Dimensional Space Research Articles

Evaluating the Predictive Modeling Performance of Kernel Trick SVM, Market Basket Analysis and Naive Bayes in Terms of Efficiency

Among many corresponding matters in predictive modeling, the efficiency and effectiveness of the several approaches are the most significant. This study delves into a comprehensive comparative analysis of three distinct methodologies: Finally, Kernel Trick Support Vector Machines (SVM), market basket analysis (MBA), and naive Bayes classifiers invoked. The research we aim at clears the advantages and benefits of these approaches in terms of providing the correct information, their accuracy, the complexity of their computation, and how much they are applicable in different domains. Kernel function SVMs that are acknowledged for their ability to tackle the problems of non-linear data transfer to a higher dimensional space, the essence of which is what to expect from them in complex classification are probed. The feature of their machine-based learning relied on making exact confusing decision boundaries detailed, with an analysis of different kernel functions that more the functionality. The performance of the Market Basket Analysis, a sophisticated tool that exposes the relationship between the provided data in transactions, helped me to discover a way of forecasting customer behavior. The technique enables paints suitable recommendation systems and leaders to make strategic business decisions using the purchasing habits it uncovers. The research owes its effectiveness to processing large volumes of data, looking for meaningful patterns, and issuing beneficial recommendations. Along with that, an attempt to understand a Bayes classifier of naive kind will be made, which belongs to a class of probabilistic models that are used largely because of their simplicity and efficiency. The author outlines the advantages and drawbacks of its assumption in terms of the attribute independence concept when putting it to use in different classifiers. The research scrutinizes their effectiveness in text categorization and image recognition as well as their ability to adapt to different tasks. In this way, the investigation aims to find out how to make the application more appropriate for various uses. The study contributes value to the competencies of readers who will be well informed about the accuracy, efficiency, and the type of data, domain, or problem for which a model is suitable for the decision on a particular model choice.

Global Solution and Stability of a Haptotaxis Mathematical Model for Complex MAP

A critical function of polymeric matrices in biological systems is to exert selective control over the transport of thousands of nanoparticulate species. Utilizing “third-party” molecular anchors to crosslink nanoparticulates to the matrix is an effective strategy, and a trapped nanoparticulate formed a desired complex MAP that is necessary to keep the nanoparticulate immobilized at any given time. In this paper, the global solution and stability of a parabolic–ordinary-parabolic haptotaxis system to complex MAP are studied. First, the existence of a local classical solution to system () has been observed using fixed point argument and parabolic Schauder estimates. Furthermore, some a priori estimates that can raise the regularity estimate of the solution for the relatively complicated first equation of system () from Lρ to L2ρ (ρ≥1) are given; then, the local classic solution can thus extend to the global classic solution when the space dimension N≤3. Lastly, by using various analytical methods, a threshold value ξ00(ξ00<0) is found, such that positive constant steady state (u*,v*,w*) becomes unstable when ξ<ξ00. Our results show that the haptotaxis plays a crucial role in determining the stability to the model (), that is, it can have a destabilizing effect.

A novel feature selection method based on quantum support vector machine

Feature selection is critical in machine learning to reduce dimensionality and improve model accuracy and efficiency. The exponential growth in feature space dimensionality for modern datasets directly results in ambiguous samples and redundant features, which can severely degrade classification accuracy. Quantum machine learning offers potential advantages for addressing this challenge. In this paper, we propose a novel method, quantum support vector machine feature selection (QSVMF), integrating quantum support vector machines with multi-objective genetic algorithm. QSVMF optimizes multiple simultaneous objectives: maximizing classification accuracy, minimizing selected features and quantum circuit costs, and reducing feature covariance. We apply QSVMF for feature selection on a breast cancer dataset, comparing the performance of QSVMF against classical approaches with the selected features. Experimental results show that QSVMF achieves superior performance. Furthermore, the Pareto front solutions of QSVMF enable analysis of accuracy versus feature set size trade-offs, identifying extremely sparse yet accurate feature subsets. We contextualize the biological relevance of the selected features in terms of known breast cancer biomarkers. This work highlights the potential of quantum-based feature selection to enhance machine learning efficiency and performance on complex real-world data.

