Dimensional Representation Research Articles

Improving the robustness of the Sequentially Optimized Reconstruction Strategy (SORS) for visual field testing.

Perimetry, or visual field test, estimates differential light sensitivity thresholds across many locations in the visual field (e.g., 54 locations in the 24-2 grid). Recent developments have shown that an entire visual field may be relatively accurately reconstructed from measurements of a subset of these locations using a linear regression model. Here, we show that incorporating a dimensionality reduction layer can improve the robustness of this reconstruction. Specifically, we propose to use principal component analysis to transform the training dataset to a lower dimensional representation and then use this representation to reconstruct the visual field. We named our new reconstruction method the transformed-target principal component regression (TTPCR). When trained on a large dataset, our new method yielded results comparable with the original linear regression method, demonstrating that there is no underfitting associated with parameter reduction. However, when trained on a small dataset, our new method used on average 22% fewer trials to reach the same error. Our results suggest that dimensionality reduction techniques can improve the robustness of visual field testing reconstruction algorithms.

Enabling unsupervised discovery in astronomical images through self-supervised representations

ABSTRACT Unsupervised learning, a branch of machine learning that can operate on unlabelled data, has proven to be a powerful tool for data exploration and discovery in astronomy. As large surveys and new telescopes drive a rapid increase in data size and richness, these techniques offer the promise of discovering new classes of objects and of efficient sorting of data into similar types. However, unsupervised learning techniques generally require feature extraction to derive simple but informative representations of images. In this paper, we explore the use of self-supervised deep learning as a method of automated representation learning. We apply the algorithm Bootstrap Your Own Latent to Galaxy Zoo DECaLS images to obtain a lower dimensional representation of each galaxy, known as features. We briefly validate these features using a small supervised classification problem. We then move on to apply an automated clustering algorithm, demonstrating that this fully unsupervised approach is able to successfully group together galaxies with similar morphology. The same features prove useful for anomaly detection, where we use the framework astronomaly to search for merger candidates. While the focus of this work is on optical images, we also explore the versatility of this technique by applying the exact same approach to a small radio galaxy data set. This work aims to demonstrate that applying deep representation learning is key to unlocking the potential of unsupervised discovery in future data sets from telescopes such as the Vera C. Rubin Observatory and the Square Kilometre Array.

Linguistic representation of cultural dimensions

Linguistic representation of cultural dimensions

Socioecological justice in urban street greenery based on green view index-A case study within the Fuzhou Third Ring Road

Urban green space equity relates to the efficient allocation of natural resources and the equalization of public service facilities. Street (road) greenery provides substantial ecological, social and cultural benefits. Thus, in this study, a subdistrict-level evaluation framework for the fairness of the spatial distribution of street greenery was proposed, taking a case study within the Third Ring Road of Fuzhou City in Fujian, China. Street view images may capture the green information in a vertical dimension for the indirect representation of people’s perspective on the ground. The green view index, which was estimated based on Baidu Street View images, was employed to represent the urban street greenery, and the results were combined using deep learning technology. The Gini coefficient, share index and location entropy were used as evaluation indicators for the fairness of the spatial distribution of the street green view index. Furthermore, this framework combined socioeconomic data and population census data to explore the correlation among socioeconomic status, age, and evaluation index at the subdistrict level. In addition, we analyzed street greenery distribution inequalities from the perspective of socioecological justice. The results showed that in Fuzhou, there is a significant correlation among the Gini coefficient, green view index and socioeconomic status. In addition, subdistricts with a lower green view index have a less equitable street greenery distribution, people with low socioeconomic status may suffer from green injustice, and seniors have a lower accessibility to street green space than people with the average social status. Our analytical approach is applicable for other cities, and the findings are useful for greenery spatial planning processes and evaluating construction effects.

