arXiv subjects

Santosh Kumar

Publications and source records attributed to Santosh Kumar.

At least 73 records · Page 4Linked to original sources

arXiv2021

Robust and Efficient Single-Pixel Image Classificationwith Nonlinear Optics

We present a hybrid image classifier by mode-selective image upconversion, single pixel photodetection, and deep learning, aiming at fast processing a large number of pixels. It utilizes partial Fourier transform to extract the signature features of images in both the original and Fourier domains, thereby significantly increasing the classification accuracy and robustness. Tested on the MNIST handwritten digit images, it boosts the accuracy from 81.25% to 99.23%, and achieves an 83% accuracy for highly contaminated images whose signal-to-noise ratio is only -17 dB. Our approach could prove useful for fast lidar data processing, high resolution image recognition, occluded target identification, atmosphere monitoring, and so on.

physics.optics↗

arXiv2021

Latent Factor Modeling of Users Subjective Perception for Stereoscopic 3D Video Recommendation

Numerous stereoscopic 3D movies are released every year to theaters and created large revenues. Despite the improvement in stereo capturing and 3D video post-production technology, stereoscopic artifacts which cause viewer discomfort continue to appear even in high-budget films. Existing automatic 3D video quality measurement tools can detect distortions in stereoscopic images or videos, but they fail to consider the viewer's subjective perception of those artifacts, and how these distortions affect their choices. In this paper, we introduce a novel recommendation system for stereoscopic 3D movies based on a latent factor model that meticulously analyse the viewer's subjective ratings and influence of 3D video distortions on their preferences. To the best of our knowledge, this is a first-of-its-kind model that recommends 3D movies based on stereo-film quality ratings accounting correlation between the viewer's visual discomfort and stereoscopic-artifact perception. The proposed model is trained and tested on benchmark Nama3ds1-cospad1 and LFOVIAS3DPh2 S3D video quality assessment datasets. The experiments revealed that resulting matrix-factorization based recommendation system is able to generalize considerably better for the viewer's subjective ratings.

cs.MM↗

arXiv2020

Differential recurrences for the distribution of the trace of the $β$-Jacobi ensemble

Examples of the $β$-Jacobi ensemble specify the joint distribution of the transmission eigenvalues in scattering problems. In this context, there has been interest in the distribution of the trace, as the trace corresponds to the conductance. Earlier, in the case $β= 1$, the trace statistic was isolated in studies of covariance matrices in multivariate statistics, where it is referred to as Pillai's $V$ statistic. In this context, Davis showed that for $β= 1$ the trace statistic, and its Fourier-Laplace transform, can be characterised by $(N+1) \times (N+1)$ matrix differential equations. For the Fourier-Laplace transform, this leads to a vector recurrence for the moments. However, for the distribution itself the characterisation provided was incomplete, as the connection problem of determining the linear combination of Frobenius type solutions that correspond to the statistic was not solved. We solve this connection problem for Jacobi parameter $b$ and Dyson index $β$ non-negative integers. For the other Jacobi parameter $a$ also a non-negative integer, the power series portion of each Frobenius solution terminates to a polynomial, and the matrix differential equation gives a recurrence for their computation.

math-ph↗

arXiv2020

Spectral statistics for the difference of two Wishart matrices

In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches. The first derivation involves the use of unitary group integral, while the second one relies on applying the derivative principle. The latter relates the joint probability density of eigenvalues of a matrix drawn from a unitarily invariant ensemble to the joint probability density of its diagonal elements. Exact closed form expressions for an arbitrary order correlation function are also obtained and spectral densities are contrasted with Monte Carlo simulation results. Analytical results for moments as well as probabilities quantifying positivity aspects of the spectrum are also derived. Additionally, we provide a large-dimension asymptotic result for the spectral density using the Stieltjes transform approach for algebraic random matrices. Finally, we point out the relationship of these results with the corresponding results for difference of two random density matrices and obtain some explicit and closed form expressions for the spectral density and absolute mean.

