Dimensional Sets Research Articles

On the propagation of regularity for solutions of the Zakharov–Kuznetsov equation

In this paper, we focus on the Zakharov–Kuznetsov (ZK) equation in the [Formula: see text]-dimensional setting with [Formula: see text] and investigate its smoothness properties. We extend the well-known regularity propagation phenomenon observed in the 2D and 3D cases, where the regularity of the initial data on certain half-spaces propagates with infinite speed, to the case where the regularity of the initial data is measured on a fractional scale. To achieve this, we introduce new localization formulas that enable us to describe the regularity of the solution on a specific class of subsets in Euclidean space. This work provides insights into the regularity behavior of solutions of the ZK equation in higher dimensions and with more general initial data.

Nonlinear viscoelastic model for time-dependent mechanical characterization of PMMA acrylic bone cements

Acrylic bone cement materials are widely used in prosthetic implants, orthopaedics and others trauma surgery. From the mechanical constitutive behaviour viewpoint, experimental analyses have provided ample evidence that such materials exhibit time-dependent properties. In this context, this work addresses the formulation of a nonlinear viscoelastic model for the behaviour of PMMA bone cements under compressive creep loading. Relying upon experimental data available for four PMMA bone cement types, a nonlinear Burgers-like rheological model is formulated and related parameters calibrated for the mechanical description of the time-dependent behaviour of these materials under isothermal conditions and one dimensional setting. The proposed model reveals relevant in reproducing both instantaneous and delayed properties of studied PMMA bone cements.

Neural network approximation of continuous functions in high dimensions with applications to inverse problems

The remarkable successes of neural networks in a huge variety of inverse problems has fueled their adoption in disciplines ranging from medical imaging to seismic analysis over the past decade. However, the high dimensionality of such inverse problems has simultaneously left current theory, which predicts that networks should scale exponentially in the dimension of the problem, unable to explain why the seemingly small networks used in these settings work as well as they do in practice. To reduce this gap between theory and practice, a general method for bounding the complexity required for a neural network to approximate a Hölder continuous function (as well as uniformly continuous functions that admit a specified modulus of continuity) defined on a high-dimensional set with a low-complexity structure is provided herein. The idea for the approach is based on the observation that the existence of a linear Johnson–Lindenstrauss embedding A∈Rd×D of a given high-dimensional set S⊂RD into a low dimensional cube [−M,M]d implies that for any Hölder (or uniformly) continuous function f:S→Rp, there exists a Hölder (or uniformly) continuous function g:[−M,M]d→Rp such that g(Ax)=f(x) for all x∈S. Hence, if one has a neural network which approximates g:[−M,M]d→Rp, then a layer can be added that implements the JL embedding A to obtain a neural network that approximates f:S→Rp. By pairing JL embedding results along with results on approximation of Hölder (or uniformly) continuous functions by neural networks, one then obtains results which bound the complexity required for a neural network to approximate Hölder (or uniformly) continuous functions on high dimensional sets. The end result is a general theoretical framework which can then be used to better explain the observed empirical successes of smaller networks in a wider variety of inverse problems than current theory allows.

Nonlinear model order reduction of resonant piezoelectric micro-actuators: An invariant manifold approach

This paper presents a novel derivation of the direct parametrisation method for invariant manifolds able to build simulation-free reduced-order models for nonlinear piezoelectric structures, with a particular emphasis on applications to Micro Electro Mechanical Systems. The constitutive model adopted accounts for the hysteretic and electrostrictive response of the piezoelectric material by resorting to the Landau-Devonshire theory of ferroelectrics. Results are validated with full-order simulations operated with a harmonic balance finite element method to highlight the reliability of the proposed reduction procedure. Numerical results show a remarkable gain in terms of computing time as a result of the dimensionality reduction process over low dimensional invariant sets. Results are also compared with experimental data to highlight the remarkable benefits of the proposed model order reduction technique.

Free boundary partial regularity in the thin obstacle problem

AbstractFor the thin obstacle problem in , , we prove that at all free boundary points, with the exception of a ‐dimensional set, the solution differs from its blow‐up by higher order corrections. This expansion entails a C1, 1‐type free boundary regularity result, up to a codimension 3 set.