Automated State Estimation for Summarizing the Dynamics of Complex Urban Systems Using Representation Learning

Complex urban systems can be difficult to monitor, diagnose and manage because the complete states of such systems are only partially observable with sensors. State estimation techniques can be used to determine the underlying dynamic behavior of such complex systems with their highly non-linear processes and external time-variant influences. States can be estimated by clustering observed sensor readings. However, clustering performance degrades as the number of sensors and readings (i.e. feature dimension) increases. To address this problem, we propose a framework that learns a feature-centric lower dimensional representation of data for clustering to support analysis of system dynamics. We propose Unsupervised Feature Attention with Compact Representation (UFACR) to rank features contributing to a cluster assignment. These weighted features are then used to learn a reduced-dimension temporal representation of the data with a deep-learning model. The resulting low-dimensional representation can be effectively clustered into states. UFACR is evaluated on real-world and synthetic wastewater treatment plant data sets, and feature ranking outcomes were validated by Wastewater treatment domain experts. Our quantitative and qualitative experimental analyses demonstrate the effectiveness of UFACR for uncovering system dynamics in an automated and unsupervised manner to offer guidance to wastewater engineers to enhance industrial productivity and treatment efficiency.

Learning manifolds from non-stationary streams

Streaming adaptations of manifold learning based dimensionality reduction methods, such as Isomap, are based on the assumption that a small initial batch of observations is enough for exact learning of the manifold, while remaining streaming data instances can be cheaply mapped to this manifold. However, there are no theoretical results to show that this core assumption is valid. Moreover, such methods typically assume that the underlying data distribution is stationary and are not equipped to detect, or handle, sudden changes or gradual drifts in the distribution that may occur when the data is streaming. We present theoretical results to show that the quality of a manifold asymptotically converges as the size of data increases. We then show that a Gaussian Process Regression (GPR) model, that uses a manifold-specific kernel function and is trained on an initial batch of sufficient size, can closely approximate the state-of-art streaming Isomap algorithms, and the predictive variance obtained from the GPR prediction can be employed as an effective detector of changes in the underlying data distribution. Results on several synthetic and real data sets show that the resulting algorithm can effectively learn lower dimensional representation of high dimensional data in a streaming setting, while identifying shifts in the generative distribution. For instance, key findings on a Gas sensor array data set show that our method can detect changes in the underlying data stream, triggered due to real-world factors, such as introduction of a new gas in the system, while efficiently mapping data on a low-dimensional manifold.

Socialness effects in lexical-semantic processing.

Contemporary theories of semantic representation posit that social experience is an important source of information for deriving meaning. However, there is a lack of behavioral evidence in support of this proposal. The aim of the present work was to test whether words' degree of social relevance, or socialness, influences lexical-semantic processing. In Study 1, across a series of item-level regression analyses, we found that (a) socialness can facilitate responses in lexical, semantic, and memory tasks, and (b) limited evidence for an interaction of socialness with concreteness. In Studies 2-3, we tested the preregistered hypothesis that social words, compared to nonsocial words, will be associated with faster and more accurate responses during a syntactic classification task. We found that socialness has a facilitatory effect on noun decisions (Study 3), but not verb decisions (Study 2). Overall, our results suggest that the socialness of a word affects lexical-semantic processing but also that this is task-dependent. These findings constitute novel evidence in support of proposals that social information is an important dimension of semantic representation. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

On intrinsic Hodge-Tate-ness of Galois representations of dimension two

On intrinsic Hodge-Tate-ness of Galois representations of dimension two

Representation zeta function of a family of maximal class groups: Non-exceptional primes

Abstract We use a constructive method to obtain all but finitely many 𝑝-local representation zeta functions of a family of finitely generated nilpotent groups M n M_{n} with maximal nilpotency class. For representation dimensions coprime to all primes p < n p<n , we construct all irreducible representations of M n M_{n} by defining a standard form for the matrices of these representations.

