Dimensional Space Research Articles

Measuring exploration: evaluation of modelling to generate alternatives methods in capacity expansion models

Abstract As decarbonization agendas mature, macro-energy systems modelling studies have increasingly focused on enhanced decision support methods that move beyond least-cost modelling to improve consideration of additional objectives and tradeoffs. One candidate is Modeling to Generate Alternatives (MGA), which systematically explores new objectives without explicit stakeholder elicitation. This paper provides comparative testing of four existing MGA methodologies and proposes a new Combination vector selection approach. We examine each existing method’s runtime, parallelizability, new solution discovery efficiency, and spatial exploration in lower dimensional (N ≤ 100) spaces, as well as spatial exploration for all methods in a three-zone, 8760-hour capacity expansion model case. To measure convex hull volume expansion, this paper formalizes a computationally tractable high-dimensional volume estimation algorithm. We find Random Vector provides the broadest exploration of the near-optimal feasible region and Variable Min/Max provides the most extreme results, while the two tie on computational speed. The new Combination method provides an advantageous mix of the two. Additional analysis is provided on MGA variable selection, in which we demonstrate MGA problems formulated over generation variables fail to retain cost-optimal dispatch and are thus not reflective of real operations of equivalent hypothetical capacity choices. As such, we recommend future studies utilize a parallelized combined vector approach over the set of capacity variables for best results in computational speed and spatial exploration while retaining optimal dispatch.

Hausdorff dimension of the parameters for (α,β)-shifts with the specification property

In this paper, we consider the specification property for ( α , β ) -shifts. When α = 0 , Schmeling shows that the set of β > 1 for which the β-shift has the specification property has the Lebesgue measure zero but has the full Hausdorff dimension [Schmeling. Symbolic dynamics for β-shifts and self-normal numbers, Ergodic Theory Dyn. Syst. 17 (1997), pp. 675–694]. So it is natural to ask what happens when α > 0 . Buzzi shows that for fixed α the set of β > 1 for which the ( α , β ) -shift has the specification property has Lebesgue measure zero. Hence we consider the Hausdorff dimension of the parameter space of ( α , β ) -shifts.

Bayesian Federated Learning with Hamiltonian Monte Carlo: Algorithm and Theory

This work introduces a novel and efficient Bayesian federated learning algorithm, namely, the Federated Averaging stochastic Hamiltonian Monte Carlo (FA-HMC), for parameter estimation and uncertainty quantification. We establish rigorous convergence guarantees of FA-HMC on non-iid distributed datasets, under the strong convexity and Hessian smoothness assumptions. Our analysis investigates the effects of parameter space dimension, noise on gradients and momentum, and the frequency of communication (between the central node and local nodes) on the convergence and communication costs of FA-HMC. Beyond that, we establish the tightness of our analysis by showing that the convergence rate cannot be improved even for continuous FA-HMC process. Moreover, extensive empirical studies demonstrate that FA-HMC outperforms the existing Federated Averaging-Langevin Monte Carlo (FA-LD) algorithm. Supplementary materials for this article are available online.

Forecasting Urban Traffic States with Sparse Data Using Hankel Temporal Matrix Factorization

Forecasting urban traffic states is crucial to transportation network monitoring and management, playing an important role in the decision-making process. Despite the substantial progress that has been made in developing accurate, efficient, and reliable algorithms for traffic forecasting, most existing approaches fail to handle sparsity, high-dimensionality, and nonstationarity in traffic time series and seldom consider the temporal dependence between traffic states. To address these issues, this work presents a Hankel temporal matrix factorization (HTMF) model using the Hankel matrix in the lower dimensional spaces under a matrix factorization framework. In particular, we consider an alternating minimization scheme to optimize the factor matrices in matrix factorization and the Hankel matrix in the lower dimensional spaces simultaneously. To perform traffic state forecasting, we introduce two efficient estimation processes on real-time incremental data, including an online imputation (i.e., reconstruct missing values) and an online forecasting (i.e., estimate future data points). Through extensive experiments on the real-world Uber movement speed data set in Seattle, Washington, we empirically demonstrate the superior forecasting performance of HTMF over several baseline models and highlight the advantages of HTMF for addressing sparsity, nonstationarity, and short time series. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: This research was supported by the Institute for Data Valorisation, the Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, the National Natural Science Foundation of China [Grants 12371456, 72101049, 72232001], the Sichuan Science and Technology Program [Grant 2024NSFJQ0038], and the Fundamental Research Funds for the Central Universities [Grant DUT23RC(3)045].

