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Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research. [ABSTRACT FROM AUTHOR]

Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms; leading algorithms use a near-term quantum computer to solve the ground state properties of molecules, simulate dynamics of different quantum systems, and so on. In the literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular and efficacious optimizers and assess their performance in variational quantum algorithms for applications in quantum chemistry in a realistic noisy setting. We benchmark the optimizers with critical analysis based on quantum simulations of simple molecules, such as hydrogen, lithium hydride, beryllium hydride, water, and hydrogen fluoride. The errors in the ground state energy, dissociation energy, and dipole moment are the parameters used as yardsticks. All the simulations were carried out with an ideal quantum circuit simulator, a noisy quantum circuit simulator, and finally a noisy simulator with noise embedded from the IBM Cairo quantum device to understand the performance of the classical optimizers in ideal and realistic quantum environments. We used the standard unitary coupled cluster ansatz for simulations, and the number of qubits varied from two starting from the hydrogen molecule to ten qubits in hydrogen fluoride. Based on the performance of these optimizers in the ideal quantum circuits, the conjugate gradient, limited-memory Broyden—Fletcher—Goldfarb—Shanno bound, and sequential least squares programming optimizers are found to be the best-performing gradient-based optimizers. While constrained optimization by linear approximation (COBYLA) and Powell's conjugate direction algorithm for unconstrained optimization (POWELL) perform most efficiently among the gradient-free methods, in noisy quantum circuit conditions, simultaneous perturbation stochastic approximation, POWELL, and COBYLA are among the best-performing optimizers. [ABSTRACT FROM AUTHOR]

Boolean functions are fundamental bricks in the development of various applications in Cryptography and Coding theory by making benefit from the weights of related Boolean functions (Walsh spectrum). Towards this, the discrete Fourier transform (Walsh–Hadamard) plays a pivotal tool. The work in this paper is dedicated towards the algebraic and numerical degrees, together with the relationship between weights of Boolean function and their Walsh transforms. We introduce Walsh matrices and generalize them to any arbitrary Boolean function. This improves the complexity in computation of Walsh–Hadamard and Fourier transform in certain cases. We also discuss some useful results related to the degree of the algebraic normal form using Walsh–Hadamard transform. [ABSTRACT FROM AUTHOR]

The aphids, Myzus persicae (Sulzer) and Aphis gossypii (Glover) (Hemiptera: Aphididae) and the whiteflies, Trialeurodes vaporariorum (Westwood) and Bemisia tabaci (Gennadius) (Hemiptera: Aleyrodidae) are the most damaging pests of greenhouse crops, which cause vector-borne viral diseases and its damage includes chlorosis, necrosis, and fruit abortion. This review article addresses the protected cultivation of vegetable crops (cucumber, capsicum, tomato, and gerbera), important insect pests of greenhouse crops in India along with its management by entomopathogenic fungi (EPF) and increase in the virulence by different genetically modified techniques. Due to excessive and indiscriminate use of insecticides over the years, these insect pests became resistant to these insecticides. So, there is a need for the effectual substitutes to manage these pests. Biological control is a foundation of integrated pest management (IPM) that plays a key role in the repression of arthropod pests. Among different IPM program, the uses of different microbial formulations are ecofriendly and safe for life and proven a boon for the farmers and entrepreneurs. EPF are the most effective in reducing aphid and whitefly populations on vegetable crops recommending its organic production under greenhouse conditions and could be a part of IPM. In the future, these insect pests will become more resistant to entomopathogens. Some novel techniques such as genetic engineering of fungal formulations will be required to increase the efficiency of various entomopathogens as these techniques are well adopted by countries like the USA, China, and European countries but its use in India and needs to be improved in the near future. [ABSTRACT FROM AUTHOR]

The peach aphid, Myzus persicae (Hemiptera: Aphididae) and silver leaf whitefly, Bemisia tabaci (Hemiptera: Aleyrodidae) are the major pests of capsicum under protected cultivation. The entomopathogenic fungi (EPF) are environmentally safe than the chemical pesticides. In the present study, different EPF formulations, Beauveria bassiana Balsamo (Vuillemin), Lecanicillium lecanii (Zimmerman) Viegas, Metarhizium anisopliae (Metschnikoff) Sorokin, were evaluated along with Azadirachtin 1% for the management of the aphid and the whitefly on capsicum under protected conditions. Result showed that talc formulation of L. lecanii MTCC 956 at 10 and 12 g/l caused 60.5 and 61.6% population reduction for aphid and 60.0 and 61.6% population reduction for whitefly, whereas Azadirachtin 1% at 4 and 5 ml/l caused 71.2 and 74.7% population reduction for aphid and 68.5 and 71.0% population reduction for whitefly after 3rd spray, respectively and were effective in reducing aphid and whitefly populations on capsicum recommending its organic production under protected cultivation and could be a part of integrated pest management program. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel method for constructing maximum distance separable (MDS) codes based on the extended invertibility and orthogonality of quasigroups. We provide various methods of constructing an orthogonal system of k-ary operations over Q2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$Q^2$$\end{document} using a special type of k-ary operations over Q, where Q is any arbitrary finite set. Then we use concepts of strong orthogonality of k-ary operations to establish a connection between orthogonality and linear recursive MDS codes. We illustrate these new classes of MDS codes using the proposed techniques and enumerate such codes using SageMath. [ABSTRACT FROM AUTHOR]

