Binary Configurations Research Articles

Binary associative memory networks: A review of mathematical framework and capacity analysis

In recent years, heightened interest has been ignited in associative memory networks, largely attributed to their perceived equivalence with the attention mechanism, a fundamental component of the Transformer architecture. The opaque nature of deep neural networks, often characterized as “black boxes”, has intensified the pursuit of explainability, positioning associative memory networks as promising candidates for illuminating the inherent complexities of deep learning models. Despite their increasing prominence, the mathematical analysis of their capacity remains a significant research gap, which constitutes the central focus of this paper. To address this gap, we commence with a review of the mathematical framework underpinning associative memory networks, with particular emphasis on their binary configurations, drawing insights from the derivation of the dense associative memory model. Additionally, we review a systematic methodology for analyzing the capacity of binary associative memory networks, building upon established studies of dense associative memory networks. Utilizing this analytical framework, we derive the capacity of several prominent associative memory networks, including binary modern Hopfield networks and binary spherical Hopfield networks. Through comprehensive discussions and rigorous deductions, we aim to elucidate the characteristics of binary associative memory networks, thereby providing valuable insights and practical guidance for their effective application in real-world scenarios.

Quantum eigensolver on extension of optimized binary configurations

Quantum eigensolver on extension of optimized binary configurations

Adaptive Merkle trees for enhanced blockchain scalability

The scalability of blockchain technology remains a critical challenge, hindering its widespread adoption across various sectors. This study introduces an innovative approach to address this challenge by proposing the adaptive restructuring of Merkle trees, fundamental components of blockchain architecture responsible for ensuring data integrity and facilitating efficient verification processes. Unlike traditional static tree structures, our adaptive model dynamically adjusts the configuration of these trees based on usage patterns, significantly reducing the average path length required for verification and, consequently, the computational overhead associated with these processes. Through a comprehensive conceptual framework, we delineate the methodology for adaptive restructuring, encompassing both binary and non-binary tree configurations. This framework is validated through a series of detailed examples, demonstrating the practical feasibility and the efficiency gains achievable with our approach. To empirically assess the effectiveness of our proposed method, we conducted rigorous experiments using real-world data from the Ethereum blockchain. The results provide compelling evidence for the superiority of adaptive Merkle trees, with efficiency gains of up to 30% and higher observed during the initial stages of tree restructuring. Moreover, we present a comparative analysis with existing scalability solutions, highlighting the unique advantages of adaptive restructuring in terms of simplicity, security, and efficiency enhancement without introducing additional complexities or dependencies. This study’s implications extend beyond theoretical advancements, offering a scalable, secure, and efficient method for blockchain data verification that could facilitate broader adoption of blockchain technology in finance, supply chain management, and beyond. As the blockchain ecosystem continues to evolve, the principles, methodologies, and empirical findings outlined herein are poised to contribute significantly to its growth and maturity. Statement The findings of this article were presented at ETHDenver 2024 (https://www.ethdenver.com/), a leading innovation festival that champions the Web3 community’s role in shaping the future of blockchain technology. A video of our presentation can be found at https://www.youtube.com/watch?v=-jjYVCAQkNE. The original manuscript of this article is available on the preprint archive at https://arxiv.org/abs/2403.00406.

Wind Roche-lobe Overflow in Low-mass Binaries: Exploring the Origin of Rapidly Rotating Blue Lurkers

Wind Roche-lobe overflow (WRLOF) is a mass-transfer mechanism proposed by Mohamed and Podsiadlowski for stellar binaries wherein the wind acceleration zone of the donor star exceeds its Roche-lobe radius, allowing stellar wind material to be transferred to the accretor at enhanced rates. WRLOF may explain characteristics observed in blue lurkers and blue stragglers. While WRLOF has been implemented in rapid population synthesis codes, it has yet to be explored thoroughly in detailed binary models such as MESA (a 1D stellar evolution code), and over a wide range of initial binary configurations. We incorporate WRLOF accretion in MESA to investigate wide low-mass binaries at solar metallicity. We perform a parameter study over the initial orbital periods and stellar masses. In most of the models where we consider angular momentum transfer during accretion, the accretor is spun up to the critical (or breakup) rotation rate. Then we assume the star develops a boosted wind to efficiently reduce the angular momentum so that it could maintain subcritical rotation. Balanced by boosted wind loss, the accretor only gains ∼2% of its total mass, but can maintain a near-critical rotation rate during WRLOF. Notably, the mass-transfer efficiency is significantly smaller than in previous studies in which the rotation of the accretor is ignored. We compare our results to observational data of blue lurkers in M67 and find that the WRLOF mechanism can qualitatively explain the origin of their rapid rotation, their location on the H-R diagram, and their orbital periods.

