arXiv subjects

Ravi Kumar

Publications and source records attributed to Ravi Kumar.

At least 163 records · Page 9Linked to original sources

arXiv2019

Semi-Online Bipartite Matching

In this paper we introduce the \emph{semi-online} model that generalizes the classical online computational model. The semi-online model postulates that the unknown future has a predictable part and an adversarial part; these parts can be arbitrarily interleaved. An algorithm in this model operates as in the standard online model, i.e., makes an irrevocable decision at each step. We consider bipartite matching in the semi-online model, for both integral and fractional cases. Our main contributions are competitive algorithms for this problem that are close to or match a hardness bound. The competitive ratio of the algorithms nicely interpolates between the truly offline setting (no adversarial part) and the truly online setting (no predictable part).

cs.DS↗

arXiv2019

Testing Mixtures of Discrete Distributions

There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example, over a domain of size $n$, distinguishing the uniform distribution from distributions that are far from uniform in $\ell_1$-distance uses only $O(\sqrt{n})$ samples. However, the picture is very different in the presence of arbitrary noise, even when the amount of noise is quite small. In this case, one must distinguish if samples are coming from a distribution that is $ε$-close to uniform from the case where the distribution is $(1-ε)$-far from uniform. The latter task requires nearly linear in $n$ samples [Valiant 2008, Valian and Valiant 2011]. In this work, we present a noise model that on one hand is more tractable for the testing problem, and on the other hand represents a rich class of noise families. In our model, the noisy distribution is a mixture of the original distribution and noise, where the latter is known to the tester either explicitly or via sample access; the form of the noise is also known a priori. Focusing on the identity and closeness testing problems leads to the following mixture testing question: Given samples of distributions $p, q_1,q_2$, can we test if $p$ is a mixture of $q_1$ and $q_2$? We consider this general question in various scenarios that differ in terms of how the tester can access the distributions, and show that indeed this problem is more tractable. Our results show that the sample complexity of our testers are exactly the same as for the classical non-mixture case.

math.ST↗

arXiv2019

The X-ray photoemission and Co K -Edge X-ray absorption of Ba2CoWO6

The structural, electronic and optical properties of cubic double perovskite BaCoWO6 have been studied. Neutron powder diffraction data is collected on this sample from 6K to 300K. The crystal structure is face centered cubic, space group being Fm3m (No. 225). We did not find evidence for long range magnetic ordering in this system in this temperature range. The band-gap is estimated using Uv-vis spectroscopy. The Co-K edge X-ray absorption (XAFS) spectra of Ba2CoWO6 was analysed together with those Co-foil, which was used as reference compounds. X-ray photoemission spectroscopy (XPS), X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) studies give the insight of the electronic and structural information on the Co local environment for Ba2CoWO6.

cond-mat.mtrl-sci↗

arXiv2019

Electronic properties of A2Zr2O7 (A= Gd, Nd) ceramic

The density functional theory with generalized gradient approximation has been used to investigate the electronic structure of gadolinium pyrochlore A2Zr2O7 (A=Gd, Nd) ceramic synthesized in polycrystalline form by solid state reaction. Structural characterization of the compound was done through X-ray diffraction (XRD) followed by Rietveld analysis of the XRD pattern. The Zr-K edge X-ray absorption (XAFS) spectra of A2Zr2O7 (A=Gd, Nd) were analysed together with those Zr-foil, which was used as reference compounds. X-ray photoemission spectroscopy (XPS), X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) for A2Zr2O7 (A=Gd, Nd) has been employed to obtain quantitative structural information on the Zr-local environment. The band gap is estimated using UV-Vis spectroscopy. The crystal structure is face centered cubic, space group being Fd-3m (No. 227). The total energies in this work were calculated using the generalized gradient approximation to DFT plus on-site repulsion (U) method.

cond-mat.mtrl-sci↗

arXiv2019

Clustering without Over-Representation

In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in any cluster. This problem is motivated by practical clustering settings, e.g., in clustering news articles where the color of an article is its source, it is preferable that no single news source dominates any cluster. For the most general version of this problem, we obtain an algorithm that has provable guarantees of performance; our algorithm is based on finding a fractional solution using a linear program and rounding the solution subsequently. For the special case of the problem where no color has an absolute majority in any cluster, we obtain a simpler combinatorial algorithm also with provable guarantees. Experiments on real-world data shows that our algorithms are effective in finding good clustering without over-representation.

cs.DS↗

arXiv2019

On the Learnability of Deep Random Networks

In this paper we study the learnability of deep random networks from both theoretical and practical points of view. On the theoretical front, we show that the learnability of random deep networks with sign activation drops exponentially with its depth. On the practical front, we find that the learnability drops sharply with depth even with the state-of-the-art training methods, suggesting that our stylized theoretical results are closer to reality.

cs.LG↗

arXiv2019

Electric dipole polarizability of group-IIIA ions using PRCC: Large correlation effects from nonlinear terms

