Linear Combination Research Articles

ON THE GAUSSIAN CURVATURE FUNCTIONAL IN THE CLASS OF SURFACES OF POSITIVE GAUSSIAN CURVATURE

The paper establishes the form of the Gaussian curvature functional defined on the class of infinitely differentiable horizontal surfaces of positive Gaussian curvature. With respect to admissible surfaces, it is assumed that they admit a global semi-geodetic parametrization. The paper proves that the first variation of the functional on the class of variations of admissible surfaces admitting connections between the coefficients of the first quadratic form and their geodesic lines similar to the axisymmetric case is determined by the Gaussian curvature of the varied surface. The considerations of the type are closely connected with the problems of the study of the equilibrium forms having one of the main curvatures sufficiently small. In this case, the classical Laplace formula fails. Thus, there appear a necessity to take into account more subtle processes leading to the adequate description of the equilibrium state of the two-phased system. In particular, it is quite natural to introduce into the study an intermediate layer consisting of the molecules of the two different phases, one of the Maxwell’s ideas. The calculations of the work spended by the pressure forces for the formation of intermediate layer leads us to the necessity to introduce Gauss functional into consideration. Linear combination of mean curvature and gaussian curvature functionals gives possibility to construct variational solution of generalized Laplace equation.

Entanglement and Mutual Information in Molecules: Comparing Localized and Delocalized Orbitals.

The use of the mutual information (MI) as a measure of the entanglement in quantum systems has gained a consensus in recent years, even if there is an ongoing effort to distinguish the classical and quantum contributions contained therein. This quantity has been first introduced in condensed matter physics, in particular, in studies based on the density matrix renormalization group method. This method has been successfully adapted to quantum chemistry problems, opening the way to compute MI also in molecular systems. A key aspect of this quantity is its dependence on the one-electron (orbital) basis set, even for wave functions that are invariant under unitary transformation of the orbitals. In this work, we investigate the role of the orbital basis set (delocalized or localized, following different strategies) for wave functions expressed as linear combinations of Slater determinants and we give the analytic expression for the MI for a few special cases. This study aims to improve the knowledge of the relationship between the characteristics of the chemical bond (considering a few paradigmatic molecules, H2, F2, N2, and short linear polyenes) and the properties of interest in the field of quantum information theory.

Using IT in Area Suitability Modeling To Plan Urban Areas: Case of Kabul City, Afghanistan

The goal of this work was to determine the optimal locations for urban growth in Kabul city using an integrated GIS-AHP model and Land Suitability Analysis (LSA). The study’s findings demonstrated that GIS-AHP is a useful approach for urban planning and ecological management. Maps were normalized using the pairwise comparison matrix technique using the generated criteria. Each model’s weights were created by comparing them according to their relative importance. Weight Age Average (OWA) and Weighted Linear Combination (WLC) were used to combine criteria weights and maps. To assess if a piece of land is suitable for urban development to determine which area was suitable for urban development, six thematic layers—slope, road, land use, river, settlement, and elevation—were used. AHP calculated their weighted scores based on the pairwise comparison. The linear combination approach was used to multiply each factor’s weight and score, and the outcome was then multiplied to make the urban development appropriate. 45.3 square kilometers of land were deemed highly suitable, 191.77 square kilometers were deemed fairly acceptable, 72.14 square kilometers were deemed marginally suitable, and 0.79 square kilometers were deemed unsuitable.

The Predictive Power of the Yield Spread Under the Veil of Time

Abstract This paper studies the sources of cyclical information delivered by the term spread for output growth predictability in the U.S. I use a wavelet-based time-frequency decomposition to decompose the predictive power of the yield spread across time scales, both in-sample and out-of-sample, over various forecast horizons. Spreads between interest rates on 10-year and 3-month Treasuries have a predictive ability for output growth that changes largely over different time scales. I find evidence of a negative correlation between the spread and future GDP growth for fluctuations with a frequency of 4 to 8 years per cycle. A linear combination among filtered yield spreads shows a sizable improvement in forecasting out-of-sample. The time-frequency decomposition is also used to propose an interpretation for the breakdown of in-sample predictability documented by Dotsey (1998) that arises after 1985. JEL classification numbers: C19, E43, E27. Keywords: Multiresolution analysis, Term structure, Predictability.

