Discrete Space Research Articles

Research on Leak Detection of Low-Pressure Gas Pipelines in Buildings Based on Improved Variational Mode Decomposition and Robust Kalman Filtering.

Aiming at the complex characteristics of negative pressure waves in low-pressure pipelines inside of buildings, we proposed an estimation method of pressure fluctuation trends based on the robust Kalman filter and the improved VMD, which can be used for leakage detection. The reconstructed baseline signal can accurately describe the fluctuation trend of the negative pressure wave after the pressure drop, and quantitatively express the characteristic difference between the leakage condition and the gas usage condition. The robust Kalman filter was used to estimate the pressure fluctuations. The parameters of VMD were adaptively calculated based on the WAA and discrete scale space. The trend components contained in the IMFs were separated by a reconstruction based on the Fourier series. Based on the simulation signal, the method can accurately restore the trend component contained in the complex pressure signal. Based on the actual signals, the accuracy of small leakage detection is 96.7% and the accuracy of large leakage detection is 73.3%.

Influence of control parameters on the stabilization of an Euler-Bernoulli flexible beam

In this work, we numerically study the influence of control parameters on the stabilization of a flexible Euler-Bernoulli beam fixed at one end and subjected at the other end to a force control and a punctual moment control proportional respectively to velocity and rotation velocity. First, we analyze the displacement stabilization and the asymptotic behavior of the beam energy using a stable numerical scheme, resulting from the Crank-Nicholson algorithm for time discretization and the finite element method based on the approximation by Hermite's cubic polynomial functions, for discretization in space. Then, by means of the finite element method, we represent the spectrum of the operator associated with this beam problem and we carry out a qualitative study of thelocus of the eigenvalues according to the positive control parameters. From these studies we conclude that rotation velocity control has more effect on the stabilization of the beam compared to velocity control. Finally, this result is confirmed by a sensitivity study on the control parameters involved in the stabilization of the beam.

Aging suppression in Multistrip Multigap Resistive Plate Chambers for high counting rate experiments

A long term operation of Multi-Strip Multi-Gap Resistive Plate Chambers (MSMGRPC) with gas mixtures based on C2H2F4 and SF6 leads to aging effects observed as depositions on the surface of the resistive electrodes, especially in the region of the spacers used for defining the gas gaps between the resistive electrodes. The observed higher noise rate and dark current has a negative impact on the performance of the chamber and leads to an increase of the data volume in a free running readout mode operation. MSMGRPC prototypes designed with a direct gas flow through the gas gaps and minimization of the number of spacers in the active area were developed as mitigation solution. Three new prototypes of different granularities were assembled using fishing line as spacers and investigated for aging effects. Although a significant reduction in the dark current and dark counting rate was evidenced, noise rate localized around the fishing line spacers, even though reduced, still remains. In this paper, a new generation of direct flow chambers based on discrete spacers is presented. The results of their aging investigations show that, even at lower gas flows, the aging effects become negligible.

Gradient-based optimization for quantum architecture search

Quantum Architecture Search (QAS) has shown significant promise in designing quantum circuits for Variational Quantum Algorithms (VQAs). However, existing QAS algorithms primarily explore circuit architectures within a discrete space, which is inherently inefficient. In this paper, we propose a Gradient-based Optimization for Quantum Architecture Search (GQAS), which leverages a circuit encoder, decoder, and predictor. Initially, the encoder embeds circuit architectures into a continuous latent representation. Subsequently, a predictor utilizes this continuous latent representation as input and outputs an estimated performance for the given architecture. The latent representation is then optimized through gradient descent within the continuous latent space based on the predicted performance. The optimized latent representation is finally mapped back to a discrete architecture via the decoder. To enhance the quality of the latent representation, we pre-train the encoder on a substantial dataset of circuit architectures using Self-Supervised Learning (SSL). Our simulation results on the Variational Quantum Eigensolver (VQE) indicate that our method outperforms the current Differentiable Quantum Architecture Search (DQAS).

