High-dimensional Research Articles

Robot-assisted optimized array design for accurate multi-component gas quantification

Designing sensor arrays is a common strategy for detecting mixtures. However, a sensor array designed based on human experience leads to inaccuracies due to cross-sensitivity and information overlap. This difficulty led to the realization that arrays should be optimized as a whole. The conventional array optimizing method involves selecting the best subarray from a limited sensor pool. However, this method did not consider the vast continuous multi-dimensional variable space of each sensing element’s recipe, thus only generating a simpler array with limited detection capacity. To address this problem, we developed a Robot-assisted Optimized Array Design (ROAD) method. This innovative method holistically optimizes the sensor array across a continuous and vast variable space, overcoming the bottlenecks of high dimensionality and high-quality data collection. We applied ROAD to an optoelectronic nose, tasked with detecting a mixture of CO2, NH3, and water vapor. The method explored an immense space, estimated at the order of 2^(10^7). The implementation of ROAD led to a revolutionary quantitative accuracy, achieving an average relative standard deviation of 1.90%. This advancement has propelled the application of optoelectronic nose from qualitative to quantitative. The successful ROAD of system-wide array optimization has been demonstrated in the optoelectronic nose, validating the potential of the holistically optimized sensor array for accurately quantifying each component in a gas mixture.

The dynamical analysis of simplicial SAIS epidemic model with awareness programs by media

In this paper, we propose an SAIS epidemic model with awareness programs by media on higher-order networks to study the impact of media and higher-order networks on disease transmission, in which the simplicial complex is utilized to construct a social network that describes connections between nodes, where a single link can connect more than two individuals. We use the cumulative density of awareness programs to quantify the impact of media and use the Microscopic Markov Chains method to get the probability evolution equation of each node. In order to solve the computational difficulties caused by the excessively high dimension of the equation, we use the mean field method to reduce the dimension of the equation to get the equilibrium of the system. Through dynamical analysis, we obtain the threshold of disease outbreak and conditions for the existence and stability of the disease-free equilibrium and the endemic equilibrium. The numerical simulations of SAIS model prove that the mean field method has good predictive performance. We also obtain the influence of parameters on threshold and system dynamical behavior through sensitivity analysis. The results show that: on one hand, the introduce of 2-simplex increases the probability of disease transmission in healthy populations, and the system appears discontinuous transition and bistable coexistence of health state and disease epidemic state, on the other hand, awareness programs by media can increase the threshold of disease outbreak, decrease the final density of infected individuals and inhibit the explosive growth of disease, thus effectively control the spread of diseases.

Hotelling $$T^2$$ test in high dimensions with application to Wilks outlier method

Hotelling $$T^2$$ test in high dimensions with application to Wilks outlier method

Accurate identification of single-cell types via correntropy-based Sparse PCA combining hypergraph and fusion similarity

ABSTRACT The advent of single-cell RNA sequencing (scRNA-seq) technology enables researchers to gain deep insights into cellular heterogeneity. However, the high dimensionality and noise of scRNA-seq data pose significant challenges to clustering. Therefore, we propose a new single-cell type identification method, called CHLSPCA, to address these challenges. In this model, we innovatively combine correntropy with PCA to address the noise and outliers inherent in scRNA-seq data. Meanwhile, we integrate the hypergraph into the model to extract more valuable information from the local structure of the original data. Subsequently, to capture crucial similarity information not considered by the PCA model, we employ the Gaussian kernel function and the Euclidean metric to mine the similarity information between cells, and incorporate this information into the model as the similarity constraint. Furthermore, the principal components (PCs) of PCA are very dense. A new sparse constraint is introduced into the model to gain sparse PCs. Finally, based on the principal direction matrix learned from CHLSPCA, we conduct extensive downstream analyses on real scRNA-seq datasets. The experimental results show that CHLSPCA performs better than many popular clustering methods and is expected to promote the understanding of cellular heterogeneity in scRNA-seq data analysis and support biomedical research.

Predicting Stock Trends Using Web Semantics and Feature Fusion

Stock data are characterized by high dimensionality and sparsity, making stock trend prediction highly challenging. Although the Light Gradient Boosting Machine (LightGBM), based on web semantics, excels at capturing global features and efficiently performs in stock trend prediction, it does not consider the issue of declining prediction performance caused by the changing distribution of stock data over time (concept drift phenomenon). Accordingly, this work introduces the Convolutional Neural Network (CNN) into the prediction model to leverage its ability to effectively capture local features. Additionally, local features are combined with global features to obtain a comprehensive set of feature information. Lastly, the model processes new data in real-time, continuously learns new knowledge, updates model parameters, and effectively addresses the decline in model performance caused by concept drift. Experimental results demonstrate that the proposed model outperforms other models indicating its ability to efficiently perform well in stock trend prediction.

