Lower Dimension Research Articles

Computing the alpha complex using dual active set quadratic programming

The alpha complex is a fundamental data structure from computational geometry, which encodes the topological type of a union of balls B(x;r)⊂Rm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B(x;r) \\subset {\\mathbb {R}}^m$$\\end{document} for x∈S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x\\in S$$\\end{document}, including a weighted version that allows for varying radii. It consists of the collection of “simplices” σ={x0,...,xk}⊂S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma =\\{x_0,...,x_k\\} \\subset S$$\\end{document}, which correspond to nonempty (k+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(k+1)$$\\end{document}-fold intersections of cells in a radius-restricted version of the Voronoi diagram Vor(S,r)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\ extrm{Vor}\\,}}(S,r)$$\\end{document}. Existing algorithms for computing the alpha complex require that the points reside in low dimension because they begin by computing the entire Delaunay complex, which rapidly becomes intractable, even when the alpha complex is of a reasonable size. This paper presents a method for computing the alpha complex without computing the full Delaunay triangulation by applying Lagrangian duality, specifically an algorithm based on dual quadratic programming that seeks to rule simplices out rather than ruling them in.

Stereologically adapted Crofton formulae for tensor valuations

The classical Crofton formula explains how intrinsic volumes of a convex body K in n-dimensional Euclidean space can be obtained from integrating a measurement function at sections of K with invariantly moved affine flats. We generalize this idea by constructing stereologically adapted Crofton formulae for translation invariant Minkowski tensors, expressing a prescribed tensor valuation as an invariant integral of a measurement function of section profiles with flats. The measurement functions are weighed sums of powers of the metric tensor times Minkowski valuations. The weights are determined explicitly from known Crofton formulae using Zeilberger's algorithm. The main result is an exhaustive set of measurement functions where the invariant integration is over flats.With the main result at hand, a Blaschke-Petkantschin formula allows us to establish new measurement functions valid when the invariant integration over flats is replaced by an invariant integration over subspaces containing a fixed subspace of lower dimension. Likewise, a stereologically adapted Crofton formula valid in the scheme of vertical sections is constructed. Only some special cases of this result have been stated explicitly before, with even the three-dimensional case yielding a new stereological formula. Here, we obtain new vertical section formulae for the surface tensors of even rank.

Evaluation of the Komlos Conjecture Using Multi-Objective Optimization

The Komlos conjecture, which explores the existence of a constant upper bound in the realm of n-dimensional vectors, specifically addresses the function K(n). This function, intricately defined as encapsulates the maximal discrepancy within a set of n -dimensional vectors. This paper endeavors to unravel the mysteries of K(n), by meticulously evaluating its behavior for lower dimensions . Our findings revealed through systematic exploration, showcase intriguing values such as , , , and , shedding light on the intricate relationships within n-dimensional spaces. Venturing into higher dimensions, we introduce the function as a potentially robust lower bound for K(n). This innovative approach aims to provide a deeper understanding of the limiting behavior of K(n) as the dimensionality expands. As a culmination of our comprehensive analysis, we arrive at a significant revelation the Komlos conjecture stands refuted. This conclusion stems from the suspected divergence of K(n), as n approaches infinity, as evidenced by . This seminal result challenges established notions and added a valuable dimension to the ongoing discourse in optimization and discrepancy theory.

Is it possible to find the single nearest neighbor of a query in high dimensions?

We investigate an open question in the study of the curse of dimensionality: Is it possible to find the single nearest neighbor of a query in high dimensions? Using the notion of (in)distinguishability to examine whether the feature map of a kernel is able to distinguish two distinct points in high dimensions, we analyze this ability of a metric-based Lipschitz continuous kernel as well as that of the recently introduced Isolation Kernel. Between the two kernels, we show that only Isolation Kernel has distinguishability and it performs consistently well in four tasks: indexed search for exact nearest neighbor search, anomaly detection using kernel density estimation, t-SNE visualization and SVM classification in both low and high dimensions, compared with distance, Gaussian and three other existing kernels.