ANÁLISE MULTICRITÉRIO E GEOPROCESSAMENTO NA SELEÇÃO DE ÁREAS PARA ATERROS SANITÁRIOS NA ÁREA SUL DA RIDE/DF

Population growth and changes in consumption patterns are the main activities contributing to the increase in the generation of Urban Solid Waste (USW). With the significant increase in USW generation, these wastes, in most Brazilian cities, are disposed of in an entirely inadequate manner, such as in open-air dumps, putting the environment as a whole at risk. This situation is evident in the Integrated Region of the Federal District and Surrounding Areas (RIDE), a region consisting of 22 municipalities and the Federal District. This research aimed to select suitable areas for sanitary landfills in the southern part of RIDE/DF to assist in the management of USW in the region. For this, maps of land use and land cover on a multi-temporal scale were produced, and criteria were defined, which were weighted by experts through the application of questionnaires. The weights of the criteria were calculated using the Analytic Hierarchy Process (AHP) methodology. The criteria, represented as geographic data layers, were standardized and combined using the Weighted Linear Combination (WLC) method to produce the map of potential areas for sanitary landfills. Four alternatives for landfill areas were defined, and through multi-criteria methodology, alternative 1, located 27 km south of Luziânia, was selected. The results indicate that the proposed objectives were achieved, and the AHP method integrated with GIS provides a procedure for the precise location of areas for landfills that should meet the needs of all stakeholders.

Deep contextual bandits-based energy-efficient beamforming for integrated sensing and communication

In this paper, a transmit beamforming design is considered to jointly improve the communication and sensing functionalities in an integrated sensing and communication (ISAC) system, where a dual-functional base station (BS) serves a set of communication users (UEs) while sensing some potential targets (TGs). To this end, a multi-objective beamforming optimization problem is formulated to maximize the weighted linear combination of the communication energy efficiency (EE) and sensing beampattern gains. Using the normalized weighted sum method, the multi-objective problem is relaxed to a single-objective problem. For dealing with the non-convexity nature of the considered problem and the continuity of the beamforming space, a novel deep contextual bandits (DCB) scheme inspired by the soft actor-critic (S-DCB) method is proposed in which the channel state information of UEs is used as the context. Both the reward and policy functions are approximated to solve the problem. Simulation results indicate that the multi-objective function enables an adjustable trade-off between the communication and sensing functionalities. Besides, the effectiveness of the proposed S-DCB algorithm is verified through a comprehensive comparison with the state-of-the-art DCB-DDPG and the upper bound benchmarks.

Application of Z-number based fuzzy MCDM in solar power plant location selection problem in Spatial planning

In order to achieve sustainable energy consumption and development goals, it is of great importance to find suitable locations for the construction of solar power plants. In this study, Geographic Information System (GIS) and Z-Number iteration of Fuzzy Logarithm Additive Weights Methodology (F-LMAW), a recently adopted Multi-Criteria Decision Making Analysis (MCDA) technique, are used to identify the best locations for solar power plant construction in Mersin province. Nineteen criteria were selected for the study and their relative weights and usefulness in ranking the solar power plant locations were estimated. The Weighted Linear Combination (WLC) technique was used to determine the suitability index for solar power plant siting in the study area. According to the analysis made by taking into account the expert opinions for the site selection of solar power plants, the solar radiation criterion was the most important criterion with a weight value of 0,0664, while the distance from the river criterion was the least important criterion with a weight value of 0,0265. A potential suitability map for the solar power plant was produced with the suitability index values. According to the suitability index values, the study area exhibited suitability degrees for solar power plant siting ranging from “suitable (0,0038 %)” to “moderately suitable (0,0034 %)” and “very slightly suitable (0,0033 %)”. Silifke and Mut regions are considered as good locations for solar power plants in Mersin province. The robustness of the proposed technique was determined by sensitivity analysis.