Tidal turbine hydrofoil design and optimization based on deep learning

The optimal design of hydrofoils is critical to improve the hydrodynamic performance of the tidal turbine. However, the global optimization of hydrofoils is limited by the high dimensionality of the design space, which requires extensive computational fluid dynamics simulations. This paper proposes an interactive framework for hydrofoil design and optimization based on deep learning. Generative adversarial networks are used to parameterize the hydrofoil design, which automatically learns representations from existing hydrofoils and controls new hydrofoil generation using fewer variables to reduce optimization dimensions. Moreover, the surrogate model based on convolutional neural networks is constructed, which realizes the mapping of hydrofoil design and operating parameters to hydrodynamic performance parameters. The framework can generate a large number of smooth and realistic hydrofoils with three design variables and quickly predict the performance, enabling effective optimization design of hydrofoils. The results show that the optimized hydrofoil shapes have larger lift-to-drag ratios than those of the common hydrofoils. Furthermore, the optimized hydrofoil is applied to the design of 3D horizontal axis tidal turbine blades. The simulation results show that the framework is effective and stable, which can facilitate the design of tidal turbine rotors and provide hydrofoils with higher power coefficients.

A muti-modal feature fusion method based on deep learning for predicting immunotherapy response

Immune checkpoint therapy (ICT) has greatly improved the survival of cancer patients in the past few years, but only a small number of patients respond to ICT. To predict ICT response, we developed a multi-modal feature fusion model based on deep learning (MFMDL). This model utilizes graph neural networks to map gene-gene relationships in gene networks to low dimensional vector spaces, and then fuses biological pathway features and immune cell infiltration features to make robust predictions of ICT. We used five datasets to validate the predictive performance of the MFMDL. These five datasets span multiple types of cancer, including melanoma, lung cancer, and gastric cancer. We found that the prediction performance of multi-modal feature fusion model based on deep learning is superior to other traditional ICT biomarkers, such as ICT targets or tumor microenvironment-associated markers. In addition, we also conducted ablation experiments to demonstrate the necessity of fusing different modal features, which can improve the prediction accuracy of the model.

Demonstrating a new evaluation method on ReLU based Neural Networks for classification problems

Deep neural networks, which have proven to be effective methods to solve complex problems, can even be applied in decision systems controlling critical processes. However, in such applications the outcomes of the neural network must be checked if it we have a clear understanding regarding the operation of network at given input intervals. The most straightforward, though often computationally expensive approach for this checking process evaluates the network at discrete input points and estimates the expected outputs at the given interval. The present research aims to develop a novel approach that can identify in the case of specific input intervals whether the operation process and the output of a neural network can be considered as known or unknown. During the presented case study, we investigated the ReLU (Rectified Linear Unit) and Sigmoid activation functions, using the double moon and the Banknote Authentication classification problems for demonstration.Our method can be applied to identify certain input intervals where the given neural network cannot support critical decisions. The evaluation is performed based on a nonlinear system of equations and inequalities built on arbitrary continuous activation functions. To define the critical intervals of the input variables (i.e. where the decision-making system should not be relied on), those input variable combinations are identified which result in a non-expected output value. This inverse logic is intended to identify intervals of the input variables where the response of the system and the correct decision are not identical. The presented demonstration examples supported our assumption that the number of the neurons and the dimension of the decision space have a significant impact on the complexity of the evaluation process.

PAPAYA: A library for performance analysis of SQL-based RDF processing systems

Prescriptive Performance Analysis (PPA) has shown to be more useful than traditional descriptive and diagnostic analyses for making sense of Big Data (BD) frameworks’ performance. In practice, when processing large (RDF) graphs on top of relational BD systems, several design decisions emerge and cannot be decided automatically, e.g., the choice of the schema, the partitioning technique, and the storage formats. PPA, and in particular ranking functions, helps enable actionable insights on performance data, leading practitioners to an easier choice of the best way to deploy BD frameworks, especially for graph processing. However, the amount of experimental work required to implement PPA is still huge. In this paper, we present PAPAYA,11 https://github.com/DataSystemsGroupUT/PAPyA a library for implementing PPA that allows (1) preparing RDF graphs data for a processing pipeline over relational BD systems, (2) enables automatic ranking of the performance in a user-defined solution space of experimental dimensions; (3) allows user-defined flexible extensions in terms of systems to test and ranking methods. We showcase PAPAYA on a set of experiments based on the SparkSQL framework. PAPAYA simplifies the performance analytics of BD systems for processing large (RDF) graphs. We provide PAPAYA as a public open-source library under an MIT license that will be a catalyst for designing new research prescriptive analytical techniques for BD applications.

