Application Of Computation Research Articles

Mathematical Foundations of Real Numbers and its Application in Computation

The study of Real Numbers (R) is a fundamental pillar of Mathematical Analysis, serving as the cornerstone for a broad spectrum of Mathematical principles and practical applications. Real Numbers are examined both in theory and in practice, impacting fields like pure Mathematics, physics, engineering, and economics. This paper thoroughly explores Real Numbers, looking at their properties, how they are represented, and their significant role in Mathematical research and various applications. We highlight the importance of Real Numbers in advancing our understanding of Mathematics. This research article provides a comprehensive overview of the Mathematical foundations on Real Numbers and its application in computation. It explores historical developments, theoretical frameworks, Mathematical proofs, comparative analyses, applications, and future directions in the study of Real Numbers. The study aims to synthesize existing knowledge, highlight key contributions, theoretical framework and application in computation.

Recent Developments on Novel 2D Materials for Emerging Neuromorphic Computing Devices

The rapid advancement of artificial intelligent and information technology has led to a critical need for extremely low power consumption and excellent efficiency. The capacity of neuromorphic computing to handle large amounts of data with low power consumption has garnered a lot of interest during the last few decades. For neuromorphic applications, 2D layered semiconductor materials have shown a pivotal role due to their distinctive properties. This comprehensive review provides an extensive study of the recent advancements in 2D materials‐based neuromorphic devices especially in multiterminal synaptic devices, two‐terminal synaptic devices, neuronal devices, and the integration of synaptic and neuronal devices. Herein, a wide range of potential applications of memory, computation, adaptation, and artificial intelligence is incorporated. Finally, the limitations and challenges of neuromorphic devices based on novel 2D materials are discussed. Thus, this review aims to illuminate the design and fabrication of neuromorphic devices based on van der Waals (vdW) heterostructure materials, leveraging promising engineering techniques to excel the applications and potential of neuromorphic computing for hardware implementations.

Calibration of stochastic, agent-based neuron growth models with approximate Bayesian computation.

Understanding how genetically encoded rules drive and guide complex neuronal growth processes is essential to comprehending the brain's architecture, and agent-based models (ABMs) offer a powerful simulation approach to further develop this understanding. However, accurately calibrating these models remains a challenge. Here, we present a novel application of Approximate Bayesian Computation (ABC) to address this issue. ABMs are based on parametrized stochastic rules that describe the time evolution of small components-the so-called agents-discretizing the system, leading to stochastic simulations that require appropriate treatment. Mathematically, the calibration defines a stochastic inverse problem. We propose to address it in a Bayesian setting using ABC. We facilitate the repeated comparison between data and simulations by quantifying the morphological information of single neurons with so-called morphometrics and resort to statistical distances to measure discrepancies between populations thereof. We conduct experiments on synthetic as well as experimental data. We find that ABC utilizing Sequential Monte Carlo sampling and the Wasserstein distance finds accurate posterior parameter distributions for representative ABMs. We further demonstrate that these ABMs capture specific features of pyramidal cells of the hippocampus (CA1). Overall, this work establishes a robust framework for calibrating agent-based neuronal growth models and opens the door for future investigations using Bayesian techniques for model building, verification, and adequacy assessment.

Spontaneous parametric downconversion in a laser-poled lithium niobate nonlinear photonic crystal with nanoscale resolution.

Based on quasi-phase-matching (QPM) theory, nonlinear photonic crystals (NPCs) are capable of realizing efficient spontaneous parametric downconversion (SPDC) for the generation of photonic entangled states. However, the traditional electric field poling techniques employed in NPC fabrication often result in non-negligible processing errors of a few hundred nanometers, thus impeding the production of quantum photon pairs as intended. In this work, we investigate the SPDC photon pairs generated in a laser-poled lithium niobate (LN) NPC. By using the recently developed laser poling technique, the processing error of the NPC is substantially reduced to approximately 15 nm. Consequently, the coincidence counts of the generated photon pairs in the experiment reach 83.6% of the designed value. Our result paves the way for on-demand production of high-quality quantum sources, which has potential applications in quantum communications and quantum computations.

