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Rahul Kumar

Publications and source records attributed to Rahul Kumar.

At least 55 records · Page 3Linked to original sources
arXiv2024

Generative AI-Based Text Generation Methods Using Pre-Trained GPT-2 Model

This work delved into the realm of automatic text generation, exploring a variety of techniques ranging from traditional deterministic approaches to more modern stochastic methods. Through analysis of greedy search, beam search, top-k sampling, top-p sampling, contrastive searching, and locally typical searching, this work has provided valuable insights into the strengths, weaknesses, and potential applications of each method. Each text-generating method is evaluated using several standard metrics and a comparative study has been made on the performance of the approaches. Finally, some future directions of research in the field of automatic text generation are also identified.

cs.CL↗
arXiv2024

The Bergman-Fridman invariant on some classes of pseudoconvex domains

We study the boundary behaviour of a variant of the Fridman's invariant function (defined in terms of the Bergman metric) on Levi corank one domains, strongly pseudoconvex domains, smoothly bounded convex domains in $ \mathbb{C}^n $ and polyhedral domains in $ \mathbb{C}^2 $.

math.CV↗
arXiv2024

Code Generation for a Variety of Accelerators for a Graph DSL

Sparse graphs are ubiquitous in real and virtual worlds. With the phenomenal growth in semi-structured and unstructured data, sizes of the underlying graphs have witnessed a rapid growth over the years. Analyzing such large structures necessitates parallel processing, which is challenged by the intrinsic irregularity of sparse computation, memory access, and communication. It would be ideal if programmers and domain-experts get to focus only on the sequential computation and a compiler takes care of auto-generating the parallel code. On the other side, there is a variety in the number of target hardware devices, and achieving optimal performance often demands coding in specific languages or frameworks. Our goal in this work is to focus on a graph DSL which allows the domain-experts to write almost-sequential code, and generate parallel code for different accelerators from the same algorithmic specification. In particular, we illustrate code generation from the StarPlat graph DSL for NVIDIA, AMD, and Intel GPUs using CUDA, OpenCL, SYCL, and OpenACC programming languages. Using a suite of ten large graphs and four popular algorithms, we present the efficacy of StarPlat's versatile code generator.

cs.DC↗
arXiv2023

Sharing nonlocality in a network using the quantum violation of chain network inequality

Based on the quantum violation of suitable $n$-local inequality in a star network for arbitrary $m$ inputs, we demonstrate the sharing of nonlocality in the network. Such a network features an arbitrary $n$ number of independent sources, $n$ edge parties, and a central party. Each party receives arbitrary $m$ inputs. We consider two different types of sharing of nonlocality in the network. i) The symmetric case - when the sharing of nonlocality is considered across all edge parties. ii) The asymmetric case - when the sharing of nonlocality is considered across only one edge party. For simplicity, we first consider the bilocal scenario $(n=2)$ with three inputs $m=3$ and demonstrate that while in the symmetric case at most two sequential observers can share nonlocality, in the asymmetric case at most four sequential observers can share nonlocality. We extend the study to $n$-local scenario by assuming each party receives three inputs and show that in the symmetric case the result remains the same for any $n$, but in the asymmetrical case, an unbounded number of sequential observers can share nonlocality across one edge for a sufficiently large value of $n$. We further extend our result for arbitrary $m$ input in $n$-local scenario. We demonstrate that for $m\geq 4$, in the symmetric case at most one sequential observer can share nonlocality irrespective of the value of $n$. For the asymmetric case, we analytically show that there exists $n(k)$ for which an arbitrary $k$ number of sequential observers can share the nonlocality across one edge. The optimal quantum violation of $m$-input $n$-local inequality is derived through an elegant SOS approach without specifying the dimension of the quantum system.

quant-ph↗
arXiv2023

Tuning Dipolar and Multipolar Resonances of Chiral Silicon Nanostructures for Control of Near field Superchirality

Chiral materials display a property called optical activity, which is the capability to interact differentially with left and right circularly polarised light. This leads to the ability to manipulate the polarisation state of light, which has a broad range of applications spanning from energy efficient displays to quantum technologies. Both synthesised and engineered chiral nanomaterials are exploited in such devices. The design strategy for optimising the optical activity of a chiral material is typically based on maximising a single parameter, the electric dipole magnetic dipole response. Here we demonstrate an alternative approach of controlling optical activity by manipulating both the dipole and multipolar response of a nanomaterial. This provides an additional parameter for material design, affording greater flexibility. The exemplar systems used to illustrate the strategy are nanofabricated chiral silicon structures. The multipolar response of the structures, and hence their optical activity, can be controlled simply by varying their height. This phenomenon allows optical activity and the creation of so called superchiral fields, with enhanced asymmetries, to be controlled over a broader wavelength range, than is achievable with just the electric dipole magnetic dipole response. This work adds to the material design toolbox providing a route to novel nanomaterials for optoelectronics and sensing applications.