Intelligent decision-making for a “Three-Variable” frequency-hopping pattern based on OC-CDRL

The frequency hopping pattern of the existing frequency hopping communication system is not designed according to the electromagnetic interference environment, resulting in blind anti-jamming. Therefore, to address this problem, a “three-variable” frequency-hopping pattern is proposed, where the frequency, hopping rate, and instantaneous bandwidth of the frequency-hopping signal vary randomly based on the background electromagnetic interference. The decision-making problem of the “three-variable” frequency-hopping pattern is modeled as a Markov decision process (MDP) by constructing the state-action-reward tuple. The designed frequency varies continuously within a small frequency band selected from a pseudo-random sequence to alleviate the problem of dimension explosion in decision-making. At the same time, discrete values for the hopping rate and instantaneous bandwidth are designed. To solve this MDP problem efficiently, a combined deep reinforcement learning algorithm (OC-CDRL) based on optimistic exploration and conservative estimation is proposed, which combines the features of TD3 and D3QN algorithms and designs the corresponding states, actions, and rewards to deal with continuous and discrete action spaces, respectively. To address the problem that the D3QN algorithm tends to fall into local optimal solutions, an optimistic exploration strategy (OES) for action selection is proposed to improve the degree of exploration. Moreover, the loss function is improved by conservatively estimating state–action pairs outside the experience replay buffer, reducing the overestimation of the optimistic action-value function and increasing the stability and convergence of the algorithm. Comparative simulation results of the algorithms in different electromagnetic interference environments show that the OC-CDRL algorithm effectively avoids most regions with higher interference and has better adaptability and anti-jamming capability.

Microscopic simulation of bicycle traffic flow incorporating cyclists’ heterogeneous dynamics and non-lane-based movement strategies

Cycling as a mode of transport is on an upward trend as a low-emission alternative to driving in urbanized areas nowadays. With the increasing number of cyclists, it is of great importance to assess the capacity of cycling infrastructure in practice. Simulation models are useful tools to investigate bicycle flow performance considering cyclists’ distinct moving behaviors. However, existing bicycle simulation models are restricted by either space discretization, lane-based setup, adaptation from models for car traffic, or complicated calibration requirement in a force-based environment. In addition, cyclists’ decision-making ability in the operational-level cycling behavior are not well-captured in these models. This paper proposes a comprehensible microscopic bicycle simulation model which includes a detailed decision-making process and the ability to simulate continuous-space lateral movement. The model consists of three levels, maneuver decision, movement planning, and physical acceleration. It is able to simulate bicycle flow dynamics in undersaturated traffic conditions on an exclusive bike path. As we do not intend to show the empirical validity of the proposed model, the simulation experiment aims at verifying the model and exploring bicycle flow performance in various scenarios by estimating the fundamental diagrams (FDs). The effect of different path widths on bicycle flow capacity is first explored. Other behavioral factors, including desired speed heterogeneity, overtaking incentive, and safety region size perceived by cyclists, which can potentially influence the shape of the FD are also tested. The model can be further extended to simulate relatively complex cycling behavior with cooperative and anticipative strategies and investigate bicycle flow characteristics in congested traffic conditions.

Neural Solving Uninterpreted Predicates with Abstract Gradient Descent

Uninterpreted predicate solving is a fundamental problem in formal verification, including loop invariant and Constrained Horn Clauses predicate solving. Existing approaches have been mostly in symbolic ways. While achieving sustainable progress, they still suffer from inefficiency and seem unable to leverage the ever-increasing computility such as GPU. Recently, Neural Relaxation has been proposed to tackle this problem. They treat the uninterpreted predicate-solving task as an optimization problem by relaxing the discrete search process into a learning process of neural networks. However, two bottlenecks keep them from being valid. First, relaxed neural networks cannot match the original semantics rigorously; second, the neural networks are difficult to train to reach global optimization. Therefore, this paper presents a novel discrete neural architecture with the Abstract Gradient Decent (AGD) algorithm to directly solve uninterpreted predicates in the discrete hypothesis space. The abstract gradient is for discrete neurons whose calculation rules are designed in an abstract domain. Our approach conforms to the original semantics, and the proposed AGD algorithm can achieve global optimization satisfactorily. We implement Dasp in the Boxes Abstract Domain to solve uninterpreted predicates in the QF-NIA SMT theory. In the experiments, Dasp has outperformed 7 state-of-the-art tools across three predicate synthesis tasks.

