arXiv subjects
Publications and source records attributed to Sourav Dutta.
This is a short communication in reference to the comments in (arXiv: 1605.05147) of our paper in Int. J. Mod. Phys. D 25, 1650051 (2016). We have tried to answer to the comments or criticism in the paper.
Many Web applications require efficient querying of large Knowledge Graphs (KGs). We propose KOGNAC, a dictionary-encoding algorithm designed to improve SPARQL querying with a judicious combination of statistical and semantic techniques. In KOGNAC, frequent terms are detected with a frequency approximation algorithm and encoded to maximise compression. Infrequent terms are semantically grouped into ontological classes and encoded to increase data locality. We evaluated KOGNAC in combination with state-of-the-art RDF engines, and observed that it significantly improves SPARQL querying on KGs with up to 1B edges.
The present work deals with a quintom model of dark energy in the framework of a spatially flat isotropic and homogeneous Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. At first, Lie point symmetry is imposed to the system and the unknown coupled potential of the model is determined. Then Noether symmetry, which is also a point like symmetry of the Lagrangian, is imposed on the physical system and the potential takes a general form. It is shown that the Lie algebra of Noether symmetry is a sub-algebra of the corresponding Lie algebra of the Lie symmetry. Finally, a point transformation in the three dimensional augmented space is performed suitably so that one of the variables become cyclic and as a result there is considerable simplification to the physical system. Hence conserved quantities (i.e, constants of motion) are expressed in a compact form and cosmological solutions are evaluated and analyzed in the present context.
Sorting, a classical combinatorial process, forms the bedrock of numerous algorithms with varied applications. A related problem involves efficiently finding the corresponding ranks of all the elements - catering to rank queries, data partitioning and allocation, etc. Although, the element ranks can be subsequently obtained by initially sorting the elements, such procedures involve O(n log n) computations and might not be suitable with large input sizes for hard real-time systems or for applications with data re-ordering constraints. This paper proposes SONIK, a non-comparison linear time and space algorithm using bit operations inspired by radix sort for computing the ranks of all input integer elements, thereby providing implicit sorting. The element ranks are generated in-situ, i.e., directly at the corresponding element position without re-ordering or recourse to any other sorting mechanism.
The paper deals with phantom scalar field cosmology in Einstein gravity. At first using Lie symmetry, the coupling function to the kinetic term and the potential function of the scalar field and the equation of state parameter of the matter field are determined and a simple solution is obtained. Subsequently, Noether symmetry is imposed on the Lagrangian of the system. The symmetry vector is obtained and the potential takes a very general form from which potential using Lie Symmetry can be obtained as a particular case. Then we choose a point transformation $(a,ϕ)\rightarrow(u,v)$ such that one of the transformed variables (say u) is a cyclic for the Lagrangian. Using conserved charge (corresponding to the cyclic coordinate) and the constant of motion, solutions are obtained.
The present work is an attempt for emergent universe scenario with modified Chaplygin gas. The universe is chosen as spatially flat FRW space-time with modified Chaplygin gas as the only cosmic substratum. It is found that emergent scenario is possible for some specific (unrealistic) choice of the parameters in the equation of state for modified Chaplygin gas.
We report the formation of ultracold $^{7}$Li$^{85}$Rb molecules in the $a^{3}Σ^{+}$ electronic state by photoassociation (PA) and their detection via resonantly enhanced multiphoton ionization (REMPI). With our dual-species Li and Rb magneto-optical trap (MOT) apparatus, we detect PA resonances with binding energies up to ~62 cm$^{-1}$ below the $^{7}$Li 2s $^{2}S_{1/2}$ $+$ $^{85}$Rb 5p $^{2}P_{1/2}$ asymptote. In addition, we use REMPI spectroscopy to probe the $a^{3}Σ^{+}$ state and excited electronic $3^{3} Π$ and $4^{3} Σ^{+}$ states, and identify $a^{3}Σ^{+} (v" = 7 - 13)$, $3^{3} Π(v'_Π = 0 - 10)$ and $4^{3} Σ^{+} (v'_Σ = 0 - 5)$ vibrational levels. Our line assignments agree well with ab initio calculations. These preliminary spectroscopic studies on previously unobserved electronic states are crucial to discovering transition pathways for transferring ultracold LiRb molecules created via PA to deeply bound rovibrational levels of the electronic ground state.
