Lower Dimension Research Articles

Orthogonal projection based statistical feature extraction for continuous process monitoring

Multivariate statistical techniques have been widely applied in industrial processes to detect abnormal behaviors, while their performance could be unsatisfactory due to insufficient extraction of complex data characteristics. A method named Orthogonal transformed statistics Mahalanobis distance (OTSMD) is developed to handle this issue. As a feature-based method, OTSMD simultaneously considers various data characteristics through monitoring statistical features of process variables. Orthogonal transformed components (OTCs) are first calculated to capture variable correlation, and a set of statistical features is determined to extract other crucial characteristics, especially for the process non-stationarity. Statistical features of OTCs, which reveals implied process information, are continuously obtained using a sliding window, and a Mahalanobis distance index is utilized for fault detection. Compared with existing methods, OTSMD extracts data characteristics more comprehensively with a lower dimension, making it more effective in monitoring various faults. The results are illustrated through a numerical example, and two chemical industrial processes.

Mod2VQLS: A Variational Quantum Algorithm for Solving Systems of Linear Equations Modulo 2

This paper presents a system for solving binary-valued linear equations using quantum computers. The system is called Mod2VQLS, which stands for Modulo 2 Variational Quantum Linear Solver. As far as we know, this is the first such proposal. The design is a classical–quantum hybrid. The quantum components are a new circuit design for implementing matrix multiplication modulo 2, and a variational circuit to be optimized. The classical components are the optimizer, which measures the cost function and updates the quantum parameters for each iteration, and the controller that runs the quantum job and classical optimizer iterations. We propose two alternative ansatze or templates for the variational circuit and present results showing that the rotation ansatz designed specifically for this problem provides the most direct path to a valid solution. Numerical experiments in low dimensions indicate that Mod2VQLS, using the custom rotations ansatz, is on par with the block Wiedemann algorithm, which is the best-known to date solution for this problem.

On some Lie-theoretic solutions of the tt*-Toda equations with integer Stokes data

We describe some solutions of the tt*-Toda equations with integer Stokes data, based on a Lie-theoretic approach. In particular, we find all such solutions in a certain 1-parameter family. For general solutions, we compare the results of Guest–Its–Lin (based on solving the equations) with the original classification of Cecotti–Vafa (based on braid group orbits of Stokes matrices for hypothetical solutions), and find that these agree in low dimensions.

Two-Dimensional Ferroelectrics: A Review on Applications and Devices

Over the last few years, research activities have seen two-dimensional (2D) materials become protagonists in the field of nanotechnology. In particular, 2D materials characterized by ferroelectric properties are extremely interesting, as they are better suited for the development of miniaturized and high-performing devices. Here, we summarize the recent advances in this field, reviewing the realization of devices based on 2D ferroelectric materials, like FeFET, FTJ, and optoelectronics. The devices are realized with a wide range of material systems, from oxide materials at low dimensions to 2D materials exhibiting van der Waals interactions. We conclude by presenting how these materials could be useful in the field of devices based on magnons or surface acoustic waves.

Effect of uniaxial compressive strain on the thermoelectric properties of two-dimensional HfNF

Two-dimensional transition metal nitride halides have shown promise in thermoelectric applications due to their low dimensionality, excellent electron transfer properties, and quantum confinement of carriers. This study focuses on investigating the impact of uniaxial compressive strain on the stability, electronic and thermoelectric properties of monolayer HfNF through first-principles calculations. The research findings reveal that the semiconductor properties of monolayer HfNF remain unchanged under various strain conditions. Furthermore, the thermoelectric properties of monolayer HfNF materials are examined using Slack model and the Boltzmann transport theory under different strain conditions. The findings indicate that applying uniaxial compressive strains at temperatures of 500 K, 700 K, and 900 K increase the Seebeck coefficients of n-type and p-type HfNF, resulting in an enhanced power factor for the material. Specifically, the power factor of p-type HfNF under uniaxial compressive strain increased by 83%, with the ZT value reaching 2.01 at 900 K, which is approximately 40% higher than the ZT value without strain. These results suggest that strain can be utilized as a modulation method to enhance the thermoelectric properties of materials. Moreover, the study suggests that two-dimensional HfNF holds great promise for thermoelectric applications when subjected to uniaxial compressive strain.