Optimization design of a hybrid thermal runaway propagation mitigation system for power battery module using high-dimensional surrogate models

The demand for high energy density in lithium-ion battery packs for electric vehicles poses a challenge to maintaining its optimum operating temperature while reducing the risk of thermal runaway (TR) propagation. This study proposes a novel hybrid TR propagation mitigation system that balances heat transfer and thermal insulation requirements using low and high thermal conductivity phase change materials (PCM), heat pipes (HP), and air-cooling. The design and optimization of such a mitigation system are complex due to the many design parameters involved. The Adaptive-Kriging-High dimensional model representation (Adaptive-Kriging-HDMR) is used to establish a surrogate model of the system, and the sensitivity of the system's design parameters is evaluated with the maximum battery temperature and the system weight as the targets, thereby improving the efficiency of model calculation and reducing the dimension of optimization parameters. Then, the design of the sensitive parameters is optimized using an extended elitist non‐dominated sorting genetic algorithm (E-NSGA-II) multi-objective optimization algorithm. The results show that the modeling difficulty and optimization calculation time are significantly reduced by using a surrogate model. The calculation time for a single surrogate model only takes a few seconds instead of several hours for the original three-dimensional heat transfer and flow calculation. The thermal conductivity of high thermal conductivity-PCM, the distance between battery and low thermal conductivity-PCM, the battery spacing, and the HP length significantly affect the system. The optimized system substantially reduces the overall weight of the battery system while ensuring its good heat dissipation capability. In the case of TR in a single battery, the system succeeds in limiting the TR propagation to the same row, with the maximum battery temperature in the second row being only 64.3 °C, well below the battery TR trigger point. Under more severe conditions, such as TR occurring in two batteries simultaneously, the maximum battery temperature in the second row is 155.5 °C, and no TR spreads to the adjacent row. This study provides a rapid and effective method for designing a TR propagation mitigation system. It can serve as a reference for the engineering design and optimization of battery thermal management systems.

Spectral equivalence of smooth group schemes over principal ideal local rings

Let G be a smooth linear group scheme of finite type. For any positive integer k and a finite field F, let Wk(F) be the ring of Witt vectors of length k over F. We show that the group algebras of G(F[t]/(tk)) and G(Wk(F)) are isomorphic (i.e. the multi-sets of the dimensions of the irreducible representations are equal) for any positive integer k and finite field F with large enough characteristic. We also prove that if charF is large enough, then the cardinality of the set {dim⁡ρ|ρ∈irr(G(F))} is bounded uniformly in F.

Matrices for finite group representations that respect Galois automorphisms

AbstractWe are given a finite group H, an automorphism $$\tau $$ τ of H of order r, a Galois extension L/K of fields of characteristic zero with cyclic Galois group $$\langle \sigma \rangle $$ ⟨ σ ⟩ of order r, and an absolutely irreducible representation $$\rho :H\rightarrow \textsf {GL} (n,L)$$ ρ : H → GL ( n , L ) such that the action of $$\tau $$ τ on the character of $$\rho $$ ρ is the same as the action of $$\sigma $$ σ . Then the following are equivalent. $$\bullet $$ ∙ $$\rho $$ ρ is equivalent to a representation $$\rho ':H\rightarrow \textsf {GL} (n,L)$$ ρ ′ : H → GL ( n , L ) such that the action of $$\sigma $$ σ on the entries of the matrices corresponds to the action of $$\tau $$ τ on H, and $$\bullet $$ ∙ the induced representation $$\textsf {ind} _{H,H\rtimes \langle \tau \rangle }(\rho )$$ ind H , H ⋊ ⟨ τ ⟩ ( ρ ) has Schur index one; that is, it is similar to a representation over K. As examples, we discuss a three dimensional irreducible representation of $$A_5$$ A 5 over $$\mathbb {Q}[\sqrt{5}]$$ Q [ 5 ] and a four dimensional irreducible representation of the double cover of $$A_7$$ A 7 over $$\mathbb {Q}[\sqrt{-7}]$$ Q [ - 7 ] .