The multichannel quantum defect theory (MQDT) in combination with the frame transformation (FT) approach is applied to model the Fano-Feshbach resonances measured for $^{7}$Li$^{87}$Rb and $^{6}$Li$^{87}$Rb [Marzok {\it et al.} Phys. Rev. A {\bf 79} 012717 (2009)]. The MQDT results show a level of accuracy comparable to that of previous models based on direct, fully numerical solutions of the the coupled channel Schrödinger equations (CC). Here, energy levels deduced from 2-photon photoassociation spectra for $^{7}$Li$^{85}$Rb are assigned by applying the MQDT approach, obtaining the bound state energies for the coupled channel problem. Our results confirm that MQDT yields a compact description of photoassociation observables as well as the Fano-Feshbach resonance positions and widths.
We present spectra of ultracold $^7$Li$^{85}$Rb molecules in their electronic ground state formed by spontaneous decay of weakly bound photoassociated molecules. Beginning with atoms in a dual species magneto-optical trap (MOT), weakly bound molecules are formed in the 4(1) electronic state, which corresponds to the B$^1Π$ state at short range. These molecules spontaneously decay to the electronic ground state and we use resonantly enhanced multiphoton ionization (REMPI) to determine the vibrational population distribution in the electronic ground states after spontaneous emission. Many of the observed lines from the spectra are consistent with transitions from the X$^1Σ^+$ ground electronic state to either the B$^1Π$ or D$^1Π$ electronic states that have been previously observed, with levels possibly as low as X$^1Σ^+$ $(v'' = 2)$ being populated. We do not observe decay to weakly bound vibrational levels of the X$^1Σ^+$ or a$^3Σ^+$ electronic states in the spectra. We also deduce a lower bound of 3900 cm$^{-1}$ for the dissociation energy of the LiRb$^+$ molecular ion.
We extend our recently developed inversion method to extract excited state potentials from fluorescence line positions and line strengths. We consider a previous limitation of the method arising due to insufficient input data in cases where the relatively weaker emission data are not experimentally available. We develop a solution to this problem by "regenerating" these weak transition lines via applying a model potential, e.g. a Morse potential. The result of this procedure, illustrated for the Q-branch emission from the lowest three vibrational levels of the B($^1 Π)$ state of LiRb, is shown to have an error of $0.29$ cm$^{-1}$ in the classically allowed region and a global error of $5.67$ cm$^{-1}$ for $V\le E(ν'=10)$. The robustness of this procedure is also demonstrated by considering the statistical error in the measured line intensities.
In this article, we report the measurement of collision-induced loss rate coefficients β_{Li,Rb} and β_{Rb,Li}, and also discuss means to significantly suppress such collision induced losses. We first describe our dual-species magneto-optical trap (MOT) that allows us to simultaneously trap > 5x10^8 7Li atoms loaded from a Zeeman slower and > 2x10^8 85Rb atoms loaded from a dispenser. We observe strong interspecies collision-induced losses in the MOTs which dramatically reduce the maximum atom number achievable in the MOTs. We measure the trap loss rate coefficients β_{Li,Rb} and β_{Rb,Li}, and, from a study of their dependence on the MOT parameters, determine the cause for the losses observed. Our results provide valuable insights into ultracold collisions between 7Li and 85Rb, guide our efforts to suppress collision induced losses, and also pave the way for the production of ultracold 7Li85Rb molecules.
