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Gyan Prakash

Publications and source records attributed to Gyan Prakash.

17 recordsLinked to original sources
arXiv2026

Learning to replenish: A hybrid deep reinforcement learning for dynamic inventory management in the pharmaceutical supply chains

Pharmaceutical supply chains (PSCs) struggle with inventory management (IM) due to unpredictable demand patterns and variable lead times associated with restocking. This complexity is further compounded by the finite shelf lives of pharmaceutical products, which necessitate a delicate balance between adequate stock and minimal waste. These intertwined factors create a complex optimization problem that requires sophisticated inventory strategies to ensure both product availability and PSC efficiency. This study aims to develop an optimal inventory replenishment policy for pharmaceutical products that can handle the stochasticity arising from uncertain demand and variable PSC conditions. The objective is to maximize the profitability of the PSC while maintaining a high patient service level. We formulate the problem as a Markov decision process and propose a deep reinforcement learning (DRL) approach, specifically, a hybrid asynchronous advantage actor critic distributed proximal policy optimization (A3C DPPO)algorithm. The A3C DPPO algorithm is tailored to handle the continuous action space inherent in IM. The numerical results demonstrate that the proposed algorithm adaptively updates the inventory replenishment strategy under dynamic scenarios, resulting in lower inventory costs compared to various benchmarks. We also conduct numerical validation using real-world pharmaceutical inventory data to confirm the practical feasibility of the proposed algorithm.

cs.AI↗
arXiv2025

Ultrasensitive Polarization-Resolved Probing of Transient Dynamics in MoS$_2$ on Silicon Nitride Microresonators

We present an ultrasensitive technique for probing transient optical changes in atomically thin molybdenum disulfide (MoS$_2$) layers integrated onto silicon nitride (Si$_3$N$_4$) ring resonators. The MoS$_2$ is illuminated by a femtosecond laser, while a tunable near-infrared (NIR) continuous-wave laser probes the microresonator resonance. The NIR light polarization can be adjusted to either transverse electric (TE, parallel to the 2D material) or transverse magnetic (TM, perpendicular), a configuration that is impossible to achieve with conventional normal-incidence pump-probe techniques. By capturing the transmitted signal on a fast oscilloscope, we detect transient optical shifts with unprecedented sensitivity, observing phenomena over time scales ranging from picoseconds to microseconds. Our results reveal both a rapid, carrier-induced nonlinear optical shift in the resonance, and a slower thermo-optic transient. The ability to simultaneously measure these fast and slow dynamics offers new insight into the complex optoelectronic behavior of 2D materials when integrated with microresonators. This method provides a significant advance over traditional pump-probe approaches, enabling the detection of exceedingly small transient signals and opening new avenues for exploring the optical properties of atomically thin materials. Our findings highlight the potential of this approach for investigating polarization-dependent nonlinear effects, with applications in photonics, sensing, and optoelectronics.

physics.optics↗
arXiv2025

Adaptive Inventory Strategies using Deep Reinforcement Learning for Dynamic Agri-Food Supply Chains

Agricultural products are often subject to seasonal fluctuations in production and demand. Predicting and managing inventory levels in response to these variations can be challenging, leading to either excess inventory or stockouts. Additionally, the coordination among stakeholders at various level of food supply chain is not considered in the existing body of literature. To bridge these research gaps, this study focuses on inventory management of agri-food products under demand and lead time uncertainties. By implementing effective inventory replenishment policy results in maximize the overall profit throughout the supply chain. However, the complexity of the problem increases due to these uncertainties and shelf-life of the product, that makes challenging to implement traditional approaches to generate optimal set of solutions. Thus, the current study propose a novel Deep Reinforcement Learning (DRL) algorithm that combines the benefits of both value- and policy-based DRL approaches for inventory optimization under uncertainties. The proposed algorithm can incentivize collaboration among stakeholders by aligning their interests and objectives through shared optimization goal of maximizing profitability along the agri-food supply chain while considering perishability, and uncertainty simultaneously. By selecting optimal order quantities with continuous action space, the proposed algorithm effectively addresses the inventory optimization challenges. To rigorously evaluate this algorithm, the empirical data from fresh agricultural products supply chain inventory is considered. Experimental results corroborate the improved performance of the proposed inventory replenishment policy under stochastic demand patterns and lead time scenarios. The research findings hold managerial implications for policymakers to manage the inventory of agricultural products more effectively under uncertainty.