Phase field modeling and numerical algorithm for two-phase dielectric fluid flows

We develop a method for modeling and simulating a class of two-phase flows consisting of two immiscible incompressible dielectric fluids and their interactions with imposed external electric fields in two and three dimensions. We first present a thermodynamically-consistent and reduction-consistent phase field model for two-phase dielectric fluids. The model honors the conservation laws and thermodynamic principles, and has the property that, if only one fluid component is present in the system, the two-phase formulation will exactly reduce to that of the corresponding single-phase system. In particular, this model accommodates an equilibrium solution that is compatible with the zero-velocity requirement based on physics. This property leads to a simpler method for simulating the equilibrium state of two-phase dielectric systems. We further present an efficient numerical algorithm, together with a spectral-element (for two dimensions) or a hybrid Fourier-spectral/spectral-element (for three dimensions) discretization in space, for simulating this class of problems. This algorithm computes different dynamic variables successively in an un-coupled fashion, and involves only coefficient matrices that are time-independent in the resultant linear algebraic systems upon discretization, even when the physical properties (e.g. permittivity, density, viscosity) of the two dielectric fluids are different. This property is crucial and enables us to employ fast Fourier transforms for three-dimensional problems. Ample numerical simulations of two-phase dielectric flows under imposed voltage are presented to demonstrate the performance of the method herein and to compare the simulation results with theoretical models and experimental data.

Актуализация подходов к исследованию неоднородности экономического пространства

The article distinguishes the categories of “heterogeneity of economic space” and “interregional social differentiation”, as well as the ways of their assessment. On the basis of the theories of new economic geography and center-periphery theory, the nature of spatial heterogeneity is revealed. The heterogeneity of Russia’s economic space is analyzed through the prism of two key properties of space, i.e., density and connectivity. It is shown that the spatial heterogeneity in terms of population density is growing against the background of decreasing differentiation of space in terms of economic density, measured as GRP per 1 km 2 and volume of investment in fixed capital per 1 km 2 , which can be explained by the fact that the economy is in a phase of recession. A positive correlation between population density and highway density is revealed, which can be explained by the discreteness of space. Based on empirical data, the authors conclude that communicative compression of economic space is characteristic of regions with high population density and economic density and regions with extremely low population density and transport connectivity. In the first case, it is evidence of high business activity in the territory, while in the second case it is a way to increase the availability of services. Based on the comparison of population density and economic density of space, four types of territories were identified: territories of spatial compression; territories with growing population density against the background of high economic density of space; and territories characterized by high population density with relatively low density of economic space; territories with relatively low population density and a trend for its further reduction against the background of high economic density of space. The priorities of spatial development are defined for each type of territory.

Analysis of a positivity-preserving splitting scheme for some semilinear stochastic heat equations

We construct a positivity-preserving Lie–Trotter splitting scheme with finite difference discretization in space for approximating the solutions to a class of semilinear stochastic heat equations with multiplicative space-time white noise. We prove that this explicit numerical scheme converges in the mean-square sense, with rate 1/4 in time and rate 1/2 in space, under appropriate CFL conditions. Numerical experiments illustrate the superiority of the proposed numerical scheme compared with standard numerical methods which do not preserve positivity.

Adaptive Space Search-based Molecular Evolution Optimization Algorithm.