Projected state ensemble of a generic model of many-body quantum chaos

Abstract The projected ensemble is based on the study of the quantum state of a subsystem A conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the kth moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension q, we find that all moments converge simultaneously with a time scaling linearly in the size of region A, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite q on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times t k = O ( log ⁡ k ) . Our results are supported with numerical simulations performed at q = 2.

Minimal cover of high-dimensional chaotic attractors by embedded recurrent patterns

We propose a general method for constructing a minimal cover of high-dimensional chaotic attractors by embedded unstable recurrent patterns. By minimal cover we mean a subset of available patterns such that the approximation of chaotic dynamics by a minimal cover with a predefined proximity threshold is as good as the approximation by the full available set. The proximity measure, based on the concept of a directed Hausdorff distance, can be chosen with considerable freedom and adapted to the properties of a given chaotic system. In the context of a spatiotemporally chaotic attractor of the Kuramoto–Sivashinsky system on a periodic domain, we demonstrate that the minimal cover can be faithfully constructed even when the proximity measure is defined within a subspace of dimension much smaller than the dimension of space containing the attractor. We discuss how the minimal cover can be used to provide a reduced description of the attractor structure and the dynamics on it.

Homogeneous Riemannian structures in Thurston geometries and contact Riemannian geometries

We give explicit parametrizations for all the homogeneous Riemannian structures on model spaces of Thurston geometry. As an application, we give all the homogeneous contact metric structures on $3$-dimensional Sasakian space forms.

Scaling Learning based Policy Optimization for Temporal Logic Tasks by Controller Network Dropout

This paper introduces a model-based approach for training feedback controllers for an autonomous agent operating in a highly nonlinear (albeit deterministic) environment. We desire the trained policy to ensure that the agent satisfies specific task objectives and safety constraints, both expressed in Discrete-Time Signal Temporal Logic (DT-STL). One advantage for reformulation of a task via formal frameworks, like DT-STL, is that it permits quantitative satisfaction semantics. In other words, given a trajectory and a DT-STL formula, we can compute the robustness , which can be interpreted as an approximate signed distance between the trajectory and the set of trajectories satisfying the formula. We utilize feedback control, and we assume a feed forward neural network for learning the feedback controller. We show how this learning problem is similar to training recurrent neural networks (RNNs), where the number of recurrent units is proportional to the temporal horizon of the agent's task objectives. This poses a challenge: RNNs are susceptible to vanishing and exploding gradients, and naïve gradient descent-based strategies to solve long-horizon task objectives thus suffer from the same problems. To tackle this challenge, we introduce a novel gradient approximation algorithm based on the idea of dropout or gradient sampling. One of the main contributions is the notion of controller network dropout , where we approximate the NN controller in several time-steps in the task horizon by the control input obtained using the controller in a previous training step. We show that our control synthesis methodology, can be quite helpful for stochastic gradient descent to converge with less numerical issues, enabling scalable backpropagation over long time horizons and trajectories over high dimensional state spaces. We demonstrate the efficacy of our approach on various motion planning applications requiring complex spatio-temporal and sequential tasks ranging over thousands of time-steps.

A variational approach to stability relative to a set of single-valued and set-valued mappings

Based on the limiting normal cone relative to a set, we present in this paper the novel versions of the limiting coderivative relative to a set and subdifferentials relative to a set of multifunctions and singleton mappings, respectively. In addition to giving the necessary and sufficient conditions for the Aubin property relative to a set of multifunctions, the limiting coderivative relative to a set also provides a coderivative criterion for the metric regularity relative to a set of multifunctions. Besides, our study establishes sudifferential characteristics of the metric regularity and the locally Lipschitz continuity relative to a set for single-valued mappings. In finite dimensional spaces, our results are more general than the previous results. Furthermore, we also give examples to illustrate our results.