We compute the ground-state electric dipole polarizability of group-IIIA ions using the perturbed relativistic coupled-cluster (PRCC) theory. To account for the relativistic effects and QED corrections, we use the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy. The effects of triple excitations are considered perturbatively in the PRCC. Our PRCC results for $α$ are good in agreement with the previous theoretical results for all the ions. From our computations we find that the nonlinear terms in PRCC have significant contributions and must be included to obtain the accurate value of $α$ for group-IIIA ions. For the correction from the Breit interaction, we find that it is largest for Al$^+$ and decreases as we go towards the heavier ions. The corrections from the vacuum polarization and the self-energy increase from lighter to heavier ions.

physics.atom-ph↗

arXiv2018

Fair Clustering Through Fairlets

We study the question of fair clustering under the {\em disparate impact} doctrine, where each protected class must have approximately equal representation in every cluster. We formulate the fair clustering problem under both the $k$-center and the $k$-median objectives, and show that even with two protected classes the problem is challenging, as the optimum solution can violate common conventions---for instance a point may no longer be assigned to its nearest cluster center! En route we introduce the concept of fairlets, which are minimal sets that satisfy fair representation while approximately preserving the clustering objective. We show that any fair clustering problem can be decomposed into first finding good fairlets, and then using existing machinery for traditional clustering algorithms. While finding good fairlets can be NP-hard, we proceed to obtain efficient approximation algorithms based on minimum cost flow. We empirically quantify the value of fair clustering on real-world datasets with sensitive attributes.

cs.LG↗

arXiv2018

Dicke model simulation via cavity-assisted Raman transitions

The Dicke model is of fundamental importance in quantum mechanics for understanding the collective behaviour of atoms coupled to a single electromagnetic mode. In this paper, we demonstrate a Dicke-model simulation using cavity-assisted Raman transitions in a configuration using counter-propagating laser beams. The observations indicate that motional effects should be included to fully account for the results and these results are contrasted with the experiments using single-beam and co-propagating configurations. A theoretical description is given that accounts for the beam geometries used in the experiments and indicates the potential role of motional effects. In particular a model is given that highlights the influence of Doppler broadening on the observed thresholds.

quant-ph↗

arXiv2017

Algorithms for $\ell_p$ Low Rank Approximation

We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entrywise $\ell_p$-approximation error, for any $p \geq 1$; the case $p = 2$ is the classical SVD problem. We obtain the first provably good approximation algorithms for this version of low-rank approximation that work for every value of $p \geq 1$, including $p = \infty$. Our algorithms are simple, easy to implement, work well in practice, and illustrate interesting tradeoffs between the approximation quality, the running time, and the rank of the approximating matrix.

cs.DS↗

arXiv2017

Linear Additive Markov Processes

We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parametrization. LAMP also allows the specific dependence on history to be learned efficiently from data. We characterize some theoretical properties of LAMP, including its steady-state and mixing time. We then give an algorithm based on alternating minimization to learn LAMP models from data. Finally, we perform a series of real-world experiments to show that LAMP is more powerful than first-order Markov processes, and even holds its own against deep sequential models (LSTMs) with a negligible increase in parameter complexity.

cs.LG↗

arXiv2016

Non-equilibrium phase transition in a spin-1 Dicke model

We realize a spin-1 Dicke model using magnetic sub-levels of the lowest F=1 hyperfine level of $^{87}$Rb atoms confined to a high finesse cavity. We study this system under conditions of imbalanced driving, which is predicted to have a rich phase diagram of nonequilibrium phases and phase transitions. We observe both super-radiant and oscillatory phases from the cavity output spectra as predicted by theory. Exploring the system over a wide range of parameters, we obtain the boundaries between the normal, super-radiant and the oscillatory phases, and compare with a theoretical model.

quant-ph↗

arXiv2016

Conversational flow in Oxford-style debates

Public debates are a common platform for presenting and juxtaposing diverging views on important issues. In this work we propose a methodology for tracking how ideas flow between participants throughout a debate. We use this approach in a case study of Oxford-style debates---a competitive format where the winner is determined by audience votes---and show how the outcome of a debate depends on aspects of conversational flow. In particular, we find that winners tend to make better use of a debate's interactive component than losers, by actively pursuing their opponents' points rather than promoting their own ideas over the course of the conversation.

cs.CL↗

arXiv2015

Multi-level cascaded electromagnetically induced transparency in cold atoms using an optical nanofibre interface