Machine learning and the prediction of changes in profitability

AbstractThis study uses machine‐learning methods to predict next‐period change in profitability based on a model proposed by Penman and Zhang (2004, Working paper, Columbia University and University of California, Berkeley; “PZ”). We find that new machine‐learning methods predict out of sample substantially better than traditional regression methods and provide richer interpretations about the role and impact of different predictor variables through their nonlinear relationships and interaction effects. For example, our results contrast with previous research by showing that both components of the DuPont decomposition (change in profit margin and change in asset turnover) are informative of next‐period changes in profitability. Our results are robust across different performance metrics, alternative machine‐learning models, and software. Furthermore, an unconstrained machine‐learning model using a larger feature space could not significantly improve the performance of the PZ model. PZ variables alone accounted for most of the explanatory power of the unconstrained model, suggesting the PZ model is both well specified (in terms of feature selection) and robust in higher dimensional settings. With respect to the economic significance of this information, we find mixed results. The market appears to adjust its expectations more in line with the machine‐learning predictions relative to the PZ model but the portfolio returns are not significantly different.

Non-Gaussian Measures in Infinite Dimensional Spaces: the Gamma-Grey Noise

In the context of non-Gaussian analysis, Schneider [29] introduced grey noise measures, built upon Mittag-Leffler functions; analogously, grey Brownian motion and its generalizations were constructed (see, for example, [6, 7, 9, 27]). In this paper, we construct and study a new non-Gaussian measure, by means of the incomplete-gamma function (exploiting its complete monotonicity). We label this measure Gamma-grey noise and we prove, for it, the existence of Appell system. The related generalized processes, in the infinite dimensional setting, are also defined and, through the use of the Riemann-Liouville fractional operators, the (possibly tempered) Gamma-grey Brownian motion is consequently introduced. A number of different characterizations of these processes are also provided, together with the integro-differential equation satisfied by their transition densities. They allow to model anomalous diffusions, mimicking the procedures of classical stochastic calculus.

A Novel Clustering and Matrix Based Computation for Big Data Dimensionality Reduction and Classification

For higher dimensional or "Big Data (BD)" clustering and classification, the dimensions of documents have to be considered. The overhead of classifying methods might also be reduced by resolving the volumetric issue of documents. However, the dimensions of the shortened collection of documents might potentially generate noise and abnormalities. Previous noise and abnormality information removal strategies include several different approaches that have already been established throughout time. To increase classification accuracy, current classifications or new classification methods that has created to conduct classification, must deal with some of the most difficult issues in BD document categorization and clustering. Hence, the goals of this research are derived from the issues that can be solved only by expanding classification accuracy of classifiers. Superior clusters may also be achieved by using effective "Dimensionality Reduction (DR)". As the first step in this research, we introduce a unique DR approach that preserves word frequency in the document collection, allowing the classification algorithm to obtain improved (or) at least equal classification levels of accuracy with a lower dimensionality set of documents. When clustering "Word Patterns (WPs)" during "WP Clustering (WPC)", we imply a new WP "Similarity Function (SF)" for "Similarity Computation (SC)" to be used as part of WPC. DR of the document collection is accomplished with the use of information gained from various WP clusters. Finally, we provide "Similarity Measures" for SC of high dimensional texts and deliver SF for document classification and deliver SF for document classification. With assessment criteria like "Information-Ratio for Dimension-Reduction", "Accuracy", and "Recall", we discovered that the proposed method WP paired with SC (WP-SC) scaled extremely effectively to higher dimensional "Dataset’s (DS)" and surpasses the current technique AFO-MKSVM. According to the findings, the WP-SC approach produced more favorable outcomes than the LDA-SVM and AFO-MKSVM approaches.

Clarifying the link between psychopathologies and heart rate variability, and the sex differences: Can neuropsychological features serve as mediators?