We report the production of ultracold heteronuclear 7Li85Rb molecules in excited electronic states by photoassociation (PA) of ultracold 7Li and 85Rb atoms. PA is performed in a dual-species 7Li-85Rb magneto-optical trap (MOT) and the PA resonances are detected using trap loss spectroscopy. We identify several strong PA resonances below the Li (2s 2S1/2) + Rb (5p 2P3/2) asymptote and experimentally determine the long range C6 dispersion coefficients. We find a molecule formation rate (P_LiRb) of 3.5x10^7 s^-1 and a PA rate coefficient (K_PA) of 1.3x10^-10 cm^3/s, the highest among heteronuclear bi-alkali molecules. At large PA laser intensity, we observe the saturation of the PA rate coefficient (K_PA) close to the theoretical value at the unitarity limit.
We report the production of ultracold 7Li85Rb molecules by photoassociation (PA) below the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote. We perform PA spectroscopy in a dual-species 7Li-85Rb magneto-optical trap (MOT) and detect the PA resonances using trap loss spectroscopy. We observe several strong PA resonances corresponding to the last few bound states, assign the lines and derive the long range C6 dispersion coefficients for the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote. We also report an excited-state molecule formation rate (P_LiRb) of ~10^7 s^-1 and a PA rate coefficient (K_PA) of ~4x10^-11 cm^3/s, which are both among the highest observed for heteronuclear bi-alkali molecules. These suggest that PA is a promising route for the creation of ultracold ground state LiRb molecules.
Applications involving telecommunication call data records, web pages, online transactions, medical records, stock markets, climate warning systems, etc., necessitate efficient management and processing of such massively exponential amount of data from diverse sources. De-duplication or Intelligent Compression in streaming scenarios for approximate identification and elimination of duplicates from such unbounded data stream is a greater challenge given the real-time nature of data arrival. Stable Bloom Filters (SBF) addresses this problem to a certain extent. . In this work, we present several novel algorithms for the problem of approximate detection of duplicates in data streams. We propose the Reservoir Sampling based Bloom Filter (RSBF) combining the working principle of reservoir sampling and Bloom Filters. We also present variants of the novel Biased Sampling based Bloom Filter (BSBF) based on biased sampling concepts. We also propose a randomized load balanced variant of the sampling Bloom Filter approach to efficiently tackle the duplicate detection. In this work, we thus provide a generic framework for de-duplication using Bloom Filters. Using detailed theoretical analysis we prove analytical bounds on the false positive rate, false negative rate and convergence rate of the proposed structures. We exhibit that our models clearly outperform the existing methods. We also demonstrate empirical analysis of the structures using real-world datasets (3 million records) and also with synthetic datasets (1 billion records) capturing various input distributions.
The tremendous expanse of search engines, dictionary and thesaurus storage, and other text mining applications, combined with the popularity of readily available scanning devices and optical character recognition tools, has necessitated efficient storage, retrieval and management of massive text databases for various modern applications. For such applications, we propose a novel data structure, INSTRUCT, for efficient storage and management of sequence databases. Our structure uses bit vectors for reusing the storage space for common triplets, and hence, has a very low memory requirement. INSTRUCT efficiently handles prefix and suffix search queries in addition to the exact string search operation by iteratively checking the presence of triplets. We also propose an extension of the structure to handle substring search efficiently, albeit with an increase in the space requirements. This extension is important in the context of trie-based solutions which are unable to handle such queries efficiently. We perform several experiments portraying that INSTRUCT outperforms the existing structures by nearly a factor of two in terms of space requirements, while the query times are better. The ability to handle insertion and deletion of strings in addition to supporting all kinds of queries including exact search, prefix/suffix search and substring search makes INSTRUCT a complete data structure.
