Binary Field Research Articles

Electromagnetic fields in compact binaries: Post-Newtonian wave generation and application to double white dwarfs systems

Electromagnetic fields in compact binaries: Post-Newtonian wave generation and application to double white dwarfs systems

A Prime-Order Group with Complete Formulas from Even-Order Elliptic Curves

This paper describes a generic methodology for obtaining unified, and then complete formulas for a prime-order group abstraction homomorphic to a subgroup of an elliptic curve with even order. The method is applicable to any curve with even order, in finite fields of both even and odd characteristic; it is most efficient on curves with order equal to 2 modulo 4, dubbed "double-odd curves". In large characteristic fields, we obtain doubling formulas with cost as low as 1M + 5S, and the resulting group allows building schemes such as signatures that outperform existing fast solutions, e.g. Ed25519. In binary fields, the obtained formulas are not only complete but also faster than previously known incomplete formulas; we can sign and verify in as low as 18k and 27k cycles on x86 CPUs, respectively.

Image Segmentation and Classification Fields Are Generated Using Binary Random Fields Based on Planar Graph and Neighborhood Spanning Tree

Image analysis plays a pivotal role in computer vision, with image segmentation and classification being fundamental tasks in this domain. This abstract presents a novel approach to image processing that leverages Binary Random Fields (BRF) with a foundation in planar graphs and neighborhood spanning trees. This innovative methodology seeks to enhance the accuracy and efficiency of image segmentation and classification, addressing key challenges in computer vision applications. Binary Random Fields (BRF) is probabilistic graphical models that have proven effective in capturing spatial dependencies and contextual information within images. Our proposed method extends the utility of BRF by incorporating planar graph theory and neighborhood spanning trees to refine the segmentation and classification processes. Planar graphs offer a structured representation of image data, preserving topological relationships among pixels, while neighborhood spanning trees provide a hierarchical framework for modeling image regions

Augmented LT codes over binary extension fields with increased ratio of full‐degree columns

AbstractThis letter proposes an augmented scheme of LT codes to improve the decoding success rate. The method involves substituting the 1‐s in full‐degree columns of the generator matrix of conventional LT codes with binary extension field elements and simultaneously increasing the ratio of full‐degree columns in the ideal soliton distribution. For non‐full‐degree columns, we retain the nonzero elements as 1‐s in the conventional LT codes generator matrix to preserve computational efficiency. Compared to conventional LT codes, the proposed method enhances the linear independence of the generator matrix, leading to a higher decoding success rate with minimal data packets. Experimental results demonstrate the effectiveness of the method at improving the performance of LT codes, with close to 100% decoding success rate achieved with around 5% data redundancy.

Topology Optimization Method of Stamping Structures Based on the Directional Density Field.

The stamping process produces thin-walled structures that, in general, have uniform wall thickness and no enclosed cavity. However, it is difficult to satisfy the above geometric requirements with the current density-based topology optimization method, since configuring the related geometric constraints is challenging. In order to solve this problem, a topology optimization method for stamping structures based on a directional density field is proposed. Specifically, the directional density field is developed to enable the adding and removing of materials only along the stamping direction, so as to avoid internal voids and concave features. The geometric control for uniform wall thickness is realized by tuning the truncation threshold of the Heaviside projection that processes the directional density field into the 0-1 binary field. At the same time, a calibrated filter radius of the truncation thresholds will facilitate the drawing angle control of the stamping ribs. The effectiveness of the established method has been verified by a number of numerical case studies. Results show that the proposed method can perform topology optimization for stamping structures with tunable uniform thickness and drawing angle control of the ribs. No internal voids or undercuts appear in the results. The results also disclose that a constant truncation threshold increment does not guarantee uniform wall thickness, and varying the threshold increments through surface offset and polynomial fitting is necessary.

Explaining heatwaves with machine learning

AbstractHeatwaves are known to arise from the interplay between large‐scale climate variability, synoptic weather patterns, and regional to local‐scale surface processes. Though recent research has made important progress for each individual contributing factor, ways to properly incorporate multiple or all of them in a unified analysis are still lacking. In this study, we consider a wide range of possible predictor variables from the ERA5 Reanalysis version 5 and ask how much information on heatwave occurrence in Europe can be learned from each of them. To simplify the problem, we first adapt the recently developed logistic principal component analysis to the task of compressing large binary heatwave fields to a small number of interpretable principal components. The relationships between heatwaves and various climate variables can then be learned by a neural network. Starting from the simple notion that the importance of a variable is given by its impact on the performance of our statistical model, we arrive naturally at the definition of Shapley values. Classic results of game theory show that this is the only fair way of distributing the overall success of a model among its inputs. We find a nonlinear model that explains 70% of reduced heatwave variability. The biggest individual contribution (27% of the 70%) comes from upper level geopotential; top‐level soil moisture is in second place (15%). Beyond this decomposition, Shapley interaction values enable us to quantify overlapping information and positive synergies between all pairs of predictors.

