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Abhinav Kumar

Publications and source records attributed to Abhinav Kumar.

At least 109 records · Page 6Linked to original sources

Streaming Video QoE Modeling and Prediction: A Long Short-Term Memory Approach

HTTP based adaptive video streaming has become a popular choice of streaming due to the reliable transmission and the flexibility offered to adapt to varying network conditions. However, due to rate adaptation in adaptive streaming, the quality of the videos at the client keeps varying with time depending on the end-to-end network conditions. Further, varying network conditions can lead to the video client running out of playback content resulting in rebuffering events. These factors affect the user satisfaction and cause degradation of the user quality of experience (QoE). It is important to quantify the perceptual QoE of the streaming video users and monitor the same in a continuous manner so that the QoE degradation can be minimized. However, the continuous evaluation of QoE is challenging as it is determined by complex dynamic interactions among the QoE influencing factors. Towards this end, we present LSTM-QoE, a recurrent neural network based QoE prediction model using a Long Short-Term Memory (LSTM) network. The LSTM-QoE is a network of cascaded LSTM blocks to capture the nonlinearities and the complex temporal dependencies involved in the time varying QoE. Based on an evaluation over several publicly available continuous QoE databases, we demonstrate that the LSTM-QoE has the capability to model the QoE dynamics effectively. We compare the proposed model with the state-of-the-art QoE prediction models and show that it provides superior performance across these databases. Further, we discuss the state space perspective for the LSTM-QoE and show the efficacy of the state space modeling approaches for QoE prediction.

cs.MM↗

Inose's construction and elliptic K3 surfaces with Mordell-Weil rank 15 revisited

We describe two constructions of elliptic K3 surfaces starting from the Kummer surface of the Jacobian of a genus 2 curve. These parallel the base-change constructions of Kuwata for the Kummer surface of a product of two elliptic curves. One of these also involves the analogue of an Inose fibration. We use these methods to provide explicit examples of elliptic K3 surfaces over the rationals of geometric Mordell-Weil rank 15.

math.AG↗

Modeling Continuous Video QoE Evolution: A State Space Approach

A rapid increase in the video traffic together with an increasing demand for higher quality videos has put a significant load on content delivery networks in the recent years. Due to the relatively limited delivery infrastructure, the video users in HTTP streaming often encounter dynamically varying quality over time due to rate adaptation, while the delays in video packet arrivals result in rebuffering events. The user quality-of-experience (QoE) degrades and varies with time because of these factors. Thus, it is imperative to monitor the QoE continuously in order to minimize these degradations and deliver an optimized QoE to the users. Towards this end, we propose a nonlinear state space model for efficiently and effectively predicting the user QoE on a continuous time basis. The QoE prediction using the proposed approach relies on a state space that is defined by a set of carefully chosen time varying QoE determining features. An evaluation of the proposed approach conducted on two publicly available continuous QoE databases shows a superior QoE prediction performance over the state-of-the-art QoE modeling approaches. The evaluation results also demonstrate the efficacy of the selected features and the model order employed for predicting the QoE. Finally, we show that the proposed model is completely state controllable and observable, so that the potential of state space modeling approaches can be exploited for further improving QoE prediction.

cs.MM↗

Resource Allocation for CoMP in Cellular Networks with Base Station Switching

Base station switching (BSS) can results in significant reduction in energy consumption of cellular networks during low traffic conditions. We show that the coverage loss due to BSS can be compensated via coordinated multi-point (CoMP) based transmission in a cluster of base stations. For a BSS with CoMP based system, we propose various BSS patterns to achieve suitable trade-offs between energy savings and throughput. We formulate the CoMP resource allocation and user scheduling as a joint optimization problem. We derive the optimal time fraction and user scheduling for this problem and use it to formulate a simplified BSS with CoMP optimization problem. A heuristic that solves this problem is presented. Through extensive simulations, we show that suitable trade-offs among energy, coverage, and rate can be achieved by appropriately selecting the BSS pattern, CoMP cluster, and rate threshold.

cs.NI↗

Neural Signatures for Licence Plate Re-identification

The problem of vehicle licence plate re-identification is generally considered as a one-shot image retrieval problem. The objective of this task is to learn a feature representation (called a "signature") for licence plates. Incoming licence plate images are converted to signatures and matched to a previously collected template database through a distance measure. Then, the input image is recognized as the template whose signature is "nearest" to the input signature. The template database is restricted to contain only a single signature per unique licence plate for our problem. We measure the performance of deep convolutional net-based features adapted from face recognition on this task. In addition, we also test a hybrid approach combining the Fisher vector with a neural network-based embedding called "f2nn" trained with the Triplet loss function. We find that the hybrid approach performs comparably while providing computational benefits. The signature generated by the hybrid approach also shows higher generalizability to datasets more dissimilar to the training corpus.