In drug development process, a significant portion of budget and research time are dedicated to the lead compound optimization procedure in order to identify potential drugs. This procedure focuses on enhancing the pharmacological and bioactive properties of compounds by optimizing their local substructures. However, due to the vast and discrete chemical structure space and the unpredictable element combinations within this space, the optimization process is inherently complex. Various structure enumeration-based combinatorial optimization methods have shown certain advantages. However, they still have limitations. Those methods fail to consider the differences between molecules and struggle to explore the unknown outer search space. In this study, we propose an adaptive space search-based molecular evolution optimization algorithm (ASSMOEA). It consists of three key modules: construction of molecule-specific search space, molecular evolutionary optimization, and adaptive expansion of molecule-specific search space. Specifically, we design a fragment similarity tree in molecule-specific search space, and apply a dynamic mutation strategy in this space to guide molecular optimization. Then we utilize an encoder-encoder structure to adaptively expand the space. Those three modules are circled iteratively to optimize molecules. Our experiments demonstrate that ASSMOEA outperforms existing methods in terms of molecular optimization. It not only enhances the efficiency of the molecular optimization process, but also exhibits a robust ability to search for correct solutions. The code is freely available on the web at https://github.com/bbbbb-b/MEOAFST. Supplementary data are available at Bioinformatics online.

Time-dependent dynamical energy analysis via convolution quadrature

Dynamical Energy Analysis was introduced in 2009 as a novel method for predicting high-frequency acoustic and vibrational energy distributions in complex engineering structures. In this paper we introduce the first time-dependent Dynamical Energy Analysis method. Time-domain models are important in numerous applications including sound simulation in room acoustics, predicting shock-responses in structural mechanics and modelling electromagnetic scattering from conductors. The first step is to reformulate Dynamical Energy Analysis in the time-domain by means of a convolution integral operator. We are then able to employ the Convolution Quadrature method to provide a link between the previous frequency-domain implementations of Dynamical Energy Analysis and fully time-dependent solutions by means of the Z-transform. By combining a modified multistep Convolution Quadrature approach for the time discretisation, together with Galerkin and Petrov-Galerkin methods for the space and momentum discretisations, respectively, we are able to accurately track the propagation of high-frequency transient signals through phase-space. The implementation here is detailed for finite two-dimensional spatial domains and we demonstrate the versatility of our approach by performing a range of numerical experiments for regular, non-convex and irregular geometries as well as different types of wave source.

A memory interaction quadratic interpolation whale optimization algorithm based on reverse information correction for high-dimensional feature selection

Feature selection is a key technique for data dimensionality reduction, and there are many challenges in facing the exponential expansion phenomenon of high-dimensional decision space. In order to improve the quality of feature selection, we propose a memory interaction quadratic interpolation whale optimization algorithm based on reverse information correction (RQWOA). First, in order to improve the convergence capability of the Whale Optimization Algorithm (WOA) in high-dimensional space, we propose a quadratic interpolation mechanism with memory information interaction, improve the quality of the datum points used for quadratic interpolation through the proposed memory interaction mechanism, and accelerate the convergence speed and accuracy of the algorithm with the help of the quadratic interpolation on the algorithm exploitation capability. In addition, to address the invalid probability flip in the feature selection subset when mapping to the discrete space, we propose a reverse information correction mechanism to judge and correct each dimension in the feature subset by using the reverse complementary information provided by individuals with poor fitness values in the population, so as to better remove invalid or redundant features and improve the quality of feature selection. Finally, in the 15 high-dimensional feature datasets compared with the comparison methods, the accuracy of RQWOA is improved by 7.49 % on average, and the number of features is compressed by 80.42 % on average, which indicates that the RQWOA algorithm has stronger feature identification and redundancy removal capabilities and can better solve the feature selection problem.

Topology Meets Number Theory

Liouville proved the existence of a set L of transcendental real numbers now known as Liouville numbers. Erdős proved that while L is a small set in that its Lebesgue measure is zero, and even its s-dimensional Hausdorff measure, for each s > 0, equals zero, it has the Erdős property, that is, every real number is the sum of two numbers in L . He proved L is a dense G δ -subset of R and every dense G δ -subset of R has the Erdős property. While being a dense G δ -subset of R is a purely topological property, all such sets contain c Liouville numbers. Each dense G δ -subset of R , including L , is homeomorphic to the product N ℵ 0 of copies of the discrete space N of all natural numbers. Also this product space is homeomorphic to the space P of all irrational real numbers and the space T of all transcendental real numbers. Hence every dense G δ -subset of R has cardinality c . Indeed, any dense G δ -subset of R has a chain Xm , m ∈ ( 0 , ∞ ) of homeomorphic dense G δ -subsets such that X m ⊂ X n , for n < m, and X n ∖ X m has cardinality c . Finally, every real number r ≠ 1 is equal to ab , for some a , b ∈ L .