A Gradient-Based Optimizer Method for Improving the Feature Extraction Capability of Network Architecture and Its Application to Condition Monitoring of Rotating Machinery

Aiming at the problem of inaccurate feature extraction under the massive data of rotating machinery, this paper proposes a feature extraction capability enhancement method based on Gradient-Based Optimizer for trusted network architecture to monitor the conditions of bearings, which firstly transforms the original signal into a wavelet time-frequency image and visualizes the high-dimensional and difficult-to-visualize data in low dimensions. Then, different convolutional neural network architectures are tested by implanting different noise intensities to determine the most robust network architecture. Secondly, this paper adopts the grid method as well as the swarm optimization algorithm to guide the parameters of the model to achieve the best feature extraction effect, compares the optimization effect of several swarm optimization algorithms horizontally, and determines the most effective GBO algorithm among them. Finally, to improve the credibility of the best network model, this paper combines the grad-cam method with the trusted fusion method to improve the accuracy and reliability of the model. Validated by the bearing data of Case Western Reserve University, it shows that the proposed model in this paper has good credibility and accuracy.

Breaking Boundaries: Giant Ultraviolet Birefringence in Dimension‐Reduced Zn‐Based Crystals

AbstractBirefringent crystals have essential applications in optical communication areas. Low‐dimensional structures with inherited structural anisotropy are potential systems for investigating birefringent materials with large birefringence. In this work, the zero‐dimensional (0D) [(p‐C5H5NO)2ZnCl2] (1) and [p‐C5H6NO]2[ZnCl4] (2) were obtained by introducing the π‐conjugated p‐C5H5NO (4HP) into the three‐dimensional (3D) ZnCl2. Remarkably, 1 exhibits a giant birefringence of 0.482@546 nm, which is the largest among Zn‐based ultraviolet (UV) compounds and 160 times that of ZnCl2. According to structural and theoretical calculation analyses, the large optical polarizability, high spatial density, ideal distribution of the [(4HP)2ZnCl2]0 cluster, and the low dimension of 1 result in the dramatically increased birefringence compared to ZnCl2. This work will provide a valid route for accelerating the design and synthesis of compounds with excellent birefringence in low‐dimensional systems.

(Invited) Resonant Exciton Transfer in Mixed-Dimensional Heterostructures for Overcoming Dimensional Restrictions in Optical Processes

Nanomaterials exhibit unique optical phenomena, in particular excitonic quantum processes occurring at room temperature. The low dimensionality, however, imposes strict requirements for conventional optical excitation, and an approach for bypassing such restrictions is desirable. Here we report on exciton transfer in carbon-nanotube/tungsten-diselenide heterostructures, where band alignment can be systematically varied. The mixed-dimensional heterostructures display a pronounced exciton reservoir effect where the longer-lifetime excitons within the two-dimensional semiconductor are funneled into carbon nanotubes through diffusion. This new excitation pathway presents several advantages, including larger absorption areas, broadband spectral response, and polarization-independent efficiency. When band alignment is resonant, we observe substantially more efficient excitation via tungsten diselenide compared to direct excitation of the nanotube. We further demonstrate simultaneous bright emission from an array of carbon nanotubes with varied chiralities and orientations. Our findings show the potential of mixed-dimensional heterostructures and band alignment engineering for energy harvesting and quantum applications through exciton manipulation.Parts of this study are supported by JSPS (KAKENHI JP22K14624, JP22K14625, JP21K14484, JP22F22350, JP22K14623, JP21H05233, JP23H00262, JP20H02558) and MEXT (ARIM JPMXP1222UT1135). Y.R.C. is supported by JSPS (International Research Fellow). N.F. and C.F.F. are supported by RIKEN Special Postdoctoral Researcher Program. We thank the Advanced Manufacturing Support Team at RIKEN for technical assistance.[1] N. Fang, D. Yamashita, S. Fujii, M. Maruyama, Y. Gao, Y. R. Chang, C. F. Fong, K. Otsuka, K. Nagashio, S. Okada, Y. K. Kato, "Resonant exciton transfer in mixed-dimensional heterostructures for overcoming dimensional restrictions in optical processes," Nature Commun., accepted (2023). Preprint at arXiv:2307.07124.