cs.CV↗

Optimality and uniqueness of the Leech lattice among lattices

We prove that the Leech lattice is the unique densest lattice in R^24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R^24 can exceed the Leech lattice's density by a factor of more than 1+1.65*10^(-30), and we give a new proof that E_8 is the unique densest lattice in R^8.

math.MG↗

Elliptic K3 surfaces associated with the product of two elliptic curves: Mordell-Weil lattices and their fields of definition

To a pair of elliptic curves, one can naturally attach two K3 surfaces: the Kummer surface of their product and a double cover of it, called the Inose surface. They have prominently featured in many interesting constructions in algebraic geometry and number theory. There are several more associated elliptic K3 surfaces, obtained through base change of the Inose surface; these have been previously studied by Kuwata. We give an explicit description of the geometric Mordell-Weil groups of each of these elliptic surfaces in the generic case (when the elliptic curves are non-isogenous). In the non-generic case, we describe a method to calculate explicitly a finite index subgroup of the Mordell-Weil group, which may be saturated to give the full group. Our methods rely on several interesting group actions, the use of rational elliptic surfaces, as well as connections to the geometry of low degree curves on cubic and quartic surfaces. We apply our techniques to compute the full Mordell-Weil group in several examples of arithmetic interest, arising from isogenous elliptic curves with complex multiplication, for which these K3 surfaces are singular.

math.AG↗

Chemical exfoliation of MoS2 leads to semiconducting 1T' phase and not the metallic 1T phase

A trigonal phase existing only as small patches on chemically exfoliated few layer, thermodynamically stable 1H phase of MoS2 is believed to influence critically properties of MoS2 based devices. This phase has been most often attributed to the metallic 1T phase. We investigate the electronic structure of chemically exfoliated MoS2 few layered systems using spatially resolved (lesser than 120 nm resolution) photoemission spectroscopy and Raman spectroscopy in conjunction with state-of-the-art electronic structure calculations. On the basis of these results, we establish that the ground state of this phase is a small gap (~90 meV) semiconductor in contrast to most claims in the literature; we also identify the specific trigonal (1T') structure it has among many suggested ones.

cond-mat.mtrl-sci↗

Metacommutation of Hurwitz primes

Conway and Smith introduced the operation of metacommutation for pairs of primes in the ring of Hurwitz integers in the quaternions. We study the permutation induced on the primes of norm p by a prime of norm q under metacommutation, where p and q are distinct rational primes. In particular, we show that the sign of this permutation is the quadratic character of q modulo p.

math.NT↗

Room temperature dynamic correlation between methylammonium molecules in lead-iodine based perovskites: An ab-initio molecular dynamics perspective

The high efficiency of lead organo-metal-halide perovskite solar cells has raised many questions about the role of the methylammonium (MA) molecules in the Pb-I framework. Experiments indicate that the MA molecules are able to 'freely' spin around at room temperature even though they carry an intrinsic dipole moment. We have performed large supercell (2592 atoms) finite temperature ab-initio molecular dynamics calculations to study the correlation between the molecules in the framework. An underlying long range anti-ferroelectric ordering of the molecular dipoles is observed. The dynamical correlation between neighboring molecules shows a maximum around room temperature in the mid-temperature phase. In this phase, the rotations are slow enough to (partially) couple to neighbors via the Pb-I cage. This results in a collective motion of neighboring molecules in which the cage acts as the mediator. At lower and higher temperatures the motions are less correlated.

cond-mat.mtrl-sci↗

Formal duality and generalizations of the Poisson summation formula

We study the notion of formal duality introduced by Cohn, Kumar, and Schürmann in their computational study of energy-minimizing particle configurations in Euclidean space. In particular, using the Poisson summation formula we reformulate formal duality as a combinatorial phenomenon in finite abelian groups. We give new examples related to Gauss sums and make some progress towards classifying formally dual configurations.

math.NT↗

Estimation of Bandlimited Grayscale Images From the Single Bit Observations of Pixels Affected by Additive Gaussian Noise