Stacking based ensemble learning framework for identification of nitrotyrosine sites

Protein nitrotyrosine is an essential post-translational modification that results from the nitration of tyrosine amino acid residues. This modification is known to be associated with the regulation and characterization of several biological functions and diseases. Therefore, accurate identification of nitrotyrosine sites plays a significant role in the elucidating progress of associated biological signs. In this regard, we reported an accurate computational tool known as iNTyro-Stack for the identification of protein nitrotyrosine sites. iNTyro-Stack is a machine-learning model based on a stacking algorithm. The base classifiers in stacking are selected based on the highest performance. The feature map employed is a linear combination of the amino composition encoding schemes, including the composition of k-spaced amino acid pairs and tri-peptide composition. The recursive feature elimination technique is used for significant feature selection. The performance of the proposed method is evaluated using k-fold cross-validation and independent testing approaches. iNTyro-Stack achieved an accuracy of 86.3% and a Matthews correlation coefficient (MCC) of 72.6% in cross-validation. Its generalization capability was further validated on an imbalanced independent test set, where it attained an accuracy of 69.32%. iNTyro-Stack outperforms existing state-of-the-art methods across both evaluation techniques. The github repository is create to reproduce the method and results of iNTyro-Stack, accessible on: https://github.com/waleed551/iNTyro-Stack/

Healthful plant-based diets are negatively associated with the rate of biological aging: A national study based on US adults

Plant-based diets are recognized for their health benefits. However, evidence on the association between plant-based diet quality and aging in the US population is limited. This study aimed to investigate the association between different plant-based diet indices, phenotypic age acceleration (PhenoAgeAccel), and biological age acceleration (BioAgeAccel). We hypothesized that healthful plant-based diets would negatively affect PhenoAgeAccel and BioAgeAccel in US adults. The cross-sectional analysis included 22,363 participants, and information was obtained from the National Health and Nutrition Examination Survey database. The quality of plant-based diet was assessed using three indices: overall plant-based diet index (PDI), healthful PDI (hPDI), and unhealthful PDI (uPDI). Phenotypic age (PA) and biological age (BA) was calculated based on a linear combination of chronological age and 12 multi-system clinical chemistry biomarkers in accordance with the previously established method. PhenoAgeAccel and BioAgeAccel are the residuals of the PA and BA. Weighted linear regression analyses were performed to evaluate the relationships between PDI, hPDI and uPDI, and PhenoAgeAccel and BioAgeAccel. After adjusting for all covariates, we observed that a 10-unit higher PDI score was associated with 0.80 years lower PhenoAgeAccel (β: −0.80, 95% confidence interval [CI]: -0.94,-0.67), and 1.91 years lower BioAgeAccel (β: −1.91, 95% CI: -2.42,-1.40). A 10-unit higher hPDI score was associated with 0.83 years lower PhenoAgeAccel (β: −0.83, 95% CI: -0.96,-0.70), and 1.76 years lower BioAgeAccel (β: −1.76, 95% CI: -2.18,-1.34). Conversely, a 10-unit higher uPDI score was associated with 0.77 years higher PhenoAgeAccel (β: 0.77, 95% CI: 0.66,0.89) and 1.21 years higher BioAgeAccel (β: 1.21, 95% CI: 0.80,1.62). These findings suggest that US adults may be able to slow the aging process by increasing adherence to a healthy plant-based diet.

Scenario Superposition Method for Real‐Time Tsunami Prediction Using a Bayesian Approach

AbstractIn this study, we propose a scenario superposition method for real‐time tsunami wave prediction. In the offline phase, prior to actual tsunami occurrence, hypothetical tsunami scenarios are created, and their wave data are decomposed into spatial modes and scenario‐specific coefficients by the singular value decomposition. Then, once an actual tsunami event is observed, the proposed method executes an online phase, which is a novel contribution of this study. Specifically, the predicted waveform is represented by a linear combination of training scenarios consisting of precomputed tsunami simulation results. To make such a prediction, a set of weight parameters that allow for appropriate scenario superposition is identified by the Bayesian update process. At the same time, the probability distribution of the weight parameters is obtained as reference information regarding the reliability of the prediction. Then, the waveforms are predicted by superposition with the estimated weight parameters multiplied by the waveforms of the corresponding scenarios. To validate the performance and benefits of the proposed method, a series of synthetic experiments are performed for the Shikoku coastal region of Japan with the subduction zone of the Nankai Trough. All tsunami data are derived from numerical simulations and divided into a training data set used as scenario superposition components and a test data set for an unknown real event. The predicted waveforms at the synthetic gauges closest to the Shikoku Islands are compared to those obtained using our previous prediction method incorporating sequential Bayesian updating.

