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Sourav Das

Publications and source records attributed to Sourav Das.

At least 37 records · Page 2Linked to original sources
arXiv2026

A new class of coherent states involving Fox-Wright functions and their generalization in the bicomplex framework

In this work, an extensive class of coherent states is introduced by taking the Fox Wright function as the normalization function. It is demonstrated that these states satisfy the key requirements of continuity, normalizability and resolution of unity. Furthermore, coherent states associated with the continuous spectrum are obtained through a discrete to continuous limiting procedure. Moreover, FW generalized multi parameter nu function is introduced and shown to act as the normalization function for the Fox Wright coherent states in the continuous spectrum. Later the Fox Wright function with bicomplex arguments has been introduced and its existence has been investigated. Bicomplex Fox Wright coherent states are also developed for the discrete spectrum based on this new function and their properties are analyzed. Subsequently, the results regarding Fox Wright coherent states are generalized to the bicomplex setting. In addition, a bicomplex FW generalized multi-parameter nu function is defined to demonstrate that it provides the normalization for these states in the continuous spectrum.

quant-ph↗
arXiv2025

Pulsed single-photon spectroscopy of an emitter with vibrational coupling

We analytically derive the quantum state of a single-photon pulse scattered from a single quantum two-level emitter interacting with a vibrational bath. This solution for the quadripartite system enables an information-theoretic characterization of vibrational effects in quantum light spectroscopy. We show that vibration-induced dephasing reduces the quantum Fisher information (QFI) for estimating the emitter's linewidth, largely reflecting the Franck-Condon suppression of light-matter coupling. Comparing time- and frequency-resolved photodetection, we find the latter to be more informative in estimating the emitter's linewidth for stronger vibrational coupling.

quant-ph↗
arXiv2025

A survey and a result on inhomogeneous quadratic forms

We survey recent work done on the values at integer points of irrational inhomogeneous quadratic forms, namely, inhomogeneous analogues of the famous Oppenheim conjecture. We also prove that the set of such forms in two variables whose set of values at integer points avoids a given countable set not containing zero, has full Hausdorff dimension. Moreover, we consider the more refined variant of this problem, where the shift is fixed and the form is allowed to vary. The strategy is to translate the problems to homogeneous dynamics and deduce the theorems from their dynamical counterparts. While our approach is inspired by the work of Kleinbock and Weiss, the dynamical results can be deduced from more general results of An, Guan, and Kleinbock.

math.NT↗
arXiv2025

Data Integration and spatio temporal statistics can quantify relative risk of medico-legal reforms: the example of police emergency mental health responses in Queensland (Australia)

This study examined the spatial-temporal dynamics of Emergency Examination Order or Authority (EE-O/A) admissions in Far Northern Queensland (FNQ) from 2009 to 2020, using 13,035 unique police records aggregated across 83 postcodes. A two-stage modelling framework was used: Lasso was used to identify a parsimonious set of socio economic and health-service covariates, and a Conditional Autoregressive (CAR) model incorporated these predictors with structured spatial and temporal random effects. This research demonstrates that socio-economic disadvantage and service accessibility drive EE-O/A incidence, underscoring the need for targeted mental-health interventions and resource allocation in impoverished FNQ communities. Limitations include reliance on cross-sectional census data for covariates and potential ecological bias from data fusion.

stat.ME↗
arXiv2025

Optimal quantum spectroscopy using single-photon pulses

We provide the ultimate precision attainable in spectroscopy of a quantum emitter using single-photon pulses. We find the maximum for estimating the linewidth to be independent of the details of the emitter's bare Hamiltonian while that for the detunings not to be so. We also identify optimal pulse shapes attaining these precisions.

quant-ph↗
arXiv2025

On the Bessel function and $n$-dimensional Hankel transform with Bicomplex arguments and coherent states

In this work, we introduce bicomplex Bessel function and analyze its region of convergence. Important properties of the bicomplex Bessel function, such as recurrence relations, integral representations, differential relations are explored. Moreover a differential equation satisfied by the bicomplex Bessel function is established. Furthermore, we investigate bicomplex holomorphicity and discuss its asymptotic behavior. Finally, we define $n$-dimensional bicomplex Hankel transformation by using bicomplex Bessel function and show that it is an isomorphism between two suitably defined function spaces. The application of the $n$-dimensional bicomplex Hankel transform has been effectively demonstrated by solving some partial differential equations. Additionally, a new extension of coherent states is built based on the use of the bicomplex Bessel function and demonstrate that these states fulfill the conditions of normalizability, continuity and the resolution of unity.