Non-evolutionary effects on period change in Magellanic Cepheids

Context. Period change studies offer a novel way to probe the evolution and dynamics of Cepheids. While evolutionary period changes have been well studied both observationally and theoretically, non-evolutionary period changes lack a systematic and quantitative description. Here, we deal with one such aspect of non-evolutionary period changes related to a crucial property, namely, the binarity-based nature of a Cepheid. With the advent of long-term photometry surveys covering Magellanic fields, the census of classical Cepheids in binary (or multiple) systems outside the Milky Way is timely. This may have implications for crucial aspects such as the period-luminosity relationship calibrations and our understanding of the nature of Cepheid companions. Aims. The overall objective is to have a quantitative understanding of the full picture of non-evolutionary period changes in Cepheids to develop a formalism to disentangle it from the secular evolutionary period change. In the first paper in the series, we aim to conduct a systematic search for non-evolutionary period changes to look for Cepheids in likely binary configurations and quantify their incidence rates in the Magellanic Clouds. Methods. We collected more than a decade-long time-series photometry from the publicly available, Optical Gravitational Lensing Experiment (OGLE) survey, with more than 7200 Cepheids altogether from the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC). Our sample contains both fundamental-mode and first-overtone mode Cepheids. Then, we calculate d the observed minus calculated (O–C) diagrams to reveal the light-travel time effect (LTTE). Finally, we calculated the minimum companion masses of the Cepheids and compared them with the predictions from Cepheid population synthesis results. Results. In our search, out of an overall sample of more than 7200 Cepheids, we found 52 candidate Cepheid binary systems in the LMC (30 fundamental and 22 first-overtone mode) and 145 in the SMC (85 fundamental and 60 first-overtone mode). The majority of the sample is characterized by orbital periods of 2000–4000 d and eccentricities of 0.2–0.5. Moreover, we report two candidates in each galaxy with the Cepheid likely existing with a giant companion. The incidence rate ratio for SMC to LMC calculated from our sample is in agreement with binary Cepheid population synthesis predictions. Conclusions. In our attempt to quantify the non-evolutionary period change connected with the LTTE, our systematic search has enriched the Cepheid binary sample by a factor of about 2 in both galaxies. The future spectroscopic follow-up can confirm the binarity nature of our sample and constrain the orbital parameters.

Formation and non-covalent interactions of binary and ternary complexes based on β-casein, Lentinus edodes mycelia polysaccharide, and taxifolin

Polyphenols, polysaccharides, and proteins are essential nutrients and functional substances present in food, and when present together these components often interact with each other to influence their structure and function. Proteins and polysaccharides are also excellent carrier materials for polyphenols. In this context, this study investigated the non-covalent interactions between taxifolin (TAX), Lentinus edodes mycelia polysaccharide (LMP), and β-casein (β-CN). β-CN and LMP spontaneously formed nanocomplexes by hydrogen bonds and van der Waals forces. The quenching constant and binding constant were (1.94 ± 0.02) × 1013 L mol−1 s−1 and (3.22 ± 0.17) × 105 L mol−1 at 298 K, respectively. The altered conformation of β-CN, resulting from the binding to LMP, affected the interaction with TAX. LMP significantly enhanced the binding affinity of TAX and β-CN, but did not change the static quenching binding mode. The binding constant for β-CN-TAX was (3.96 ± 0.09) × 1013 L mol−1, and that for the interaction between TAX and β-CN-LMP was (32.06 ± 0.05) × 1013 L mol−1. In summary, β-CN-LMP nanocomplexes have great potential as a nanocarrier for polyphenols, and this study provides a theoretical foundation for the rational design of non-covalent complexes involving LMP and β-CN, both in binary and ternary configurations.