Data-driven FEM cluster-based basis reduction method for ultimate load-bearing capacity prediction of structures under variable loads

The structural ultimate load-bearing capacity plays an influential role in engineering applications. Melan’s static shakedown theorem offers a valuable approach for predicting the lower bound of shakedown loading factors and providing a safer shakedown domain when the structures are subjected to cyclic variable loads. However, the associated nonlinear mathematical programming is plagued by substantial computational expenses due to excessive design variables and constraints. Inspired by the data-driven FEM Cluster-based Analysis (FCA) [44–47] for predicting nonlinear effective properties of RVE of heterogeneous materials very efficiently, this paper introduces a novel FEM cluster-based basis reduction method to predict the shakedown domain of structures. Firstly, the FEM elements of discretized structures are grouped into several clusters using the elastic strain tensor under different load vertex cases, which differs from the orthogonal loading conditions for clustering RVE. In this way, similar mechanical behavior in each cluster of the structures is expected in future loading. Then, the cluster eigenstrain-driven algorithm is employed to construct the self-equilibrium stress (SES) basis vectors, which should satisfy the equilibrium equation and statical boundary condition. Furthermore, the essential time-independent beneficial residual stress in the static shakedown analysis is represented as a linear combination of the constructed SES basis vectors based on the basis reduction method, which can reduce a large number of time-independent residual stress to several linear combination coefficients. In addition, the reduced-order model (ROM) is constructed by the cluster SES, which are volume averaged stresses of the element SES basis vectors within each cluster. Based on the ROM, a constraint reduction strategy (CRS) is introduced to selectively remove stress constraints significantly below yield stress from the enormous element-wise yield constraint set. These innovations decrease the number of design variables and nonlinear constraints in the shakedown optimization, thus significantly enhancing computational efficiency. Several numerical examples illustrate the effectiveness and efficiency of the proposed shakedown analysis method of FCA.

Bayesian Inference for Long Memory Stochastic Volatility Models

We explore the application of integrated nested Laplace approximations for the Bayesian estimation of stochastic volatility models characterized by long memory. The logarithmic variance persistence in these models is represented by a Fractional Gaussian Noise process, which we approximate as a linear combination of independent first-order autoregressive processes, lending itself to a Gaussian Markov Random Field representation. Our results from Monte Carlo experiments indicate that this approach exhibits small sample properties akin to those of Markov Chain Monte Carlo estimators. Additionally, it offers the advantages of reduced computational complexity and the mitigation of posterior convergence issues. We employ this methodology to estimate volatility dependency patterns for both the SP&500 index and major cryptocurrencies. We thoroughly assess the in-sample fit and extend our analysis to the construction of out-of-sample forecasts. Furthermore, we propose multi-factor extensions and apply this method to estimate volatility measurements from high-frequency data, underscoring its exceptional computational efficiency. Our simulation results demonstrate that the INLA methodology achieves comparable accuracy to traditional MCMC methods for estimating latent parameters and volatilities in LMSV models. The proposed model extensions show strong in-sample fit and out-of-sample forecast performance, highlighting the versatility of the INLA approach. This method is particularly advantageous in high-frequency contexts, where the computational demands of traditional posterior simulations are often prohibitive.

Bayesian Fictitious Play in Oligopoly: The Case of Risk-Averse Agents

A number of learning models have been suggested to analyze the repeated interaction of boundedly rational agents competing in oligopolistic markets. The agents form a model of the environment that they are competing in, which includes the market demand and price formation process, as well as their expectations of their rivals’ actions. The agents update their model based on the observed output and price realizations and then choose their next period output levels according to an optimization criterion. In previous works, the global dynamics of price movement have been analyzed when risk-neutral agents maximize their expected rewards at each round. However, in many practical settings, agents may be concerned with the risk or uncertainty in their reward stream, in addition to the expected value of the future rewards. Learning in oligopoly models for the case of risk-averse agents has received much less attention. In this paper, we present a novel learning model that extends fictitious play learning to continuous strategy spaces where agents combine their prior beliefs with market price realizations in previous periods to learn the mean and the variance of the aggregate supply function of the rival firms in a Bayesian framework. Next, each firm maximizes a linear combination of the expected value of the profit and a penalty term for the variance of the returns. Specifically, each agent assumes that the aggregate supply of the remaining agents is sampled from a parametric distribution employing a normal-inverse gamma prior. We prove the convergence of the proposed dynamics and present simulation results to compare the proposed learning rule to the traditional best response dynamics.