The Multiple Millionaires' Problem: New Algorithmic Approaches and Protocols

We study a fundamental problem in Multi-Party Computation, which we call the Multiple Millionaires Problem (MMP). Given a set of private integer inputs, the problem is to identify the subset of inputs that equal the maximum (or minimum) of that set, without revealing any further information on the inputs beyond what is implied by the desired output. Such a problem is a natural extension of the Millionaires Problem, which is the very first Multi-Party Computation problem that was presented in Andrew Yaos seminal work (FOCS 1982). A closely related problem is MaxP, in which the value of the maximum is sought. We study these fundamental problems and describe several algorithmic approaches and protocols for their solution. In addition, we compare the performance of the protocols under several selected settings. As applications of privacy-preserving computation are more and more commonly implemented in industrial systems, MMP and MaxP become important building blocks in privacy-preserving statistics, machine learning, auctions and other domains. One of the prominent advantages of the protocols that we present here is their simplicity. As they solve fundamental problems that are essential building blocks in various application scenarios, we believe that the presented solutions to those problems, and the comparison between them, will serve well future researchers and practitioners of secure distributed computing.

Strain-Controlled Electronic and Magnetic Properties of Janus Nitride MXene Monolayer MnCrNO2

Two-dimensional (2D) van der Waals (vdW) magnetic materials show potential for the advancement of high-density, energy-efficient electronic and spintronic applications in future memory and computation. Here, by using first-principles density functional theory (DFT) calculations, we predict a new 2D Janus nitride MXene MnCrNO2 monolayer. Our results suggest that the optimized MnCrNO2 monolayer possesses a hexagonal structure and exhibits good dynamical stability. The intrinsic monolayer MnCrNO2 exhibits semiconductive properties and adopts a ferromagnetic ground state with an out-of-plane easy axis. It can sustain strain effects within a wide range of strains from −10% to +8%, as indicated by the phonon dispersion spectra. Under the biaxial tensile strain, a remarkable decrease in the bandgap of the MnCrNO2 is induced, which is attributed to the distinct roles played by Mn and Cr in the VBM or CBM bands. Furthermore, when the compressive strain reaches approximately −8%, the magnetic anisotropy undergoes a transition from an out-of-plane easy axis to an in-plane easy axis. This change is mainly influenced by the efficient hybridization of the d orbitals, particularly in Mn atoms. Our study of the Janus MXene MnCrNO2 monolayer indicates its potential as a promising candidate for innovative electronic and spintronic devices; this potential is expected to create interest in its synthesis.

Monolith: Circuit-Friendly Hash Functions with New Nonlinear Layers for Fast and Constant-Time Implementations

Hash functions are a crucial component in incrementally verifiable computation (IVC) protocols and applications. Among those, recursive SNARKs and folding schemes require hash functions to be both fast in native CPU computations and compact in algebraic descriptions (constraints). However, neither SHA-2/3 nor newer algebraic constructions, such as Poseidon, achieve both requirements. In this work we overcome this problem in several steps. First, for certain prime field domains we propose a new design strategy called Kintsugi, which explains how to construct nonlinear layers of high algebraic degree which allow fast native implementations and at the same time also an efficient circuit description for zeroknowledge applications. Then we suggest another layer, based on the Feistel Type-3 scheme, and prove wide trail bounds for its combination with an MDS matrix. We propose a new permutation design named Monolith to be used as a sponge or compression function. It is the first arithmetization-oriented function with a native performance comparable to SHA3-256. At the same time, it outperforms Poseidon in a circuit using the Merkle tree prover in the Plonky2 framework. Contrary to previously proposed designs, Monolith also allows for efficient constant-time native implementations which mitigates the risk of side-channel attacks.

Programming Fast DNA Amplifier Circuits with Versatile Toehold Exchange Pathway.

DNA amplifier circuits establish powerful tools to dynamically control molecular assembly for computation, sensing, and biological applications. However, the slow reaction speed remains a major barrier to their practical utility. Here, diverse fast DNA amplifier circuits termed toehold exchange polymerization (TEP) and toehold exchange catalysis (TEC) using toehold exchange-mediated assembly as a fundamental mechanism are built. Both TEP and TEC with a duplex and a hairpin can respond within minutes to diverse nucleic acid inputs with high fidelity. In addition, the circuits can amplify live-cell signals for fluorescence imaging target RNA dynamics and discriminating different cell lines. Compared with existing DNA circuits that involve time scales of hours for transducing small signals, TEP and TEC exhibit much faster dynamics, simpler design, and comparable sensitivity. These features make TEP and TEC promising platforms to develop programmable nucleic acid tools and devices and to create fast sensing and processing systems, amenable to wide practical applications.