math-ph↗

arXiv2020

Single-Pixel Pattern Recognition with Coherent Nonlinear Optics

We propose and experimentally demonstrate a nonlinear-optics approach to pattern recognition with single-pixel imaging and deep neural network. It employs mode selective image up-conversion to project a raw image onto a set of coherent spatial modes, whereby its signature features are extracted nonlinear-optically. With 40 projection modes, the classification accuracy reaches a high value of 99.49% for the MNIST handwritten digit images, and up to 95.32% even when they are mixed with strong noise. Our experiment harnesses rich coherent processes in nonlinear optics for efficient machine learning, with potential applications in online classification of large size images, fast lidar data analyses, complex pattern recognition, and so on.

physics.optics↗

arXiv2020

Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance

Hilbert-Schmidt distance is one of the prominent distance measures in quantum information theory which finds applications in diverse problems, such as construction of entanglement witnesses, quantum algorithms in machine learning, and quantum state tomography. In this work, we calculate exact and compact results for the mean square Hilbert-Schmidt distance between a random density matrix and a fixed density matrix, and also between two random density matrices. In the course of derivation, we also obtain corresponding exact results for the distance between a Wishart matrix and a fixed Hermitian matrix, and two Wishart matrices. We verify all our analytical results using Monte Carlo simulations. Finally, we apply our results to investigate the Hilbert-Schmidt distance between reduced density matrices generated using coupled kicked tops.

quant-ph↗

arXiv2020

Risk assessment of airborne transmission of COVID-19 by asymptomatic individuals under different practical settings

The lack of quantitative risk assessment of airborne transmission of COVID-19 under practical settings leads to large uncertainties and inconsistencies in our preventive measures. Combining in situ measurements and numerical simulations, we quantify the exhaled particles from normal respiratory behaviors and their transport under elevator, small classroom and supermarket settings to evaluate the risk of inhaling potentially virus-containing particles. Our results show that the design of ventilation is critical for reducing the risk of particle encounters. Inappropriate design can significantly limit the efficiency of particle removal, create local hot spots with orders of magnitude higher risks, and enhance particle deposition causing surface contamination. Additionally, our measurements reveal the presence of substantial fraction of crystalline particles from normal breathing and its strong correlation with breathing depth.

physics.med-ph↗

arXiv2020

A Super-resolution Optical Classifier with High Photon Efficiency

We propose and demonstrate a photon-efficient optical classifier to overcome the Rayleigh limit in spatial resolution. It utilizes mode-selective sum frequency generation and single-pixel photon detection to resolve closely spaced incoherent sources based on photon counting statistics. Super-resolving and photon efficient, this technique can find applications in microscopy, light detection and ranging (LiDAR), and astrophysics.

quant-ph↗

arXiv2020

Computable structural formulas for the distribution of the $β$-Jacobi edge eigenvalues

The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy's largest root test in multivariate statistics) and smallest (e.g.~condition numbers of linear systems) eigenvalues. We identify three ranges of parameter values for which the gap probability determining these distributions is a finite sum with respect to particular bases, and moreover make use of a certain differential-difference system fundamental in the theory of the Selberg integral to provide a recursive scheme to compute the corresponding coefficients.

math-ph↗

arXiv2020

Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles

The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to compute in analyzing the spectrum of a general system. The Wigner-surmise-like results for the ratio distribution are known for the invariant classes of Gaussian random matrices. However, for the crossover ensembles, which are useful in modeling systems with partially broken symmetries, corresponding results have remained unavailable so far. In this work, we derive exact results for the distribution and average of the ratio of two consecutive level spacings in the Gaussian orthogonal to unitary crossover ensemble using a $3\times 3$ random matrix model. This crossover is useful in modeling time-reversal symmetry breaking in quantum chaotic systems. Although based on a $3\times 3$ matrix model, our results can also be applied in the study of large spectra, provided the symmetry-breaking parameter facilitating the crossover is suitably scaled. We substantiate this claim by considering Gaussian and Laguerre crossover ensembles comprising large matrices. Moreover, we apply our result to investigate the violation of time-reversal invariance in the quantum kicked rotor system.