cs.AI↗
arXiv2024

Terahertz Antenna Impedance Matched to a Graphene Photodetector

Developing low-power, high-sensitivity photodetectors for the terahertz (THz) band that operate at room temperature is an important challenge in optoelectronics. In this study, we introduce a photo-thermal-electric (PTE) effect detector based on quasi-free standing bilayer graphene (BLG) on a silicon carbide (SiC) substrate, designed for the THz frequency range. Our detector's performance hinges on a quasi-optical coupling scheme, which integrates an aspherical silicon lens, to optimize impedance matching between the THz antenna and the graphene p-n junction. At room temperature, we achieved a noise equivalent power (NEP) of less than 300 $pW/\sqrt{Hz}$. Through an impedance matching analysis, we coupled a planar antenna with a graphene p-n junction, inserted in parallel to the nano-gap of the antenna, via two coupling capacitors. By adjusting the capacitors and the antenna arm length, we tailored the antenna's maximum infrared power absorption to specific frequencies. The sensitivity, spectral properties, and scalability of our material make it an ideal candidate for future development of far-infrared detectors operating at room temperature.

physics.ins-det↗
arXiv2019

Plasmon-induced efficient hot carrier generation in graphene on gold ultrathin film with periodic array of holes: Ultrafast pump-probe spectroscopy

Using ultrafast pump-probe reflectivity with 3.1 eV pump and coherent white light probe (1.1 to 2.6 eV), we show that graphene on gold nanostructures exhibits a strong coupling to the plasmonic resonances of the ordered lattice hole array, thus injecting a high density of hot carriers in graphene through plasmons. The system being studied is single-layer graphene on ultrathin film of gold with periodic arrangements of holes showing anomalous transmission. A comparison is made with gold film with and without hole array. By selectively probing transient carrier dynamics in the spectral regions corresponding to plasmonic resonances, we show efficient plasmon-induced hot carrier generation in graphene. We also show that due to high electromagnetic field intensities at the edge of the sub-micron holes, fast decay time (10-100 fs) and short decay length (1 nm) of plasmons, a highly confined density of hot carriers (very close to edge of the holes) is generated by Landau damping of plasmons within the holey gold film. A contribution to transient decay dynamics due to diffusion of initial non-uniform distribution of hot carriers away from the hole edges is observed. Our results are important for future applications of novel hot carrier device concepts where hot carriers with tunable energy can be generated in different graphene regions connected seamlessly.

cond-mat.mes-hall↗
arXiv2019

Anomalous temperature dependence of optical and acoustic phonons in Bi$_2$Se$_3$ arising from stacking faults

The class of layered 3D-topological insulators have shown intriguingly anomalous temperature dependence in their thermal expansion coefficients. It was proposed that stacking faults are the origin of the observed anomalous thermal expansion. Here, using femtosecond pump-probe differential reflectivity measurements we probe the carrier and coherently generated totally symmetric A1g1 optical phonons in Bi2Se3. Transient signals also show a low frequency (~GHz) oscillations due to coherent longitudinal acoustic phonons. We extract temperature dependence of optical constants, sound velocity and Young's modulus of Bi2Se3 using the strain pulse propagation model. A remarkable anomalous behavior around ~180 K is observed in the temperature dependence of optical and acoustic phonons as well as the optical constants. First-principles density functional theory (DFT) reveals that thermally activated formation of stacking faults is responsible for the anomalies observed in Bi2Se3, similar to case of Sb2Te3. We also show that inclusion of spin-orbit coupling plays an important role in reducing the total energy difference between the pristine and the faulted structures.

cond-mat.mtrl-sci↗
arXiv2019

Carrier dynamics in ultrathin gold nanowires: Role of Auger processes

Carrier dynamics in metallic nanostructures is strongly influenced by their confining dimensions. Gold nanoparticles of size $\sim 2$ nm lie at the boundary separating metallic and non-metallic behavior. In this work, we report carrier dynamics in high aspect ratio ultrathin gold nanowires (Au-UNWs) of average diameter $\sim$2 nm using pump (3.1 eV) and coherent white light continuum as probe in the spectral range of 1.15 eV to 2.75 eV. The transient carrier dynamics in Au-UNWs under extreme excitation regime is slower than predicted by the often used two temperature model. We identify Auger-assisted carrier heating process which slows down the hot carrier cooling dynamics. The rate equation model fitted to the data yields an estimate of Auger coefficient for gold nanostructures.

cond-mat.mes-hall↗
arXiv2019

On sum-product bases

Besides various asymptotic results on the concept of sum-product bases in $\mathbb{N}_0$, we consider by probabilistic arguments the existence of thin sets $A,A'$ of integers such that $AA+A=\mathbb{N}_0$ and $A'A'+A'A'=\mathbb{N}_0$.