Volatility dynamics in energy and agriculture markets: An analysis of domestic and global uncertainty factors

PurposeThis study aims to explore the intricate relationship between uncertainty indicators and volatility of commodity futures, with a specific focus on agriculture and energy sectors.Design/methodology/approachThe authors analyse the volatility of Indian agriculture and energy futures using the GARCH-MIDAS model, taking into account different types of uncertainty factors. The evaluation of out-sample predictive capability involves the application of out-sample R-squared test and computation of various loss functions.FindingsThe research outcomes underscore the significant impact of diverse uncertainty factors such as domestic economic policy uncertainty (EPU), global EPU (GEPU), US EPU and geopolitical risk (GPR) on long-run volatility of Indian energy and agriculture (agri) futures. Additionally, the study demonstrates that GPR exhibits superior predictive capability for crude oil futures volatility, while domestic EPU stands out as an effective predictor for agri futures, particularly castor seed and guar gum.Practical implicationsThe study offers practical implications for market participants and policymakers to adopt a comprehensive perspective, incorporating diverse uncertainty factors, for informed decision-making and effective risk management in commodity markets.Originality/valueThe research makes an inaugural attempt to examine the impact of domestic and global uncertainty indicators on modelling and predicting volatility in energy and agri futures. The distinctive feature of considering an emerging market also adds a novel dimension to the research landscape.

A new generalized perspective to establish vortex beams

Vortex beams are powerful primitives for optical operations and communications. We propose general mathematical methods to establish new vortex beams and optimize existing vortex beams. Based on these methods, two new types of vortex beams are demonstrated theoretically and experimentally. The propagation characteristics of these vortex beams can be finely controlled through specific parameters. Additionally, influences of periodic discontinuities and orbital angular momentum of two vortex beams are analyzed. The innovative concept of beam modulation and the introduction of new vortex beams in this paper indicate significant potential for applications in particle trapping, spatial communication, and quantum computation.

A hybrid quantum computing pipeline for real world drug discovery

Quantum computing, with its superior computational capabilities compared to classical approaches, holds the potential to revolutionize numerous scientific domains, including pharmaceuticals. However, the application of quantum computing for drug discovery has primarily been limited to proof-of-concept studies, which often fail to capture the intricacies of real-world drug development challenges. In this study, we diverge from conventional investigations by developing a hybrid quantum computing pipeline tailored to address genuine drug design problems. Our approach underscores the application of quantum computation in drug discovery and propels it towards more scalable system. We specifically construct our versatile quantum computing pipeline to address two critical tasks in drug discovery: the precise determination of Gibbs free energy profiles for prodrug activation involving covalent bond cleavage, and the accurate simulation of covalent bond interactions. This work serves as a pioneering effort in benchmarking quantum computing against veritable scenarios encountered in drug design, especially the covalent bonding issue present in both of the case studies, thereby transitioning from theoretical models to tangible applications. Our results demonstrate the potential of a quantum computing pipeline for integration into real world drug design workflows.

Raman Sideband Cooling of Molecules in an Optical Tweezer Array to the 3D Motional Ground State

Ultracold polar molecules are promising for quantum information processing and searches for physics beyond the standard model. Laser cooling to ultracold temperatures is an established technique for trapped diatomic and triatomic molecules. Further cooling of the molecules to near the motional ground state is crucial for reducing various dephasings in quantum and precision applications. In this work, we demonstrate Raman sideband cooling (RSC) of CaF molecules in optical tweezers to near their motional ground state, with average motional occupation quantum numbers of n¯x=0.16(12), n¯y=0.17(17) (radial directions), and n¯z=0.22(16) (axial direction), and a 3-D motional-ground-state probability of 54±18% of the molecules that survive the RSC. This process paves the way to increase molecular coherence times in optical tweezers for robust quantum computation and simulation applications. Published by the American Physical Society 2024