math-ph↗

arXiv2020

Large-scale Ising Emulation with Four-Body Interaction and All-to-All Connection

We propose and demonstrate a nonlinear optics approach to emulate Ising machines containing up to a million spins and with tailored two and four-body interactions with all-to-all connections. It uses a spatial light modulator to encode and control the spins in the form of the binary phase values of wavelets in coherent laser beams, and emulates the high-order interaction with frequency conversion in a nonlinear crystal at the Fourier plane. By adaptive feedback control, the system can be evolved into effective spin configurations that well approximate the ground states of Ising Hamiltonians with all-to-all connected many-body interactions. Our technique could serve as a new tool to probe complex, many-body physics and give rise to exciting applications in big data optimization, computing, and analytics.

physics.optics↗

arXiv2019

Recursion scheme for the largest $β$-Wishart-Laguerre eigenvalue and Landauer conductance in quantum transport

The largest eigenvalue distribution of the Wishart-Laguerre ensemble, indexed by Dyson parameter $β$ and Laguerre parameter $a$, is fundamental in multivariate statistics and finds applications in diverse areas. Based on a generalization of the Selberg integral, we provide an effective recursion scheme to compute this distribution explicitly in both the original model, and a fixed-trace variant, for $a,β$ non-negative integers and finite matrix size. For $β= 2$ this circumvents known symbolic evaluation based on determinants which become impractical for large dimensions. Our exact results have immediate applications in the areas of multiple channel communication and bipartite entanglement. Moreover, we are also led to the exact solution of a long standing problem of finding a general result for Landauer conductance distribution in a chaotic mesoscopic cavity with two ideal leads. Thus far, exact closed-form results for this were available only in the Fourier-Laplace space or could be obtained on a case-by-case basis.

math-ph↗

arXiv2019

Machine Learning Holography for 3D Particle Field Imaging

We propose a new learning-based approach for 3D particle field imaging using holography. Our approach uses a U-net architecture incorporating residual connections, Swish activation, hologram preprocessing, and transfer learning to cope with challenges arising in particle holograms where accurate measurement of individual particles is crucial. Assessments on both synthetic and experimental holograms demonstrate a significant improvement in particle extraction rate, localization accuracy and speed compared to prior methods over a wide range of particle concentrations, including highly-dense concentrations where other methods are unsuitable. Our approach can be potentially extended to other types of computational imaging tasks with similar features.

eess.IV↗

arXiv2019

Mode Selective Image Upconversion over Turbulence

We experimentally study a nonlinear optical approach to selective manipulation and detection of structured images mixed with turbulent noise. Unlike any existing adaptive-optics method by applying compensating modulation directly on the images, here we account for the turbulence indirectly, by modulating only the pump driving the nonlinear process but not the images themselves. This indirect approach eliminates any signal modulation loss or noise, while allowing more flexible and capable operations. Using specifically sum frequency generation in a lithium niobate crystal, we demonstrate selective upconversion of Laguerre-Gaussian spatial modes mixed with turbulent noise. The extinction reaches $\sim$40 dB without turbulence, and maintains $\sim$20 dB in the presence of strong turbulence. This technique could find utilities in classical and quantum communications, compressive imaging, pattern recognition, and so on.

physics.optics↗

arXiv2019

Bures-Hall Ensemble: Spectral Densities and Average Entropies

We consider an ensemble of random density matrices distributed according to the Bures measure. The corresponding joint probability density of eigenvalues is described by the fixed trace Bures-Hall ensemble of random matrices which, in turn, is related to its unrestricted trace counterpart via a Laplace transform. We investigate the spectral statistics of both these ensembles and, in particular, focus on the level density, for which we obtain exact closed-form results involving Pfaffians. In the fixed trace case, the level density expression is used to obtain an exact result for the average Havrda-Charvát-Tsallis (HCT) entropy as a finite sum. Averages of von Neumann entropy, linear entropy and purity follow by considering appropriate limits in the average HCT expression. Based on exact evaluations of the average von Neumann entropy and the average purity, we also conjecture very simple formulae for these, which are similar to those in the Hilbert-Schmidt ensemble.

math-ph↗

arXiv2019

Coulomb blockade in an atomically thin quantum dot coupled to a tunable Fermi reservoir