Ultrathin optical fibres integrated into cold atom setups are proving to be ideal building blocks for atom-photon hybrid quantum networks. Such optical nanofibres (ONF) can be used for the demonstration of nonlinear optics and quantum interference phenomena in atomic media. Here, we report on the observation of multilevel cascaded electromagnetically induced transparency (EIT) using an optical nanofibre to interface cold $^{87}$Rb atoms through the intense evanescent fields that can be achieved at ultralow probe and coupling powers. Both the probe (at 780 nm) and the coupling (at 776 nm) beams propagate through the nanofibre. The observed multipeak transparency spectra of the probe beam could offer a method for simultaneously slowing down multiple wavelengths in an optical nanofibre or for generating ONF-guided entangled beams, showing the potential of such an atom-nanofibre system for quantum information. We also demonstrate all-optical-switching in the all fibred system using the obtained EIT effect.

physics.atom-ph↗

arXiv2015

Sketching, Embedding, and Dimensionality Reduction for Information Spaces

Information distances like the Hellinger distance and the Jensen-Shannon divergence have deep roots in information theory and machine learning. They are used extensively in data analysis especially when the objects being compared are high dimensional empirical probability distributions built from data. However, we lack common tools needed to actually use information distances in applications efficiently and at scale with any kind of provable guarantees. We can't sketch these distances easily, or embed them in better behaved spaces, or even reduce the dimensionality of the space while maintaining the probability structure of the data. In this paper, we build these tools for information distances---both for the Hellinger distance and Jensen--Shannon divergence, as well as related measures, like the $χ^2$ divergence. We first show that they can be sketched efficiently (i.e. up to multiplicative error in sublinear space) in the aggregate streaming model. This result is exponentially stronger than known upper bounds for sketching these distances in the strict turnstile streaming model. Second, we show a finite dimensionality embedding result for the Jensen-Shannon and $χ^2$ divergences that preserves pair wise distances. Finally we prove a dimensionality reduction result for the Hellinger, Jensen--Shannon, and $χ^2$ divergences that preserves the information geometry of the distributions (specifically, by retaining the simplex structure of the space). While our second result above already implies that these divergences can be explicitly embedded in Euclidean space, retaining the simplex structure is important because it allows us to continue doing inference in the reduced space. In essence, we preserve not just the distance structure but the underlying geometry of the space.

cs.DS↗

arXiv2015

Autler-Townes splitting via frequency upconversion at ultra-low power levels in cold $^{87}$Rb atoms using an optical nanofiber

The tight confinement of the evanescent light field around the waist of an optical nanofiber makes it a suitable tool for studying nonlinear optics in atomic media. Here, we use an optical nanofiber embedded in a cloud of laser-cooled 87Rb for near-infrared frequency upconversion via a resonant two-photon process. Sub-nW powers of the two-photon beams, at 780 nm and 776 nm, co-propagate through the optical nanofiber and generation of 420 nm photons is observed. A measurement of the Autler-Townes splitting provides a direct measurement of the Rabi frequency of the 780 nm transition. Through this method, dephasings of the system can be studied. In this work, the optical nanofiber is used as an excitation and detection tool simultaneously, and it highlights some of the advantages of using fully fibered systems for nonlinear optics with atoms.

physics.optics↗

arXiv2014

Development of high power quantum well lasers at RRCAT

We at RRCAT have recently developed high power laser diodes in the wavelength range of 740 to 1000 nm. A typical semiconductor laser structure is consisted of about 10 epilayers with different composition, thickness and doping values. For example, a laser diode operating at 0.8 micron has either GaAs or GaAsP quantum well as an active layer. The quantum well is sandwiched between AlGaAs wider bandgap waveguide and cladding layers. The complete laser structure is grown by metal organic vapour phase epitaxy technique and devices are fabricated through standard procedure using photolithography. We recently achieved about 5.3 Watt peak power at 853 nm. These laser diodes were tested under pulsed operation at room temperature for 500 nanosecond pulse duration with a duty cycle of 1:1000. Laser diode arrays consisting of 6-10 elements were also developed and tested for operation in pulsed mode at room temperature.

physics.optics↗

arXiv2014

Interaction of laser-cooled $^{87}$Rb atoms with higher order modes of an optical nanofiber

Optical nanofibres are used to confine light to subwavelength regions and are very promising tools for the development of optical fibre-based quantum networks using cold, neutral atoms. To date, experimental studies on atoms near nanofibres have focussed on fundamental fibre mode interactions. In this work, we demonstrate the integration of a few-mode optical nanofibre into a magneto-optical trap for $^{87}$Rb atoms. The nanofibre, with a waist diameter of $\sim$700 nm, supports both the fundamental and first group of higher order modes and is used for atomic fluorescence and absorption studies. In general, light propagating in higher order fibre modes has a greater evanescent field extension around the waist in comparison with the fundamental mode. By exploiting this behaviour, we demonstrate that the detected signal of fluorescent photons emitted from a cloud of cold atoms centred at the nanofibre waist is larger ($\sim$6 times) when higher order guided modes are considered as compared to the fundamental mode. Absorption of on-resonance, higher order mode probe light by the laser-cooled atoms is also observed. These advances should facilitate the realisation of atom trapping schemes based on higher order mode interference.

physics.atom-ph↗