Dimensional Space Research Articles

Structure-preserving semi-convex-splitting numerical scheme for a Cahn–Hilliard cross-diffusion system in lymphangiogenesis

A fully discrete semi-convex-splitting finite-element scheme with stabilization for a Cahn–Hilliard cross-diffusion system is analyzed. The system consists of parabolic fourth-order equations for the volume fraction of the fiber phase and solute concentration, modeling pre-patterning of lymphatic vessel morphology. The existence of discrete solutions is proved, and it is shown that the numerical scheme is energy stable up to stabilization, conserves the solute mass, and preserves the lower and upper bounds of the fiber phase fraction. Numerical experiments in two space dimensions using FreeFem illustrate the phase segregation and pattern formation.

Fixed-Point Theorems for Fuzzy Mappings

Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra.

Exploration-Exploitation and Suicidal Behavior in Borderline Personality Disorder and Depression

Clinical theory and behavioral studies suggest that people experiencing suicidal crisis are often unable to find constructive solutions or incorporate useful information into their decisions, resulting in premature convergence on suicide and neglect of better alternatives. However, prior studies of suicidal behavior have not formally examined how individuals resolve the tradeoffs between exploiting familiar options and exploring potentially superior alternatives. To investigate exploration and exploitation in suicidal behavior from the formal perspective of reinforcement learning. Two case-control behavioral studies of exploration-exploitation of a large 1-dimensional continuous space and a 21-day prospective ambulatory study of suicidal ideation were conducted between April 2016 and March 2022. Participants were recruited from inpatient psychiatric units, outpatient clinics, and the community in Pittsburgh, Pennsylvania, and underwent laboratory and ambulatory assessments. Adults diagnosed with borderline personality disorder (BPD) and midlife and late-life major depressive disorder (MDD) were included, with each sample including demographically equated groups with a history of high-lethality suicide attempts, low-lethality suicide attempts, individuals with BPD or MDD but no suicide attempts, and control individuals without psychiatric disorders. The MDD sample also included a subgroup with serious suicidal ideation. Behavioral (model-free and model-derived) indices of exploration and exploitation, suicide attempt lethality (Beck Lethality Scale), and prospectively assessed suicidal ideation. The BPD group included 171 adults (mean [SD] age, 30.55 [9.13] years; 135 [79%] female). The MDD group included 143 adults (mean [SD] age, 62.03 [6.82] years; 81 [57%] female). Across the BPD (χ23 = 50.68; P < .001) and MDD (χ24 = 36.34; P < .001) samples, individuals with high-lethality suicide attempts discovered fewer options than other groups as they were unable to shift away from unrewarded options. In contrast, those with low-lethality attempts were prone to excessive behavioral shifts after rewarded and unrewarded actions. No differences were seen in strategic early exploration or in exploitation. Among 84 participants with BPD in the ambulatory study, 56 reported suicidal ideation. Underexploration also predicted incident suicidal ideation (χ21 = 30.16; P < .001), validating the case-control results prospectively. The findings were robust to confounds, including medication exposure, affective state, and behavioral heterogeneity. The findings suggest that narrow exploration and inability to abandon inferior options are associated with serious suicidal behavior and chronic suicidal thoughts. By contrast, individuals in this study who engaged in low-lethality suicidal behavior displayed a low threshold for taking potentially disadvantageous actions.

Community childhood obesity assessment in elementary school, anthropometric indices as screening tools: a community cross-sectional study in Indonesia

BackgroundRepresentative anthropometric epidemiological data are needed to formulate screening and intervention methods to prevent obesity in children. This study aims to conduct community childhood obesity assessment in elementary school based...

Cube is a good form: Hyperspectral band selection via multi-dimensional and high-order structure preserved clustering

As an effective strategy for reducing the noisy and redundant information for hyperspectral imagery (HSI), hyperspectral band selection intends to select a subset of original hyperspectral bands, which boosts the subsequent different tasks. In this paper, we introduce a multi-dimensional high-order structure preserved clustering method for hyperspectral band selection, referred to as MHSPC briefly. By regarding original hyperspectral images as a tensor cube, we apply the tensor CP (CANDECOMP/PARAFAC) decomposition on it to exploit the multi-dimensional structural information as well as generate a low-dimensional latent feature representation. In order to capture the local geometrical structure along the spectral dimension, a graph regularizer is imposed on the new feature representation in the lower dimensional space. In addition, since the low rankness of HSIs is an important global property, we utilize a nuclear norm constraint on the latent feature representation matrix to capture the global data structure information. Different to most of previous clustering based hyperspectral band selection methods which vectorize each band as a vector without considering the 2-D spatial information, the proposed MHSPC can effectively capture the spatial structure as well as the spectral correlation of original hyperspectral cube in both local and global perspectives. An efficient alternatively updating algorithm with theoretical convergence guarantee is designed to solve the resultant optimization problem, and extensive experimental results on four benchmark datasets validate the effectiveness of the proposed MHSPC over other state-of-the-arts.