math.CV↗
arXiv2025

The Latency Price of Threshold Cryptosystem in Blockchains

Threshold cryptography is essential for many blockchain protocols. For example, many protocols rely on threshold common coin to implement asynchronous consensus, leader elections, and provide support for randomized applications. Similarly, threshold decryption and threshold time-lock puzzles are often necessary for privacy. In this paper, we study the interplay between threshold cryptography and a class of blockchains that use Byzantine-fault tolerant (BFT) consensus protocols with a focus on latency. More specifically, we focus on blockchain-native threshold cryptosystem, where the blockchain validators seek to run a threshold cryptographic protocol once for every block with the block contents as an input to the threshold cryptographic protocol. All existing approaches for blockchain-native threshold cryptosystems introduce a latency overhead of at least one message delay for running the threshold cryptographic protocol. In this paper, we first propose a mechanism to eliminate this overhead for blockchain-native threshold cryptosystems with tight thresholds, i.e., in threshold cryptographic protocols where the secrecy and reconstruction thresholds are the same. However, many real-world proof-of-stake-based blockchain-native threshold cryptosystems rely on ramp thresholds, where reconstruction thresholds are strictly greater than secrecy thresholds. For these blockchains, we formally demonstrate that the additional delay is unavoidable. We then introduce a mechanism to minimize this delay in the optimistic case. We implement our optimistic protocol for the proof-of-stake distributed randomness scheme on the Aptos blockchain. Our measurements from the Aptos mainnet show that the optimistic approach reduces latency overhead by 71%.

cs.CR↗
arXiv2025

True Solid-State Electrical Conduction of Proteins shows them to be Efficient Transport Media

While solid-state protein junctions have shown efficient electron transport over lengths that surpass those of conventional organic semiconducting systems, interfacial or contact effects may obscure the intrinsic protein charge transport properties. Therefore, contact resistance (RC) effects need to be quantified and then minimized, which poses a problem if 4-probe geometries cannot be used. Here we show how RC can be extracted quantitatively from the measured junction resistance (RP) by using the extrapolated zero-length resistance (RZLR) and short-circuit resistance (RS). We used AC (impedance spectroscopy) and DC measurements to examine charge transport in junctions of human serum albumin (HSA) and bacteriorhodopsin (bR) films with varying thicknesses. Three contact configurations, Si-Au, Au-EGaIn, and, in a micropore device (MpD), Au-Pd, were compared. While Si-Au and Au-EGaIn junctions exhibit substantial RC that we ascribe to interfacial oxides and electrostatic protein-electrode interactions, MpD effectively eliminates RC, enabling measuring the intrinsic electron transport across HSA and bR films. The exponential length dependence of RP shows a transport decay constant (beta) that varies with interfacial conditions, underscoring the role of contact engineering. By minimizing RC, exceptionally low beta values (0.7 to 1.1 per nm) are found, proving that, indeed, proteins can have outstanding charge transport efficiencies.

physics.bio-ph↗
arXiv2025

An Equisingular Specialisation of the Compactified Jacobian and its applications

For any positive integer $k$, let $X_k$ be a projective irreducible nodal curve with $k$ nodes. We show that the Betti numbers and the mixed Hodge numbers of the compactified Jacobian $\overline{J_{k}}$ of an irreducible nodal curve $X_k$ with $k$ nodes are the same as the Betti numbers and the mixed Hodge numbers of $J_0\times R^k$, where $J_0$ is the Jacobian of the normalisation of the irreducible nodal curve and $R$ denotes the rational nodal curve with one node. We prove it by constructing a topologically locally trivial family of projective varieties containing $\overline{J_{k}}$ and $J_0\times R^k$ as fibres.

math.AG↗
arXiv2025

Subordination Involving Gauss Hypergeometric Function

The primary objective of this work is to obtain some sufficient conditions so that normalized Gauss hypergeometric function satisfies exponential starlikeness and convexity in the unit disk. Moreover, conditions on parameter of this function has been derived for being Janowski convexity and starlikeness with the help of differential subordination. Results established in this work are presumably new and their significance is illustrated by several consequences.

math.CV↗
arXiv2025

Shoal++: High Throughput DAG BFT Can Be Fast!