Peak response regularization for localization

Deep convolutional neural networks approaches often assume that the feature response has a Gaussian distribution with target-centered peak response, which can be used to guide the target location and classification. Nevertheless, such an assumption is implausible when there is progressive interference from other targets and/or background noise, which produces sub-peaks on the tracking response map and causes model drift. In this paper, we propose a feature response regularization approach for sub-peak response suppression and peak response enforcement and aim to handle progressive interference systematically. Our approach, referred to as Peak Response Regularization (PRR), applies simple-yet-efficient method to aggregate and align discriminative features, which convert local extremal response in discrete feature space to extremal response in continuous space, which enforces the localization and representation capability of convolutional features. Experiments on human pose detection, object detection, object tracking, and image classification demonstrate that PRR improves the performance of image tasks with a negligible computational cost.

On Entropic Learning from Noisy Time Series in the Small Data Regime.

In this work, we present a novel methodology for performing the supervised classification of time-ordered noisy data; we call this methodology Entropic Sparse Probabilistic Approximation with Markov regularization (eSPA-Markov). It is an extension of entropic learning methodologies, allowing the simultaneous learning of segmentation patterns, entropy-optimal feature space discretizations, and Bayesian classification rules. We prove the conditions for the existence and uniqueness of the learning problem solution and propose a one-shot numerical learning algorithm that-in the leading order-scales linearly in dimension. We show how this technique can be used for the computationally scalable identification of persistent (metastable) regime affiliations and regime switches from high-dimensional non-stationary and noisy time series, i.e., when the size of the data statistics is small compared to their dimensionality and when the noise variance is larger than the variance in the signal. We demonstrate its performance on a set of toy learning problems, comparing eSPA-Markov to state-of-the-art techniques, including deep learning and random forests. We show how this technique can be used for the analysis of noisy time series from DNA and RNA Nanopore sequencing.

Total ankle arthroplasty improves discrete and continuous stance phase gait symmetry

BackgroundTotal ankle arthroplasty (TAA) is used to treat symptomatic end-stage ankle arthritis (AA). However, little is known about TAA's effects on gait symmetry. Research questionDetermine if symmetry changes from before surgery through two years following TAA utilizing the normalized symmetry index (NSI) and statistical parametric mapping (SPM). Methods141 patients with end-stage unilateral AA were evaluated from a previously collected prospective database, where each participant was tested within two weeks of surgery (Pre-Op), one year and two years following TAA. Walking speed, hip extension angle and moment, hip flexion angle, ankle plantarflexion angle and moment, ankle dorsiflexion angle, weight acceptance (GRF1), and propulsive (GRF2) vertical ground reaction forces were calculated for each limb. Gait symmetry was assessed using the NSI. A linear mixed effects model with a single response for each gait symmetry variable was used to examine the fixed effect of follow-up time (Pre-Op, Post-1 yr, Post-2 yr) and the random effect of participant with gait speed as a covariate in the model. A one-dimensional repeated measures analysis of variance (ANOVA) statistical parameter mapping (SPM) was completed to examine differences in the time-series NSI to determine regions of significant differences between follow-up times. ResultsRelative to Pre-Op values, GRF1, and GRF2 showed increased symmetry for discrete metrics and the time-series NSI across sessions. Hip extension moment had the largest symmetry improvement. Ankle plantarflexion angle was different between Pre-Op and Post-2 yr (p=0.010); and plantarflexion moment was different between Pre- Op and each post-operative session (p<0.001). The time-series Ankle Angle NSI was greater during the early stance phase in the Pre-Op session compared to Post-2 yr. SignificanceSymmetry across most of the stance phase improved following TAA indicating that TAA successfully improves gait symmetry and future work should determine if these improvements restore symmetry to levels equivalent with health age-match controls.