Extremal Functions for Trudinger–Moser Inequalities Involving Various $L^{p}$-norms in High Dimension

Extremal Functions for Trudinger–Moser Inequalities Involving Various $L^{p}$-norms in High Dimension

Non-invertible symmetries and higher representation theory I

The purpose of this paper is to investigate the global categorical symmetries that arise when gauging finite higher groups in three or more dimensions. The motivation is to provide a common perspective on constructions of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. This paper focusses on gauging finite groups and split 2-groups in three dimensions. In addition to topological Wilson lines, we show that this generates a rich spectrum of topological surface defects labelled by 2-representations and explain their connection to condensation defects for Wilson lines. We derive various properties of the topological defects and show that the associated symmetry category is the fusion 2-category of 2-representations. This allows us to determine the full symmetry categories of certain gauge theories with disconnected gauge groups. A subsequent paper will examine gauging more general higher groups in higher dimensions.

Two-sample testing with local community depth

AbstractIn this paper, we investigate nonparametric two-sample hypothesis testing with local community depth, a measure of data depth calculated from pairwise distances between observations. Unlike many common “center-outwards” measures of data depth, local community depth captures local features of a distribution such as multimodality and can adapt to modes with different scales. This gives local community depth greater power to detect scale changes in multimodal distributions, and importantly the method is parameter-free. The local depth employed supplements existing adaptations of depth to local regions and is computationally cheaper in high dimensions than many classic depths such as halfspace depth, regression depth, simplicial depth, and Mahalanobis depth. We test hypotheses by using local community depth in the Liu–Singh test and give conditions under which our method is consistent against fixed alternatives (and has a limiting null distribution). In simulations and an application to diagnosing dengue fever, we show that local community depth outperforms other depths when the underlying distribution is multimodal or asymmetric, and is comparable to other methods when the data is unimodal and symmetric.

Integration of simulated annealing into pigeon inspired optimizer algorithm for feature selection in network intrusion detection systems.

In the context of the 5G network, the proliferation of access devices results in heightened network traffic and shifts in traffic patterns, and network intrusion detection faces greater challenges. A feature selection algorithm is proposed for network intrusion detection systems that uses an improved binary pigeon-inspired optimizer (SABPIO) algorithm to tackle the challenges posed by the high dimensionality and complexity of network traffic, resulting in complex models, reduced accuracy, and longer detection times. First, the raw dataset is pre-processed by uniquely one-hot encoded and standardized. Next, feature selection is performed using SABPIO, which employs simulated annealing and the population decay factor to identify the most relevant subset of features for subsequent review and evaluation. Finally, the selected subset of features is fed into decision trees and random forest classifiers to evaluate the effectiveness of SABPIO. The proposed algorithm has been validated through experimentation on three publicly available datasets: UNSW-NB15, NLS-KDD, and CIC-IDS-2017. The experimental findings demonstrate that SABPIO identifies the most indicative subset of features through rational computation. This method significantly abbreviates the system's training duration, enhances detection rates, and compared to the use of all features, minimally reduces the training and testing times by factors of 3.2 and 0.3, respectively. Furthermore, it enhances the F1-score of the feature subset selected by CPIO and Boost algorithms when compared to CPIO and XGBoost, resulting in improvements ranging from 1.21% to 2.19%, and 1.79% to 4.52%.

On K-contact metric manifolds satisfying an almost gradient Ricci–Bourguignon soliton

The main purpose of the paper is to study an almost gradient Ricci–Bourguignon soliton (RB soliton) within the framework of [Formula: see text]-contact manifolds and [Formula: see text]-contact manifolds. First, we prove that if complete [Formula: see text]-contact manifold endows a gradient RB soliton, then the manifold is compact Sasakian and isometric to unit sphere [Formula: see text]. Next, we show that if a complete contact metric satisfies an almost RB soliton with a non-zero potential vector field is collinear with the Reeb vector field [Formula: see text] and the Reeb vector field [Formula: see text] acting as an eigenvector of the Ricci operator, then it is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field [Formula: see text]. Lastly, we prove that if the metric of a non-Sasakian [Formula: see text]-contact manifold is an almost gradient RB soliton, then it is flat in dimension 3 and in higher dimensions it is locally isometric to [Formula: see text].