(Invited) Silicon Nanocrystals and Electrum Nanoclusters with High Quantum Yield for Light Converting Applications

While QDs are typically made of semiconductors, metals at low dimensions also turn to discrete electronic structure. The characteristic transition size from bulk to nanodot is lower, because Fermi level position is at the band middle, while discretization of levels starts from the band edge. Therefore, only for sizes of a metal entity ~ 1 nm a QD-like behavior manifests.Here we show that metal nanoclusters Au16Ag7 of an electrum alloy (gold-silver) with adamantanethiolate ligands possess PL quantum yield of ~ 70% in a thiol-ene polymer matrix [1]. PL is in NIR range with a large Stokes shift. Due to parity-forbidden transition the PL lifetime is in microseconds. These characteristics are similar to silicon QDs, where optical transition is also partly forbidden. Luminescence from Si QDs (5-10 nm size) may also feature high quantum efficiency when a defect-free core with good surface passivation is prepared. We have demonstrated a new synthesis method, which can reduce precursor cost by an order of magnitude from the established HSQ-based technique [2]. Si QDs prepared in this way have near-unity internal and > 50% external (quantum yield) efficiency with a large Stokes shift. In both nanomaterials the re-absorption is suppressed, which is of value for several applications.One such application is a semi-transparent photovoltaics for glazing in building-integration. It is based on a luminescent solar concentrator concept, where high efficiency and a large Stokes shift are necessary requirements for nanophosphors. In this configuration absorbed solar light is re-emitted and a large fraction of it is guided by total internal reflection to the edges for collection by standard solar cells. As a proof-of-concept we fabricated 20x20 cm2 prototypes, where Si QD-doped polymer layer is sandwiched between glass plates in a triplex geometry. Such “solar windows” feature high transparency (>80%), low haze (<3%), high color rendering index (~ 88) and, at the same time, deliver up to 0.6 W of electrical peak power under one sun [3]. Original measurement techniques were developed to characterize large-area devices [4,5].

(Invited) Two-Dimensional Layered Materials and Their Mixed-Dimensional Hybrids for Electrochemical Applications

Compared with their 3D counterparts, two-dimensional (2D) van der Waals (vdW) materials exhibit quantum confinement where charge carriers are spatially confined at the physical boundaries. Particularly, when mixing 2D materials with other low-dimensional (LD) materials, they exhibit enormous potential in electrochemical energy applications due to the unique properties arising from reduced dimensionality and, more importantly, material integration synergy.In this work, 2D transition metal dichalcogenides (MoS2) and their mixed low-dimensional hybrids (MLDHs) are introduced with an emphasis on the hybrid structure construction using the one-step solvothermal synthesis technique and their electrochemical applications. Fundamental insight into the synergistic effect of the MLDHs integration in terms of active site exposure, surface area enlargement, electrical conductivity improvement, and structural phase engineering for advancing the development of Li-ion batteries (LIBs) and electrocatalytic hydrogen evolution reaction (HER) will also be discussed. Specifically, in the case of LIBs, 2D-based binary hybrids (i.e., MoS2/MXene) deliver a Li-ion storage capacity of 540 mA h g−1 at 100 mA g−1 and a stable cycle performance up to 300 cycles. In sharp contrast, the 2D-based ternary MLDHs (i.e., MoS2/MXene/CNT) exhibit a higher Li-ion storage capacity (1500 mAh g−1 at 100 mA g−1), outstanding cycle stability (up to 300 cycles) and excellent rate capability (500 mAh g−1 at 4000 mA g−1) as an anode of LIBs. In the case of HER, the MLDH heterostructures show an overpotential of 169 mV with a low Tafel slope of 51 mV/dec and can be cycled to 1000 cycles. Leveraging the unique microreactor platform based on the 2D vdW platform, a mechanistic understanding of charge transport dynamics at the electrified electrode and current collector interface will be highlighted.The knowledge gained on how mixed-dimensional physics and chemistry will shed light on the design principle of the electrode materials for electrochemical energy storage and conversion and deepen the understanding of the process-structural-property-performance (PSPP) relationship of the vdW-based hybrid structures.