physics.optics↗
arXiv2023

Attomole enantiomeric discrimination of small molecules using an achiral SERS reporter and chiral plasmonics

Biologically important molecules span a size range from very large biomacromolecules, such as proteins to small metabolite molecules. Consequently, spectroscopic techniques which can detect and characterize the structure of inherently chiral biomolecules over this range of scale at the femtomole level are necessary to develop novel biosensing and diagnostic technologies. Nanophotonic platforms uniquely enable chirally sensitive structural characterisation of biomacromolecules at this ultrasensitive level. However, they are less successful at achieving the same level of sensitivity for small chiral molecules, with less than nanomole typical. This poorer performance can be attributed to the optical response of the platform being sensitive to a much larger volume of the near field than is occupied by the small molecule. Here we show that by combining chiral plasmonic metasurfaces with Raman reporters, which can detect changes in electromagnetic environment at molecular dimensions, chiral discrimination can be achieved for attomole quantities of a small molecule, the amino acid cysteine. The signal-to-noise, and hence ultimate sensitivity, of the measurement can be further improved by combining the metasurfaces with gold achiral nanoparticles. This indirect enantiomeric detection is 9 orders of magnitude more sensitive than strategies relying on monitoring the Raman response of target chiral molecules directly. Given the generic nature of the phenomenon,this study provides a framework for developing novel technologies for detecting a broad spectrum of small biomolecules, which would be useful tools in the field of metabolomics.

physics.optics↗
arXiv2023

Aerodynamic performance and flow mechanism of 3D flapping wing using discrete vortex method

In this work, we have performed numerical simulations of the flapping motion of a rectangular wing in a three-dimensional flow field using the discrete vortex method (DVM). The DVM method is computationally more convenient because it does not require the generation of a grid for the flow field at each time step as in other conventional simulation methods. In addition to the rigid wing case, the aerodynamic characteristics of a deformable wing are also investigated. The deformable wing is studied in various configurations, such as bending, twisting, and bending-twisting coupling (BTC). The investigation of all four modes involves a detailed analysis of the flow mechanisms and vortex dynamics, which play a crucial role in influencing the aerodynamic forces, namely lift and thrust. The study aims to understand how these flow patterns change under different operating conditions and how these changes impact the generation of lift and thrust. The lift, thrust, and propulsive efficiency of all four modes are compared to provide a detailed understanding of their aerodynamic characteristics. The bent wing showed more lift compared to the rigid wing, but minimal improvements in thrust. In contrast, the twisted wing showed greater improvements in both lift and thrust. The BTC wing proves to be the most efficient method to improve aerodynamic performance during flapping. The parametric dependence of kinematic parameters such as asymmetric ratio (downstroke speed to upstroke speed), aspect ratio and reduced frequency on the aerodynamic performance was also investigated.

physics.flu-dyn↗
arXiv2023

Arithmetic properties of the Herglotz-Zagier-Novikov function

In this article, we undertake the study of the function $\mathscr{F}(x;u,v)$, which we refer to as the Herglotz-Zagier-Novikov function. This function appears in Novikov's work on the Kronecker limit formula, which was motivated by Zagier's paper where he obtained the Kronecker limit formula in terms of the Herglotz function $F(x)$. Two, three, and six-term functional equations satisfied by $\mathscr{F}(x;u,v)$ are exhibited. These are cohomological relations coming from the action of an involution and SL$_2(\mathbb{Z})$ on $\mathbb{C}\times {\mathbb{D}_1}^2$ (the unit circle ${\mathbb{D}_1})$. We also provide the special values of $\mathscr{F}(x;u,v)$ at rational arguments of $x$. Importantly, $\mathscr{F}(x;u,v)$ serves as a unified generalization of three other interesting functions, namely $F(x)$, $J(x)$, and $T(x)$, which also appear in various Kronecker limit formulas and are previously studied by Cohen, Herglotz, Muzaffar and Williams, and Radchenko and Zagier. Consequently, our study not only reveals the numerous elegant properties of $\mathscr{F}(x;u,v)$ but also helps us to further develop the theories of functions related to its special cases such as $J(x)$ and $T(x)$.

math.NT↗
arXiv2023

A note on odd zeta values over any number field and Extended Eisenstein series

In this article, we have studied transformation formulas of zeta function at odd integers over an arbitrary number field which in turn generalizes Ramanujan's identity for the Riemann zeta function. The above transformation leads to a new number field extension of Eisenstein series, which satisfies the transformation $z \mapsto -1/z$ like an integral weight modular form over SL$_2(\Z)$. The results provide number of important applications, which are important in studying the behaviour of odd zeta values as well as Lambert series in an arbitrary number field.