The estimation of grayscale images using their single-bit zero mean Gaussian noise-affected pixels is presented in this paper. The images are assumed to be bandlimited in the Fourier Cosine transform (FCT) domain. The images are oversampled over their Nyquist rate in the FCT domain. We propose a non-recursive approach based on first order approximation of Cumulative Distribution Function (CDF) to estimate the image from single bit pixels which itself is based on Banach's contraction theorem. The decay rate for mean squared error of estimating such images is found to be independent of the precision of the quantizer and it varies as $O(1/N)$ where $N$ is the "effective" oversampling ratio with respect to the Nyquist rate in the FCT domain.

cs.CV↗

Hilbert modular surfaces for square discriminants and elliptic subfields of genus 2 function fields

We compute explicit rational models for some Hilbert modular surfaces corresponding to square discriminants, by connecting them to moduli spaces of elliptic K3 surfaces. Since they parametrize decomposable principally polarized abelian surfaces, they are also moduli spaces for genus-2 curves covering elliptic curves via a map of fixed degree. We thereby extend classical work of Jacobi, Hermite, Bolza etc., and more recent work of Kuhn, Frey, Kani, Shaska, Völklein, Magaard and others, producing explicit families of reducible Jacobians. In particular, we produce a birational model for the moduli space of pairs (C,E) of a genus 2 curve C and elliptic curve E with a map of degree n from C to E, as well as a tautological family over the base, for 2 <= n <= 11. We also analyze the resulting models from the point of view of arithmetic geometry, and produce several interesting curves on them.

math.AG↗

Algebraic models and arithmetic geometry of Teichmüller curves in genus two

A Teichmüller curve is an algebraic and isometric immersion of an algebraic curve into the moduli space of Riemann surfaces. We give the first explicit algebraic models of Teichmüller curves of positive genus. Our methods are based on the study of certain Hilbert modular forms and the use of Ahlfors's variational formula to identify eigenforms for real multiplication on genus two Jacobians. We also present evidence that Teichmüller curves admit a rich arithmetic geometry by exhibiting examples with small primes of bad reduction and notable divisors supported at their cusps.

math.AG↗

Real multiplication through explicit correspondences

We compute equations for real multiplication on the divisor classes of genus two curves via algebraic correspondences. We do so by implementing van Wamelen's method for computing equations for endomorphisms of Jacobians on examples drawn from the algebraic models for Hilbert modular surfaces computed by Elkies and Kumar. We also compute a correspondence over the universal family for the Hilbert modular surface of discriminant 5 and use our equations to prove a conjecture of A. Wright on dynamics over the moduli space of Riemann surfaces.

math.AG↗

Orbit Parametrizations for K3 Surfaces

We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits of a representation are in bijection with K3 surfaces (up to suitable equivalence) whose Néron-Severi lattice contains a given lattice. An immediate consequence is that the corresponding moduli spaces of these lattice-polarized K3 surfaces are all unirational. Our constructions also produce many fixed-point-free automorphisms of positive entropy on K3 surfaces in various families associated to these representations, giving a natural extension of recent work of Oguiso.

math.AG↗

Evolution of fusion hindrance for asymmetric systems at deep sub barrier energies

Measurements of fusion cross-sections of 7Li and 12C with 198Pt at deep sub-barrier energies are reported to unravel the role of the entrance channel in the occurrence of fusion hindrance. The onset of fusion hindrance has been clearly observed in 12C + 198Pt system but not in 7Li + 198Pt system, within the measured energy range. Emergence of the hindrance, moving from lighter (6,7Li) to heavier (12C,16O) projectiles is explained employing a model that considers a gradual transition from a sudden to adiabatic regime at low energies. The model calculation reveals a weak effect of the damping of coupling to collective motion for the present systems as compared to that obtained for systems with heavier projectiles.

nucl-ex↗

Gravitational potential wells and the cosmic bulk flow

The bulk flow is a volume average of the peculiar velocities and a useful probe of the mass distribution on large scales. The gravitational instability model views the bulk flow as a potential flow that obeys a Maxwellian Distribution. We use two N-body simulations, the LasDamas Carmen and the Horizon Run, to calculate the bulk flows of various sized volumes in the simulation boxes. Once we have the bulk flow velocities as a function of scale, we investigate the mass and gravitational potential distribution around the volume. We found that matter densities can be asymmetrical and difficult to detect in real surveys, however, the gravitational potential and its gradient may provide better tools to investigate the underlying matter distribution. This study shows that bulk flows are indeed potential flows and thus provides information on the flow sources. We also show that bulk flow magnitudes follow a Maxwellian distribution on scales $>10\ h^{-1}$Mpc.

astro-ph.CO↗