Pions from higher-dimensional gluons: general realizations and stringy models

In this paper we revisit the general phenomenon that scattering amplitudes of pions can be obtained from “dimensional reduction” of gluons in higher dimensions in a more general context. We show that such “dimensional reduction” operations universally turn gluons into pions regardless of details of interactions: under such operations any amplitude that is gauge invariant and contains only local simple poles becomes one that satisfies Adler zero in the soft limit. As two such examples, we show that starting from gluon amplitudes in both superstring and bosonic string theories, the operations produce “stringy” completion of pion scattering amplitudes to all orders in α′, with leading order given by non-linear sigma model amplitudes. Via Kawai-Lewellen-Tye relations, they give closed-stringy completion for Born-Infeld theory and the special Galileon theory, which are directly related to gravity amplitudes in closed-string theories. We also discuss how they naturally produce stringy models for mixed amplitudes of pions and colored scalars.

Characterizing Biphoton Spatial Wave Function Dynamics with Quantum Wavefront Sensing.

With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally characterize the multiphoton spatial wave function including the entangled amplitude and phase information at different evolutionary stages. However, there is no effective method to measure it. Quantum state tomography is costly, and quantum holography requires additional references. Here, we introduce quantum Shack-Hartmann wavefront sensing to perform efficient and reference-free measurement of the biphoton spatial wave function. The joint probability distribution of photon pairs at the back focal plane of a microlens array is measured and used for amplitude extraction and phase reconstruction. In the experiment, we observe that the biphoton amplitude correlation becomes weak while phase correlation shows up during free-space propagation. Our work is a crucial step in quantum physical and adaptive optics and paves the way for characterizing quantum optical fields with high-order correlations or topological patterns.

F-PICNN: A physics-informed convolutional neural network for partial differential equations with space-time domain

The physics and interdisciplinary problems in science and engineering are mainly described as partial differential equations (PDEs). Recently, a novel method using physics-informed neural networks (PINNs) to solve PDEs by employing deep neural networks with physical constraints as data-driven models has been pioneered for surrogate modelling and inverse problems. However, the original PINNs based on fully connected neural networks pose intrinsic limitations and poor performance for the PDEs with nonlinearity, drastic gradients, multiscale characteristics or high dimensionality in which the complex features are hard to capture. This leads to difficulties in convergence to correct solutions and high computational costs. To address the above problems, in this paper, a novel physics-informed convolutional neural network framework based on finite discretization schemes with a stack of a series of nonlinear convolutional units (NCUs) for solving PDEs in the space-time domain without any labelled data (f-PICNN) is proposed, in which the memory mechanism can considerably speed up the convergence. Specifically, the initial conditions (ICs) are hard-encoded into the network as the first time-step solution and used to extrapolate the next time-step solution. The Dirichlet boundary conditions (BCs) are constrained by soft BC enforcement while the Neumann BCs are hard enforced. Furthermore, the loss function is designed as a set of discretized PDE residuals and optimized to conform to physics laws. Finally, the proposed auto-regressive model has been proven to be effective in a wide range of 1D and 2D nonlinear PDEs in both space and time under different finite discretization schemes (e.g., Euler, Crank Nicolson and fourth-order Runge-Kutta). The numerical results demonstrate that the proposed framework not only shows the ability to learn the PDEs efficiently but also provides an opportunity for greater conceptual simplicity, and potential for extrapolation from learning the PDEs using a limited dataset.

Organic-Inorganic Hybrid Cuprous-Based Metal Halides with Unique Two-Dimensional Crystal Structure for White Light-Emitting Diodes.

Ternary cuprous (Cu+)-based metal halides, represented by cesium copper iodide (e.g., CsCu2I3 and Cs3Cu2I5), are garnering increasing interest for light-emitting applications owing to their intrinsically high photoluminescence quantum yield and direct band gap. Toward electrically driven light-emitting diodes (LEDs), it is highly desirable for the light emitters to have a high structural dimensionality as it may favor efficient electrical injection. However, unlike lead-based halide perovskites whose light-emitting units can be facilely arranged in three-dimensional (3D) ways, to date, nearly all ternary Cu+-based metal halides crystallize into 0D or 1D networks of Cu-X (X=Cl, Br, I) polyhedra, whereas 3D and even 2D structures remain mostly uncharted. Here, by employing a fluorinated organic cation, we report a new kind of ternary Cu+-based metal halides, (DFPD)CuX2 (DFPD+=4,4-difluoropiperidinium), which exhibits unique 2D layered crystal structure. Theoretical calculations reveal a highly dispersive conduction band of (DFPD)CuBr2, which is beneficial for charge carrier injection. It is also of particular significance to find that the 2D (DFPD)CuBr2 crystals show appealing properties, including improved ambient stability and an efficient warm white-light emission, making it a promising candidate for single-component lighting and display applications.