Distinct High-Pressure Responses of Halide Perovskites from Bulk to Low Dimension

Hybrid organic-inorganic perovskites (HOIPs) are low-cost and highly efficient optoelectronic and photovoltaic materials for applications in solar cells, light emitting diodes (LEDs), and so on, which is correlated with their intrinsic structures. Now the hybrid perovskite families include three-dimensional (3D) (CH3NH3PbBr3), two-dimensional (2D) ((C4H9NH3)2(CH3NH3)n-1PbnI3n+1) and nanostructured ((CH3NH3PbBr3 nanoparticles) materials. Herein, well understanding the relationship between the cystal structures and the related functional properties of HOIP materials is essential to the application point of view. High pressure up to gigapascal, offers a comprehensive way to study the structure-property correlation of solid materials in the atomic level, where both crystal structures and electronic properties are changed dramatically.In this presentation, high pressure induced dramatically inorganic and organic part changes in 2D HOIPs are comprehensively studied[1,2], as shown in Figure 1. On the other hand, structural phase transition and morphology changes are also explored in 3D HOIP and their nanoparticles[3], as shown in Figure 2. All the high pressure-induced inorganic structural transition is resolved by in situ X-ray powder diffraction (XRD) measurements, morphology change is resolved by transmission electron microscopy (TEM), the correlated optical responses are investigated by absorption and photoluminescence spectroscopy. And the rotational isomerism is evidenced by the vibrational properties of the organic BA chain by Raman spectroscopy combined with the Ab initio calculations.Reference:[1] T Yin, B Liu, J Yan, Y Fang, M Chen, WK Chong, S Jiang, J-L Kuo, J Fang, P L, S-H W, K-P Loh, T-C Sum, T J. White, and Z Xiang, J. Am. Chem. Soc. 141, 1235 (2019).[2] Yin T, Yan H, Abdelwahab I, Lekina Y, Lü X, Yang W, Sun H, Leng K, Cai Y, Shen Z, Loh KP, Nat. Commun. 14, 411 (2023).[3] T Yin, Y Fang, WK Chong, KT Ming, S Jiang, X Li, J-L Kuo, J Fang, T-C Sum, T J. White, J Yan, and Z Xiang, Adv. Mater. 30, 1705017 (2018). Figure 1

Deciphering the Interplay of Structure and Charge Carrier Dynamics in Reduced-Dimensional Perovskites

Reduced-dimensional perovskites (RDPs) have advanced the development of perovskite solar cells (PSCs) due to their tunable energy landscape, structure, and orientation. Thus, we aim for an increase in the understanding of structure-photophysical properties of Dion-Jacobson (DJ) and Ruddlesden-Popper (RP) RDPs with different dimensionalities. Our findings reveal that RP RDPs with lower dimensionality exhibits a dominant n=2 phase, preferential out-of-plane orientation, and longer charge carrier lifetime compared with DJ RDPs, as evidenced by X-ray scattering technique and transient absorption spectroscopy. In addition, we unveil the film growth of respective RDPs by in-situ X-ray scattering, showing the stoichiometry-determined phase growth. The formation of lower-n phases in RP RDPs with higher dimensionality is thermodynamically favored, while those phases are likely in the form of “intermediate phase”, which bridge the 3d-like and lower-n phases in DJ RDPs. DJ RDPs with higher dimensionality demonstrate comparable phase purity, giving rise to more sufficient energy transfer and longer charge carrier lifetime. As such, DJ-based PSCs (n=4) demonstrate better device stability under ISOS-I-L conditions compared to RP-based PSCs. Leveraging these structural and photophysical insights, our work paves the way for dictating the utilization of RDPs in 3D PSCs and the fabrication of quasi-2D solar cells.