MGDHGS[formula omitted] Gene-bridged metabolite-disease relationships prediction via GraphSAGE and self-attention mechanism

Metabolites represent the underlying information of biological systems. Revealing the links between metabolites and diseases can facilitate the development of targeted drugs. Traditional biological experiments can be used to validate the relationships of metabolite-disease, but these methods are time-consuming and labor-intensive. In contrast, the prevailing computational methods have improved efficiency but primarily rely on the metabolite-disease interactions, overlooking the impact of other biological components. To remedy the problem, we present a novel computational framework (MGDHGS) based on metabolite-gene-disease heterogeneous network to forecast potential associations. Specifically, we initially integrate data from multiple sources to construct metabolite-gene-disease heterogeneous network that includes known associations and computationally-derived similarities. Then, the GraphSAGE is harnessed to learn the low dimensional neighborhood representation in the heterogeneous network and self-attention mechanism is applied to effectively capture the connectivity patterns, which contributions to combine with nodes intrinsic and extrinsic features. Finally, the ultimate relationships probability scores are predicted by linear regression based on the these characteristics. The five-fold cross-validation showcases impressive AUC (0.9734) and PR (0.9718) for MGDHGS compared with five state-of-the-art methods, and the case studies validate that the metabolite-disease associations predicted by MGDHGS can be substantiated through pertinent biological experiments. The findings of this study show great potential contribution in the development of targeted drugs as well as offering solid support for our understanding of the complex interactions between metabolites, genes and diseases.

Research on movement of dimensional singularities without elastic interaction in gasketed joints

Loss of clamping force due to elastic interaction is unpredictable and nonnegligible with the typical non-linear characteristics of gasketed joints. It is hard to weaken or eliminate elastic interaction by suitable joint dimensions. An analytical model of elastic interaction with dimensional representation is constructed using gasket deformation as a bridge. The influence of multi-dimensional dimensions on clamping force losses, such as bolt spacing, joint width and thickness, was explored by non-linear finite element analysis for a typical sandwich structure with two-bolt gasketed joints. Dimensional singularities without elastic interaction are validated and their approximate range is determined. It is clarified that initial clamping force or joint material can cause dimensional singularity movement. This paper provides a theoretical basis for solving the problem of clamping force losses and inhomogeneities effected by elastic interactions in engineering.

Disentangled deep generative models reveal coding principles of the human face processing network.

Despite decades of research, much is still unknown about the computations carried out in the human face processing network. Recently, deep networks have been proposed as a computational account of human visual processing, but while they provide a good match to neural data throughout visual cortex, they lack interpretability. We introduce a method for interpreting brain activity using a new class of deep generative models, disentangled representation learning models, which learn a low-dimensional latent space that "disentangles" different semantically meaningful dimensions of faces, such as rotation, lighting, or hairstyle, in an unsupervised manner by enforcing statistical independence between dimensions. We find that the majority of our model's learned latent dimensions are interpretable by human raters. Further, these latent dimensions serve as a good encoding model for human fMRI data. We next investigate the representation of different latent dimensions across face-selective voxels. We find that low- and high-level face features are represented in posterior and anterior face-selective regions, respectively, corroborating prior models of human face recognition. Interestingly, though, we find identity-relevant and irrelevant face features across the face processing network. Finally, we provide new insight into the few "entangled" (uninterpretable) dimensions in our model by showing that they match responses in the ventral stream and carry information about facial identity. Disentangled face encoding models provide an exciting alternative to standard "black box" deep learning approaches for modeling and interpreting human brain data.

SHARE-Topic: Bayesian interpretable modeling of single-cell multi-omic data

Multi-omic single-cell technologies, which simultaneously measure the transcriptional and epigenomic state of the same cell, enable understanding epigenetic mechanisms of gene regulation. However, noisy and sparse data pose fundamental statistical challenges to extract biological knowledge from complex datasets. SHARE-Topic, a Bayesian generative model of multi-omic single cell data using topic models, aims to address these challenges. SHARE-Topic identifies common patterns of co-variation between different omic layers, providing interpretable explanations for the data complexity. Tested on data from different technological platforms, SHARE-Topic provides low dimensional representations recapitulating known biology and defines associations between genes and distal regulators in individual cells.