Large Skew-t Copula Models and Asymmetric Dependence in Intraday Equity Returns

Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio allows for a higher level of pairwise asymmetric dependence than two popular alternative skew-t copulas. Estimation of this copula in high dimensions is challenging, and we propose a fast and accurate Bayesian variational inference (VI) approach to do so. The method uses a generative representation of the skew-t distribution to define an augmented posterior that can be approximated accurately. A stochastic gradient ascent algorithm is used to solve the variational optimization. The methodology is used to estimate skew-t factor copula models with up to 15 factors for intraday returns from 2017 to 2021 on 93 U.S. equities. The copula captures substantial heterogeneity in asymmetric dependence over equity pairs, in addition to the variability in pairwise correlations. In a moving window study we show that the asymmetric dependencies also vary over time, and that intraday predictive densities from the skew-t copula are more accurate than those from benchmark copula models. Portfolio selection strategies based on the estimated pairwise asymmetric dependencies improve performance relative to the index.

Testing independence based on Spearman’s footrule in high dimensions

. Spearman’s footrule is a widely used tool to discover the relationship between two continuous random variables, mainly because of its robustness, natural interpretation, and simplicity of calculation. In this article, we propose a new test statistic based on the sum of squares of pairwise Spearman’s footrule, to test the mutual independence of a high dimensional random vector. The large sample properties of the proposed test method are established. Simulation results show that the new test has higher power than existing test methods under some circumstances. An example with real life data is discussed to illustrate the usefulness and effectiveness of the proposed test statistic.

Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice.

The two-channel Kondo lattice likely hosts a rich array of phases, including hastatic order, a channel symmetry breaking heavy Fermi liquid. We revisit its one-dimensional phase diagram using density matrix renormalization group and, in contrast to previous work, find algebraic hastatic orders generically for stronger couplings. These are heavy Tomonaga-Luttinger liquids with nonanalyticities at Fermi vectors captured by hastatic density waves. We also find a predicted additional nonlocal order parameter due to interference between hastatic spinors, not present at large N, and residual repulsive interactions at strong coupling suggesting non-Fermi-liquid physics in higher dimensions.

More power by using fewer permutations

Abstract It is conventionally believed that permutation-based testing methods should ideally use all permutations. We challenge this by showing that we can sometimes obtain dramatically more power by using a tiny subgroup. As the subgroup is tiny, this also comes at a much lower computational cost. Moreover, the method remains valid for the same hypotheses. We exploit this to improve the popular permutation-based Westfall and Young MaxT multiple testing method. We analyse the relative efficiency in a Gaussian location model, and find the largest gain in high dimensions.

An event-triggered and dimension learning scheme WOA for PEMFC modeling and parameter identification

Aiming at the high dimension and complexity of parameters identification problem, a whale optimization algorithm based on event-triggered and dimension learning scheme (EDWOA) is presented, which is specifically designed for the proton exchange membrane fuel cell (PEMFC) model. Drawing inspiration from group optimization strategies, a novel dimensional learning method is introduced to enhance the dynamic search capabilities of the algorithm. To assess the efficacy of the proposed algorithm, benchmark function testing was conducted, and its fitness surpassed common heuristic algorithms on over 15 objective functions. The results clearly indicate that the EDWOA algorithm outperforms its counterparts in terms of global search performance. Its ability to navigate complex search spaces sets it apart from other algorithms. Finally, the proposed EDWOA algorithm is successfully applied to parameter identification in the PEMFC model. Through a comparative analysis with existing research findings, it was found that the identified PEMFC model exhibited a notable enhancement in fitness, ranging from 0.02 to 0.93. This underscores the effectiveness of the EDWOA algorithm in improving the performance and dynamic output of PEMFC models.

General measurements with limited resources and their application to quantum unambiguous state discrimination

In this report, we present a framework for implementing an arbitrary n-outcome generalized quantum measurement (POVM) on an m-qubit register as a sequence of two-outcome measurements requiring only single ancillary qubit. Our procedure offers a particular construction for the two-outcome partial measurements which can be composed into a full implementation of the measurement on any gate architecture. This implementation in general requires classical feedback; we present specific cases when this is not the case. We apply this framework on the unambiguous state discrimination and analyze possible strategies. In the simplest case, it gives the same construction as is known, if we opt for performing conclusiveness measurement first. However, it also offers possibility of performing measurement for one of the state outcomes first, leaving conclusiveness measurement for later. This shows flexibility of presented framework and opens possibilities for further optimization. We present discussion also on biased qubit case as well as general case of unambiguous quantum state discrimination in higher dimension.