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Arun Kumar

Publications and source records attributed to Arun Kumar.

100 records · Page 6Linked to original sources

Mittag-Leffler Lévy Processes

In this article, we introduce Mittag-Leffler Lévy process and provide two alternative representations of this process. First, in terms of Laplace transform of the marginal densities and next as a subordinated stochastic process. Both these representations are useful in analyzing the properties of the process. Since integer order moments for this process are not finite, we obtain fractional order moments. Its density function and corresponding Lévy measure density is also obtained. Further, heavy tailed behavior of densities and stochastic self-similarity of the process is demonstrated. Our results generalize and complement the results available on Mittag-Leffler distribution in several directions.

math.PR↗

Kleene Algebras and Logic: Boolean and Rough Set Representations, 3-valued, Rough and Perp Semantics

A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets. Further, we show that negation with the Kleene property (called the `Kleene negation') always arises from the set theoretic complement. The corresponding propositional logic is then studied through a 3-valued and rough set semantics. It is also established that Kleene negation can be considered as a modal operator, and enables giving a perp semantics to the logic. One concludes with the observation that all the semantics for this logic are equivalent.

math.LO↗

Search for a heavy Higgs boson in $H\rightarrow ZZ\rightarrow 2\ell2ν$ channel in pp collisions with CMS detector at the LHC

A search for a heavy Higgs boson in the $H\rightarrow ZZ\rightarrow 2\ell2ν$ decay channel, where $\ell$ = e or $μ$, in pp collisions at a centre-of-mass energy of 7 and 8 TeV is presented. The search is optimized separately for the vector boson fusion and the gluon fusion production processes. No significant excess is observed above the background expectation. A re-interpretation of the results as a search for an electroweak singlet extension of the Standard Model is also presented.

hep-ex↗

Search for the standard model Higgs boson in the H->ZZ->2l2nu decay channel in the CMS Experiment

A search for the Standard Model Higgs boson in the H->ZZ->2l2nu decay channel, where l = e or mu, in pp collisions at a center-of-mass energy of both 7 and 8 TeV is presented. The data were collected at the LHC, with the CMS detector, and correspond to an integrated luminosity of 5.0 fb-1 at 7 TeV and 5.0 fb-1 at 8 TeV. The search is optimized separately for the vector boson fusion and the gluon fusion production processes.No significant excess is observed above the background expectation, and upper limits are set on the Higgs boson production cross section. The presence of the standard model Higgs boson with a mass in the 278-600 GeV/c2 range is excluded at 95% confidence level.

hep-ex↗

The MADlib Analytics Library or MAD Skills, the SQL

MADlib is a free, open source library of in-database analytic methods. It provides an evolving suite of SQL-based algorithms for machine learning, data mining and statistics that run at scale within a database engine, with no need for data import/export to other tools. The goal is for MADlib to eventually serve a role for scalable database systems that is similar to the CRAN library for R: a community repository of statistical methods, this time written with scale and parallelism in mind. In this paper we introduce the MADlib project, including the background that led to its beginnings, and the motivation for its open source nature. We provide an overview of the library's architecture and design patterns, and provide a description of various statistical methods in that context. We include performance and speedup results of a core design pattern from one of those methods over the Greenplum parallel DBMS on a modest-sized test cluster. We then report on two initial efforts at incorporating academic research into MADlib, which is one of the project's goals. MADlib is freely available at http://madlib.net, and the project is open for contributions of both new methods, and ports to additional database platforms.

cs.DB↗

Towards a Unified Architecture for in-RDBMS Analytics

The increasing use of statistical data analysis in enterprise applications has created an arms race among database vendors to offer ever more sophisticated in-database analytics. One challenge in this race is that each new statistical technique must be implemented from scratch in the RDBMS, which leads to a lengthy and complex development process. We argue that the root cause for this overhead is the lack of a unified architecture for in-database analytics. Our main contribution in this work is to take a step towards such a unified architecture. A key benefit of our unified architecture is that performance optimizations for analytics techniques can be studied generically instead of an ad hoc, per-technique fashion. In particular, our technical contributions are theoretical and empirical studies of two key factors that we found impact performance: the order data is stored, and parallelization of computations on a single-node multicore RDBMS. We demonstrate the feasibility of our architecture by integrating several popular analytics techniques into two commercial and one open-source RDBMS. Our architecture requires changes to only a few dozen lines of code to integrate a new statistical technique. We then compare our approach with the native analytics tools offered by the commercial RDBMSes on various analytics tasks, and validate that our approach achieves competitive or higher performance, while still achieving the same quality.

