arXiv subjects
Publications and source records attributed to Ankit Anand.
We have parameterized the degeneracy factor in terms of temperature and using this we have tried to compare and study the LQCD(Lattice Quantum Chromodynamics) data with our data.
We have studied the collisional time and relaxation time of a QGP(Quark-Gluon Plasma) by parameterizing them by temperature. From this parameterization we have obtained the decay rate parameterized by temperature which further helps us to calculate and compare the shear viscosity to entropy density ratio of a QGP with the KSS(Kovtun-Son-Starinets) result.
We have attempted to build first some simplified model to map the interaction of quarks and gluons, which can be contained by their thermodynamical quantity like entropy density, obtained from calculation of lattice quantum chromo dynamics (LQCD). With respect to entropy density of the standard non-interacting massless quark gluon plasma (QGP), its interacting values from LQCD simulation are reduced as we go from higher to lower temperature through the cross-over of quark-hadron phase transition. By parameterizing increasing degeneracy factor or increasing interaction-fugacity or decreasing thermal width of quarks and gluons with temperature, we have matched LQCD data.Using that interaction picture, shear viscosity and electrical conductivity are calculated. For getting nearly perfect fluid nature of QGP, interaction might have some role when we consider temperature dependent thermal width.
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in understanding stochastic process and fractal dynamics. In this paper, we apply the techniques of fractional calculus to study some specific modifications of the geometry of submanifolds. Our generalisation is applied to extend the Israel formalism which is used to glue together two spacetimes across a timelike, spacelike or a null hypersurface. In this context, we show that the fractional extrapolation leads to some striking new results. More precisely we demonstrate that, in contrast to the original Israel formalism, where many spacetimes can only be joined together through an intermediate thin hypersurface of matter satisfying some non- standard energy conditions, the fractional generalisation allows these spacetimes to be smoothly sewed together without any such requirements on the stress tensor of the matter fields. We discuss the ramifications of these results for spacetime structure and the possible implications for gravitational physics.
One popular way for lifted inference in probabilistic graphical models is to first merge symmetric states into a single cluster (orbit) and then use these for downstream inference, via variations of orbital MCMC [Niepert, 2012]. These orbits are represented compactly using permutations over variables, and variable-value (VV) pairs, but they can miss several state symmetries in a domain. We define the notion of permutations over block-value (BV) pairs, where a block is a set of variables. BV strictly generalizes VV symmetries, and can compute many more symmetries for increasing block sizes. To operationalize use of BV permutations in lifted inference, we describe 1) an algorithm to compute BV permutations given a block partition of the variables, 2) BV-MCMC, an extension of orbital MCMC that can sample from BV orbits, and 3) a heuristic to suggest good block partitions. Our experiments show that BV-MCMC can mix much faster compared to vanilla MCMC and orbital MCMC.
Lifted inference algorithms commonly exploit symmetries in a probabilistic graphical model (PGM) for efficient inference. However, existing algorithms for Boolean-valued domains can identify only those pairs of states as symmetric, in which the number of ones and zeros match exactly (count symmetries). Moreover, algorithms for lifted inference in multi-valued domains also compute a multi-valued extension of count symmetries only. These algorithms miss many symmetries in a domain. In this paper, we present first algorithms to compute non-count symmetries in both Boolean-valued and multi-valued domains. Our methods can also find symmetries between multi-valued variables that have different domain cardinalities. The key insight in the algorithms is that they change the unit of symmetry computation from a variable to a variable-value (VV) pair. Our experiments find that exploiting these symmetries in MCMC can obtain substantial computational gains over existing algorithms.
There is a vast body of theoretical research on lifted inference in probabilistic graphical models (PGMs). However, few demonstrations exist where lifting is applied in conjunction with top of the line applied algorithms. We pursue the applicability of lifted inference for computer vision (CV), with the insight that a globally optimal (MAP) labeling will likely have the same label for two symmetric pixels. The success of our approach lies in efficiently handling a distinct unary potential on every node (pixel), typical of CV applications. This allows us to lift the large class of algorithms that model a CV problem via PGM inference. We propose a generic template for coarse-to-fine (C2F) inference in CV, which progressively refines an initial coarsely lifted PGM for varying quality-time trade-offs. We demonstrate the performance of C2F inference by developing lifted versions of two near state-of-the-art CV algorithms for stereo vision and interactive image segmentation. We find that, against flat algorithms, the lifted versions have a much superior anytime performance, without any loss in final solution quality.
An important approach for efficient inference in probabilistic graphical models exploits symmetries among objects in the domain. Symmetric variables (states) are collapsed into meta-variables (meta-states) and inference algorithms are run over the lifted graphical model instead of the flat one. Our paper extends existing definitions of symmetry by introducing the novel notion of contextual symmetry. Two states that are not globally symmetric, can be contextually symmetric under some specific assignment to a subset of variables, referred to as the context variables. Contextual symmetry subsumes previous symmetry definitions and can rep resent a large class of symmetries not representable earlier. We show how to compute contextual symmetries by reducing it to the problem of graph isomorphism. We extend previous work on exploiting symmetries in the MCMC framework to the case of contextual symmetries. Our experiments on several domains of interest demonstrate that exploiting contextual symmetries can result in significant computational gains.