Considering product life cycle characteristics and industry background in environmental impact analysis and application: a case study of a television.

Life cycle assessment (LCA) is widely used to evaluate product's life cycle environmental impact and identify the environmental weaknesses. However, it is difficult for existing LCA software to perform flexible LCA analysis based on the product life cycle characteristics and industry background. Meanwhile, under the existing LCA research model, product designers and manufacturers are usually not LCA evaluators, resulting in a certain time gap between the evaluation results and product improvement. Designers with less experience in green design often find it difficult to identify high environmental impact links in products at different life cycle stages and product levels, and updated products are challenging to meet various environmental restrictions. This paper establishes a multi-module product life cycle analysis model that combines product industry background that includes basic information, assessment information, structural information, and restriction information to achieve the multi-scenario of product LCA in different dimensions in a typical domain. The calculated mechanism of the dynamic power emission factor is built according to the service time and space dimensions. The proposed method forms an integrated environmental performance evaluation of household appliance (EPEHA) system. A software assessment and an optimization method are proposed to improve the EPEHA system. The results of this study show that these proposed methods can improve the timeliness and diversity of results analysis of product LCA in the field of household appliances in China. The universal data exchange format and simple operation interface of the EPEHA system enable people related to the product to quickly understand the environmental impact of the product in different scenarios, even if they lack green design knowledge and professional software training.

Heat stress resilience assessment of urban form from physical space dimension: A case study of Guangdong-Hong Kong-Macao Greater Bay Area

Improving urban resilience is crucial to counteract rising high-temperature disasters. This study constructed a framework for a process-based heat stress resilience (HSR_phy) assessment from the urban physical space dimension. Based on the universal thermal climate index (UTCI), the Weather Research and Forecasting (WRF) model, and the Local Climate Zone (LCZ) map generated through WUDAPT, an HSR_phy evaluation method with high spatiotemporal accuracy is proposed. The Guangdong-Hong Kong-Macao Greater Bay Area (GBA) was studied for heat stress resilience patterns in July 2021. Boosted regression tree (BRT) models analyzed LCZ landscape patterns' impacts on HSR_phy. The results indicated that HSR_phy during the daytime was significantly lower than that at night. The HSR_phy of GBA showed the characteristics of low inland and high periphery. Significant differences in HSR_phy existed among most LCZs. LCZA, LCZC, and LCZ9 showed strong HSR_phy, whereas LCZ2, LCZ8, and LCZ7 were opposite. At the 1500 m scale, the Percentage of Landscape (PLAND), Landscape Shape Index (LSI), and Shannon's Diversity Index (SHDI) of LCZ4, LCZ5, and LCZ6 were the key factors affecting HSR_phy. Our research demonstrates how to quantify heat stress resilience and impact factors of urban physical spaces to provide a basis for developing climate-sensitive urban design strategies.

Amino acid-specific isotopes reveal changing five-dimensional niche segregation in Pacific seabirds over 50 years

Hutchison’s niche theory suggests that coexisting competing species occupy non-overlapping hypervolumes, which are theoretical spaces encompassing more than three dimensions, within an n-dimensional space. The analysis of multiple stable isotopes can be used to test these ideas where each isotope can be considered a dimension of niche space. These hypervolumes may change over time in response to variation in behaviour or habitat, within or among species, consequently changing the niche space itself. Here, we use isotopic values of carbon and nitrogen of ten amino acids, as well as sulphur isotopic values, to produce multi-isotope models to examine niche segregation among an assemblage of five coexisting seabird species (ancient murrelet Synthliboramphus antiquus, double-crested cormorant Phalacrocorax auritus, Leach’s storm-petrel Oceanodrama leucorhoa, rhinoceros auklet Cerorhinca monocerata, pelagic cormorant Phalacrocorax pelagicus) that inhabit coastal British Columbia. When only one or two isotope dimensions were considered, the five species overlapped considerably, but segregation increased in more dimensions, but often in complex ways. Thus, each of the five species occupied their own isotopic hypervolume (niche), but that became apparent only when factoring the increased information from sulphur and amino acid specific isotope values, rather than just relying on proxies of δ15N and δ13C alone. For cormorants, there was reduction of niche size for both species consistent with a decline in their dominant prey, Pacific herring Clupea pallasii, from 1970 to 2006. Consistent with niche theory, cormorant species showed segregation across time, with the double-crested demonstrating a marked change in diet in response to prey shifts in a higher dimensional space. In brief, incorporating multiple isotopes (sulfur, PC1 of δ15N [baselines], PC2 of δ15N [trophic position], PC1 and PC2 of δ13C) metrics allowed us to infer changes and differences in food web topology that were not apparent from classic carbon–nitrogen biplots.