Prediction of fetal brain gestational age using multihead attention with Xception

Accurate gestational age (GA) prediction is crucial for monitoring fetal development and ensuring optimal prenatal care. Traditional methods often face challenges in terms of precision and prediction efficiency. In this context, leveraging modern deep learning (DL) techniques is a promising solution. This paper introduces a novel DL approach for GA prediction using fetal brain images obtained via magnetic resonance imaging (MRI), which combines the strength of the Xception pretrained model with a multihead attention (MHA) mechanism. The proposed model was trained on a diverse dataset comprising 52,900 fetal brain images from 741 patients. The images encompass a GA ranging from 19 to 39 weeks. These pretrained models served as feature extraction components during the training process. The extracted features were subsequently used as the inputs of different configurable MHAs, which produced GA predictions in days. The proposed model achieved promising results with 8 attention heads, 32 dimensionality of the key space and 32 dimensionality of the value space, with an R-squared (R2) value of 96.5 %, a mean absolute error (MAE) of 3.80 days, and a Pearson correlation coefficient (PCC) of 98.50 % for the test set. Additionally, the 5-fold cross-validation results reinforce the model's reliability, with an average R2 of 95.94 %, an MAE of 3.61 days, and a PCC of 98.02 %. The proposed model excels in different anatomical views, notably the axial and sagittal views. A comparative analysis of multiple planes and a single plane highlights the effectiveness of the proposed model against other state-of-the-art (SOTA) models reported in the literature. The proposed model could help clinicians accurately predict GA.

Eigenbin compression for reducing photon-counting CT data size.

Photon-counting CT (PCCT) systems acquire multiple spectral measurements at high spatial resolution, providing numerous image quality benefits while also increasing the amount of data that must be transferred through the gantry slip ring. This study proposes a lossy method to compress photon-counting CT data using eigenvector analysis, with the goal of providing image quality sufficient for applications that require a rapid initial reconstruction, such as to confirm anatomical coverage, scan quality, and to support automated advanced applications. The eigenbin compression method was experimentally evaluated on a clinical silicon PCCT prototype system. The proposed eigenbin method performs principal component analysis (PCA) on a set of PCCT calibration measurements. PCA finds the orthogonal axes or eigenvectors, which capture the maximum variance in the N dimensional photon-count data space, where N is the number of acquired energy bins. To reduce the dimensionality of the PCCT data, the data are linearly transformed into a lower dimensional space spanned by the M<N eigenvectors with highest eigenvalues (i.e., the vectors that account for most of the information in the data). Only M coefficients are then transferred per measurement, which we term eigenbin values. After transmission, the original N energy-bin measurements are estimated as a linear combination of the M eigenvectors. Two versions of the eigenbin method were investigated: pixel-specific and pixel-general. The pixel-specific eigenbin method determines eigenvectors for each individual detector pixel, while the more practically realizable pixel-general eigenbin method finds one set of eigenvectors for the entire detector array. The eigenbin method was experimentally evaluated by scanning a 20cm diameter Gammex Multienergy phantom with different material inserts on a clinical silicon-based PCCT prototype. The method was evaluated with the number of eigenbins varied between two and four. In each case, the eigenbins were used to estimate the original 8-bin data, after which material decomposition was performed. The mean, standard deviation, and contrast-to-noise ratio (CNR) of values in the reconstructed basis and virtual monoenergetic images (VMI) were compared for the original 8-bin data and for the eigenbin data. The pixel-specific eigenbin method reduced photon-counting CT data size by a factor of four with<5% change in mean values and a small noise penalty (mean change in noise of<12%, maximum change in noise of 20% for basis images). The pixel-general eigenbin compression method reduced data size by a factor of 2.67 with<5% change in mean values and a less than 10% noise penalty in the basis images (average noise penalty≤5%). The noise penalty and errors were less for the VMIs than for the basis images, resulting in<5% change in CNR in the VMIs. The eigenbin compression method reduced photon-counting CT data size by a factor of two to four with less than 5% change in mean values, noise penalty of less than 10%-20%, and change in CNR ranging from 15% decrease to 24% increase. Eigenbin compression reduces the data transfer time and storage space of photon-counting CT data for applications that require rapid initial reconstructions.