Coded Caching for Dense-user Combination Network in Binary Field

Coded Caching for Dense-user Combination Network in Binary Field

Analysis of the self-consistency of nucleation in the diffuse interface limit of binary alloy phase field models

This paper examines the process of nucleation in phase field (PF) models, with the aim of elucidating how the use of diffuse interfaces often employed for quantitative modelling of solidification affects nucleation rates and distribution statistics in relation to the predictions of classical nucleation theory. Nucleation is simulated through the use of noise in a quantitative binary alloy PF model using different interface widths. Our results reveal that the rate of nucleation in the PF model is found to be strongly dependent on the scale of the interface width and the numerical discretization, but that careful control of these quantities offers the possibility of a consistent interpretation of nucleation rate. The paper ends by assessing some of the practical merits of seeded versus noise-induced nucleation in PF modelling in the diffuse-interface limit, while also emphasizing how nucleation in this limit is fundamentally flawed from a quantitative perspective.

Comparative Analysis of Genetic and Greedy Algorithm for Optimal Drone Flight Route Planning in Agriculture

In this study, the performance of the Genetic Algorithm (GA) in optimizing the agricultural drone flight route was compared with the Greedy Algorithm, revealing that GA produce routes that are, on average, 17.44 % more efficient. This efficiency, measured over 500 generations in a static field model, suggests substantial potential for saving resources and time in agricultural operations. Despite the effectiveness of the GA, its computational intensity limits real-time field applications, but offers advantages in offline route planning for pre-mapped areas. A t-test between flight lengths created by the algorithms highlighted a significant difference, with a p-value of approximately 7.18×10−9, indicating the GA's superior performance. Future research should aim to bridge the gap between the simplified binary field model used in simulations and the complexities of real-world agricultural landscapes to improve the practical deployment of GAs in drone route optimization.

Binary spatial random field reconstruction from non-Gaussian inhomogeneous time-series observations

We develop a new model for spatial random field reconstruction of a binary-valued spatial phenomenon. In our model, sensors are deployed in a wireless sensor network across a large geographical region. Each sensor measures a non-Gaussian inhomogeneous temporal process which depends on the spatial phenomenon. Two types of sensors are employed: one collects point observations at specific time points, while the other collects integral observations over time intervals. Subsequently, the sensors transmit these time-series observations to a Fusion Center (FC), and the FC infers the spatial phenomenon from these observations. We show that the resulting posterior predictive distribution is intractable and develop a tractable two-step procedure to perform inference. Firstly, we develop algorithms to perform approximate Likelihood Ratio Tests on the time-series observations, compressing them to a single bit for both point sensors and integral sensors. Secondly, once the compressed observations are transmitted to the FC, we utilize a Spatial Best Linear Unbiased Estimator (S-BLUE) to reconstruct the binary spatial random field at any desired spatial location. The performance of the proposed approach is studied using simulation. We further illustrate the effectiveness of our method using a weather dataset from the National Environment Agency (NEA) of Singapore with fields including temperature and relative humidity.

Power Efficient Implementation of ECC Using LCSLA Based Dual Field Vedic Multiplier

The Elliptic Curve Cryptographic (ECC) technique is employed for security standards such as Security Key Management (SKM), digital signature, data authentication and so on. The ECC technique is capable of sequential and parallel mode processes through a unified design. It is used for both equally binary fields and prime fields of cryptosystems. The DMM structure has been developed using CSA. This adder requires a greater amount of Full Adder circuits, which occupy more area. To overcome this problem, this paper discusses four different methods, such as DMM-Optimized Carry Look Ahead Adder, DMM-Optimized Carry Bypass Adder, DMM-Look up Table Carry Select Adder, and Dual Field Vedic Multiplier – LCSLA, which is used to increase the performance of the ECC. The parameters like power utilization, time delay information, and hardware area overhead are analyzed and compared with existing methods. Among those four methods, the DVM-LCSLA method gave better results in FPGA and ASIC performances.