Finite variation sensitivity analysis in the design of isotropic metamaterials through discrete topology optimization

AbstractThis article extends recently developed finite variation sensitivity analysis (FVSA) approaches to an inverse homogenization problem. The design of metamaterials with prescribed mechanical properties is stated as a discrete density‐based topology optimization problem, in which the design variables define the microstructure of the periodic base cell. The FVSA consists in estimating the finite variations of the objective and constraint functions after independently switching the state of each variable. It is used to properly linearize the functions of binary variables so the optimization problem can be solved through sequential integer linear programming. Novel sensitivity expressions were developed and it was shown that they are more accurate than the ones conventionally used in literature. Referred to as the conjugate gradient sensitivity (CGS) approach, the proposed strategy was quantitatively evaluated through numerical examples. In these examples, metamaterials with prescribed homogenized Poisson's ratios and minimal homogenized Young's moduli were obtained. A hexagonal base cell with dihedral symmetry was used to produce only metamaterials with isotropic properties. It was shown that, by using the CGS approach instead of the conventional sensitivity analysis, the sensitivity error was substantially reduced for the considered problem. The proposed developments effectively improved the stability and robustness of the discrete optimization procedures. In all the considered examples, when more accurate sensitivity analyses were performed, the parameters of the topology optimization method could be tuned more easily, yielding effective solutions even if the settings were not ideal.

Topological derivative based sensitivity analysis for three-dimensional discrete variable topology optimization

This study introduces a novel Topological Derivative-based Sensitivity Analysis (TDSA) methodology for three-dimensional (3D) discrete variable topology optimization. Recently, the authors pointed out that the discrete variable sensitivity can be related to the topological derivative, and thus can be rationally approximated by the specially customized topological derivative for plane stress problems. However, the 3D discrete variable sensitivity requires the 3D topological derivative with element-shaped (e.g., unit cube) domain perturbation, whose analytical solution is not available in the literature. This paper proposes a unified parameter fitting framework to calculate the 3D topological derivative with arbitrary shape 3D domain perturbation. The formula for spherical hole perturbation obtained through this parameter fitting framework is identical to the well-known analytical topological derivative formula. Further, the 3D discrete variable sensitivity can be easily obtained through element-shaped domain perturbation. With the recently proposed Sequential Approximate Integer Programming (SAIP), numerical examples demonstrate that TDSA is precise not only for the self-adjoint 3D minimum compliance problems but also for the non-adjoint 3D compliant mechanism design problems. In sum, numerical examples have been conducted by feeding the derived sensitivity to the SAIP optimization algorithms, and the correctness of the sensitivity information has been well demonstrated. This research further solidifies the foundation of rational discrete variable sensitivity analysis in 3D topology optimization.

Coordinated configuration of hybrid energy storage for electricity-hydrogen integrated energy system

This paper proposes an optimal coordinated configuration method of hybrid electricity and hydrogen storage for the electricity‑hydrogen integrated energy system (EH-ES) to promote the renewable energy source (RES) utilization and reduce the deployment cost. To simulate the practical operation of EH-ES, an energy hub framework with a discrete state space system matrix is designed to characterize the internal interconnection topology and quantify the steady-state production, storage, conversion and utilization processes of electricity and hydrogen energy carriers within EH-ES. A chronological operation simulation based electricity and hydrogen storage configuration model over a year-round time horizon is formulated to collaboratively optimize the capacity of the electrolyzer, fuel cell, battery energy storage (BES) and hydrogen storage tank. In this model, the power and capacity complementarity of BES and generalized hydrogen storage is fully exploited to compensate for power and energy imbalances, and additional capacity configuration of BES is considered to mitigate the drastic electrolytic power fluctuation. Besides, a typical source-load scenario reduction method based on K-means and ordered clustering is developed to avoid a large number of operation variables due to year-round hourly simulation. Comparative studies demonstrate that the proposed methodology can achieve the RES consumption rate of 98.873 % while the equipment investment cost can be reduced by 10.034 %.