure based on the singular value decomposition (SVD) with a guarantee on the quality of the approximation. Second, we propose an exact algorithm (that is, an algorithm that finds an optimal solution), also based on the SVD, for a certain class of matrices (including nonnegative irreducible matrices) from which we derive an initialization for matrices not belonging to that class. Numerical experiments illustrate that this second approach performs extremely well, and allows us to compute optimal semi-NMF decompositions in many situations. Finally, we analyze the computational complexity of semi-NMF proving its NP-hardness, already in the rank-one case (that is, for $r = 1$), and we show that semi-NMF is sometimes ill-posed (that is, an optimal solution does not exist).

math.NA↗

arXiv2015

A Shell Model for Buoyancy-Driven Turbulence

In this paper we present a unified shell model for stably stratified and convective turbulence. Numerical simulation of this model for stably stratified flow shows Bolgiano-Obukhbov scaling in which the kinetic energy spectrum varies as $k^{-11/5}$. We also observe a dual scaling ($k^{-11/5}$ and $k^{-5/3}$) for a limited range of parameters. The shell model of convective turbulence yields Kolmogorov's spectrum. These results are consistent with the energy flux and energy feed due to buoyancy, and are in good agreement with direct numerical simulations of Kumar {\em et al.} [Phys. Rev. E {\bf 90}, 023016 (2014)].

physics.flu-dyn↗

arXiv2014

Prefrontal Cortex Motivated Cognitive Architecture for Multiple Robots

In this paper, we introduce a cerebral cortex inspired architecture for robots in which we have mapped hierarchical cortical representation of human brain to logic flow and decision making process. Our work focuses on the two major features of human cognitive process, viz. the perception action cycle and its hierarchical organization, and the decision making process. To prove the effectiveness of our proposed method, we incorporated this architecture in our robot which we named as Cognitive Insect Robot inspired by Brain Architecture (CIRBA). We have extended our research to the implementation of this cognitive architecture of CIRBA in multiple robots and have analyzed the level of cognition attained by them

cs.RO↗

arXiv2014

Energy Spectrum of Buoyancy-Driven Turbulence

Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux $Π_u$, we demonstrate that for stably stratified flows, the kinetic energy spectrum $E_u(k) \sim k^{-11/5}$, the entropy spectrum $E_θ(k) \sim k^{-7/5}$, and $Π_u(k) \sim k^{-4/5}$, consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence $E_u(k)$ follows Kolmogorov's spectrum with a constant energy flux. For Rayleigh Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing $Π_u(k)$ with $k$, thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant $Π_u(k)$ and $E_u(k) \sim k^{-5/3}$ for a narrow band of wavenumbers.

physics.flu-dyn↗

arXiv2014

Energy spectrum of Buoyancy-driven Flows

Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux $Π_u$, we demonstrate that for stably stratified flows, the kinetic energy spectrum $E_u(k) \sim k^{-11/5}$, the entropy spectrum $E_θ(k) \sim k^{-7/5}$, and $Π_u(k) \sim k^{-4/5}$ (Bolgiano-Obukhov scaling). This scaling is due to the depletion of kinetic energy because of buoyancy. For weaker buoyancy in stratified flows, $E_u(k)$ follows Kolmgorov's spectrum with a constant energy flux. We also argue that for Rayleigh Bénard convection, the Bolgiano-Obukhov scaling will not hold for the bulk flow due to the positive energy supply by buoyancy and non-decreasing $Π_u(k)$.

physics.flu-dyn↗

arXiv2013

Near-separable Non-negative Matrix Factorization with $\ell_1$- and Bregman Loss Functions

Recently, a family of tractable NMF algorithms have been proposed under the assumption that the data matrix satisfies a separability condition Donoho & Stodden (2003); Arora et al. (2012). Geometrically, this condition reformulates the NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. In this paper, we develop several extensions of the conical hull procedures of Kumar et al. (2013) for robust ($\ell_1$) approximations and Bregman divergences. Our methods inherit all the advantages of Kumar et al. (2013) including scalability and noise-tolerance. We show that on foreground-background separation problems in computer vision, robust near-separable NMFs match the performance of Robust PCA, considered state of the art on these problems, with an order of magnitude faster training time. We also demonstrate applications in exemplar selection settings.

stat.ML↗

arXiv2013

Very Light Scalar Top Quarks at the LHC

A very light scalar top (stop) superpartner is motivated by naturalness and electroweak baryogenesis. When the mass of the stop is less than the sum of the masses of the top quark and the lightest neutralino superpartner, as well as the of the masses of the lightest chargino and the bottom quark, the dominant decay channels of the stop will be three-body, four-body, or flavour violating. In this work, we investigate the direct and indirect constraints on a light stop, we compute the relative decay branching fractions to these channels, and we study the sensitivity of existing LHC searches to each of them.

hep-ph↗

arXiv2013

Tracking Down the Top Quark Forward-Backward Asymmetry with Monotops

We revisit the possibility that the top quark forward-backward asymmetry arises from the on-shell production and decay of scalar top partners to top-antitop pairs with missing transverse energy. Although the asymmetry is produced by t-channel exchange of a light mediator, the model remains unconstrained by low energy atomic parity violation tests. An interesting connection to the active neutrino sector through a Type-I seesaw operator helps to evade stringent monojet constraints and opens up a richer collider phenomenology. After performing a global fit to top data from both the Tevatron and the LHC, we obtain a viable region of parameter space consistent with all phenomenological and collider constraints. We also discuss the discovery potential of a predicted monotop signal and related lepton charge asymmetry at the LHC.

hep-ph↗

arXiv2013

Actomyosin contractility rotates the cell nucleus

The nucleus of the eukaryotic cell functions amidst active cytoskeletal filaments, but its response to the stresses carried by these filaments is largely unexplored. We report here the results of studies of the translational and rotational dynamics of the nuclei of single fibroblast cells, with the effects of cell migration suppressed by plating onto fibronectin-coated micro-fabricated patterns. Patterns of the same area but different shapes and/or aspect ratio were used to study the effect of cell geometry on the dynamics. On circles, squares and equilateral triangles, the nucleus undergoes persistent rotational motion, while on high-aspect-ratio rectangles of the same area it moves only back and forth. The circle and the triangle showed respectively the largest and the smallest angular speed. We show that our observations can be understood through a hydrodynamic approach in which the nucleus is treated as a highly viscous inclusion residing in a less viscous fluid of orientable filaments endowed with active stresses. Lowering actin contractility selectively by introducing blebbistatin at low concentrations drastically reduced the speed and persistence time of the angular motion of the nucleus. Time-lapse imaging of actin revealed a correlated hydrodynamic flow around the nucleus, with profile and magnitude consistent with the results of our theoretical approach. Coherent intracellular flows and consequent nuclear rotation thus appear to be a generic property that cells must balance by specific mechanisms in order to maintain nuclear homeostasis.

physics.bio-ph↗

arXiv2013

Top-flavored dark matter and the forward-backward asymmetry

We propose a simple model where dark matter (DM) carries top flavor and couples to the Standard Model through the top quark within a framework of minimal flavor violation (MFV). Top-flavored DM can explain the anomalous top forward-backward asymmetry observed at the Tevatron, while remaining consistent with other top observables at colliders. By virtue of its large coupling to top, DM acquires a sizable loop coupling to the Z boson, and the relic density is set by annihilation through the Z. We also discuss contraints from current direct detection searches, emphasizing the role of spin-dependent searches to probe this scenario.

hep-ph↗