math.NT↗
arXiv2023

Symmetry control of strong chiral light matter interactions in photonic nanocavities for efficient circularly polarised emission

Chiral excited electronic states of molecules have an intrinsic sense of handedness, or twist, and are the active component in energy efficient display technologies and in new photosynthetic routes to produce pharmaceuticals. Creating chiral states is achieved by manipulating the twistiness of the geometric molecular structure. This is a demanding problem adding complexity due to the need to precisely control molecular geometry. Here we demonstrate a novel concept for creating chiral excited states which does not rely on molecular structure. Instead, it depends on hybridising a non chiral molecule with a chiral electromagnetic field, producing a hybrid light matter chiral polariton state. This is achieved by a symmetry controlled strong chiral-light matter interaction between an electromagnetic mode of a chiral nanocavity and an achiral molecule, a concept referred to as the electromagnetic enantiomer. This electromagnetic mechanism simplifies the creation of chiral electronic states since it is far less demanding in terms of materials design. We have illustrated the concept using an exemplar system relevant to organic optoelectronic technology, producing efficient circularly polarised emission from a non-chiral emitter molecule.

physics.optics↗
arXiv2023

Applications of Lipschitz summation formula and a generalization of Raabe's cosine transform

General summation formulas have been proved to be very useful in analysis, number theory and other branches of mathematics. The Lipschitz summation formula is one of them. In this paper, we give its application by providing a new transformation formula which generalizes that of Ramanujan. Ramanujan's result, in turn, is a generalization of the modular transformation of Eisenstein series $E_k(z)$ on SL$_2(\mathbb{Z})$, where $z\to-1/z, z\in\mathbb{H}$. The proof of our result involves delicate analysis containing Cauchy Principal Value integrals. A simpler proof of a recent result of ours with Kesarwani giving a non-modular transformation for $\sum_{n=1}^{\infty}σ_{2m}(n)e^{-ny}$ is also derived using the Lipschitz summation formula. In the pursuit of obtaining this transformation, we naturally encounter a new generalization of Raabe's cosine transform whose several properties are also demonstrated. As a corollary of this result, we get a generalization of Wright's asymptotic estimate for the generating function of the number of plane partitions of a positive integer $n$.

math.NT↗
arXiv2023

Tunable Resonance and Electron-Phonon Coupling in Layered MoS2

Resonance Raman scattering, a very effective and sensitive technique for atomically thin semiconducting transition metal dichalcogenide, can be used to observe the phonons from the entire Brillouin zone. In addition to the significance of resonance effect on the Raman spectrum it may also be used to probe the electron-phonon coupling. Our study is devoted to understand the phonons in layered MoS2, especially for very low frequency range (i.e. below 100 cm-1), as a function of temperature under the resonance effect. Understanding the phonon-phonon and electron-phonon coupling and the effects of temperature on the Raman spectrum are the central points of the present study. We observe the anomalous softening and broadening of a very low frequency phonon mode P3 (~34 cm-1) at low temperature ( i.e below 150 K). We attributed the observed anomalous trend in frequency and linewidth of this low frequency phonon to the electron-phonon coupling. Furthermore, our work also highlights the temperature induced tuning of resonance condition via understanding the intensity of phonon modes as a function of temperature.

cond-mat.mtrl-sci↗
arXiv2023

Emergence of field-induced memory effect in spin ices

Out-of-equilibrium investigation of strongly correlated materials deciphers the hidden equilibrium properties. Herein, we have investigated the out-of-equilibrium magnetic properties of polycrystalline Dy2Ti2O7 and Ho2Ti2O7 spin ices. The experimental results show the emergence of magnetic field-induced anomalous hysteresis observed only in temperature/magnetic field-dependent ac susceptibility measurements. The observed memory effect (anomalous thermomagnetic hysteresis) strongly depends on the driving thermal and non-thermal variables. Contrary, in the absence of the magnetic field, dipolar interaction induced Ising paramagnetic to spin ice crossover develops a liquid-gas transition type hysteresis below 4 K. Unlike field-induced hysteresis, it shows weak dependency on thermal and non-thermal variables. Due to the non-colinear spin structure, the applied dc bias magnetic field produces quench disorder sites in the cooperative Ising spin matrix and suppresses the spin-phonon coupling. These quench disorders create dynamic spin correlations governed by quantum fluctuations, having slow spin relaxation and quick decay times, which additionally contribute to ac susceptibility. The initial conditions and measurement protocol decide the magnitude and sign of this dynamical term contributing to ac susceptibility. It has been suggested that such kind of out-of-equilibrium properties emerge by the cumulative effect of geometric frustration, disorder, quantum fluctuations, and the cooperative nature of spin dynamics of these materials.