Parallel finite-element codes for the Bogoliubov-de Gennes stability analysis of Bose-Einstein condensates

We present and distribute a parallel finite-element toolbox written in the free software FreeFEM for computing the Bogoliubov-de Gennes (BdG) spectrum of stationary solutions to one- and two-component Gross-Pitaevskii (GP) equations, in two or three spatial dimensions. The parallelization of the toolbox relies exclusively upon the recent interfacing of FreeFEM with the PETSc library. The latter contains itself a wide palette of state-of-the-art linear algebra libraries, graph partitioners, mesh generation and domain decomposition tools, as well as a suite of eigenvalue solvers that are embodied in the SLEPc library. Within the present toolbox, stationary states of the GP equations are computed by a Newton method. Branches of solutions are constructed using an adaptive step-size continuation algorithm. The combination of mesh adaptivity tools from FreeFEM with the parallelization features from PETSc makes the toolbox efficient and reliable for the computation of stationary states. Their BdG spectrum is computed using the SLEPc eigenvalue solver. We perform extensive tests and validate our programs by comparing the toolbox's results with known theoretical and numerical findings that have been reported in the literature. Program summaryProgram Title: FFEM_BdG_ddm_toolbox.zipCPC Library link to program files:https://doi.org/10.17632/w9hg964wpb.1Licensing provisions: GPLv3Programming language:FreeFEM (v 4.12) free software (www.freefem.org)Nature of problem: Among the plethora of configurations that may exist in Gross-Pitaevskii (GP) equations modeling one or two-component Bose-Einstein condensates, only the ones that are deemed spectrally stable (or even, in some cases, weakly unstable) have high probability to be observed in realistic ultracold atoms experiments. To investigate the spectral stability of solutions requires the numerical study of the linearization of GP equations, the latter commonly known as the Bogoliubov-de Gennes (BdG) spectral problem. The present software offers an efficient and reliable tool for the computation of eigenvalues (or modes) of the BdG problem for a given two- or three-dimensional GP configuration. Then, the spectral stability (or instability) can be inferred from its spectrum, thus predicting (or not) its observability in experiments.Solution method: The present toolbox in FreeFEM consists of the following steps. At first, the GP equations in two (2D) and three (3D) spatial dimensions are discretized by using P2 (piece-wise quadratic) Galerkin triangular (in 2D) or tetrahedral (in 3D) finite elements. For a given configuration of interest, mesh adaptivity in FreeFEM is deployed in order to reduce the size of the problem, thus reducing the toolbox's execution time. Then, stationary states of the GP equations are obtained by a Newton method whose backbone involves the use of a reliable and efficient linear solver judiciously selected from the PETSc1 library. Upon identifying stationary configurations, to trace branches of such solutions a parameter continuation method over the chemical potential in the GP equations (effectively controlling the number of atoms in a BEC) is employed with step-size adaptivity of the continuation parameter. Finally, the computation of the stability of branches of solutions (i.e. the BdG spectrum), is carried out by accurately solving, at each point in the parameter space, the underlying eigenvalue problem by using the SLEPc2 library. Three-dimensional computations are made affordable in the present toolbox by using the domain decomposition method (DDM). In the course of the computation, the toolbox stores not only the solutions but also the eigenvalues and respective eigenvectors emanating from the solution to the BdG problem. We offer examples for computing stationary configurations and their BdG spectrum in one- and two-component GP equations.Running time: From minutes to hours depending on the mesh resolution and space dimension.

Radiation of the energy-critical wave equation with compact support

We prove exterior energy lower bounds for (nonradial) solutions to the energy-critical nonlinear wave equation in space dimensions 3≤d≤5, with compactly supported initial data. In particular, it is shown that nontrivial global solutions with compact spatial support must be radiative in a sharp sense. In space dimensions 3 and 4, a nontrivial soliton background is also considered. As an application, we obtain partial results on the rigidity conjecture concerning solutions with the compactness property, including a new proof for the global existence of such solutions.