New fractal dimensions of measures and decompositions of singularly continuous measures

By introducing a novel expression for the Hausdorff and packing measures with respect to gauge functions, we establish a connection between different approaches to defining the exact Hausdorff and packing dimensions of measures. Furthermore, we define the upper and lower Hausdorff and packing dimensions of a Borel probability measure and demonstrate that these dimensions can be represented using an entropy formula. This paper also addresses an intriguing question raised multiple times regarding the structural representation of singular probability measures. We provide an affirmative response to this question by utilizing characteristic measures.

CLUSTERING-BASED OBJECTS STATE DIAGNOSTICS IN CONDITIONS OF FUZZY SOURCE DATA

У The problem of distribution of a set of objects, the state of which is determined by a set of controlled parameters, into a set of subsets of objects maximally homogeneous in their properties is considered. Relevance of the problem and important advantage of the clustering procedure: when its implementing it is possible to reduce the initial difficult problem of high dimensionality objects analysing to the solution of a number of simpler problems of lower dimensionality. This circumstance acquires additional attractiveness and importance if the initial data of the problem contain uncertainty, for example, are vaguely defined. Research object is the procedure of partitioning a set of objects into clusters under conditions of uncertainty. In this regard, the purpose of the study is to develop a method for solving the problem of clustering in conditions where the initial data on objects controlled parametersthe values contain uncertainty. The method of solving the problem is based on clustering procedure mathematical model development, containing analytical expressions for the criterion of its effectiveness, written in the form of a twice fractionally quadratic function. The impossibility of mathematical programming problem direct solution initiated the development of a heuristic algorithm for its solution. As a result, an iterative method was obtained and applied to solve the clustering problem under conditions of fuzzy initial data. The developed computational procedure is based on a reasonable system of rules for performing operations on fuzzy numbers. The situations when the belonging functions of problem fuzzy parameters are defined on infinite or compact media are considered. The developed system of rules allows to correctly perform operations in the metric of fuzzy defined states between clustering objects. The proposed method is easily generalised to the case when the uncertainty of the initial data is hierarchical.

Bicontinuous microemulsion in binary blends of complementary diblock copolymers.

The phase behavior of binary blends of AB diblock copolymers of compositions f and 1 - f is examined using field-theoretic simulations. Highly asymmetric compositions (i.e., f ≈ 0) behave like homopolymer blends macrophase separating into coexisting A- and B-rich phases as the segregation is increased, whereas more symmetric diblocks (i.e., f ≈ 0.5) microphase separate into an ordered lamellar phase. In self-consistent field theory, these behaviors are separated by a Lifshitz critical point at f = 0.2113. However, its lower critical dimension is believed to be four, which implies that the Lifshitz point should be destroyed by fluctuations. Consistent with this, it is found to transform into a tricritical point. Furthermore, the highly swollen lamellar phase near the mean-field Lifshitz point disorders into a bicontinuous microemulsion (BμE), consisting of large interpenetrating A- and B-rich microdomains. BμE has been previously reported in ternary blends of AB diblock copolymer with its parent A- and B-type homopolymers, but in that system the homopolymers have a tendency to macrophase separate. Our alternative system for creating BμE is free of this macrophase separation.