A topological approach for semi-supervised learning

Nowadays, Machine Learning and Deep Learning methods have become the state-of-the-art approach to solve data classification tasks. In order to use those methods, it is necessary to acquire and label a considerable amount of data; however, this is not straightforward in some fields, since data annotation is time consuming and might require expert knowledge. This challenge can be tackled by means of semi-supervised learning methods that take advantage of both labelled and unlabelled data. In this work, we present new semi-supervised learning methods based on techniques from Topological Data Analysis (TDA). In particular, we have created two semi-supervised learning methods following two topological approaches. In the former, we have used a homological approach that consists in studying the persistence diagrams associated with the data using the bottleneck and Wasserstein distances. In the latter, we have considered the connectivity of the data. In addition, we have carried out a thorough analysis of the developed methods using 9 tabular datasets with low and high dimensionality. The results show that the developed semi-supervised methods outperform the results obtained with models trained with only manually labelled data, and are an alternative to other classical semi-supervised learning algorithms.

An enhanced AlexNet-Based model for femoral bone tumor classification and diagnosis using magnetic resonance imaging

ObjectiveBone tumors, known for their infrequent occurrence and diverse imaging characteristics, require precise differentiation into benign and malignant categories. Existing diagnostic approaches heavily depend on the laborious and variable manual delineation of tumor regions. Deep learning methods, particularly convolutional neural networks (CNNs), have emerged as a promising solution to tackle these issues. This paper introduces an enhanced deep-learning model based on AlexNet to classify femoral bone tumors accurately. MethodsThis study involved 500 femoral tumor patients from July 2020 to January 2023, with 500 imaging cases (335 benign and 165 malignant). A CNN was employed for automated classification. The model framework encompassed training and testing stages, with 8 layers (5 Conv and 3 FC) and ReLU activation. Essential architectural modifications included Batch Normalization (BN) after the first and second convolutional filters. Comparative experiments with various existing methods were conducted to assess algorithm performance in tumor staging. Evaluation metrics encompassed accuracy, precision, sensitivity, specificity, F-measure, ROC curves, and AUC values. ResultsThe analysis of precision, sensitivity, specificity, and F1 score from the results demonstrates that the method introduced in this paper offers several advantages, including a low feature dimension and robust generalization (with an accuracy of 98.34 %, sensitivity of 97.26 %, specificity of 95.74 %, and an F1 score of 96.37). These findings underscore its exceptional overall detection capabilities. Notably, when comparing various algorithms, they generally exhibit similar classification performance. However, the algorithm presented in this paper stands out with a higher AUC value (AUC=0.848), signifying enhanced sensitivity and more robust specificity. ConclusionThis study presents an optimized AlexNet model for classifying femoral bone tumor images based on convolutional neural networks. This algorithm demonstrates higher accuracy, precision, sensitivity, specificity, and F1-score than other methods. Furthermore, the AUC value further confirms the outstanding performance of this algorithm in terms of sensitivity and specificity. This research makes a significant contribution to the field of medical image classification, offering an efficient automated classification solution, and holds the potential to advance the application of artificial intelligence in bone tumor classification.

Numerical and computational analysis on a dissipative dynamical system: Slow invariant manifold for complex chemical mechanism

This article presents the notion about Slow Invariant Manifold (SIM) and their fundamental role in model reduction techniques (MRTs) for challenges encountered in mechanical engineering within dissipative systems of chemical kinetics. Focusing on the reaction routes of complex mechanisms, we construct and compare primary approximations of the SIM through MRTs, including the Spectral Quasi Equilibrium Manifold (SQEM) and Intrinsic Low Dimensional Manifold (ILDM). These methods effectively transform high-dimensional complex problems into lower dimensions, solving them without compromising crucial information about the complex systems modified for homogeneous reactive systems. Employing the sensitivity analysis by using the MATLAB's toolbox, we present the numerical findings in a tabular format obtained through MRTs. This study provides the understanding about the accessible exploration of numerical solutions, improving insights of the complex variation within the system.