Rare earth element (REE) speciation in municipal solid waste incineration ash

A robust and sustainable supply of rare earth elements (REE) is critically needed for clean-energy technologies, which has stimulated substantial interests in REE recovery from waste streams. Municipal solid waste incineration ash (MSWIA) was recently recognized as a potentially important REE resource, yet REE speciation in MSWIA remains poorly understood. This study employed synchrotron X-ray spectroscopy and microscopy techniques to elucidate the speciation of representative REE (Y, Ce, and Nd) in different MSWIA samples. Linear combination fitting of bulk X-ray absorption near edge structure (XANES) data indicated that Y-bearing Al/Fe oxides and phosphates are the primary Y-hosting phases. Micro-XANES of individual Y-containing particles identified by micro X-ray fluorescence (μXRF) mapping revealed notably different Y speciation at micro-scale from the bulk, consistent with the highly heterogeneous nature of MSWIA samples. The main REE-bearing phases in different size-fractionated MSWIA are similar: Y and Nd as oxides and xenotime/monazite, and Ce as apatite and monazite. Our results provide important insights for designing pre-screening processes (e.g., density separation) and optimizing extraction methods (e.g., pH, use of ligands) for cost-effective REE recovery from MSWIA.

Predicting and Explaining Assessment Center Judgments: A Cross‐Validated Behavioral Approach to Performance Judgments in Interpersonal Assessment Center Exercises

ABSTRACTAlthough Assessment Center (AC) role‐play assessments have received ample attention in past research, their reliance on actual behavioral information is still unclear. Uncovering the behavioral basis of AC role‐play assessments is, however, a prerequisite for the optimization of existing and the development of novel automated AC procedures. This work provides a first data‐driven benchmark for the behavioral prediction and explanation of AC performance judgments. We used machine learning models trained on behavioral cues (C = 36) to predict performance judgments in three interpersonal AC exercises from a real‐life high‐stakes AC (selection of medical students, N = 199). Three main findings emerged: First, behavioral prediction models showed substantial predictive performance and outperformed prediction models representing potential judgment biases. Comparisons with in‐sample results revealed overfitting of traditional approaches, highlighting the importance of out‐of‐sample evaluations. Second, we demonstrate that linear combinations of behavioral cues can be strong predictors of assessors' judgments. Third, we identified consistent exercise‐specific patterns of individual cues and cross‐exercise consistent behavioral patterns of behavioral dimensions and interpersonal strategies that were especially predictive of the assessors' judgments. We discuss implications for future research and practice.

Approximation of Time-Frequency Shift Equivariant Maps by Neural Networks

Based on finite-dimensional time-frequency analysis, we study the properties of time-frequency shift equivariant maps that are generally nonlinear. We first establish a one-to-one correspondence between Λ-equivariant maps and certain phase-homogeneous functions and also provide a reconstruction formula that expresses Λ-equivariant maps in terms of these phase-homogeneous functions, leading to a deeper understanding of the class of Λ-equivariant maps. Next, we consider the approximation of Λ-equivariant maps by neural networks. In the case where Λ is a cyclic subgroup of order N in ZN×ZN, we prove that every Λ-equivariant map can be approximated by a shallow neural network whose affine linear maps are simply linear combinations of time-frequency shifts by Λ. This aligns well with the proven suitability of convolutional neural networks (CNNs) in tasks requiring translation equivariance, particularly in image and signal processing applications.