NeuroDAVIS: A neural network model for data visualization

The task of dimensionality reduction and visualization of high-dimensional datasets remains a challenging problem since long. Modern high-throughput technologies produce large datasets having multiple views with relatively new data types. Visualization of these datasets require efficient algorithms that can uncover hidden patterns in the data without affecting the local and global structures, and bring out the inherent non-linearity within the data. To this end, however, very few such methodologies exist, which can realize this task. In this work, we have introduced a novel unsupervised deep neural network model, called NeuroDAVIS, for data visualization. NeuroDAVIS is capable of extracting important features from the data, without assuming any data distribution, visualize effectively in low dimension, and preserve both local and global structures simultaneously. It has been shown theoretically that neighbourhood relationship of the data in high dimension remains preserved in lower dimension. The performance of NeuroDAVIS has been evaluated on a wide variety of synthetic and real high-dimensional datasets including numeric, textual, image and biological data. NeuroDAVIS has been highly competitive against t-Distributed Stochastic Neighbor Embedding (t-SNE), Uniform Manifold Approximation and Projection (UMAP), Principal Component Analysis (PCA) and Random Projection (RP) with respect to visualization quality, preservation of data size, shape, and both local and global structure. It has outperformed Fast interpolation-based t-SNE (Fit-SNE), a variant of t-SNE, for most of the datasets. For the biological datasets, besides t-SNE, UMAP, Fit-SNE, PCA and RP, NeuroDAVIS has also performed well as compared to other state-of-the-art algorithms, like Potential of Heat-diffusion for Affinity-based Trajectory Embedding (PHATE) and the siamese neural network-based method, called IVIS. Downstream classification and clustering analyses have also revealed favourable results for NeuroDAVIS-generated embeddings.

Health-related quality of life in Mexican women with obesity

Obesity creates a burden of disease that affects the health-related quality of life (HRQoL) of women and in those between 20 to 59 years of age it implies greater morbidity and mortality compared to men or other age groups. To evaluate the HRQoL of Mexican women aged 20 to 59 years with obesity. Observational, cross-sectional, prospective, and retrospective study. It was obtained a sample of 104 women from 20 to 59 years of age diagnosed with obesity according to the NOM-008-SSA3-2017 Standard. The participants' main clinical and sociodemographic characteristics were collected, and their HRQoL was evaluated with the SF-36 questionnaire. For the analysis of the collected variables, descriptive statistics were used. To identify the association of these variables with HRQoL, the Kruskal-Wallis test was used. 104 women with a median age of 40.0 years participated. Of these, 66.3% had grade I obesity, 21.2% grade II, and 12.5% grade III. In the overall sample, general health and vitality were the lowest dimensions. In the comparison by groups, the physical role and the emotional role had statistically significant differences (p = 0.007 and p = 0.009, respectively), with the most affected group being obesity grade II. Obesity mainly affected the perception of general health and vitality; likewise, those with grade II had a greater impact on the physical role and the emotional role.

Optoelectronic Properties of Cold Plasma-Deposited, Oxidized Sn-C Thin Films.

We report on investigating the structural and electronic properties of semiconducting and insulating layers produced in a process resembling percolation in a unique cold plasma fabrication method (plasma-enhanced chemical vapor deposition-PECVD). Amorphous carbon-tin films (Sn-C) produced from tetramethyl tin (TMT) with an acoustic-frequency glow discharge in a three-electrode reactor were investigated. The layers, after air exposure, oxidized to SnO2/Sn-C. Depending on the coupling capacitance applied to the plasma reactor, the films could be obtained in the form of an amorphous semiconductor or an amorphous insulator. We assume that the semiconductor consists of an internal network of channels auto-organized during deposition. The insulator does not demonstrate any internal structure features. An investigation on conductive filaments creating low-dimensional (LD) nanojunctions in the semiconductor and the location of energetic levels in the insulator was performed. The main parameters of the electronic band structure of the insulating film, such as the transport gap EG (5.2 eV), optical gap Eopt (3.1 eV), electron affinity Χ (2.1 eV), and ionization potential J (7.3 eV), were determined. We have demonstrated a simple approach for developing a catalyst candidate consisting of amorphous semiconductor-insulator nanojunctions for (photo)catalytic hydrogen evolution or CO2 reduction.

A very general framework for fractal interpolation functions

M. Barnsley introduced the concept of fractal interpolation function as an alternative method for construction of interpolation functions. Such a function is the attractor of an iterated function system comprising Banach contractions (on the product of two real compact intervals) with respect to the second variable. In the present paper we enlarge classical Barnsley's framework by allowing the constitutive functions of the system to be Edelstein contractions in the second variable. As the class of Edelstein contractions contains the class of Matkowski contractions, the class of Meir-Keeler contractions, the class of F-contractions and the class of θ-contractions, we provide a much more flexible framework for the construction of fractal interpolation functions. We also obtain a result concerning the estimation of lower and upper box dimensions of the graph of a fractal interpolation function constructed via our general method.