cs.DB↗

Probabilistic Management of OCR Data using an RDBMS

The digitization of scanned forms and documents is changing the data sources that enterprises manage. To integrate these new data sources with enterprise data, the current state-of-the-art approach is to convert the images to ASCII text using optical character recognition (OCR) software and then to store the resulting ASCII text in a relational database. The OCR problem is challenging, and so the output of OCR often contains errors. In turn, queries on the output of OCR may fail to retrieve relevant answers. State-of-the-art OCR programs, e.g., the OCR powering Google Books, use a probabilistic model that captures many alternatives during the OCR process. Only when the results of OCR are stored in the database, do these approaches discard the uncertainty. In this work, we propose to retain the probabilistic models produced by OCR process in a relational database management system. A key technical challenge is that the probabilistic data produced by OCR software is very large (a single book blows up to 2GB from 400kB as ASCII). As a result, a baseline solution that integrates these models with an RDBMS is over 1000x slower versus standard text processing for single table select-project queries. However, many applications may have quality-performance needs that are in between these two extremes of ASCII and the complete model output by the OCR software. Thus, we propose a novel approximation scheme called Staccato that allows a user to trade recall for query performance. Additionally, we provide a formal analysis of our scheme's properties, and describe how we integrate our scheme with standard-RDBMS text indexing.

cs.DB↗

Alice Meets Bob: A Comparative Usability Study of Wireless Device Pairing Methods for a "Two-User" Setting

When users want to establish wireless communication between/among their devices, the channel has to be bootstrapped first. To prevent any malicious control of or eavesdropping over the communication, the channel is desired to be authenticated and confidential. The process of setting up a secure communication channel between two previously unassociated devices is referred to as "Secure Device Pairing". When there is no prior security context, e.g., shared secrets, common key servers or public key certificates, device pairing requires user involvement into the process. The idea usually involves leveraging an auxiliary human-perceptible channel to authenticate the data exchanged over the insecure wireless channel. We observe that the focus of prior research has mostly been limited to pairing scenarios where a single user controls both the devices. In this paper, we consider more general and emerging "two-user" scenarios, where two different users establish pairing between their respective devices. Although a number of pairing methods exists in the literature, only a handful of those are applicable to the two-user setting. We present the first study to identify the methods practical for two-user pairing scenarios, and comparatively evaluate the usability of these methods. Our results identify methods best-suited for users, in terms of efficiency, error-tolerance and of course, usability. Our work sheds light on the applicability and usability of pairing methods for emerging two-user scenarios, a topic largely ignored so far.

cs.CR↗

Fractional Normal Inverse Gaussian Process

Normal inverse Gaussian (NIG) process was introduced by Barndorff-Nielsen (1997) by subordinating Brownian motion with drift to an inverse Gaussian process. Increments of NIG process are independent and stationary. In this paper, we introduce dependence between the increments of NIG process, by subordinating fractional Brownian motion to an inverse Gaussian process and call it fractional normal inverse Gaussian (FNIG) process. The basic properties of this process are discussed. Its marginal distributions are scale mixtures of normal laws, infinitely divisible for the Hurst parameter 1/2<=H< 1 and are heavy tailed. First order increments of the process are stationary and possess long-range dependence (LRD) property. It is shown that they have persistence of signs LRD property also. A generalization of the FNIG process called n-FNIG process is also discussed which allows Hurst parameter H in the interval (n-1, n). Possible applications to mathematical finance and hydraulics are also pointed out

math.PR↗