Innovative Mathematical Insights through Artificial Intelligence (AI): Analysing Ramanujan Series and the Relationship between e and π\pi

This paper presents a comprehensive case study on the application of Artificial Intelligence (AI) in mathematics, focusing on the Ramanujan series and the intricate relationship between the mathematical constants e and π. The study explores how AI, particularly machine learning and pattern recognition techniques, can be harnessed to discover new mathematical series and patterns, thereby extending the pioneering work of the legendary mathematician Srinivasa Ramanujan. The paper begins with an overview of the Ramanujan series, illustrating their significance and applications in mathematical computations. It then delves into the specifics of AI methodologies employed to unearth new series for e and π, highlighting the algorithms and models used. Through detailed analysis and experimentation, the study demonstrates how AI can generate new series expansions for e and π, offering enhanced convergence rates and computational efficiencies. Furthermore, the paper examines the relationship between these two constants, providing insights into their interconnected nature through AI-discovered series and patterns. Practical applications of these new series in fields such as numerical methods, cryptography, and theoretical physics are also discussed. By showcasing the successful integration of AI in the realm of mathematical research, this case study underscores the potential of AI to revolutionize traditional mathematical approaches, fostering the discovery of new knowledge and the refinement of existing theories. The findings contribute to a deeper understanding of the interplay between e and π, reinforcing the profound impact of Ramanujan's work in modern mathematics and the transformative power of AI in advancing this legacy.

The application of evolutionary computation in generative adversarial networks (GANs): a systematic literature survey

As a subfield of deep learning (DL), generative adversarial networks (GANs) have produced impressive generative results by applying deep generative models to create synthetic data and by performing an adversarial training process. Nevertheless, numerous issues related to the instability of training need to be urgently addressed. Evolutionary computation (EC), using the corresponding paradigm of biological evolution, overcomes these problems and improves evolutionary-based GANs’ ability to deal with real-world applications. Therefore, this paper presents a systematic literature survey combining EC and GANs. First, the basic theories of GANs and EC are analyzed and summarized. Second, to provide readers with a comprehensive view, this paper outlines the recent advances in combining EC and GANs after detailed classification and introduces each of them. These classifications include evolutionary GANs and their variants, GANs with evolutionary strategies and differential evolution, GANs combined with neuroevolution, evolutionary GANs related to different optimization problems, and applications of evolutionary GANs. Detailed information on the evaluation metrics, network structures, and comparisons of these models is presented in several tables. Finally, future directions and possible perspectives for further development are discussed.

Electric-magnetic duality and Z2 symmetry enriched Abelian lattice gauge theory

Kitaev’s quantum double model is a lattice realization of Dijkgraaf–Witten topological quantum field theory. Its topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory. We investigate the Z2 symmetry enriched generalization of the model for the Abelian group in a categorical framework and present an explicit Hamiltonian construction. This model provides a lattice realization of the Z2 symmetry of the topological phase. We discuss in detail the categorical symmetry of the phase, for which the electric-magnetic (EM) duality symmetry is a special case. The aspects of symmetry defects are investigated using the G-crossed unitary braided fusion category. By determining the corresponding anyon condensation, the gapped boundaries and boundary-bulk duality are also investigated. In the last part, an explicit lattice realization of EM duality is discussed.

Enhancement of quantum entanglement between twin beams via a four-wave mixing process with double feedback

Two-port feedback has been theoretically studied and proved to be effective in enhancing the degree of entanglement of the output beams for a four-wave mixing process. Here, to further consider the loss effects and phase delays, we use a model that is closer to practical implementation. By reasonably tuning the feedback coefficients, we find that a higher degree of entanglement and higher power of the output beams can be achieved, and a loose requirement for phase-locking accuracy can be obtained. This scheme may have promising applications in practical quantum computation and quantum communication.