Comparative study of homogenization techniques for evaluating the bearing capacity of bimsoils under shallow foundations

Bimsoils, characterized by discrete blocks within a finer-grained matrix, pose challenges in evaluating the bearing capacity of shallow foundations due to their spatial variability. To address this, a binary random field coupled with a Finite-Element model is used to simulate the variability of bimsoils. This study focuses on investigating the effect of the blocks spatial fraction (γ), the isotropic and anisotropic spatial correlations, and the undrained shear strength (cu) ratio between the matrix and the blocks. The results reveal that the coefficients of variation (CV) for the bearing capacity (qu), at a given γ, reach nearly 20% due to the diverse spatial configurations. This dispersion is attributed to the development of distinct failure mechanisms. However, optimizing the local average area used to evaluate γ can help reduce these CV values. The average qu for a given γ can be accurately determined using the Bruggeman symmetric effective medium (BEM) equation, ensuring safe design compared to traditional homogenization techniques. The BEM equation considers γ and the cu ratio, providing an accurate estimation of bearing capacity for an equivalent homogeneous model suitable for probabilistic analyses.

An Optimized Flexible Accelerator for Elliptic Curve Point Multiplication over NIST Binary Fields

This article proposes a flexible hardware accelerator optimized from a throughput and area point of view for the computationally intensive part of elliptic curve cryptography. The target binary fields, defined by the National Institute of Standards and Technology, are GF(2163), GF(2233), GF(2283), GF(2409), and GF(2571). For the optimization of throughput, the proposed accelerator employs a digit-parallel multiplier. The size of the digit is 41 bits. The proposed accelerator has reused the multiplication and squaring circuit for area optimization to compute modular inversions. Flexibility is included using three additional buffers on top of the proposed accelerator architecture to load different input parameters. Finally, a dedicated controller is used to optimize control signal handling. The architecture is modeled using Verilog and implemented up to the post-place-and-route level on a Xilinx Virtex-7 field-programmable gate array. The area utilization of our accelerator in slices is 1479, 1998, 2573, 3271, and 4469 for m=163 to 571. The time needed to perform one-point multiplication is 7.15, 10.60, 13.26, 20.96, and 30.42 μs. Similarly, the throughput over area figures for the same key lengths are 94.56, 47.21, 29.30, 14.58, and 7.35. Consequently, achieved results and a comprehensive performance comparison show the suitability of the proposed design for constrained environments that demand throughput/area-efficient implementations.

A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions.

This article presents a new hybrid method (combining search based methods and direct construction methods) to generate all involutory maximum distance separable (MDS) matrices over . The proposed method reduces the search space complexity at the level of , where n represents the number of all invertible matrices over to be searched for. Hence, this enables us to generate all involutory MDS matrices over and . After applying global optimization technique that supports higher Exclusive-OR (XOR) gates (e.g., XOR3, XOR4) to the generated matrices, to the best of our knowledge, we generate the lightest involutory/non-involutory MDS matrices known over , and in terms of XOR count. In this context, we present new involutory MDS matrices over , and , which can be implemented by 13 XOR operations with depth 5, 25 XOR operations with depth 5 and 42 XOR operations with depth 4, respectively. Finally, we denote a new property of Hadamard matrix, i.e., (involutory and MDS) Hadamard matrix form is, in fact, a representative matrix form that can be used to generate a small subset of all involutory MDS matrices, where k > 1. For k = 1, Hadamard matrix form can be used to generate all involutory MDS matrices.

An Efficient Audio Encryption Scheme Based on Elliptic Curve over Finite Fields

Elliptic curve (EC) based cryptographic systems are more trustworthy than the currently used cryptographic approaches since they require less computational work while providing good security. This paper shows how to use an EC to make a good cryptosystem for encrypting digital audio. As a preliminary step, the system uses an EC of a particular type over a binary extension field to distort the digital audio pixel position. It reduces the inter-correlation between pixels in the original audio, making the system resistant to statistical attacks. In creating confusion in the data, an EC over a binary extension field is used to make a different number of substitution boxes (S-boxes). The suggested design employs a unique curve that relies on efficient EC arithmetic operations in the diffusion module. As a result, it generates high-quality pseudo-random numbers (PRNs) and achieves optimal diffusion in encrypted audio files with less processing work. Audio files of various sizes and kinds can all be encrypted using the provided algorithm. Moreover, the results show that this method effectively protects many kinds of audio recordings and is more resistant to statistical and differential attacks.

