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The structure of Markov equivalence classes (MECs) of causal DAGs has been studied extensively. A natural question in this regard is to algorithmically find the number of MECs with a given skeleton. Until recently, the known results for this problem were in the setting of very special graphs (such as paths, cycles, and star graphs). More recently, a fixed-parameter tractable (FPT) algorithm was given for this problem which, given an input graph $G$, counts the number of MECs with the skeleton $G$ in $O(n(2^{O(d^4k^4)} + n^2))$ time, where $n$, $d$, and $k$, respectively, are the numbers of nodes, the degree, and the treewidth of $G$. We give a faster FPT algorithm that solves the problem in $O(n(2^{O(d^2k^2)} + n^2))$ time when the input graph is chordal. Additionally, we show that the runtime can be further improved to polynomial time when the input graph $G$ is a tree., Comment: 53 pages, 2 figures

We consider mixed Steklov-Dirichlet eigenvalue problem on smooth bounded domains in Riemannian manifolds. Under certain symmetry assumptions on multiconnected domains in $\mathbb{R}^{n}$ with a spherical hole, we obtain isoperimetric inequalities for $k$-th Steklov-Dirichlet eigenvalues for $2 \leq k \leq n+1$. We extend Theorem 3.1 of \cite{gavitone2023isoperimetric} from Euclidean domains to domains in space forms, that is, we obtain sharp lower and upper bounds of the first Steklov-Dirichlet eigenvalue on bounded star-shaped domains in the unit $n$-sphere and in the hyperbolic space.

This paper investigates the performance of multiple reconfigurable intelligent surfaces (multi-RIS) communication systems where the RIS link with the highest signal-to-noise-ratio (SNR) is selected at the destination. In practice, all the RISs will not have the same number of reflecting elements. Hence, selecting the RIS link with the highest SNR will involve characterizing the distribution of the maximum of independent, non-identically distributed (i.n.i.d.) SNR random variables (RVs). Using extreme value theory (EVT), we derive the asymptotic distribution of the normalized maximum of i.n.i.d. non-central chi-square (NCCS) distributed SNR RVs with one degree of freedom (d.o.f) and then extend the results for k-th order statistics. Using these asymptotic results, the outage capacity and average throughput expressions are derived for the multi-RIS system. The results for independent and identically distributed (i.i.d.) SNR RVs are then derived as a special case of i.n.i.d. RVs. All the derivations are validated through extensive Monte Carlo simulations, and their utility is discussed.

Quantum computation holds the promise of solving computational problems which are believed to be classically intractable. However, in practice, quantum devices are still limited by their relatively short coherence times and imperfect circuit-hardware mapping. In this work, we present the parallelization of pre-calibrated pulses at the hardware level as an easy-to-implement strategy to optimize quantum gates. Focusing on $R_{ZX}$ gates, we demonstrate that such parallelization leads to improved fidelity and gate time reduction, when compared to serial concatenation. As measured by Cycle Benchmarking, our most modest fidelity gain was from 98.16(7)% to 99.15(3)% for the application of two $R_{ZX}(\pi/2)$ gates with one shared qubit. We show that this strategy can be applied to other gates like the CNOT and CZ, and it may benefit tasks such as Hamiltonian simulation problems, amplitude amplification, and error-correction codes.

The agricultural sector plays an essential role in the economic growth of a country. Specifically, in an Indian context, it is the critical source of livelihood for millions of people living in rural areas. Plant Disease is one of the significant factors affecting the agricultural sector. Plants get infected with diseases for various reasons, including synthetic fertilizers, archaic practices, environmental conditions, etc., which impact the farm yield and subsequently hinder the economy. To address this issue, researchers have explored many applications based on AI and Machine Learning techniques to detect plant diseases. This research survey provides a comprehensive understanding of common plant leaf diseases, evaluates traditional and deep learning techniques for disease detection, and summarizes available datasets. It also explores Explainable AI (XAI) to enhance the interpretability of deep learning models' decisions for end-users. By consolidating this knowledge, the survey offers valuable insights to researchers, practitioners, and stakeholders in the agricultural sector, fostering the development of efficient and transparent solutions for combating plant diseases and promoting sustainable agricultural practices., Comment: To appear in a Journal/Conference