Bayesian Synthesis of Astrometric Wobble and Total Light Curves in Close Binary Supermassive Black Holes

We test the potential of Bayesian synthesis of upcoming multi-instrument data to extract orbital parameters and individual light curves of close binary supermassive black holes (CB-SMBH) with subparsec separations. Next-generation interferometers, will make possible the observation of astrometric wobbles in CB-SMBH. Combining them with periodic variable time-domain data from surveys like the Vera C. Rubin Legacy Survey of Space and Time, allows for more information on CB-SMBH candidates compared to standalone observational methods. Our method reliably determines binary parameters and component fluxes from binary total flux across long-term, intermediate, and short-term binary dynamics and observational configurations, assuming 10 annual observations, even in short period “q-accrete” objects. Expected CB-SMBH astrometric wobbles constructed from binary dynamical parameters might serve in refining observational strategies for CB-SMBH. Combination of inferred mass ratio, light curves of binary components, and observed photocenter wobbles can be a proxy for the activity states of CB-SMBH components.

Secular evolution of circumbinary 2-planet systems with isotropically varying masses

ABSTRACT We investigate the secular evolution of a four-body planetary system, where two planets move around a binary star configuration on quasi-elliptic orbits. It is assumed that the masses of all bodies can change isotropically at different rates and the bodies attract each other according to Newton’s law of universal gravitation. The purpose of this work is to investigate an influence of variability of the masses of the binary stars and their planets on the dynamical evolution of the planetary system. We consider the case of small eccentricities and inclinations of the bodies orbits and assume that their orbits do not intersect during evolution. Differential equations of the perturbed motion in the osculating analogues of canonical Poincaré elements were obtained in a general case of the many-body problem with variable masses in our previous work. Here we solve these equations numerically and investigate the secular evolution of some fictitious circumbinary 2-planet system under assumption that the two stars of the binary system lose their masses independently at different rates. In order to demonstrate the dynamical features of the equations we use the known parameters of the TOI-1338 system. Comparing the results of calculations in the cases of constant and variable masses, we show that the isotropic variability of the masses of bodies can influence substantially the secular perturbation of the orbital elements.

Dynamical Structures Associated with High-Order and Secondary Resonances in the Spin–Orbit Problem

In our solar system, spin–orbit resonances are common under Sun–planet, planet–satellite, and binary asteroid configurations. In this work, high-order and secondary spin–orbit resonances are investigated by taking numerical and analytical approaches. Poincaré sections as well as two types of dynamical maps are produced, showing that there are complicated structures in the phase space. To understand numerical structures, we adopt the theory of perturbative treatments to formulate resonant Hamiltonian for describing spin–orbit resonances. The results show that there is an excellent agreement between analytical and numerical structures. It is concluded that the main V-shape structure arising in the parameter space (θ̇,α) is sculpted by the synchronous primary resonance, those minute structures inside the V-shape region are dominated by secondary resonances and those structures outside the V-shape region are governed by high-order resonances. Finally, the analytical approach is applied to binary asteroid systems (65803) Didymos and (4383) Suruga to reveal their phase-space structures.

Compact Objects with Wolf–Rayet Companions: a Key Binary Configuration to Produce Gravitational Wave Mergers

The properties of binaries hosting a Wolf–Rayet star and a compact object (black hole or neutron star) suggest that such systems could be the progenitors of binary compact objects merging via gravitational wave emission. We used the population-synthesis code SEVN to explore this possibility and account for current uncertainties in theoretical models. According to our simulations, most (more than about 83%) binary compact object mergers were once compact objects with Wolf–Rayet companions. Binaries like Cyg X-3, the only candidate hosting a Wolf–Rayet and a compact object observed in the Milky Way, are more likely (approximately 70%–100%) to become binary compact object mergers if they host a black hole. This work indicates that further characterization of systems like Cyg X-3 can unveil the formation mechanisms of binary compact object mergers.