On the limiting amplitude principle for the wave equation with variable coefficients

In this paper, we prove new results on the validity of the limiting amplitude principle (LAP) for the wave equation with nonconstant coefficients, not necessarily in divergence form. Under suitable assumptions on the coefficients and on the source term, we establish the LAP for space dimensions 2 and 3. This result is extended to one space dimension with an appropriate modification. We also quantify the LAP and thus provide estimates for the convergence of the time-domain solution to the frequency-domain solution. Our proofs are based on time-decay results of solutions of some auxiliary problems.

Intermittency analysis of charged particles generated in Xe-Xe~collisions at $\sqrt{s_{\rm{NN}}}$ = 5.44 TeV using the AMPT model

The multiplicity fluctuations are sensitive to QCD phase transition and to the presence of critical point in QCD phase diagram. At critical point a system undergoing phase transition is characterized by large fluctuations in the observables which is an important tool to understand the dynamics of particle production in heavy-ion interactions and phase changes. Multiplicity fluctuations of produced particles is an important observable to characterize the evolving system. Using scaling exponent obtained from the normalized factorial moments of the number of charged hadrons in the two dimensional (\eta,\phiη,ϕ) phase space, one can learn about the dynamics of system created in these collisions. Events generated using Xe-Xe collisions at $ = 5.44 $ TeV with string-melting (SM) version of the AMPT model are analyzed and the scaling exponent (\nu)(ν) for various p_TpT intervals is determined. It is observed that the calculated value of \nuν is larger than the universal value 1.304, as is obtained from Ginzburg-Landau theory for second order phase transition. Here we will also present the results of the dependence of the scaling exponent on the transverse momentum bin width.

A physics based machine learning model to characterize room temperature semiconductor detectors in 3D

Room temperature semiconductor radiation detectors (RTSD) for X-ray and γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document}-ray detection are vital tools for medical imaging, astrophysics and other applications. CdZnTe (CZT) has been the main RTSD for more than three decades with desired detection properties. In a typical pixelated configuration, CZT have electrodes on opposite ends. For advanced event reconstruction algorithms at sub-pixel level, detailed characterization of the RTSD is required in three dimensional (3D) space. However, 3D characterization of the material defects and charge transport properties in the sub-pixel regime is a labor intensive process with skilled manpower and novel experimental setups. Presently, state-of-art characterization is done over the bulk of the RTSD considering homogenous properties. In this paper, we propose a novel physics based machine learning (PBML) model to characterize the RTSD over a discretized sub-pixelated 3D volume which is assumed. Our novel approach is the first to characterize a full 3D charge transport model of the RTSD. In this work, we first discretize the RTSD between a pixelated electrodes spatially into 3 dimensions—x, y, and z. The resulting discretizations are termed as voxels in 3D space. In each voxel, the different physics based charge transport properties such as drift, trapping, detrapping and recombination of charges are modeled as trainable model weights. The drift of the charges considers second order non-linear motion which is observed in practice with the RTSDs. Based on the electron–hole pair injections as input to the PBML model, and signals at the electrodes, free and trapped charges (electrons and holes) as outputs of the model, the PBML model determines the trainable weights by backpropagating the loss function. The trained weights of the model represents one-to-one relation to that of the actual physical charge transport properties in a voxelized detector.

Large-N Principal Chiral Model in Arbitrary External Fields.

We report the explicit solution for the vacuum state of the two-dimensional SU(N) principal chiral model at large N for an arbitrary set of chemical potentials and any interaction strength, a unique result of such kind for an asymptotically free quantum field theory. The solution matches one-loop perturbative calculation at weak coupling, and in the opposite strong-coupling regime exhibits an emergent spacial dimension from the continuum limit of the SU(N) Dynkin diagram.