This article presents spectroscopy results of the $5s5p{\;^3}P_0 \rightarrow 5s5d{\;^3}D_1$ transition in all isotopes of laser cooled Sr atoms and the utility of this transition for repumping application. By employing the $5s5p{\;^{3} P_{0}} \rightarrow 5s5d{\;^3}D_1 $ (483 nm) transition in combination with the excitation of $5s5p{\;^3}P_2 \rightarrow 5s6s{\;^3}S_1$ (707 nm) transition, we observe a significant increase ($\sim$ 13 fold) in the steady state number of atoms in the magneto-optic trap (MOT). This enhancement is attributed to the efficient repumping of Sr atoms that have decayed into the dark $5s5p{\;^3}P_2$ state by returning them to the ground state $5s^2{\;^1}S_0$ without any loss into the other states. The absolute transition frequencies were measured with an absolute accuracy of 30 MHz. To support our measurements, we performed Fock-space relativistic coupled-cluster calculations of the relevant parameters in Sr. To further increase the accuracy of the calculated properties, corrections from the Breit, QED and perturbative triples were also included. The calculated branching ratio for the repumping state confirms the significantly increased population in the ${^3}P_1$ state. Thereby, leading to an increase of population of atoms trapped due to the enhanced repumping. Our calculated hyperfine-splitting energies are in excellent agreement with the measured values. Moreover, our calculated isotope shifts in the transition frequencies are in good agreement with our measured values., Comment: 8 pages, 4 figures

Capillary suspensions are three-phase mixtures containing a solid particulate phase, a continuous liquid phase, and a second immiscible liquid forming capillary bridges between particles. Capillary suspensions are encountered in a wide array of applications including 3D printing, porous materials, and food formulations, but despite recent progress, the micromechanics of particle clusters in flow is not fully understood. In this work, we study the dynamics of meniscus-bound particle clusters in planar extensional flow using a Stokes trap, which is an automated flow control technique that allows for precise manipulation of freely suspended particles or particle clusters in flow. Focusing on the case of a two-particle doublet, we use a combination of experiments and analytical modeling to understand how particle clusters rearrange, deform, and ultimately break up in extensional flow. The time required for cluster breakup is quantified as a function of capillary number $Ca$ and meniscus volume $V$. Importantly, a critical capillary number $Ca_{crit}$ for cluster breakup is determined using a combination of experiments and modeling. Cluster relaxation experiments are also performed by deforming particle clusters in flow, followed by flow cessation prior to breakup and observing cluster relaxation dynamics under zero-flow conditions. In all cases, experiments are complemented by an analytical model that accounts for capillary forces, lubrication forces, hydrodynamic drag forces, and hydrodynamic interactions acting on the particles. Results from the analytical models are found to be in good agreement with experiments. Overall, this work provides a new quantitative understanding of the deformation dynamics of capillary clusters in extensional flow., Comment: 15 pages, 9 figures

We present the study of four FUV stars in the field of open cluster NGC 2420 using the Ultra Violet Imaging Telescope (UVIT) mounted on AstroSat. The three stars 525, 527, and 560 are members, while star 646 is a non-member of the cluster. To characterize and determine the parameters of these stars, multi-wavelength spectral energy distributions (SEDs) are analyzed using UV, optical, and IR data sets. For all four FUV bright stars, a two-component SED model fits well. Our findings indicate that two stars, 525 and 560, are binary BSS systems. These binary BSS systems may have formed in a tertiary system due to mass transfer from an evolved outer tertiary companion. Star 527 is a binary system of a BSS and an extremely low-mass (ELM) white dwarf, while Star 646 is a binary system of a horizontal branch star and an ELM white dwarf. The effective temperatures, radii, luminosities and masses of the two ELMs are (10250, 11500) K, (0.42, 0.12) Rsun, (1.61, 0.23) Lsun, and (0.186, 0.170) Msun, respectively. The star 527 could be a post-mass transfer system and may have originated through the Case A/B mass transfer process in a low-density environment. The cooling age of the ELMs is < 1 Myr, indicating that they have only recently formed., Comment: Accepted in ApJ, 9 pages, 4 figures, 1 table