Stability of coorbital planets around binaries

In previous hydrodynamical simulations, we found a mechanism for nearly circular binary stars, such as Kepler-413, to trap two planets in a stable 1:1 resonance. Therefore, the stability of coorbital configurations becomes a relevant question for planet formation around binary stars. For this work, we investigated the coorbital planet stability using a Kepler-413 analogue as an example and then expanded the parameters to study a general n-body stability of planet pairs in eccentric horseshoe orbits around binaries. The stability was tested by evolving the planet orbits for 105 binary periods with varying initial semi-major axes and planet eccentricities. The unstable region of a single circumbinary planet is used as a comparison to the investigated coorbital configurations in this work. We confirm previous findings on the stability of single planets and find a first order linear relation between the orbit eccentricity ep and pericentre to identify stable orbits for various binary configurations. Such a linear relation is also found for the stability of 1:1 resonant planets around binaries. Stable orbits for eccentric horseshoe configurations exist with a pericentre closer than seven binary separations and, in the case of Kepler-413, the pericentre of the first stable orbit can be approximated by rc,peri = (2.90 ep + 2.46) abin.

Synergistic doping with Ag, CdO, and ZnO to overcome electron-hole recombination in TiO2 photocatalysis for effective water photo splitting reaction.

This manuscript is dedicated to a comprehensive exploration of the multifaceted challenge of fast electron-hole recombination in titanium dioxide photocatalysis, with a primary focus on its critical role in advancing the field of water photo splitting. To address this challenge, three prominent approaches-Schottky barriers, Z-scheme systems, and type II heterojunctions-were rigorously investigated for their potential to ameliorate TiO2's photocatalytic performance toward water photo splitting. Three distinct dopants-silver, cadmium oxide, and zinc oxide-were strategically employed. This research also delved into the dynamic interplay between these dopants, analyzing the synergetic effects that arise from binary and tertiary doping configurations. The results concluded that incorporation of Ag, CdO, and ZnO dopants effectively countered the fast electron-hole recombination problem in TiO2 NPs. Ag emerged as a critical contributor at higher temperatures, significantly enhancing photocatalytic performance. The photocatalytic system exhibited a departure from Arrhenius behavior, with an optimal temperature of 40°C. Binary doping systems, particularly those combining CdO and ZnO, demonstrated exceptional photocatalytic activity at lower temperatures. However, the ternary doping configuration involving Ag, CdO, and ZnO proved to be the most promising, surpassing many functional materials. In sum, this study offers valuable insights into how Schottky barriers, Z-scheme systems, and type II heterojunctions, in conjunction with specific dopants, can overcome the electron-hole recombination challenge in TiO2-based photocatalysis. The results underscore the potential of the proposed ternary doping system to revolutionize photocatalytic water splitting for efficient green hydrogen production, significantly advancing the field's understanding and potential for sustainable energy applications.

Machine Learning-Aided High-Throughput First-Principles Calculations to Predict the Formation Energy of μ Phase.

The μ phase is a type of hard and brittle constituent that exists in high-temperature alloys. The formation energy is a crucial thermochemical datum, and the accurate calculation of the formation energy of the μ phase contributes to the material design of high-temperature alloys. Traditional first-principles calculations demand significant computational time and resources. In this study, an innovative machine learning (ML)-based approach to accurately predict the formation energy of the μ phase is proposed. This approach involves the utilization of six algorithms and two model evaluation methods to construct the ML models. Leveraging a comprehensive data set containing 1036 binary configurations of the μ phase, the model trained using a 10-fold cross-validation technique, and the multilayer perceptron (MLP) algorithm achieves a mean absolute error (MAE) of 23.906 meV/atom. To validate its generalization performance, the trained model is further validated on 900 ternary configurations, resulting in an MAE of 32.754 meV/atom. Compared with solely using traditional first-principles calculations, our approach significantly reduces the computational time by at least 52%. Moreover, the ML model exhibits exceptional accuracy in predicting the lattice parameters of the μ phase. The MAE values for the a and c parameters are 0.024 and 0.214 Å, respectively, corresponding to low error rates of only 0.479 and 0.578%. Additionally, the ML model was utilized to accurately predict the formation energy of all of the possible ternary configurations. To enhance accessibility to the formation energy data of the μ phase, a user-friendly graphical user interface (GUI) was developed, ensuring convenient usability for researchers and practitioners.