In recent years, there have been a lot of research towards finding conditions under which the trinomial x r (x α (q − 1) + x β (q − 1) + 1) permutes F 2 2 m with α > β and r being positive integers. The authors of [6,10,24] have determined these conditions when α ≤ 5 for certain values of β and r. In this paper, we work for α = 6 and determine four new classes of such permutation trinomials. Our contribution encompasses the investigation of these unexplored classes. Additionally, we analyze their quasi-multiplicative equivalence with already known permutation trinomials for m ≥ 1. Through our research, we demonstrate that two of these determined classes are new, and for others, we explicitly compute the exponent for which they become equivalent. [ABSTRACT FROM AUTHOR]

Purpose: To evaluate the association between obstructive sleep apnea (OSA) and thyroid eye disease (TED) and its effect on disease activity. Methods: A prospective case–control study was conducted from January 2020 to March 2022. All TED patients (group A) were clinically evaluated. The activity of thyroid eye disease was calculated based on the clinical activity score (CAS), and grading of severity was done according to the EUGOGO classification. All TED patients (group A) were screened for OSA using the Snoring Tired Observed Pressure (STOP)-Bang survey. Age- and gender-matched control group patients (group B) without TED were screened for OSA. Results: One hundred TED patients and 138 control patients without TED were included in the respective groups. Sixty-two (62%) patients in group A and 48 (34.78%) patients in group B were having high risk of OSA, and this difference was statistically significant (P = 0.001). Further, in group A patients, on univariate analysis, TED activity was significantly associated with a high risk of OSA (P = 0.009). On multivariate logistic regression analysis, OSA also showed significant association with TED activity (odds ratio [OR]: 4.14, 95% confidence interval [CI]: 1.11-18.85 at 10% level; P = 0.05). Conclusion: Our study showed that OSA is significantly associated with TED disease and its activity. However, no significant association was found between OSA and severity of the disease. [ABSTRACT FROM AUTHOR]

Let F q denote the finite field of order q , let m 1 , m 2 , ⋯ , m ℓ be positive integers satisfying gcd ⁡ ( m i , q ) = 1 for 1 ≤ i ≤ ℓ , and let n = m 1 + m 2 + ⋯ + m ℓ . Let Λ = ( λ 1 , λ 2 , ⋯ , λ ℓ ) be fixed, where λ 1 , λ 2 , ⋯ , λ ℓ are non-zero elements of F q . In this paper, we study the algebraic structure of Λ-multi-twisted codes of length n over F q and their dual codes with respect to the standard inner product on F q n . We provide necessary and sufficient conditions for the existence of a self-dual Λ-multi-twisted code of length n over F q , and obtain enumeration formulae for all self-dual and self-orthogonal Λ-multi-twisted codes of length n over F q . We also derive some sufficient conditions under which a Λ-multi-twisted code is linear with complementary dual (LCD). We determine the parity-check polynomial of all Λ-multi-twisted codes of length n over F q and obtain a BCH type bound on their minimum Hamming distances. We also determine generating sets of dual codes of some Λ-multi-twisted codes of length n over F q from the generating sets of the codes. Besides this, we provide a trace description for all Λ-multi-twisted codes of length n over F q by viewing these codes as direct sums of certain concatenated codes, which leads to a method to construct these codes. We also obtain a lower bound on their minimum Hamming distances using their multilevel concatenated structure. [ABSTRACT FROM AUTHOR]

The multivariate public-key cryptography (MPKC) provides a promising class of post-quantum signature schemes. Its theoretical security comes from the intractability of the multivariate quadratic problem (M Q problem), which is an NP-hard problem [1]. Nevertheless, not every instance of M Q -problem is hard [2–6] while the problem itself is NP-hard. Thus, it is important to understand and analyze the nature of the quadratic systems used in existing MPKC so that the security of the multivariate schemes can be properly assessed. Herein, we present a detailed cryptanalysis of the multivariate based 'ring' signature scheme presented by Wang et al. [7]. We utilize the attacks on the underdetermined system of multivariate quadratic equations. We prove both theoretically and experimentally that the scheme (Wang et al. [7]) can be broken in polynomial time even for rings of small size. Additionally, we observed that the attack strategy we proposed in this work is not only limited to [7] , but can also be applied to break the unforgeability of other multivariate based schemes such as verifiable ring signature scheme [8] , multivariate group signature scheme [9] , and Gui and GeMSS based ring signature scheme [10,11]. [ABSTRACT FROM AUTHOR]