DMMGNet: A Discrimination Mapping and Memory Bank Mean Guidance-based Network for High-performance Few-shot Industrial Anomaly Detection

For deep learning-based industrial anomaly detection, it is still challenging to get adequate images for model training and achieve cold start for cross-product migration, restricting their practical application in real industrial production. Herein, an innovative few-shot anomaly detection network DMMGNet based on discrimination mapping and memory bank mean guidance strategies are demonstrated, which is trained by a new two-branch data augmentation technique. By separating the features stored in memory bank from the features used for training, the two-branch data augmentation method can significantly improve the robustness of few-shot model training and reduce the redundance of memory bank. In the elaborately designed discrimination mapping module, new negative samples are generated by adding dynamic Gaussian noise to normal samples along the channel dimension in feature space to solve the problem of sample imbalance. Meanwhile, the discrimination mapping module also helps to map the feature distribution of positive samples to the target domain more efficiently and reduce the deviation of feature domain, conducive to a more precise separation of positive and negative samples. In addition, a novel mean guidance approach with an optimized loss function is developed to guide the positive sample feature mapping by specifying the local feature space center to form a clear feature domain contour and enhance the detection accuracy. The multiple experimental results validate that our DMMGNet outperforms the most advanced anomaly detection counterparts on image-level AUROC, showing an increase by 0.3-3% on both MVTec AD and MPDD benchmarks under several few-shot scenarios.

Gravitational wave signal extraction against non-stationary instrumental noises with deep neural network

Sapce-borne gravitational wave antennas, such as LISA and LISA-like mission (Taiji and Tianqin), will offer novel perspectives for exploring our Universe while introduce new challenges, especially in data analysis. Aside from the known challenges like high parameter space dimension, superposition of large number of signals etc., gravitational wave detections in space would be more seriously affected by anomalies or non-stationarities in the science measurements. Considering the three types of foreseeable non-stationarities including data gaps, transients (glitches), and time-varying noise auto-correlations, which may come from routine maintenance or unexpected disturbances during science operations, we developed a deep learning model for accurate signal extractions confronted with such anomalous scenarios. Our model exhibits the same performance as the current state-of-the-art models do for the ideal and anomaly free scenario, while shows remarkable adaptability in extractions of coalescing massive black hole binary signal against all three types of non-stationarities and even their mixtures. This also provide new explorations into the robustness studies of deep learning models for data processing in space-borne gravitational wave missions.

Constructing all BPS black hole microstates from the gravitational path integral

Understanding how to prepare and count black hole micro-states by using the gravitational path integral is one of the most important problems in quantum gravity. Nevertheless, a state-by-state count of black hole microstates is difficult because the apparent number of degrees of freedom available in the gravitational effective theory can vastly exceed the entropy of the black hole, even in the special case of BPS black holes. In this paper, we show that we can use the gravitational path integral to prepare a basis for the Hilbert space of all BPS black hole microstates. We find that the dimension of this Hilbert space computed by an explicit state count is in complete agreement with the degeneracy obtained from the Gibbons-Hawking prescription. Specifically, this match includes all non-perturbative corrections in 1/GN. Such corrections are, in turn, necessary in order for this degeneracy of BPS states to match the non-perturbative terms in the 1/GN expansion in the string theory count of such microstates.

Efficient six-dimensional phase space reconstructions from experimental measurements using generative machine learning

Efficient six-dimensional phase space reconstructions from experimental measurements using generative machine learning

An automated convergence diagnostic for phylogenetic MCMC analyses.