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical randomness -- can be mapped to the paradigm of stochastic games. Subsequently, using the setup of two-player--two-action games, we explore the pure reactive strategies belonging to the set of reactive strategies, whose support in the quantum games is no longer countably finite but rather non-denumerably infinite. We find that how two pure strategies fare against each other is crucially dependent on the discount factor (the probability of occurrence of every subsequent round) and how much entangled the quantum states of the players are. We contrast the results obtained with the corresponding results in the classical setup and find fundamental differences between them: e.g, when the underlying game is the prisoner's dilemma, in the quantum game setup, always-defect strategy can be beaten by the tit-for-tat strategy for high enough discount factor.

The Pancharatnam phase is a generalization of the Berry phase that applies to discrete sequences of quantum states. Here, we show that the Pancharatnam phase is a natural invariant for a wide class of quantum many-body dynamics involving measurements. We specifically investigate how a non-trivial Pancharatnam phase arises in the trajectories of Floquet quantum error-correcting codes and show that this phase can be extracted in a "computationally-assisted" interferometry protocol, involving additional post-processing based on the measurement record that defines a given quantum many-body trajectory. This Pancharatnam phase can also be directly related to the Berry phase accrued by continuous unitary evolution within a gapped phase. For the $\mathbb Z_2$ Floquet code of Hastings and Haah, we show that the associated family of unitary evolutions is the radical chiral Floquet phase. We demonstrate this correspondence explicitly by studying an exactly-solvable model of interacting spins., Comment: 5+4 pages, 2+1 figures

Quantum key distribution (QKD) provides a method of ensuring security using the laws of physics, avoiding the risks inherent in cryptosystems protected by computational complexity. Here we investigate the feasibility of satellite-based quantum key exchange using low-cost compact nano-satellites. This paper demonstrates the first prototype of system level quantum key distribution aimed at the Cube satellite scenario. It consists of a transmitter payload, a ground receiver and simulated free space channel to verify the timing and synchronisation (T&S) scheme designed for QKD and the required high loss tolerance of both QKD and T&S channels. The transmitter is designed to be deployed on various up-coming nano-satellite missions in the UK and internationally. The effects of channel loss, background noise, gate width and mean photon number on the secure key rate (SKR) and quantum bit error rate (QBER) are discussed. We also analyse the source of QBER and establish the relationship between effective signal noise ratio (ESNR) and noise level, signal strength, gating window and other parameters as a reference for SKR optimization. The experiment shows that it can tolerate the 40 dB loss expected in space to ground QKD and with small adjustment decoy states can be achieved. The discussion offers valuable insight not only for the design and optimization of miniature low-cost satellite-based QKD systems but also any other short or long range free space QKD on the ground or in the air.

We perform a comparative study of the phase noise induced in the lasers used for Bragg diffraction in a Bose-Einstein condensate-based quantum gravimeter where the Bragg beams are generated using two different configurations. In one of the configurations, the Bragg beams that form the moving optical lattice are generated using two different acousto-optic modulators. In the second configuration, the Bragg beams are generated using a single acousto-optic modulator carrying two phase-locked frequencies. The second configuration shows a suppression of phase noise by a factor of 4.7 times in the frequency band upto 10 $kHz$, the primary source of noise, which is the background acoustic noise picked up by optical components and the optical table. We report a sensitivity of 99.7 $\mu Gal/\sqrt Hz$ for an interferometric time of 10 $ms$., Comment: 8 pages, 6 figures