Today's practical partially synchronous Byzantine Fault Tolerant (BFT) consensus protocols trade off low latency and high throughput. On the one end, traditional BFT protocols such as PBFT and its derivatives optimize for latency. They require, in fault-free executions, only 3 message exchanges to commit, the optimum for BFT consensus. However, this class of protocols typically relies on a single leader, hampering throughput scalability. On the other end, a new class of so-called DAG-BFT protocols demonstrates how to achieve highly scalable throughput by separating data dissemination from consensus, and using every replica as proposer. Unfortunately, existing DAG-BFT protocols pay a steep latency premium, requiring on average 10.5 message exchanges to commit a transactions. This work aims to soften this tension and proposes Shoal++, a novel DAG-based BFT consensus system that offers the throughput of DAGs while reducing commit latency to an average of 4.5 message exchanges. Our empirical findings are encouraging, showing that Shoal++ achieves throughput comparable to state-of-the-art DAG BFT solutions while reducing latency by up to 60%.

cs.DC↗
arXiv2024

Distilling Knowledge for Short-to-Long Term Trajectory Prediction

Long-term trajectory forecasting is an important and challenging problem in the fields of computer vision, machine learning, and robotics. One fundamental difficulty stands in the evolution of the trajectory that becomes more and more uncertain and unpredictable as the time horizon grows, subsequently increasing the complexity of the problem. To overcome this issue, in this paper, we propose Di-Long, a new method that employs the distillation of a short-term trajectory model forecaster that guides a student network for long-term trajectory prediction during the training process. Given a total sequence length that comprehends the allowed observation for the student network and the complementary target sequence, we let the student and the teacher solve two different related tasks defined over the same full trajectory: the student observes a short sequence and predicts a long trajectory, whereas the teacher observes a longer sequence and predicts the remaining short target trajectory. The teacher's task is less uncertain, and we use its accurate predictions to guide the student through our knowledge distillation framework, reducing long-term future uncertainty. Our experiments show that our proposed Di-Long method is effective for long-term forecasting and achieves state-of-the-art performance on the Intersection Drone Dataset (inD) and the Stanford Drone Dataset (SDD).

cs.CV↗
arXiv2024

Properties and applications of the Bicomplex Miller-Ross function

In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the bicomplex holomorphicity and Taylor series representation of this function are discussed, along with the derivation of a differential equation. Finally, as applications some relations of fractional order derivatives and solutions for the bicomplex extension of the generalized fractional kinetic equation involving the bicomplex Miller Ross function are derived.

math.CV↗
arXiv2024

Inhomogeneous Khitchine-Groshev type theorems on manifolds over function fields

The goal of this paper is to establish a complete Khintchine-Groshev type theorem in both homogeneous and inhomogeneous setting, on analytic nondegenerate manifolds over a local field of positive characteristic. The dual form of Diophantine approximation has been considered here. Our treatise provides the function field analogues of the various earlier results of this type, studied in the euclidean and S-adic framework, by Bernik, Kleinbock and Margulis, Beresnevich, Bernik, Kleinbock and Margulis, Badziahin, Beresnevich and Velani, Mohammadi and Golsefidy, and Datta and Ghosh.

math.NT↗
arXiv2024

Dirichlet improvability for $S$-numbers

We study the problem of improving Dirichlet's theorem of metric Diophantine approximation in the $S$-adic setting. Our approach is based on translation of the problem related to Dirichlet improvability into a dynamical one, and the main technique of our proof is the $S$-adic version of quantitative nondivergence estimate due to D. Y. Kleinbock and G. Tomanov. The main result of this paper can be regarded as the number field version of earlier works of D. Y. Kleinbock and B. Weiss, and of the second named author and Anish Ghosh. Also this in turn generalises a result of Shreyasi Datta and M. M. Radhika on singularity of vectors to any number field $K$ and $S$ containing all archimedian places.

math.NT↗
arXiv2024

Diophantine transference principle over function fields

We study the Diophantine transference principle over function fields. By adapting the approach of Beresnevich and Velani to the function field set-up, we extend many results from homogeneous Diophantine approximation to the realm of inhomogeneous Diophantine approximation over function fields. This also yields the inhomogeneous Baker-Sprindzuk conjecture over function fields as a consequence. Furthermore, we prove the upper bounds for the general non-extremal scenario.

math.NT↗
arXiv2023

Bicomplex generalized hypergeometric functions and their applications

In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation, differential relation, analyticity and contiguous relations of this function are derived. Additionally, applications in quantum information system and quantum optics are provided as a consequence.

math.CV↗