Gate-tunable quantum-mechanical tunnelling of particles between a quantum confined state and a nearby Fermi reservoir of delocalized states has underpinned many advances in spintronics and solid-state quantum optics. The prototypical example is a semiconductor quantum dot separated from a gated contact by a tunnel barrier. This enables Coulomb blockade, the phenomenon whereby electrons or holes can be loaded one-by-one into a quantum dot. Depending on the tunnel-coupling strength, this capability facilitates single spin quantum bits or coherent many-body interactions between the confined spin and the Fermi reservoir. Van der Waals (vdW) heterostructures, in which a wide range of unique atomic layers can easily be combined, offer novel prospects to engineer coherent quantum confined spins, tunnel barriers down to the atomic limit or a Fermi reservoir beyond the conventional flat density of states. However, gate-control of vdW nanostructures at the single particle level is needed to unlock their potential. Here we report Coulomb blockade in a vdW heterostructure consisting of a transition metal dichalcogenide quantum dot coupled to a graphene contact through an atomically thin hexagonal boron nitride (hBN) tunnel barrier. Thanks to a tunable Fermi reservoir, we can deterministically load either a single electron or a single hole into the quantum dot. We observe hybrid excitons, composed of localized quantum dot states and delocalized continuum states, arising from ultra-strong spin-conserving tunnel coupling through the atomically thin tunnel barrier. Probing the charged excitons in applied magnetic fields, we observe large gyromagnetic ratios (~8). Our results establish a foundation for engineering next-generation devices to investigate either novel regimes of Kondo physics or isolated quantum bits in a vdW heterostructure platform.

cond-mat.mes-hall↗

arXiv2019

Structural and magnetic properties of GdCo$_{5-x}$Ni$_x$

GdCo$_5$ may be considered as two sublattices - one of Gd and one of Co - whose magnetizations are in antiparallel alignment, forming a ferrimagnet. Substitution of nickel in the cobalt sublattice of GdCo$_5$ has been investigated to gain insight into how the magnetic properties of this prototype rare-earth/transition-metal magnet are affected by changes in the transition metal sublattice. Polycrystalline samples of GdCo$_{5-x}$Ni$_x$ for 0 $ \leq x \leq $ 5 were synthesized by arc melting. Structural characterization was carried out by powder x-ray diffraction and optical and scanning electron microscope imaging of metallographic slides, the latter revealing a low concentration of Gd$_2$(Co, Ni)$_7$ lamellae for $x \leq 2.5$. Compensation - i.e. the cancellation of the opposing Gd and transition metal moments is observed for $1 \leq x \leq 3$ at a temperature which increases with Ni content; for larger $x$, no compensation is observed below 360 K. A peak in the coercivity is seen at $x \approx 1$ at 10K coinciding with a minimum in the saturation magnetization. Density-functional theory calculations within the disordered local moment picture reproduce the dependence of the magnetization on Ni content and temperature. The calculations also show a peak in the magnetocrystalline anisotropy at similar Ni concentrations to the experimentally observed coercivity maximum.

cond-mat.mtrl-sci↗

arXiv2019

Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions

We consider a class of systems where $N$ identical particles with positions ${\bf q}_1,...,{\bf q}_N$ and momenta ${\bf p}_1,...,{\bf p}_N$ are enclosed in a box of size $L$, and exhibit the scaling $\mathcal{U}(L{\bf r}_1,...,L{\bf r}_N)=α(L)\, \mathcal{U}({\bf r}_1,...,{\bf r}_N)$ for the associated potential energy function $\mathcal{U}({\bf q}_1,...,{\bf q}_N)$. For these systems, we propose an efficient implementation of the Wang-Landau algorithm for evaluating thermodynamic observables involving energy and volume fluctuations in the microcanonical description, and temperature and volume fluctuations in the canonical description. This requires performing the Wang-Landau simulation in a scaled box of unit size and evaluating the density of states corresponding to the potential energy part only. To demonstrate the efficacy of our approach, as example systems, we consider Padmanabhan's binary star model and an ideal gas trapped in a harmonic potential within the box.

cond-mat.stat-mech↗