Balanced allocation of online balls-into-bins has long been an active area of research for efficient load balancing and hashing applications.There exists a large number of results in this domain for different settings, such as parallel allocations~\cite{parallel}, multi-dimensional allocations~\cite{multi}, weighted balls~\cite{weight} etc. For sequential multi-choice allocation, where $m$ balls are thrown into $n$ bins with each ball choosing $d$ (constant) bins independently uniformly at random, the maximum load of a bin is $O(\log \log n) + m/n$ with high probability~\cite{heavily_load}. This offers the current best known allocation scheme. However, for $d = Θ(\log n)$, the gap reduces to $O(1)$~\cite{soda08}.A similar constant gap bound has been established for parallel allocations with $O(\log ^*n)$ communication rounds~\cite{lenzen}. In this paper we propose a novel multi-choice allocation algorithm, \emph{Improved D-choice with Estimated Average} ($IDEA$) achieving a constant gap with a high probability for the sequential single-dimensional online allocation problem with constant $d$. We achieve a maximum load of $\lceil m/n \rceil$ with high probability for constant $d$ choice scheme with \emph{expected} constant number of retries or rounds per ball. We also show that the bound holds even for an arbitrary large number of balls, $m>>n$. Further, we generalize this result to (i)~the weighted case, where balls have weights drawn from an arbitrary weight distribution with finite variance, (ii)~multi-dimensional setting, where balls have $D$ dimensions with $f$ randomly and uniformly chosen filled dimension for $m=n$, and (iii)~the parallel case, where $n$ balls arrive and are placed parallely in the bins. We show that the gap in these case is also a constant w.h.p. (independent of $m$) for constant value of $d$ with expected constant number of retries per ball.
Allocation of balls into bins is a well studied abstraction for load balancing problems.The literature hosts numerous results for sequential(single dimensional) allocation case when m balls are thrown into n bins. In this paper we study the symmetric multiple choice process for both unweighted and weighted balls as well as for both multidimensional and scalar models.Additionally,we present the results on bounds on gap for (1+beta) choice process with multidimensional balls and bins. We show that for the symmetric d choice process and with m=O(n), the upper bound on the gap is O(lnln(n)) w.h.p.This upper bound on the gap is within D=f factor of the lower bound. This is the first such tight result.For the general case of m>>n the expected gap is bounded by O(lnln(n)).For variable f and non-uniform distribution of the populated dimensions,we obtain the upper bound on the expected gap as O(log(n)). Further,for the multiple round parallel balls and bins,we show that the gap is also bounded by O(loglog(n)) for m=O(n).The same bound holds for the expected gap when m>>n. Our analysis also has strong implications in the sequential scalar case.For the weighted balls and bins and general case m>>n,we show that the upper bound on the expected gap is O(log(n)) which improves upon the best prior bound of n^c.Moreover,we show that for the (1 + beta) choice process and m=O(n) the upper bound(assuming uniform distribution of f populated dimensions over D total dimensions) on the gap is O(log(n)/beta),which is within D=f factor of the lower bound.For fixed f with non-uniform distribution and for random f with Binomial distribution the expected gap remains O(log(n)/beta) independent of the total number of balls thrown. This is the first such tight result for (1 +beta) paradigm with multidimensional balls and bins.
With the explosion of information stored world-wide,data intensive computing has become a central area of research.Efficient management and processing of this massively exponential amount of data from diverse sources,such as telecommunication call data records,online transaction records,etc.,has become a necessity.Removing redundancy from such huge(multi-billion records) datasets resulting in resource and compute efficiency for downstream processing constitutes an important area of study. "Intelligent compression" or deduplication in streaming scenarios,for precise identification and elimination of duplicates from the unbounded datastream is a greater challenge given the realtime nature of data arrival.Stable Bloom Filters(SBF) address this problem to a certain extent.However,SBF suffers from a high false negative rate(FNR) and slow convergence rate,thereby rendering it inefficient for applications with low FNR tolerance.In this paper, we present a novel Reservoir Sampling based Bloom Filter,(RSBF) data structure,based on the combined concepts of reservoir sampling and Bloom filters for approximate detection of duplicates in data streams.Using detailed theoretical analysis we prove analytical bounds on its false positive rate(FPR),false negative rate(FNR) and convergence rates with low memory requirements.We show that RSBF offers the currently lowest FN and convergence rates,and are better than those of SBF while using the same memory.Using empirical analysis on real-world datasets(3 million records) and synthetic datasets with around 1 billion records,we demonstrate upto 2x improvement in FNR with better convergence rates as compared to SBF,while exhibiting comparable FPR.To the best of our knowledge,this is the first attempt to integrate reservoir sampling method with Bloom filters for deduplication in streaming scenarios.