BackgroundPatients with common mental disorders (depression, anxiety, and somatic symptoms) often exhibit lower heart rate variability (HRV) than healthy individuals. Under the hypothesis that disorder status affects cognitive function, we examined whether neuropsychological features can be mediators between psychopathologies and HRV and possible sex differences. MethodsWe recruited 359 individuals (aged 42.47 ± 12.23) with and without common mental disorders. Questionnaires were used to measure their psychopathologies. Eight tests from the Cambridge Neuropsychological Test Automated Battery were selected to measure neuropsychological functions. Resting-state HRV measurements were obtained for 5 min. The associations among these constructs were analyzed using multiple linear regression analysis and structural equation modelling. ResultsAmong women, Reaction Time (RTI, a task of psychomotor speed) indicator mediated the relationship between depression and low-frequency power (LF); Emotion Recognition Task (ERT, a task of emotional regulation) indicator mediated the relationship between health anxiety and high-frequency power (HF). Among men, Intra-Extra Dimensional Set Shift (IED, a task of shifting) indicator mediated the relationship between depression and LF; Match to Sample Visual Search (MTS, a task of selective attention) indicator mediated the relationship between health cognition and HF. The depression-RTI-LF pathway in women tended to lower HRV; whereas health anxiety-ERT-HF in women, depression-IED-LF and health cognition-MTS-HF in men tended to increase HRV. LimitationsPossible medication effects; not directly measuring brain activity; only gathering resting-state HRV. ConclusionOur findings support the notion that neuropsychological features mediate the relationship between psychopathologies and HRV, and that sex differences exist.

Artificial intelligence enabled Luong Attention and Hosmer Lemeshow Regression Window‐based attack detection in 6G

SummaryRegardless of the developments of networking and communication technologies, security is without exception a predominant feature to ensure network reliability. The future sixth‐generation (6G) network is anticipated to be carried out with artificial intelligence (AI) powered communication via machine learning (ML), post‐quantum cryptography, and so on. AI‐powered communication has been in recent years utilized in enhancing network traffic performance with respect to resource management, optimal frequency spectrum design, security, and latency. The studies of modern wireless communications and anticipated features of 6G networks revealed a prerequisite for designing a trustworthy attack detection mechanism. In this work, a method called, Luong Attention and Hosmer Lemeshow Regression Window‐based (LA‐HLRW) attack detection in 6G is proposed. Initially, with the raw Botnet Attack dataset obtained as input, preprocessing is performed to normalize network traffic features. Next, the dimensionality of network traffic feature of large‐scale network traffic data is reduced using the Luong Attention integrated with Long Short Term Memory (LSTM)‐based Feature extraction model. Finally, with the objective of classifying network traffic samples for attack detection in 6G, we analyze the low dimensional network traffic feature set produced by Luong Attention integrated with LSTM using the Hosmer Lemeshow Logistic Regression Window‐based Attack Detection model. Extensive experiments are performed with the Botnet Attack dataset to validate the efficiency of the proposed LA‐HLRW method by using different parameters such as attack detection accuracy, attack detection time, precision, and recall. The overall analysis of proposed LA‐HLRW results significantly reduced the attack detection time by 24%, and additionally improved attack detection accuracy, precision, and recall by 5%, 5%, and 6% as compared to existing attack detection methods respectively.

Variational Wasserstein Barycenters with C-cyclical Monotonicity Regularization

Wasserstein barycenter, built on the theory of Optimal Transport (OT), provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it is often intractable to precisely compute, especially for high dimensional and continuous settings. To alleviate this problem, we develop a novel regularization by using the fact that c-cyclical monotonicity is often necessary and sufficient conditions for optimality in OT problems, and incorporate it into the dual formulation of Wasserstein barycenters. For efficient computations, we adopt a variational distribution as the approximation of the true continuous barycenter, so as to frame the Wasserstein barycenters problem as an optimization problem with respect to variational parameters. Upon those ideas, we propose a novel end-to-end continuous approximation method, namely Variational Wasserstein Barycenters with c-Cyclical Monotonicity Regularization (VWB-CMR), given sample access to the input distributions. We show theoretical convergence analysis and demonstrate the superior performance of VWB-CMR on synthetic data and real applications of subset posterior aggregation.

From the distributions of times of interactions to preys and predators dynamical systems.

We consider a stochastic individual based model where each predator searches and then manipulates its prey or rests during random times. The time distributions may be non-exponential and density dependent. An age structure allows to describe these interactions and get a Markovian setting. The process is characterized by a measure-valued stochastic differential equation. We prove averaging results in this infinite dimensional setting and get the convergence of the slow-fast macroscopic prey predator process to a two dimensional dynamical system. We recover classical functional responses. We also get new forms arising in particular when births and deaths of predators are affected by the lack of food.