math.NT↗
arXiv2017

On monochromatic representation of sums of squares of primes

When the sequences of squares of primes is coloured with $K$ colours, where $K \geq 1$ is an integer, let $s(K)$ be the smallest integer such that each sufficiently large integer can be written as a sum of no more than $s(K)$ squares of primes, all of the same colour. We show that $s(K) \ll K \exp\left(\frac{(3\log 2 + {\rm o}(1))\log K}{\log \log K}\right)$ for $K \geq 2$. This improves on $s(K) \ll_ε K^{2 +ε}$, which is the best available upper bound for $s(K)$.

math.NT↗
arXiv2016

Sum-free subsets of finite abelian groups of type III

A finite abelian group $G$ of cardinality $n$ is said to be of type III if every prime divisor of $n$ is congruent to 1 modulo 3. We obtain a classification theorem for sum-free subsets of largest possible cardinality in a finite abelian group $G$ of type III. This theorem, when taken together with known results, gives a complete characterisation of sum-free subsets of the largest cardinality in any finite abelian group $G$. We supplement this result with a theorem on the structure of sum-free subsets of cardinality "close" to the largest possible in a type III abelian group $G$. We then give two applications of these results. Our first application allows us to write down a formula for the number of orbits under the natural action of ${\rm Aut}(G)$ on the set of sum-free subsets of $G$ of the largest cardinality when $G$ is of the form $({\mathbf{Z}}/m{\mathbf{Z}})^r$, with all prime divisors of $m$ congruent to 1 modulo 3, thereby extending a result of Rhemtulla and Street. Our second application provides an upper bound for the number of sum-free subsets of $G$. For finite abelian groups $G$ of type III and with {\em a given exponent} this bound is substantially better than that implied by the bound for the number of sum-free subsets in an arbitrary finite abelian group, due to Green and Ruzsa.

math.NT↗
arXiv2014

A remark on a result of Helfgott, Roton and Naslund

Let $F(X)= \prod_{i=1}^k(a_iX+b_i)$ be a polynomial with $a_i, b_i$ being integers. Suppose the discriminant of $F$ is non-zero and $F$ is admissible. Given any natural number $N$, let $S(F,N)$ denotes those integers less than or equal to $N$ such that $F(n)$ has no prime factors less than or equal to $N^{1/(4k+1)}.$ Let $L$ be a translation invariant linear equation in $3$ variables. Then any $A\subset S(F, N)$ with $δ_F(N): = \frac{|A|}{|S(F,N)|} \gg_{ε, F, L}\frac{1}{(\log \log N)^{1-ε}}$ contains a non-trivial solution of $L$ provided $N$ is sufficiently large.

math.NT↗
arXiv2009

Number of sets with small sumset and the clique number of random Cayley graphs

Let $G$ be a finite abelian group of order $n$. For any subset $B$ of $G$ with $B=-B$, the Cayley graph $G_B$ is a graph on vertex set $G$ in which $ij$ is an edge if and only if $i-j\in B.$ It was shown by Ben Green that when $G$ is a vector space over a finite field $Z/pZ$, then there is a Cayley graph containing neither a complete subgraph nor an independent set of size more than $clog nloglog n,$ where $c$ is an absolute constant. In this article we observe that a modification of his arguments shows that for an arbitrary finite abelian group of order $n$, there is a Cayley graph containing neither a complete subgraph nor an independent set of size more than $c(omega^3(n)log omega(n) +log nloglog n)$, where $c$ is an absolute constant and $omega(n)$ denotes the number of distinct prime divisors of $n$.

math.NT↗
arXiv2009

Large zero-free subsets of Z/pZ

A finite subset $A$ of an abelian group $G$ is said to be zero-free if the identity element of $G$ cannot be written as a sum of distinct elements from $A$. In this article we study the structure of zero-free subsets of $Z/pZ$ the cardinality of which is close to largest possible. In particular, we determine the cardinality of the largest zero-free subset of $Z/pZ$, when $p$ is a sufficiently large prime.

math.NT↗
arXiv2005

Sum-free set in finite abelian groups

Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. In this paper we shall characterise the largest possible sum-free subsets of G in case the order of G is only divisible by primes which are congruent to 1 modulo 3. The result is based on a recent result of Ben Green and Imre Ruzsa.

math.NT↗
arXiv2005

Asymptotic formula for sum-free sets in abelian groups

Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. Let SF(G) denotes the set of all sum-free subets of $G$ and $σ(G)$ denotes the number $ n^{-1}(\log_2 |SF(G)|) $. In this article we shall improve the error term in the asymptotic formula of $σ(G)$ which was obtained recently by Ben Green and Ruzsa. The methods used are a slight refinement of methods developed by Ben Green and Ruzsa.

math.NT↗