Dynamical Evolution of White Dwarfs in Triples in the Era of Gaia

The Gaia mission has detected many white dwarfs (WDs) in binary and triple configurations, and while observations suggest that triple-stellar systems are common in our Galaxy, not much attention was devoted to WDs in triples. For stability reasons, these triples must have hierarchical configurations, i.e., two stars are on a tight orbit (the inner binary), with the third companion on a wider orbit about the inner binary. In such a system, the two orbits torque each other via the eccentric Kozai–Lidov mechanism, which can alter the orbital configuration of the inner binary. We simulate thousands of triple-stellar systems for over 10 Gyr, tracking gravitational interactions, tides, general relativity, and stellar evolution up to their WD fate. As demonstrated here, three-body dynamics coupled with stellar evolution is a critical channel to form tight WD binaries or merge a WD binary. Among these triples, we explore their manifestations as cataclysmic variables, Type Ia supernovae, and gravitational-wave events. The simulated systems are then compared to a sample of WD triples selected from the Gaia catalog. We find that including the effect of mass-loss-induced kicks is crucial for producing a distribution of the inner binary–tertiary separations that is consistent with Gaia observations. Lastly, we leverage this consistency to estimate that, at minimum, 30% of solar-type stars in the local 200 pc were born in triples.

Double generative network (DGNet) pipeline for structure-property relation of digital composites

Deep learning's fast and accurate inference between material configurations and properties has been used to design digital composites with superior mechanical properties. However, initial training sets cannot explore a vast design space with astronomical numbers of possible combinations, and most DL methods cannot guarantee predictive power in unobserved domains that may contain optimal configurations. Active learning-based gradual DNN model update schemes were implemented, but this increased computational costs. We propose a single-shot training pipeline to predict stress/strain distribution and stiffness over configuration space far from the initial training set. Predicting a composite's load response requires predicting its stress/strain field. Two autoencoders and a cGAN predict high-resolution stress/strain fields from grid-averaged local fields inferred from binary digital composite configurations. Our pipeline accurately predicts the high-resolution stress/strain field distribution in the unseen volume fraction (VF) domain or for composites with configurations very different from the initial training set. The framework can predict high-resolution fields in many physical phenomena and design composite materials for engineering applications.

The C/N ratio from FUV spectroscopy as a constraint on evolution of the dwarf nova HS 0218 + 3229

ABSTRACT White dwarfs that accrete from non-degenerate companions show anomalous carbon and nitrogen abundances in the photospheres of their stellar components have been postulated to be descendants of supersoft X-ray binaries. Measuring the carbon-to-nitrogen abundance ratio may provide constraints on their past evolution. We fit far-ultraviolet spectroscopy of the cataclysmic variable HS 0218 + 3229 taken with the Cosmic Origins Spectrograph using Markov chain Monte Carlo methods, and found the carbon-to-nitrogen ratio is about one tenth of the Solar value $(\rm{\log \mathrm{[C/N]}}=-0.56\pm 0.15)$. We also provide estimates of the silicon and aluminium abundances, and upper limits for iron and oxygen. Using the parameters we derived for HS 0218 + 3229 we reconstruct its past. We calculated a grid of mesa models and implemented Gaussian process fits in order to determine its most likely initial binary configuration. We found that an initial mass of the donor of $M_{\rm donor;i}=0.90-0.98,\rm{\mathrm{M}_{\odot }}$ and an initial orbital period of Porb; i = 2.88 d (Porb; i = 3.12–3.16 d) for an assumed initial white dwarf mass of $\rm{M_{\mathrm{WD}}}_\mathrm{;i}=0.83\, \rm{\mathrm{M}_{\odot }}$$(\rm{M_{\mathrm{WD}}}_{\rm ;i}=0.60\, \rm{\mathrm{M}_{\odot }})$ can replicate the measured parameters. The low mass ratio, $M_{\rm donor;i} / \rm{M_{\mathrm{WD}}}_{\rm ;i} =1.08-1.18\, (1.5-1.63)$, suggests that the system did not go through a phase of hydrogen-burning on the white dwarf’s surface. However, we can not exclude a phase of thermal time-scale mass transfer in the past. We predict that HS 0218 + 3229 will evolve below the ≃ 76.2 ± 1 min period minimum for normal cataclysmic variables.