A fast, scalable and versatile tool for analysis of single-cell omics data.

Single-cell omics technologies have revolutionized the study of gene regulation in complex tissues. A major computational challenge in analyzing these datasets is to project the large-scale and high-dimensional data into low-dimensional space while retaining the relative relationships between cells. This low dimension embedding is necessary to decompose cellular heterogeneity and reconstruct cell-type-specific gene regulatory programs. Traditional dimensionality reduction techniques, however, face challenges in computational efficiency and in comprehensively addressing cellular diversity across varied molecular modalities. Here we introduce a nonlinear dimensionality reduction algorithm, embodied in the Python package SnapATAC2, which not only achieves a more precise capture of single-cell omics data heterogeneities but also ensures efficient runtime and memory usage, scaling linearly with the number of cells. Our algorithm demonstrates exceptional performance, scalability and versatility across diverse single-cell omics datasets, including single-cell assay for transposase-accessible chromatin using sequencing, single-cell RNA sequencing, single-cell Hi-C and single-cell multi-omics datasets, underscoring its utility in advancing single-cell analysis.

Dynamic scaling-based immersion and invariance adaptive pose tracking control using dual quaternions

This paper investigates the position and attitude (pose) tracking control of a rigid body with uncertain mass and inertia. By virtue of the dual quaternion description, a six-degree-of-freedom (6-DOF) relative motion model is established in an integrated and compact way. Then an adaptive pose tracking controller is proposed based on the immersion and invariance (I&I) theory, where the key integrability obstacle is overcome by the dynamic scaling technique. Compared with the existing filter system-based method that constructs a filter system to circumvent the integrability obstacle, the dynamic scaling-based method is directly designed based on the original system, which is capable of retaining all benefits of the I&I design with much lower dimension dynamic extensions. Comparisons with the filter system-based I&I method and the classical certainty equivalent method are first carried out from the theoretical analyses, which elucidate benefits of the proposed method in lower control demands. Then the comparative simulations are conducted to verify the features and effectiveness of the proposed dynamic scaling-based I&I adaptive control scheme.

Random projection using random quantum circuits

The random sampling task performed by Google's Sycamore processor gave us a glimpse of the “quantum supremacy era.” This has definitely shed some light on the power of random quantum circuits in this abstract task of sampling outputs from the (pseudo)random circuits. In this paper, we explore a practical near-term use of local random quantum circuits in dimensional reduction of large low-rank data sets. We make use of the well-studied dimensionality reduction technique called the random projection method. This method has been extensively used in various applications such as image processing, logistic regression, entropy computation of low-rank matrices, etc. We prove that the matrix representations of local random quantum circuits with sufficiently shorter depths [∼O(n)] serve as good candidates for random projection. We demonstrate numerically that their projection abilities are not far off from the computationally expensive classical principal components analysis on MNIST and CIFAR-100 image datasets. We also benchmark the performance of quantum random projection against the commonly used classical random projection in the tasks of dimensionality reduction of image data sets and computing von Neumann entropies of large low-rank density matrices. And finally, using variational quantum singular value decomposition, we demonstrate a near-term implementation of extracting the singular vectors with dominant singular values after quantum random projecting a large low-rank matrix to lower dimensions. All such numerical experiments unequivocally demonstrate the ability of local random circuits to randomize a large Hilbert space at sufficiently shorter depths with robust retention of properties of large data sets in reduced dimensions. Published by the American Physical Society 2024

Understanding and tuning magnetism in van der Waals-type metal thiophosphates.