Correction: Preimages under linear combinations of iterates of finite Blaschke products

Correction: Preimages under linear combinations of iterates of finite Blaschke products

Connectomes as holographic states

We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of states in Chern-Simons with properties similar to those of holographic states. While the holographic states are dual to classical geometries, these connectome states represent classical topologies, which satisfy a discrete analog of the Ryu-Takayanagi formula and characteristic inequalities for the entanglement entropy. Generic states are linear combinations of connectomes, and the theory also has nonperturbative states which are global spacetime defects formed by a large number of quantum fluctuations. Topological presentation of quantum states and emergence of topology from entanglement may be useful for building a generalization to geometry, that is quantum gravity. Thinking of further quantum gravity comparisons we discuss replica wormholes and conclude that similar objects exist beyond gravitational theories. The topological theory perspective suggests that the sum over all wormholes is always factorizable, even though the individual ones might not be.

Designing high-performance asymmetric and hybrid energy devices via merging supercapacitive/pseudopcapacitive and Li-ion battery type electrodes

We report a strategic development of asymmetric (supercapacitive–pseudocapacitive) and hybrid (supercapacitive/pseudocapacitive–battery) energy device architectures as generation–II electrochemical energy systems. We derived performance-potential estimation regarding the specific power, specific energy, and fast charge–discharge cyclic capability. Among the conceived group, pseudocapacitor–battery hybrid device is constructed with a high-rate intrinsic asymmetric pseudocapacitive (α − MnO2/rGO) and a high-capacity Li-ion intercalation battery type (po-nSi/rGO) electrodes. The experimental setup was developed to measure the current sharing between the two different active materials in a single device allowing us to distinguish the contribution of each active electrode material. The combined potentiostatic cyclic voltammograms and galvanostatic charge–discharge cycling profiles provided gravimetric capacity exceeding 600 F/g (or 180.5 mAh g−1 and ≥ 35mC/cm2) resulting in higher specific power and specific energy densities of 6.5 kW kg−1 and 33.5 Wh kg−1 with Coulombic efficiency (CE) and capacitance retention exceeding ≥ 85–90%, reported to date for full cell configuration, compared with symmetric or half-cell configurations (ca. 0.1 kW kg−1 and 13.7 Wh kg−1). Other systems studied provided specific energy ranged between 28 Wh kg−1 and 50 Wh kg−1 and specific power between 6.5 kW kg−1and 1.3 kW kg−1. Moreover, the behavior of such asymmetric hybrid devices represented a linear combination of the two active electrode material systems. The use of aqueous (and organic) electrolytes for asymmetric electrodes dramatically improved device performance and stability depending upon the electrode combination forming hybrid energy devices. We attribute the observed efficient performance of these hybrid devices induced by hybridized and emergent redox chemistries of merged electrode materials and dynamical processes at the electrode-electrolyte interfaces (intrinsic electroactivity, optimized double-layer and quantum capacitance) which play multiple roles. These energy devices are commercially relevant due to their potential viability in future hybrid electric vehicles, smart electric grids, electrocatalytic fuel production, space (micro-satellites), and miniaturized flexible electronic and wearable biomedical devices.

SC-VAE: Sparse coding-based variational autoencoder with learned ISTA

Learning rich data representations from unlabeled data is a key challenge towards applying deep learning algorithms in downstream tasks. Several variants of variational autoencoders (VAEs) have been proposed to learn compact data representations by encoding high-dimensional data in a lower dimensional space. Two main classes of VAEs methods may be distinguished depending on the characteristics of the meta-priors that are enforced in the representation learning step. The first class of methods derives a continuous encoding by assuming a static prior distribution in the latent space. The second class of methods learns instead a discrete latent representation using vector quantization (VQ) along with a codebook. However, both classes of methods suffer from certain challenges, which may lead to suboptimal image reconstruction results. The first class suffers from posterior collapse, whereas the second class suffers from codebook collapse. To address these challenges, we introduce a new VAE variant, termed sparse coding-based VAE with learned ISTA (SC-VAE), which integrates sparse coding within variational autoencoder framework. The proposed method learns sparse data representations that consist of a linear combination of a small number of predetermined orthogonal atoms. The sparse coding problem is solved using a learnable version of the iterative shrinkage thresholding algorithm (ISTA). Experiments on two image datasets demonstrate that our model achieves improved image reconstruction results compared to state-of-the-art methods. Moreover, we demonstrate that the use of learned sparse code vectors allows us to perform downstream tasks like image generation and unsupervised image segmentation through clustering image patches. The code is available at https://github.com/sotiraslab/SC-VAE.