Surging parametrization for gas-liquid centrifugal pumps

The present work investigates the dimensional and similarity representations of two-phase flows in centrifugal pumps. A new parametrization scheme is advanced for the capacity (ϕ=Q/ωD3) and head (ψ=gH/ω2D2) coefficients in terms of the non-dimensional parameters β (no-slip volume gas fraction) and Ω (= ωD/UM, UM = mixture velocity in the inlet pipe). The new parametrization yields universal performance curves that capture the positions of performance degradation (ϕcr and ψmax) and the appearance of surging. The new expressions are supported by a comprehensive set of experiments carried out for volume gas fractions up to 12% and four rotational speeds. The experimental conditions cover the four different flow patterns commonly described in the literature. The experiments are conducted with water and air. The flow parameters are characterized through global parameters (pressures, flow rates). The work confirms the rotation speed as a relevant parameter in the performance determination of gas–liquid systems and shows its relation to bubble breakup and the definition of the four observed flow patterns. The particularly introduced parametrization equations are limited to the geometry of the pump that is tested. The developed methodology, however, is expected to be extendable to pumps of different geometries.

Multi-Head Transformer Architecture with Higher Dimensional Feature Representation for Massive MIMO CSI Feedback

To achieve the anticipated performance of massive multiple input multiple output (MIMO) systems in wireless communication, it is imperative that the user equipment (UE) accurately feeds the channel state information (CSI) back to the base station (BS) along the uplink. To reduce the feedback overhead, an increasing number of deep learning (DL)-based networks have emerged, aimed at compressing and subsequently recovering CSI. Various novel structures are introduced, among which Transformer architecture has enabled a new level of precision in CSI feedback. In this paper, we propose a new method named TransNet+ built upon the Transformer-based TransNet by updating the multi-head attention layer and implementing an improved training scheme. The simulation results demonstrate that TransNet+ outperforms existing methods in terms of recovery accuracy and achieves state-of-the-art.

Finite dimensional irreducible representations of Lie superalgebra D (2, 1; α)

This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2, 1; α). We explicitly construct the finite dimensional representations of the superalgebra D(2, 1; α) by using the shift operator and differential operator representations. Unlike ordinary Lie algebra representation, there are typical and atypical representations for most superalgebras. Therefore, its typical and atypical representation conditions are also given. Our results are expected to be useful for the construction of primary fields of the corresponding current superalgebra of D(2, 1; α).

A Semi-Supervised Multi-Scale Arbitrary Dilated Convolution Neural Network for Pediatric Sleep Staging.

Sleep staging is essential for assessing sleep quality and diagnosing sleep disorders. However, sleep staging is a labor-intensive process, making it arduous to obtain large quantities of high-quality labeled data for automatic sleep staging. Meanwhile, most of the research on automatic sleep staging pays little attention to pediatric sleep staging. To address these challenges, we propose a semi-supervised multi-scale arbitrary dilated convolution neural network (SMADNet) for pediatric sleep staging using the scalogram with a high height-to-width ratio generated by the continuous wavelet transform (CWT) as input. To extract more extended time dimensional feature representations and adapt to scalograms with a high height-to-width ratio in SMADNet, we introduce a multi-scale arbitrary dilation convolution block (MADBlock) based on our proposed arbitrary dilated convolution (ADConv). Finally, we also utilize semi-supervised learning as the training scheme for our network in order to alleviate the reliance on labeled data. Our proposed model has achieved performance comparable to state-of-the-art supervised learning methods with 30% labels. Our model is tested on a private pediatric dataset and achieved 79% accuracy, 72% kappa, and 75% MF1. Therefore, our model demonstrates a powerful feature extraction capability and has achieved performance comparable to state-of-the-art supervised learning methods with a small number of labels.