Separation and Extraction of Compound-Fault Signal Based on Multi-Constraint Non-Negative Matrix Factorization.

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time-frequency domain with the STFT, which describes the local characteristic of the signal from the time-frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.

Exponentially improved efficient machine learning for quantum many-body states with provable guarantees

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an m-dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error ɛ, provided that a sample set (of size N) of the states can be efficiently prepared and measured. In a recent work [Huang , ], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, N=mO(1ɛ), was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension m is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the prediction error ɛ and the number of qubits, n, with N=poly(ɛ−1,n,ln1δ), where poly denotes a polynomial function, and (1−δ) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to N=poly(ɛ−1,lnnδ). Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase. Published by the American Physical Society 2024

Research on the Effective Sheltering Rates of Public Buildings in Villages in Western Sichuan, China—A Case Study of Ganbao Tibetan Village

The western region of Sichuan Province, located in the Hengduan Mountains, is one of China’s most seismically active zones. Due to limited land resources, many villages in western Sichuan Province are situated in mountainous and valley areas, facing harsh climatic conditions, lagging economic development, and insufficient infrastructure. After experiencing seismic disasters, these villages often encounter challenges, such as cut-off mountain roads, difficulties in delivering relief supplies, and sharply a significant drop in nighttime temperatures due to the high-altitude climate. Consequently, in the case of the economic underdevelopment and limited resources, how to repurpose existing buildings for disaster relief has become a crucial issue for disaster prevention and mitigation in these villages. This paper takes Ganbao Tibetan Village, located in the alpine gorge regions of western Sichuan Province, as a case study. It evaluates the interior space utilization status of different types of existing public buildings during disasters, calculates the effective utilization rate of interior space disaster reduction conversion based on the spatial layout model, and extracts the typical interior space dimensions that are conducive to disaster relief and conversion of public buildings based on the interior space utilization characteristics of disaster relief. This study provides a reference for the design of public service buildings considering the requirements of disaster resilience transformation.

Maximum principle preserving time implicit DGSEM for linear scalar hyperbolic conservation laws

The properties of the high-order discontinuous Galerkin spectral element method (DGSEM) with implicit backward Euler time stepping are investigated for the approximation of hyperbolic linear scalar conservation equation in multiple space dimensions. We first prove that the DGSEM scheme in one space dimension preserves a maximum principle for the cell-averaged solution when the time step is large enough. This property however no longer holds in multiple space dimensions and we propose to use the flux-corrected transport (FCT) limiting [5] based on a low-order approximation using graph viscosity to impose a maximum principle on the cell-averaged solution. These results allow us to use a linear scaling limiter [58] in order to impose a maximum principle at nodal values within elements, while limiting the cell average with the FCT limiter improves the accuracy of the limited solution. Then, we investigate the inversion of the linear systems resulting from the time implicit discretization at each time step. We prove that the diagonal blocks are invertible and provide efficient algorithms for their inversion. Numerical experiments in one and two space dimensions are presented to illustrate the conclusions of the present analyses.

Well-posedness and scattering for a 2D inhomogeneous NLS with Aharonov-Bohm magnetic potential

We consider the magnetic nonlinear inhomogeneous Schrödinger equationi∂tu−(−i∇+α|x|2(−x2,x1))2u=±|x|−ϱ|u|p−1u,(t,x)∈R×R2, where α∈R∖Z,ϱ>0,p>1. We establish a dichotomy between global existence and scattering versus finite-time blow-up for energy solutions below the ground state threshold in the inter-critical regime. The scattering result is obtained by employing the novel approach developed by Dodson and Murphy (A new proof of scattering below the ground state for the 3D radial focusing cubic NLS, Proc. Am. Math. Soc. (2017)). We employ Tao's scattering criteria and Morawetz estimates as the foundation of this method. The novelty of our approach lies in two aspects: firstly, we explore the case of nonzero ϱα, and secondly, we consider general energy initial data that need not be radially symmetric. The specific instance of α=0, known as INLS, has garnered significant attention in recent years. Additionally, X. Gao and C. Xu recently investigated the case of ϱ=0 in the homogeneous regime, establishing scattering theory for spherically symmetric data in their work (Scattering theory for NLS with inverse-square potential in 2D, J. Math. Anal. Appl. (2020)). In the radial framework, the aforementioned problem can be translated to the INLS with an inverse square potential, which has been extensively studied in higher-dimensional spaces. The Hardy inequality ‖|x|−1f‖L2(RN)≤2N−2‖∇f‖L2(RN), which establishes the norm equivalence ‖f‖H1≃‖f‖H1+‖|x|−1f‖L2, does not hold in two space dimensions. Consequently, it remains unclear how to handle the NLS with an inverse square potential in the H1 framework for two-dimensional space. This article stands out as the first one to address the NLS with Aharonov-Bohm magnetic potential within the inhomogeneous regime, specifically when ϱ≠0.

Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations

In this paper we prove that rectified deep neural networks do not suffer from the curse of dimensionality when approximating McKean–Vlasov SDEs in the sense that the number of parameters in the deep neural networks only grows polynomially in the space dimension d of the SDE and the reciprocal of the accuracy ϵ.

Single-camera photogrammetry using a mobile phone for low-cost documentation of corpses.

Photogrammetry is a technique for studying and defining objects' shape, dimension, and position in a three-dimensional space using measurements obtained from two-dimensional photographs. It has gained popularity following the development of computer graphics technologies and has been applied to various branches of medicine. In this study, the authors present a method for low-cost photorealistic documentation of corpses during autopsy using single-camera photogrammetry with a mobile phone. Besides representing the body by demonstrating the injured and non-injured body parts as control, evidencing the body parts on a 3D reconstruction allows easy explanation to nonmedical experts such as lawyers.

The R-mAtrIx Net

We provide a novel neural network architecture that can: i) output R-matrix for a given quantum integrable spin chain, ii) search for an integrable Hamiltonian and the corresponding R-matrix under assumptions of certain symmetries or other restrictions, iii) explore the space of Hamiltonians around already learned models and reconstruct the family of integrable spin chains which they belong to. The neural network training is done by minimizing loss functions encoding Yang–Baxter equation, regularity and other model-specific restrictions such as hermiticity. Holomorphy is implemented via the choice of activation functions. We demonstrate the work of our neural network on the spin chains of difference form with two-dimensional local space. In particular, we reconstruct the R-matrices for all 14 classes. We also demonstrate its utility as an Explorer, scanning a certain subspace of Hamiltonians and identifying integrable classes after clusterisation. The last strategy can be used in future to carve out the map of integrable spin chains with higher dimensional local space and in more general settings where no analytical methods are available.

On the Algebraic Geometry of Multiview

We study the multiviews of algebraic space curves X from n pin-hole cameras of a real or complex projective space. We assume the pin-hole centers to be known, i.e., we do not reconstruct them. Our tools are algebro-geometric. We give some general theorems, e.g., we prove that a projective curve (over complex or real numbers) may be reconstructed using four general cameras. Several examples show that no number of badly placed cameras can make a reconstruction possible. The tools are powerful, but we warn the reader (with examples) that over real numbers, just using them correctly, but in a bad way, may give ghosts: real curves which are images of the emptyset. We prove that ghosts do not occur if the cameras are general. Most of this paper is devoted to three important cases of space curves: unions of a prescribed number of lines (using the Grassmannian of all lines in a 3-dimensional projective space), plane curves, and curves of low degree. In these cases, we also see when two cameras may reconstruct the curve, but different curves need different pairs of cameras.

Multi-armed bandit algorithm for sequential experiments of molecular properties with dynamic feature selection.

Sequential optimization is one of the promising approaches in identifying the optimal candidate(s) (molecules, reactants, drugs, etc.) with desired properties (reaction yield, selectivity, efficacy, etc.) from a large set of potential candidates, while minimizing the number of experiments required. However, the high dimensionality of the feature space (e.g., molecular descriptors) makes it often difficult to utilize the relevant features during the process of updating the set of candidates to be examined. In this article, we developed a new sequential optimization algorithm for molecular problems based on reinforcement learning, multi-armed linear bandit framework, and online, dynamic feature selections in which relevant molecular descriptors are updated along with the experiments. We also designed a stopping condition aimed to guarantee the reliability of the chosen candidate from the dataset pool. The developed algorithm was examined by comparing with Bayesian optimization (BO), using two synthetic datasets and two real datasets in which one dataset includes hydration free energy of molecules and another one includes a free energy difference between enantiomer products in chemical reaction. We found that the dynamic feature selection in representing the desired properties along the experiments provides a better performance (e.g., time required to find the best candidate and stop the experiment) as the overall trend and that our multi-armed linear bandit approach with a dynamic feature selection scheme outperforms the standard BO with fixed feature variables. The comparison of our algorithm to BO with dynamic feature selection is also addressed.