cond-mat.str-el↗
arXiv2022

Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations

Multipartite nonlocality in a network is conceptually different from standard multipartite Bell nonlocality. In recent times, network nonlocality has been studied for various topologies. We consider a linear-chain topology of the network and demonstrate the quantum nonlocality (the non-$n$-locality). Such a network scenario involves $n$ number of independent sources and $n+1$ parties, two edge parties (Alice and Charlie), and $n-1$ central parties (Bobs). It is commonly assumed that each party receives only two inputs. In this work, we consider a generalized scenario where the edge parties receive an arbitrary $n$ number of inputs (equals to a number of independent sources), and each of the central parties receives two inputs. We derive a family of generalized $n$-locality inequalities for a linear-chain network for arbitrary $n$ and demonstrate the optimal quantum violation of the inequalities. We introduce an elegant sum-of-squares approach enabling the derivation of the optimal quantum violation of aforesaid inequalities \emph{without} assuming the dimension of the system. We show that the optimal quantum violation requires the observables of edge parties to mutually anticommuting. For $n=2$ and $3$, the optimal quantum violation can be obtained when each edge party shares a two-qubit entangled state with central parties. We further argue that for $n\geq 2$, a single copy of a two-qubit-entangled state may not be enough to exhibit the violation of $n$-locality inequality, but multiple copies of it can activate the quantum violation.

quant-ph↗
arXiv2022

Chiral Metafilms and Surface Enhanced Raman Scattering For Enantiomeric Discrimination of Helicoid Nanoparticles

Chiral nanophotonic platforms provide a means of creating near fields with both enhanced asymmetric properties and intensities. They can be exploited for optical measurements that allow enantiomeric discrimination at detection levels greater than 6 orders of magnitude than is achieved with conventional chirally sensitive spectroscopic methods based on circularly polarized light. The optimal approach for exploiting nanophotonic platforms for chiral detection would be to use spectroscopic methods that provide a local probe of changes in the near field environment induced by the presence of chiral species. Here we show that surface enhanced Raman spectroscopy (SERS) is such a local probe of the near field environment. We have used it to achieve enantiomeric discrimination of chiral helicoid nanoparticles deposited on left and right-handed enantiomorphs of a chiral metafilm. Hotter electromagnetic hotspots are created for matched combinations of helicoid and metafilms (left-left and right-right), while mismatched combinations leads to significantly cooler electromagnetic hotspots. This large enantiomeric dependency on hotspot intensity is readily detected using SERS with the aid of an achiral Raman reporter molecule. In effect we have used SERS to distinguish between the different EM environments of the plasmonic diastereomers produced by mixing chiral nanoparticles and metafilms. The work demonstrates that by combining chiral nanophotonic platforms with established SERS strategies new avenues in ultrasensitive chiral detection can be opened.

physics.optics↗
arXiv2022

A modular relation involving a generalized digamma function and asymptotics of some integrals containing $Ξ(t)$

A modular relation of the form $F(α, w)=F(β, iw)$, where $i=\sqrt{-1}$ and $αβ=1$, is obtained. It involves the generalized digamma function $ψ_w(a)$ which was recently studied by the authors in their work on developing the theory of the generalized Hurwitz zeta function $ζ_w(s, a)$. The limiting case $w\to0$ of this modular relation is a famous result of Ramanujan on page $220$ of the Lost Notebook. We also obtain asymptotic estimate of a general integral involving the Riemann function $Ξ(t)$ as $α\to\infty$. Not only does it give the asymptotic estimate of the integral occurring in our modular relation as a corollary but also some known results.

math.NT↗
arXiv2022

Much Easier Said Than Done: Falsifying the Causal Relevance of Linear Decoding Methods

Linear classifier probes are frequently utilized to better understand how neural networks function. Researchers have approached the problem of determining unit importance in neural networks by probing their learned, internal representations. Linear classifier probes identify highly selective units as the most important for network function. Whether or not a network actually relies on high selectivity units can be tested by removing them from the network using ablation. Surprisingly, when highly selective units are ablated they only produce small performance deficits, and even then only in some cases. In spite of the absence of ablation effects for selective neurons, linear decoding methods can be effectively used to interpret network function, leaving their effectiveness a mystery. To falsify the exclusive role of selectivity in network function and resolve this contradiction, we systematically ablate groups of units in subregions of activation space. Here, we find a weak relationship between neurons identified by probes and those identified by ablation. More specifically, we find that an interaction between selectivity and the average activity of the unit better predicts ablation performance deficits for groups of units in AlexNet, VGG16, MobileNetV2, and ResNet101. Linear decoders are likely somewhat effective because they overlap with those units that are causally important for network function. Interpretability methods could be improved by focusing on causally important units.

cs.LG↗