The Management of Natural Disasters in Cinema: The Movie “2012”

Nature offers many opportunities but also poses many risks. Opportunities offered by nature are characterized as petroleum resources, natural resources, or energy resources. People must deal with natural disasters (earthquakes, tsunamis, volcanic eruptions, floods, hurricanes, avalanche, landslide, erosion etc.). Education is critical to introduce these disasters and raise public awareness. Movies are an appropriate medium for promoting disaster education and raising public awareness. Cinema is used to communicate messages or meanings. Movies are a powerful tool for educating people about what to do before, during, and after a disaster. Through signifiers and discourses, movies can teach people how to cooperate with the government during disasters and how to manage them. This study focused on the movie "2012," which depicts more than one natural disaster. The movie was selected using purposive sampling. We chose this movie because we think that its visual, auditory, and textual components can show people what they should do before, during, and after disasters and how they can effectively manage them. We analyzed the disaster-related signs in the movie using the method of semiotic analysis based on Roland Barthes' binary relation configuration of denotation and connotation. The auditory indicators in the movie are supported by discourse analysis.

Heat transfer to proximal cylinders in hypersonic flow

Uncontrolled atmospheric entry of meteors, satellites, and spacecraft components often leads to their partial or complete demise. In this destructive process, driven by hypersonic ablation, reentry objects fragment, interact, and alter each other's aerothermal environment. The effect of these interactions on the heat transfer to the fragments has not been investigated, despite the heat transfer's importance in hypersonic ablation and reentry demise. This study focuses on the numerical investigation of heat transfer to proximal circular cylinders in a thermochemically frozen flow and in two dimensions. First, binary body configurations at Mach numbers 2, 4, and 8 revealed that the heat load and peak heat transfer can be augmented for either or both proximal bodies by +20% to −90% of an isolated body. Second, different clusters of five proximal bodies showed that the heat load to any given body can range from +40% to −90% of an isolated body. Moreover, the average heat load in a cluster is found to vary between +20% and −60% of an isolated body. Intuitively, clusters which are thin in the direction perpendicular to free-stream velocity and long in the direction parallel to the free-stream velocity have their cluster-averaged heat load reduced. In contrast, thick and thin clusters, in directions perpendicular and parallel to the free-stream velocity, are subject to an increased cluster-averaged heat load.

Programming metastable transition sequences in digital mechanical materials

The realization of unconventional computing methods in soft matter has inspired the creation of mechanological systems capable of processing information. These systems often utilize bistable mechanisms that serve as mechanically abstracted bits to perform digital logic operations. Yet, the input of such operations often requires manual control of complex cyclic loading to reach a desired configuration. This research presents a method to design digital mechanical materials that can enter a programmable sequence of metastable configurations through simple displacement-controlled inputs. Interactions between serially connected bistable units enable the transition and reset behavior of mechanical bits. An analytical model using the principle of minimum total potential energy of a single bit is presented to articulate systematic ways to tune the critical force thresholds and displacements of metastable transition sequences. This work elucidates how the application of a prescribed displacement allows for novel resetting behavior that enables simultaneous transitions of multiple bits. By combining the principles of deterministic transition sequences and mechanical computing, a mechanical analog to digital conversion (ADC) material system is introduced that digitizes a continuous force stimulus into binary configurations that perform computations within the mechanical material based on the applied load. The mechanical ADC establishes a foundation for the integration of environmental sensing, information processing, and response in a soft material system.

Polarization-insensitive liquid crystal Fresnel lens based on self-assembly polymer gravels and chiral dopant.

A polarization-insensitive liquid crystal (LC) Fresnel lens is developed with binary LC configurations of 90°-twisted nematic (TN) and vertically-aligned (VA) domains in the adjacent zones. A LC mixture comprised of nematic host, photopolymer and chiral material is initially filled into the VA cell with orthogonal rubbing treatment. After the ultraviolet irradiation on the filled LC cell through a photomask with Fresnel zone plate pattern, the interactions among orthogonal rubbing treatment, self-assembly polymer gravels, and chiral material induce the 90°-TN structure in the odd zones, whereas the initial VA structures are maintained in the even zones. The fabricated LC Fresnel lens with binary configuration emerges a maximum diffraction efficiency of around 35% at a voltage of 2.3 V, close to the theoretical diffraction limit of around 41%. The diffractive focus of the LC Fresnel lens is polarization-insensitive at the voltage above 2 V. When the voltage reaches 10 V, the diffractive focus vanishes. The numerical calculation confirms that the polarization-insensitive property appears in the primary focus of the LC Fresnel lens. This work reports a simple method to develop a highly efficient, polarization-insensitive, and electrically tunable LC Fresnel lens which is favorable for imaging system.