From Chalcogen Bonding to S-π Interactions in Hybrid Perovskite Photovoltaics.

The stability of hybrid organic-inorganic halide perovskite semiconductors remains a significant obstacle to their application in photovoltaics. To this end, the use of low-dimensional (LD) perovskites, which incorporate hydrophobic organic moieties, provides an effective strategy to improve their stability, yet often at the expense of their performance. To address this limitation, supramolecular engineering of noncovalent interactions between organic and inorganic components has shown potential by relying on hydrogen bonding and conventional van der Waals interactions. Here, the capacity to access novel LDperovskite structures that uniquely assemble through unorthodox S-mediated interactions is explored by incorporating benzothiadiazole-based moieties. The formation of S-mediated LD structures is demonstrated, including one-dimensional (1D) and layered two-dimensional (2D) perovskite phases assembled via chalcogen bonding and S-π interactions. This involved a combination of techniques, such as single crystal and thin film X-ray diffraction, as well as solid-state NMR spectroscopy, complemented by molecular dynamics simulations, density functional theory calculations, and optoelectronic characterization, revealing superior conductivities of S-mediated LD perovskites. The resulting materials are applied in n-i-p and p-i-n perovskite solar cells, demonstrating enhancements in performance and operational stability that reveal a versatile supramolecular strategy in photovoltaics.

Spiking mode-based neural networks.

Spiking neural networks play an important role in brainlike neuromorphic computations and in studying working mechanisms of neural circuits. One drawback of training a large-scale spiking neural network is that updating all weights is quite expensive. Furthermore, after training, all information related to the computational task is hidden into the weight matrix, prohibiting us from a transparent understanding of circuit mechanisms. Therefore, in this work, we address these challenges by proposing a spiking mode-based training protocol, where the recurrent weight matrix is explained as a Hopfield-like multiplication of three matrices: input modes, output modes, and a score matrix. The first advantage is that the weight is interpreted by input and output modes and their associated scores characterizing the importance of each decomposition term. The number of modes is thus adjustable, allowing more degrees of freedom for modeling the experimental data. This significantly reduces the training cost because of significantly reduced space complexity for learning. Training spiking networks is thus carried out in the mode-score space. The second advantage is that one can project the high-dimensional neural activity (filtered spike train) in the state space onto the mode space which is typically of a low dimension, e.g., a few modes are sufficient to capture the shape of the underlying neural manifolds. We successfully apply our framework in two computational tasks-digit classification and selective sensory integration tasks. Our method thus accelerates the training of spiking neural networks by a Hopfield-like decomposition, and moreover this training leads to low-dimensional attractor structures of high-dimensional neural dynamics.

Consensus dynamics under asymmetric interactions in low dimensions

AbstractWe consider a set $$N = \{ 1,\ldots ,n \}$$ N = { 1 , … , n } , $$n\ge 2$$ n ≥ 2 , of interacting agents whose individual opinions $$ x_{i}$$ x i , with $$i \in N $$ i ∈ N , take values in some domain $$\mathbb {D}\subseteq \mathbb {R}$$ D ⊆ R . The interaction among the agents represents the degree of reciprocal influence which the agents exert upon each other and it is expressed by a general asymmetric interaction matrix with null diagonal and off-diagonal coefficients in the open unit interval. The present paper examines the asymmetric generalization of the linear consensus dynamics model discussed in previous publications by the same authors, in which symmetric interaction was assumed. We are mainly interested in determining the form of the asymptotic convergence towards the consensual opinion. In this respect, we present some general results plus the study of three particular versions of the linear consensus dynamics, depending on the relation between the interaction structure and the degrees of proneness to evaluation review of the various individual opinions. In the general asymmetric case, the analytic form of the asymptotic consensual solution $$\tilde{x}$$ x ~ is highly more complex than that under symmetric interaction, and we have obtained it only in two low-dimensional cases. Nonetheless, we are able to write those complex analytic forms arranging the numerous terms in an intelligible way which might provide useful clues to the open quest for the analytic form of the asymptotic consensual solution in higher-dimensional cases.