Multidimensional Hyperbolic Equations with Nonlocal Potentials: Families of Global Solutions

In spaces of arbitrary dimensions, hyperbolic differential–difference equations with potentials undergoing translations along arbitrary spatial directions are investigated. The fundamental novelty of this study is that, unlike previous investigations, no restrictions are imposed on the symbol of the differential–difference operator contained in the equation. For the investigated equation, we succeed to explicitly construct a multiparametric family of classical global solutions.

Distributionally robust chance-constrained kernel-based support vector machine

Support vector machine (SVM) is a powerful model for supervised learning. This article addresses the nonlinear binary classification problem using kernel-based SVM with uncertainty involved in the input data specified by the first- and second-order moments. To achieve a robust classifier with small probabilities of misclassification, we investigate a distributionally robust chance-constrained kernel-based SVM model. Since the moment information in the original problem becomes unclear/unavailable in the feature space via kernel transformation, we develop a data-driven approach utilizing empirical moments to provide a second-order cone programming (SOCP) reformulation for efficient computation. To speed up the required computations for solving large-size problems in higher dimensional space and/or with more sampling points involved in estimating empirical moments, we further design an alternating direction multipliers-based algorithm for fast computations. Extensive computational results support the effectiveness and efficiency of the proposed model and solution method. Results on public benchmark datasets without any moment information indicate that the proposed approach still works and, surprisingly, outperforms some commonly used state-of-the-art kernel-based SVM models.

Validating a Curvature-Based Marker of Cervical Carotid Tortuosity for Risk Assessment in Heritable Aortopathies.

Cervical arterial tortuosity is associated with adverse outcomes in Loeys-Dietz syndrome and other heritable aortopathies. A method to assess tortuosity based on curvature of the vessel centerline in 3-dimensional space was developed. We measured cervical carotid tortuosity in 65 patients with Loeys-Dietz syndrome from baseline computed tomography angiogram/magnetic resonance angiogram and all serial images during follow-up. Relations between baseline carotid tortuosity, age, aortic root diameter, and its change over time were compared. Patients with unoperated aortic roots were assessed for clinical end point (type A aortic dissection or aortic root surgery during 4 years of follow-up). Logistic regression was performed to assess the likelihood of clinical end point according to baseline carotid tortuosity. Total absolute curvature at baseline was 11.13±5.76 and was relatively unchanged at 8 to 10 years (fold change: 0.026±0.298, P=1.00), whereas tortuosity index at baseline was 0.262±0.131, with greater variability at 8 to 10 years (fold change: 0.302±0.656, P=0.818). Baseline total absolute curvature correlated with aortic root diameter (r=0.456, P=0.004) and was independently associated with aortic events during the 4-year follow-up (adjusted odds ratio [OR], 2.64 [95% CI, 1.02-6.85]). Baseline tortuosity index correlated with age (r=0.532, P<0.001) and was not associated with events (adjusted OR, 1.88 [95% CI, 0.79-4.51]). Finally, baseline total absolute curvature had good discrimination of 4-year outcomes (area under the curve=0.724, P=0.014), which may be prognostic or predictive. Here we introduce cervical carotid tortuosity as a promising quantitative biomarker with validated, standardized characteristics. Specifically, we recommend the adoption of a curvature-based measure, total absolute curvature, for early detection or monitoring of disease progression in Loeys-Dietz syndrome.

Deal.t: an implementation of multivariate analysis suitable T-splines within the deal.ii framework

AbstractWe present a numerical framework for solving partial differential equations within an isogeometric context using T-splines in two and three space dimensions. Within this paper, we explain the data structures used for the implementation of ( with T-splines) and main differences when using in contrast to . The authors present numerical experiments with error-based refinement (2D) and a priori refinement (3D) for scalar-valued problems. A full tutorial is given in the appendix. Since the new framework is based on , T-splines may be applied to various different PDEs.

Fast Parameter Inference on Pulsar Timing Arrays with Normalizing Flows.

Pulsar timing arrays perform Bayesian posterior inference with expensive Markov chain MonteCarlo (MCMC) methods. Given a dataset of ∼10-100 pulsars and O(10^{3}) timing residuals each, producing a posterior distribution for the stochastic gravitational wave background (SGWB) can take days to a week. The computational bottleneck arises because the likelihood evaluation required for MCMC is extremely costly when considering the dimensionality of the search space. Fortunately, generating simulated data is fast, so modern simulation-based inference techniques can be brought to bear on the problem. In this Letter, we demonstrate how conditional normalizing flows trained on simulated data can be used for extremely fast and accurate estimation of the SGWB posteriors, reducing the sampling time from weeks to a matter of seconds.