Symmetry, Music and Water

There is a deep link existing between symmetry and nature that may be best apprehended by using group theory. In physics, giving a symmetry group is entirely equivalent to fix natural laws (Noether’s theorem). Within such a framework, it follows that all fundamental mechanical laws may be given by defining a group of symmetry operations belonging to the Gal (3,1) symmetry group having ten generators (3 + 3 + 3 + 1 = 10). The move to special relativity amounts simply to substitute another group ISO (3,1) to Gal (3,1) and having the same number of generators. In both cases, one immediately perceives that we live in universe with 3 dimensions of space and 1 dimension of time. A further progress could be made by looking for the symmetry group that leaves Maxwell’s equations invariant. The answer to this fundamental question is the group ISO (4,2) ⊗U (2) ⊗U (2) characterized by 23 generators: 15 = 10 + 5 for the conformal group ISO(4,2), 4 for U(2) and hence 8 = 4 + 4 for the compact part U(2) ⊗U(2) that could be related to the existence of quantum physics besides relativity. As ISO (3,1) is a sub-group of ISO (4,2), the two numbers 4 and 2 suggests that, taking into account the existence of light besides matter, we live in an universe having 4 spacelike dimensions and 2 time-like dimensions. Here, it is proposed that, as music is characterized by a scale-invariant symmetry operation (transposition by octaves) and that as time may be perceived differently in shamanic trance for instance, the two “new” dimensions of our universe may be related to music and consciousness. Related to the fifth dimension of music, the notion of diapason linking physical frequencies to a musical note is revisited. It is thus proposed to adopt a new A4 = 429.62 Hz value based on universal physical constants of our universe and on the mass of the water molecule H₂O, "The most abundant heteronuclear molecule in the entire universe". Demonstration is done that this new diapason is superior to other diapasons based on frequencies of 440 Hz or even 432 Hz.

Generation of diffraction-free beam with winding trajectory based on metasurface holography

The diffraction-free beams with curved trajectories and shaped wavefronts have wide application prospects in many fields. This paper proposes the generation of diffraction-free beam with winding trajectory and spiral wavefront based on holographic metasurface. The holographic metasurface consists of rotated rectangular nanoholes and the winding trajectory for the generated diffraction-free beam may be in two or three dimensional space under the control of the rotated nanoholes. The multiple diffraction-free beams are exemplified and the performance of holographic metasurfaces are testified by the simulation and experiment results. The utilization of compact metasurface enables the flexible generation of the diffraction-free beams with complex trajectories and tailored wavefronts. It may bring more new applications of diffraction-free beams with on-demand trajectories and customized wavefronts.

Robust space-time finite element methods for parabolic distributed optimal control problems with energy regularization

As in our previous work (SINUM 59(2):660–674, 2021) we consider space-time tracking optimal control problems for linear parabolic initial boundary value problems that are given in the space-time cylinder Q=Ω×(0,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q = \\Omega \ imes (0,T)$$\\end{document}, and that are controlled by the right-hand side zϱ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_\\varrho $$\\end{document} from the Bochner space L2(0,T;H-1(Ω))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2(0,T;H^{-1}(\\Omega ))$$\\end{document}. So it is natural to replace the usual L2(Q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2(Q)$$\\end{document} norm regularization by the energy regularization in the L2(0,T;H-1(Ω))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2(0,T;H^{-1}(\\Omega ))$$\\end{document} norm. We derive new a priori estimates for the error ‖u~ϱh-u¯‖L2(Q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Vert \\widetilde{u}_{\\varrho h} - \\overline{u}\\Vert _{L^2(Q)}$$\\end{document} between the computed state u~ϱh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{u}_{\\varrho h}$$\\end{document} and the desired state u¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{u}$$\\end{document} in terms of the regularization parameter ϱ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varrho $$\\end{document} and the space-time finite element mesh size h, and depending on the regularity of the desired state u¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{u}$$\\end{document}. These new estimates lead to the optimal choice ϱ=h2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varrho = h^2$$\\end{document}. The approximate state u~ϱh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{u}_{\\varrho h}$$\\end{document} is computed by means of a space-time finite element method using piecewise linear and continuous basis functions on completely unstructured simplicial meshes for Q. The theoretical results are quantitatively illustrated by a series of numerical examples in two and three space dimensions. We also provide performance studies for different solvers.