A New Text Encryption Scheme Suitable for Combating Sniffing Attacks in IoT Applications via Non-supersingular Elliptic Curves over Binary Extension Fields

Several research works propose the use of Elliptic Curve Cryptography (ECC) to provide security for the Internet of Things (IoT) and cloud computing due to its shorter key requirement of approximately 160-571 bits vs. 1,024-15,360 bits of the others whilst achieving the same level of security. As a result, several ECC based text encryption schemes have been proposed in recent times. However, due to the mathematical foundations behind some of these schemes, there is the need for improvement to make them efficiently suitable for applications targeting IoT platforms. In addition, many of the existing schemes are either limited to some languages and/or use lookup tables which increase their computational overheads in terms of storage and processing. Against this background that this paper proposes a new ECC based text encryption scheme using efficient elliptic curve arithmetic to reduce the computational overheads. The scheme resists the major forms of sniffing attack in software implementation of ECC-based schemes. A test implementation proves that a very high key sensitivity is also achieved.

Gravitational Redshift Detection from the Magnetic White Dwarf Harbored in RX J1712.6–2414

Gravitational redshift is a fundamental parameter that allows us to determine the mass-to-radius ratio of compact stellar objects, such as black holes, neutron stars, and white dwarfs (WDs). In the X-ray spectra of the close binary system, RX J1712.6−2414, obtained from the Chandra High Energy Transmission Grating observation, we detected significant redshifts for characteristic X-rays emitted from hydrogen-like magnesium, silicon (ΔE/E rest ∼ 7 × 10−4), and sulfur (ΔE/E rest ∼ 15 × 10−4) ions, which are over the instrumental absolute energy accuracy (ΔE/E rest ∼ 3.3 × 10−4). Considering some possible factors, such as Doppler shifts associated with the plasma flow, systemic velocity, and optical depth, we concluded that the major contributor to the observed redshift is the gravitational redshift of the WD harbored in the binary system, which is the first gravitational redshift detection from a magnetic WD. Moreover, the gravitational redshift provides us with a new method of WD mass measurement by invoking the plasma-flow theory with strong magnetic fields in close binaries. Regardless of large uncertainty, our new method estimated the WD mass to be M WD > 0.9 M ⊙.

Experimental sandbox tracer tests to characterize a two-facies aquifer via an ensemble smoother

Estimating aquifer properties and their spatial variability is the most challenging part of groundwater flow and transport simulations. In this work, an ensemble Kalman-based method, the ensemble smoother with multiple data assimilation (ES-MDA), is applied to infer the characteristics of a binary field by means of tracer test data collected in an experimental sandbox. Two different approaches are compared: the first one aims at estimating the hydraulic conductivity over the whole field assuming that the rest of the hydraulic and transport parameters are known by applying the standard ES-MDA method; the second one couples the ES-MDA with a truncated Gaussian model to simultaneously estimate the spatial distribution of two geological lithotypes and their main hydraulic and transport properties. Both procedures are tested following a fully parameterized approach and a pilot point approach. A synthetic case that mimics the sandbox experiment was developed to test the capability of the proposed methods and find out their optimal configurations to be used for the real case. The results show that the ES-MDA coupled with a truncated Gaussian model outperforms the standard ES-MDA and it reproduces well the binary field and the aquifer properties also in the presence of large measurement errors. The fully parametrized and pilot point approaches lead to comparable solutions, with less computation time required by the pilot point approach.

Electromagnetic fields in compact binaries: A post-Newtonian approach

Electromagnetic fields in compact binaries: A post-Newtonian approach

Advanced Genetic Programming vs. State-of-the-Art AutoML in Imbalanced Binary Classification

The objective of this article is to provide a comparative analysis of two novel genetic programming (GP) techniques, differentiable Cartesian genetic programming for artificial neural networks (DCGPANN) and geometric semantic genetic programming (GSGP), with state-of-the-art automated machine learning (AutoML) tools, namely Auto-Keras, Auto-PyTorch and Auto-Sklearn. While all these techniques are compared to several baseline algorithms upon their introduction, research still lacks direct comparisons between them, especially of the GP approaches with state-of-the-art AutoML. This study intends to fill this gap in order to analyze the true potential of GP for AutoML. The performances of the different tools are assessed by applying them to 20 benchmark datasets of the imbalanced binary classification field, thus an area that is a frequent and challenging problem. The tools are compared across the four categories average performance, maximum performance, standard deviation within performance, and generalization ability, whereby the metrics F1-score, G-mean, and AUC are used for evaluation. The analysis finds that the GP techniques, while unable to completely outperform state-of-the-art AutoML, are indeed already a very competitive alternative. Therefore, these advanced GP tools prove that they are able to provide a new and promising approach for practitioners developing machine learning (ML) models. Doi: 10.28991/ESJ-2023-07-04-021 Full Text: PDF