ParaLiNGAM: Parallel causal structure learning for linear non-Gaussian acyclic models

One of the key objectives in many fields in machine learning is to discover causal relationships among a set of variables from observational data. In linear non-Gaussian acyclic models (LiNGAM), it can be shown that the true underlying causal structure can be identified uniquely from merely observational data. The DirectLiNGAM algorithm is a well-known solution to learn the true causal structure in a high dimensional setting. DirectLiNGAM algorithm executes in a sequence of iterations and it performs a set of comparisons between pairs of variables in each iteration. Unfortunately, the runtime of this algorithm grows significantly as the number of variables increases. In this paper, we propose a parallel algorithm, called ParaLiNGAM, to learn casual structures based on DirectLiNGAM algorithm. We propose a threshold mechanism that can reduce the number of comparisons remarkably compared with the sequential solution. Moreover, in order to further reduce runtime, we employ a messaging mechanism between workers. We also present an implementation of ParaLiNGAM on GPU, considering hardware constraints. Experimental results on synthetic and real data show that our proposed solution outperforms DirectLiNGAM by a factor up to 4788X, and by a median of 2344X.

Polarization and Coherence in Mean Field Games Driven by Private and Social Utility

We study a mean field game in continuous time over a finite horizon, T, where the state of each agent is binary and where players base their strategic decisions on two, possibly competing, factors: the willingness to align with the majority (conformism) and the aspiration of sticking with the own type (stubbornness). We also consider a quadratic cost related to the rate at which a change in the state happens: changing opinion may be a costly operation. Depending on the parameters of the model, the game may have more than one Nash equilibrium, even though the corresponding N-player game does not. Moreover, it exhibits a very rich phase diagram, where polarized/unpolarized, coherent/incoherent equilibria may coexist, except for T small, where the equilibrium is always unique. We fully describe such phase diagram in closed form and provide a detailed numerical analysis of the N-player counterpart of the mean field game. In this finite dimensional setting, the equilibrium selected by the population of players is always coherent (favoring the subpopulation whose type is aligned with the initial condition), but it does not necessarily minimize the cost functional. Rather, it seems that, among the coherent ones, the equilibrium prevailing is the one that most benefits the underdog subpopulation forced to change opinion.

Can computerized cognitive training enhance executive functions in healthy young adults? A preliminary study

Computerized cognitive training (CCT) is a computer-based intervention that targets cognitive functioning that has become increasingly popular in the recent decade. We examined the effectiveness of RehaCom as a standard computerized cognitive training on the executive functions of healthy adults in this preliminary study. The study was a quasi-experimental study using a pretest-posttest experimental design without a control group. The participants included 10 healthy adults. The participants were evaluated before and after the intervention using the Trail Making Test (TMT), Intra-Extra Dimensional Set Shift (IED), and Stockings of Cambridge (SOC) computerized tasks. The subjects trained by RehaCom software for 45 minutes per day, one day per week, for a total of four sessions over one month. Data were analyzed in the SPSS software (version 26) using the paired t-test test. Results show significant enhancement in participants’ central executive functioning (p < 0.01), shifting (p<0.05), and planning (p<0.05). A computerized cognitive training program can improve cognitive functions of healthy adults.

Automated facial expression recognition using novel textural transformation

Facial expressions demonstrate the important information about our emotions and show the real intentions. In this study, a novel texture transformation method using graph structures is presented for facial expression recognition. Our proposed method consists of five steps. First the face image is segmented and resized. Then the proposed graph-based texture transformation is used as feature extractor. The exemplar feature extraction is performed using the proposed deep graph texture transformation. The extracted features are concatenated to obtain one dimensional feature set. This feature set is subjected to maximum pooling and principle component analysis methods to reduce the number of features. These reduced features are fed to classifiers and we have obtained the highest classification accuracy of 97.09% and 99.25% for JAFFE and TFEID datasets respectively Moreover, we have used CK + dataset to obtain comparison results and our textural transformation based model yielded 100% classification accuracy on the CK + dataset. The proposed method has the potential to be employed for security applications like counter terrorism, day care, residential security, ATM machine and voter verification.

The Modelwise Interpolation Property of Semantic Logics

In this paper we introduce the modelwise interpolation property of a logic that states that whenever \(\models\phi\to\psi\) holds for two formulas \(\phi\) and \(\psi\), then for every model \(\mathfrak{M}\) there is an interpolant formula \(\chi\) formulated in the intersection of the vocabularies of \(\phi\) and \(\psi\), such that \(\mathfrak{M}\models\phi\to\chi\) and \(\mathfrak{M}\models\chi\to\psi\), that is, the interpolant formula in Craig interpolation may vary from model to model. We compare the modelwise interpolation property with the standard Craig interpolation and with the local interpolation property by discussing examples, most notably the finite variable fragments of first order logic, and difference logic. As an application we connect the modelwise interpolation property with the local Beth definability, and we prove that the modelwise interpolation property of an algebraizable logic can be characterized by a weak form of the superamalgamation property of the class of algebras corresponding to the models of the logic.