Leveraging Temperature-Dependent (Electro)Chemical Kinetics for High-Throughput Flow Battery Characterization

The library of redox-active organics that are potential candidates for electrochemical energy storage in flow batteries is exceedingly vast, necessitating high-throughput characterization of molecular lifetimes. Demonstrated extremely stable chemistries require accurate yet rapid cell cycling tests, a demand often frustrated by time-denominated capacity fade mechanisms. We have developed a high-throughput setup for elevated temperature cycling of redox flow batteries, providing a new dimension in characterization parameter space to explore. We utilize it to evaluate capacity fade rates of aqueous redox-active organic molecules, as functions of temperature. We demonstrate Arrhenius-like behavior in the temporal capacity fade rates of multiple flow battery electrolytes, permitting extrapolation to lower operating temperatures. Collectively, these results highlight the importance of accelerated decomposition protocols to expedite the screening process of candidate molecules for long lifetime flow batteries.

Quantum projections on conceptual subspaces: A deeper dive into methodological challenges and opportunities.

In alignment with the distributional hypothesis of language, the work "Quantum Projections on Conceptual Subspaces" (Martínez-Mingo A, Jorge-Botana G, Martinez-Huertas JÁ, et al. Quantum projections on conceptual subspaces. Cogn Syst Res 2023; 82: 101154) proposed a methodology for generating conceptual subspaces from textual information based on previous work (Martinez-Mingo A, Jorge-Botana G and Olmos R. Quantum approach for similarity evaluation in LSA vector space models. 2020). These subspaces enable the utilization of the quantum model of similarity put forth by Pothos and Busemeyer (Pothos E, Busemeyer J. A quantum probability explanation for violations of symmetry in similarity judgments. In Proceedings of the annual meeting of the cognitive science society, 2011, Vol. 33, No. 33), allowing for the empirical examination of the violations of assumptions concerning symmetry and triangular inequality (Tversky A. Features of similarity. Psychol Rev 1977; 84: 327-352; Yearsley JM, Barque-Duran A, Scerrati E, et al. The triangle inequality constraint in similarity judgments. Prog Biophys Mol Biol 2017; 130: 26-32), as well as the diagnosticity effect (Tversky A. Features of similarity. Psychol Rev 1977; 84: 327-352; Yearsley JM, Pothos EM, Barque-Duran A, et al. Context effects in similarity judgments. J Exp Psychol Gen 2022; 151: 711-717), within a data-driven environment. These psychological biases, deeply studied by authors such as Tversky and Kahneman, inform us about the limitations of modeling psychological similarity measures using tools from classical geometry. This commentary aims to offer methodological clarifications, discuss theoretical and practical implications, and speculate on future directions in this field of research. Concretely, it aims to propose the use of different contours (conceptual or contextual) to generate the subspaces, which lead to subspaces of terms or contexts. Once these contours are defined, a differentiation is proposed between Aggregated Terms Subspaces (ATSs), Aggregated Contexts Subspaces (ACSs), and Aggregated Features Subspaces (AFSs) depending on whether we define the subspaces by grouping the terms or contexts within the contour, or from the latent dimensions of the semantic space obtained in the contour window. Finally, new data is provided on the violation of the triangular inequality assumption through the application of the quantum similarity model to ATSs.

Accelerated Double-Sketching Subspace Newton

This paper proposes a second-order stochastic algorithm called Accelerated Double-Sketching Subspace Newton (ADSSN) to solve large-scale optimization problems with high dimensional feature spaces and substantial sample sizes. The proposed ADSSN has two computational superiority. First, ADSSN achieves a fast local convergence rate by exploiting Nesterov’s acceleration technique. Second, by taking full advantage of the double sketching strategy, ADSSN provides a lower computational cost for each iteration than competitive approaches. Moreover, these advantages hold for actually all sketching techniques, which enables practitioners to design custom sketching methods for specific applications. Finally, numerical experiments are carried out to demonstrate the efficiency of ADSSN compared with accelerated gradient descent and two single sketching counterparts.