Over the past two decades, significant progress in two-dimensional (2D) materials has invigorated research in condensed matter and material physics in low dimensions. While traditionally studied in three-dimensional systems, magnetism has now been extended to the 2D realm. Recent breakthroughs in 2D magnetism have attracted substantial interest from the scientific community, owing to the stable magnetic order achievable in atomically thin layers of the van der Waals (vdW)-type layered magnetic materials. These advances offer an exciting platform for investigating related phenomena in low dimensions and hold promise for spintronic applications. Consequently, vdW magnetic materials with tunable magnetism have attracted significant attention. Specifically, antiferromagnetic metal thiophosphates MPX3 (M = transition metal, P = phosphorus, X = chalcogen) have been investigated extensively. These materials exhibit long-range magnetic order spanning from bulk to the 2D limit. The magnetism in MPX3 arises from localized moments associated with transition metal ions, making it tunable via substitutions and intercalations. In this review, we focus on such tuning by providing a comprehensive summary of various metal- and chalcogen-substitution and intercalation studies, along with the mechanism of magnetism modulation, and a perspective on the development of this emergent material family.

Breaking the bottleneck of lead-free perovskite solar cells through dimensionality modulation.

The emerging perovskite solar cell (PSC) technology has attracted significant attention due to its superior power conversion efficiency (PCE) among the thin-film photovoltaic technologies. However, the toxicity of lead and poor stability of lead halide materials hinder their commercialization. In this case, after a decade of effort, various categories of lead-free perovskites and perovskite-like materials have been developed, including tin halide perovskites, double perovskites, defect-structured perovskites, and rudorffites. However, the performance of the corresponding devices still falls short of expectations, especially their PCE. The limitations mainly originate from either the unstable lattice structure of these materials, which causes the distortion of their octahedra, or their low dimensionality (e.g., structural and electronic dimensionality)-correlated poor carrier transport and self-trapping effect, accelerating nonradiative recombination. Therefore, understanding the relationship between the structures and performance in these emerging candidates and leveraging these insights to design or modify new lead-free perovskites is of great significance. Herein, we review the variety of dimensionalities in different categories of lead-free perovskites and perovskite-like materials and conclude that dimensionality is an important aspect among the crucial indexes that determine the performance of lead-free PSCs. In addition, we summarize the modulation of both structural and electronic dimensionality, and the corresponding enhanced optoelectronic properties in different categories. Finally, perspectives on the future development of lead-free perovskites and perovskite-like materials for photovoltaic applications are provided. We hope that this review will provide researchers with a concise overview of these emerging materials and help them leverage dimensionality to break the bottleneck in photovoltaic applications.

Synthesis and electrocatalytic applications of hybrid nanomaterials containing low-dimensional metals

In this review, recent progress in the synthesis and electrocatalytic applications of hybrid nanomaterials containing low-dimensional metals was outlined and some promising future directions were proposed.

Enhancing Self-Awareness by Basic-Element Model

Cognitive ability plays an extremely important role in personal development. However, current methods for enhancing self-awareness suffer from issues such as one-sidedness, partiality, and low dimensionality. To better improve the capacity for self-awareness, the method of establishing basic-element model from the field of extenics is adopted. This approach enhances the systematic nature of self-awareness and inspires the direction of self-development through building models of objects, affair, relation, and conjugate analysising the aspects of physical, systematic, antithetic, and dynamic. Preliminary analysis of some case studies has verified the effectiveness of the basic-element model approach in enhancing self-awareness.

Mapping the phase-separated state in a 2D magnet.

Intrinsic 2D magnets have recently been established as a playground for studies on fundamentals of magnetism, quantum phases, and spintronic applications. The inherent instability at low dimensionality often results in coexistence and/or competition of different magnetic orders. Such instability of magnetic ordering may manifest itself as phase-separated states. In 4f 2D materials, magnetic phase separation is expressed in various experiments; however, the experimental evidence is circumstantial. Here, we employ a high-sensitivity MFM technique to probe the spatial distribution of magnetic states in the paradigmatic 4f 2D ferromagnet EuGe2. Below the ferromagnetic transition temperature, we discover the phase-separated state and follow its evolution with temperature and magnetic field. The characteristic length-scale of magnetic domains amounts to hundreds of nanometers. These observations strongly shape our understanding of the magnetic states in 2D materials at the monolayer limit and contribute to engineering of ultra-compact spintronics.