Interactions of scores derived from two groups of variables: Alternating lasso regularization avoids overfitting and finds interpretable scores.

Regression models with interaction terms are common models for moderating relationships. When effects of several predictors from one group-for example, genetic variables-are potentially moderated by several predictors from another-for example, environmental variables-many interaction terms result. This complicates model interpretation, especially when coefficient signs point in different directions. By first forming a score for each group of predictors, the interaction model's dimension is severely reduced. The hierarchical score model is an elegant one-step approach: Score weights and regression model coefficients are estimated simultaneously by an alternating optimization (AO) algorithm. Especially in high dimensional settings, scores remain an effective technique to reduce interaction model dimension, and we propose regularization to ensure sparsity and interpretability of the score weights. A nontrivial extension of the original AO algorithm is presented, which adds a lasso penalty, resulting in the alternating lasso optimization algorithm (ALOA). The hierarchical score model with ALOA is an interpretable statistical learning technique for moderation in potentially high dimensional applications, and encompasses generalized linear models for the main interaction model. In addition to the lasso regularization, a screening procedure called regularization and residualization (RR) is proposed to avoid spurious interactions. ALOA tuning parameter choice and the RR screening procedure are investigated by simulations, and two illustrative applications to depression risk are provided. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Stabilitas Dimensi dan Setting Time Bahan Cetak Anatomis Kedokteran Gigi Dari Ekstrak Natrium Alginat Rumput Laut Merah (Kappaphycus alvarezii) Dari Desa Agel, Kecamatan Jangkar, Situbondo

Alginate impression material is important in dentistry. In its clinical application, setting time is still considered too fast, and the alginate impression material must have dimensional stability in accordance with ANSI / ADA standard specification no.18. Alginate impression material has a main component, namely sodium alginate which is produced from the seaweed extraction process. In Indonesia, there are several types of seaweed, one of which is the Kappaphycus alvarezii (K. alvarezii). The seaweed from the village of Agel Situbondo has the potential to be a source of sodium alginate and has antibacterial and antioxidant effects. The aim of this study to analyze the dimensional stability and setting time of the alginate printing material with sodium alginate extract of kappaphycus alvarezii seaweed. The study was conducted using laboratory experimental methods with post-test only control group design, there were 2 groups, namely the commercial alginate printing material control group, and the alginate printing material treatment group with sodium alginate extract from the acid method, then the FTIR test was carried out. Then the two groups were tested for setting time and dimensional stability. The results of the FTIR test of red seaweed extract showed an absorption peak that was identical to that of sodium alginate. The results of the setting time test significantly took longer for the red seaweed alginate impression material than the control group, while the dimensional stability showed the same results. Conclusion: The results of the setting time test showed that the treatment group had a longer setting time than the control group and both groups had dimensional stability according to the standard. The results of the setting time test showed that the treatment group had a longer setting time than the control group and both groups already had dimensional stability in accordance with the standard.

Relationship of insight to neurocognitive function and risk of recurrence in depression: A naturalistic follow-up study.

Major depressive disorder (MDD) is a highly recurrent mental illness accompanied by impairment of neurocognitive function. Lack of insight may affect patients' motivation to seek treatment, resulting in poor clinical outcomes. This study explores the relationship of insight to neurocognitive function and the risk of recurrence of depressive episodes in patients with MDD. Demographic, clinical variables, and neurocognitive function measured with Intra-Extra Dimensional Set Shift (IED) from the Cambridge Neuropsychological Test Automated Battery (CANTAB) were collected from 277 patients with MDD. Among them, 141 participants completed a follow-up visit within 1-5 years. Insight was measured using the 17-item Hamilton Depression Rating Scale (HAM-D). To explore the factors associated with recurrence, binary logistic regression models were used. Patients with MDD, without insight, had significantly higher total and factor scores (anxiety/somatization, weight, retardation, and sleep) on the HAM-D and worse performance in the neurocognition task, compared to those with insight. Furthermore, binary logistic regression revealed that insight and retardation can predict recurrence. Lack of insight is associated with recurrence and impaired cognitive flexibility in patients with MDD.