A Proportional-Integral-One Plus Double Derivative Controller-Based Fractional-Order Kepler Optimizer for Frequency Stability in Multi-Area Power Systems with Wind Integration

This study proposes an enhanced Kepler Optimization (EKO) algorithm, incorporating fractional-order components to develop a Proportional-Integral-First-Order Double Derivative (PI–(1+DD)) controller for frequency stability control in multi-area power systems with wind power integration. The fractional-order element facilitates efficient information and past experience sharing among participants, hence increasing the search efficiency of the EKO algorithm. Furthermore, a local escaping approach is included to improve the search process for avoiding local optimization. Applications were performed through comparisons with the 2020 IEEE Congress on Evolutionary Computation (CEC 2020) benchmark tests and applications in a two-area system, including thermal and wind power. In this regard, comparisons were implemented considering three different controllers of PI, PID, and PI–(1+DD) designs. The simulations show that the EKO algorithm demonstrates superior performance in optimizing load frequency control (LFC), significantly improving the stability of power systems with renewable energy systems (RES) integration.

Confidentially Compare Rational Numbers under the Malicious Model

<p>Secure multi-party computation is a hotspot in the cryptography field, and it is also a significant means to realize privacy computation. The Millionaires’ problem is the most fundamental problem among them, which is the basic module of secure multi-party computation protocols. Although there are many solutions to this problem, there are few anti-malicious adversarial protocols besides protocols based on Yao’s garbled circuit. Only a few solutions have low efficiency, and there is no protocol for rational numbers comparison under the malicious model, which restricts the solution of many secure multi-party computation problems. In this paper, the possible malicious behaviors are analyzed in the existing Millionaires’ problem protocols. These behaviors are discovered and taken precautions against through the triangle area formula, zero-knowledge proof, and cut-and-choose method, so the protocol of comparing confidentially rational numbers is proposed under the malicious model. And this paper adopts the real/ideal model paradigm to prove the security of the malicious model protocol. Efficiency analysis indicates that the proposed protocol is more effective than existing protocols. The protocol of rational numbers comparison under the malicious model is more suitable for the practical applications of secure multi-party computation, which has important theoretical and practical significance.</p> <p> </p>

Application of Evolutionary Computation to the Optimization of Biodiesel Mixtures Using a Nature-Inspired Adaptive Genetic Algorithm

The present research work introduces a novel mixture optimization methodology for biodiesel fuels using an Evolutionary Computation method inspired by biological evolution. Specifically, the optimal biodiesel composition is deduced from the application of a nature-inspired adaptive genetic algorithm that first examines percentages of the ingredients in the optimal mixtures. The innovative approach’s effectiveness lies in problem simulation with improvements in the evaluation of the specific function and the way to define and tune the genetic algorithm. Environmental imperatives in the era of climate change currently impose the optimized production of alternative environmentally friendly biofuels to replace fossil fuels. Biodiesel in particular, appears to be more attractive in recent years, as it originates from renewable bio-derived resources. The main ingredients of the specific biofuel mixture investigated in this research are diesel and biodiesel (100% from bioresources). The assessment of the new biodiesel examined was performed using a fitness function that estimated both the density and cost of the fuel. Beyond the evaluation criterion of cost, density also influences the suitability of this biofuel for commercial use and market sale. The outcomes from the modeling process can be beneficial in saving cost and time for new biodiesel production by using this novel decision-making tool in comparison with randomized laboratory experimentations.

Unbalanced penalization: a new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms

Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical applications such as the traveling salesman problem (TSP), the bin packing problem (BPP), or the knapsack problem (KP) have inequality constraints that require a particular cost function encoding. The common approach is the use of slack variables to represent the inequality constraints in the cost function. However, the use of slack variables considerably increases the number of qubits and operations required to solve these problems using quantum devices. In this work, we present an alternative method that does not require extra slack variables and consists of using an unbalanced penalization function to represent the inequality constraints in the QUBO. This function is characterized by larger penalization when the inequality constraint is not achieved than when it is. We evaluate our approach on the TSP, BPP, and KP, successfully encoding the optimal solution of the original optimization problem near the ground state cost Hamiltonian. Additionally, we employ D-Wave Advantage and D-Wave hybrid solvers to solve the BPP, surpassing the performance of the slack variables approach by achieving solutions for up to 29 items, whereas the slack variables approach only handles up to 11 items. This new approach can be used to solve combinatorial problems with inequality constraints with a reduced number of resources compared to the slack variables approach using quantum annealing or variational quantum algorithms.