Predicting potential microbe-disease associations based on dual branch graph convolutional network.

Studying the association between microbes and diseases not only aids in the prevention and diagnosis of diseases, but also provides crucial theoretical support for new drug development and personalized treatment. Due to the time-consuming and costly nature of laboratory-based biological tests to confirm the relationship between microbes and diseases, there is an urgent need for innovative computational frameworks to anticipate new associations between microbes and diseases. Here, we propose a novel computational approach based on a dual branch graph convolutional network (GCN) module, abbreviated as DBGCNMDA, for identifying microbe-disease associations. First, DBGCNMDA calculates the similarity matrix of diseases and microbes by integrating functional similarity and Gaussian association spectrum kernel (GAPK) similarity. Then, semantic information from different biological networks is extracted by two GCN modules from different perspectives. Finally, the scores of microbe-disease associations are predicted based on the extracted features. The main innovation of this method lies in the use of two types of information for microbe/disease similarity assessment. Additionally, we extend the disease nodes to address the issue of insufficient features due to low data dimensionality. We optimize the connectivity between the homogeneous entities using random walk with restart (RWR), and then use the optimized similarity matrix as the initial feature matrix. In terms of network understanding, we design a dual branch GCN module, namely GlobalGCN and LocalGCN, to fine-tune node representations by introducing side information, including homologous neighbour nodes. We evaluate the accuracy of the DBGCNMDA model using five-fold cross-validation (5-fold-CV) technique. The results show that the area under the receiver operating characteristic curve (AUC) and area under the precision versus recall curve (AUPR) of the DBGCNMDA model in the 5-fold-CV are 0.9559 and 0.9630, respectively. The results from the case studies using published experimental data confirm a significant number of predicted associations, indicating that DBGCNMDA is an effective tool for predicting potential microbe-disease associations.

A Sparse Approximate Factor Model for High-Dimensional Covariance Matrix Estimation and Portfolio Selection

Abstract We propose a novel estimation approach for the covariance matrix based on the l1-regularized approximate factor model (AFM). Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard AFM. We prove the consistency of the covariance matrix estimator under the Frobenius norm as well as the consistency of the factor loadings and the factors. Our Monte Carlo simulations reveal that the SAF covariance estimator has superior properties in finite samples for low and high dimensions and different designs of the covariance matrix. Moreover, in an out-of-sample portfolio forecasting application, the estimator uniformly outperforms alternative portfolio strategies based on alternative covariance estimation approaches and modeling strategies including the 1/N-strategy.

Tracking and modeling the movement of Queensland fruit flies, Bactrocera tryoni, using harmonic radar in papaya fields

Determining movement parameters for pest insects such as tephritid fruit flies is critical to developing models which can be used to increase the effectiveness of surveillance and control strategies. In this study, harmonic radar was used to track wild-caught male Queensland fruit flies (Qflies), Bactrocera tryoni, in papaya fields. Experiment 1 continuously tracked single flies which were prodded to induce movement. Qfly movements from this experiment showed greater mean squared displacement than predicted by both a simple random walk (RW) or a correlated random walk (CRW) model, suggesting that movement parameters derived from the entire data set do not adequately describe the movement of individual Qfly at all spatial scales or for all behavioral states. This conclusion is supported by both fractal and hidden Markov model (HMM) analysis. Lower fractal dimensions (straighter movement paths) were observed at larger spatial scales (> 2.5 m) suggesting that Qflies have qualitatively distinct movement at different scales. Further, a two-state HMM fit the observed movement data better than the CRW or RW models. Experiment 2 identified individual landing locations, twice a day, for groups of released Qflies, demonstrating that flies could be tracked over longer periods of time.