Assessing convergence of Markov chain Monte Carlo (MCMC) based analyses is crucial but challenging, especially so in high dimensional and complex spaces such as the space of phylogenetic trees (treespace). In practice, it is assumed that the target distribution is the unique stationary distribution of the MCMC and convergence is achieved when samples appear to be stationary. Here we leverage recent advances in computational geometry of the treespace and introduce a method that combines classical statistical techniques and algorithms with geometric properties of the treespace to automatically evaluate and assess practical convergence of phylogenetic MCMC analyses. Our method monitors convergence across multiple MCMC chains and achieves high accuracy in detecting both practical convergence and convergence issues within treespace. Furthermore, our approach is developed to allow for real-time evaluation during the MCMC algorithm run, eliminating any of the chain post-processing steps that are currently required. Our tool therefore improves reliability and efficiency of MCMC based phylogenetic inference methods and makes analyses easier to reproduce and compare. We demonstrate the efficacy of our diagnostic via a well-calibrated simulation study and provide examples of its performance on real data sets. Although our method performs well in practice, a significant part of the underlying treespace probability theory is still missing, which creates an excellent opportunity for future mathematical research in this area. The open source package for the phylogenetic inference framework BEAST2, called ASM, that implements these methods, making them accessible through a user-friendly GUI, is available from https://github.com/rbouckaert/asm/. The open source Python package, called tetres, that provides an interface for these methods enabling their applications beyond BEAST2 can be accessed at https://github.com/bioDS/tetres/.

China's logistics evolution: A study of development characteristics and catalytic effects on economic growth.

The impact of logistics development on the economy covers many aspects, such as production, cost, employment, international trade, etc. It is an indispensable part of the modern economy, which helps to improve overall economic efficiency and social prosperity. This study studies the spatiotemporal dynamic evolution characteristics of China's logistics development from 2008 to 2018 and explores its impact on economic growth in multiple dimensions of time and space. The research findings indicate the following: (1) From 2008 to 2018, China's logistics development level (LDL) exhibited a clear upward trend. The differences between the eastern, central, and western regions showed fluctuating downward patterns, ultimately converging towards a high-level concentration. Concerning spatial distribution, China's logistics development demonstrated a trend towards the west and south. However, the spatial pattern of "strong in the east and weak in the west " has existed for a long time. Moreover, the "T-shaped" pattern between coastal provinces and those along the Yangtze River Basin deepened, and the LDL in the central and western regions significantly improved. (2) The advancement of China's LDL effectively promotes its economic growth, confirming that the Belt and Road Initiative enhances the role of logistics development in driving economic growth. Regarding regional differences, logistics development positively influences economic growth in the eastern and western regions, with a less significant impact on the central region. Regarding the strength of influence, logistics development has a more substantial effect on promoting high-ranking provinces in the entire country, the eastern region, and the central region, as well as boosting economic growth in low-ranking provinces in the western region.

Severity Scale of Diabetic Macular Ischemia Based on the Distribution of Capillary Nonperfusion in OCT Angiography

To evaluate the severity scales of diabetic macular ischemia (DMI) by analyzing the quantity and distribution of capillary nonperfusion using OCT angiography (OCTA) images. A single-center, prospective case series. Three hundred one eyes from 301 patients with diabetic retinopathy. We acquired 3× 3-mm swept-source OCTA images and created en face images within a central 2.5-mm circle. The circle was divided into 15× 15-pixel squares and nonperfusion squares (NPSs) were defined as those without retinal vessels. Eyes with high-dimensional spatial data were arranged on a 2-dimensional space using the uniform manifold approximation and projection (UMAP) algorithm and classified by clustering into 5 groups: Initial, Mild, Superficial, Moderate, and Severe. Development of a severity scale for DMI. Eyes arranged on a 2-dimensional UMAP space were divided into 5 clusters, based on the similarity of nonperfusion area distribution. Nonperfusion square counts in the deep layer increased in eyes of the Initial, Mild, Moderate, and Severe groups in a stepwise manner. In contrast, there were no significant changes in superficial NPS counts between eyes of the Initial and Mild groups. In the intermediate stage, eyes of the Superficial group exhibited higher NPS counts in the central sector of the superficial layer compared with those of the Moderate group. The foveal avascular zone extended into the temporal subfield of the deep layer in eyes of the Moderate group. Eyes of the Severe group had significantly poorer visual acuity that was more frequently accompanied with proliferative diabetic retinopathy. The application of dimensionality reduction and clustering has facilitated the development of a novel severity scale for DMI based on the distribution of capillary nonperfusion in OCTA images. The authors have no proprietary or commercial interest in any materials discussed in this article.