Domain Partitioning Research Articles

A Novel Method Based on the Fuzzy Entropy Measure to Optimize the Fuzziness in Trapezoidal Strong Fuzzy Partitions

Analyzing the uncertainty of outcomes based on estimates of the data’s membership degrees to fuzzy sets is essential for making decisions. These fuzzy sets are often designated by experts as strong fuzzy partitions of the data domain with trapezoidal fuzzy numbers. Some indices of the fuzzy set’s fuzziness provide an assessment of the degree of uncertainty of the results. It is feasible to bring the fuzzy sets’ fuzziness below a tolerable level by suitably redefining the strong fuzzy partition. Significant differences in the original fuzzy partition, however, result in disparities concerning the decision maker’s approximative reasoning and the interpretability of the results. In light of this, we provide in this study a technique applied to trapezoidal strong fuzzy partitions that, while not appreciably altering the original fuzzy partition, reduces the fuzziness of its fuzzy sets. The fuzziness of the fuzzy sets is assessed using the De Luca and Termini fuzzy entropy. An iterative process is then executed, with the aim of modifying the cores of the trapezoidal fuzzy partitions to decrease their fuzziness. This technique is tested on datasets containing average daily temperatures measured in various cities. The findings demonstrate that this approach strikes a great balance between the goal of lessening the fuzziness of the fuzzy sets and the goal of not appreciably altering the original fuzzy partition.

A Novel Approach for Thermoelastic Fracture Simulation in Bimaterials Using Element-Free Galerkin Method with Improved Interface Modeling

Layered materials play a crucial role in numerous essential structures, including adhesive connections, composite laminates, and various electronic components. This work focuses on proposing a novel framework of algorithms to improve the adaptability of element-free Galerkin method for modeling fracture in bimaterials exposed to thermoelastic loads. A bimaterial fracture problem is modeled as a combination of both weak and strong discontinuities — strong discontinuity owing to the presence of crack and weak discontinuity due to inherent material discontinuities. Initially, three distinct methods, comprising domain partitioning, lagrange multiplier, and jump function have been employed for interface crack modeling and error norm is used as an indicator to select the optimum one. Second, a novel interface enrichment algorithm has been introduced to effectively model the interface with limited computational costs with higher accuracy. Owing to the applicability of bimaterials in numerous applications under a combination of thermal/mechanical loads, the proposed formulation has been utilized for modeling and simulating a diverse bimaterial thermoelastic fracture problems using the proposed framework. The mixed mode (complex) stress intensity factors (SIFs) are numerically examined using modified domain form of interaction integral. A good agreement of results with available results from literature extends the computational prowess of the proposed framework in modeling a variety of thermoelastic bimaterial problems accurately and swiftly as compared to conventional EFGM.

Real-time Bayesian inversion in resin transfer moulding using neural surrogates

In Resin Transfer Moulding (RTM), local variations in reinforcement properties (porosity and permeability) and the formation of gaps along the reinforcement edges result in non-uniform resin flow patterns, which may cause defects in the produced composite component. The ensemble Kalman inversion (EKI) algorithm has previously been used to invert in-process data to estimate local reinforcement properties. However, implementation of this algorithm in some applications is limited by the requirement to run thousands of computationally expensive resin flow simulations. In this study, a machine learning approach is used to train a surrogate model which can emulate resin flow simulations near-instantaneously. A partition of the flow domain into a low-dimensional representation enables an artificial neural network (ANN) surrogate to make accurate predictions, with a simple architecture. When the ANN is integrated within the EKI algorithm, estimates for local reinforcement permeability and porosity can be achieved in real time, as was verified by virtual and lab experiments. Since EKI utilises the Bayesian framework, estimates are given within confidence intervals and statements can be made on-line regarding the probability of defects within sections of the reinforcement. The proposed framework has shown good predictive capabilities for the set of laboratory experiments and estimates for reinforcement properties were always computed within 1 s.

Reassessing the exon–foldon correspondence using frustration analysis

Protein folding and evolution are intimately linked phenomena. Here, we revisit the concept of exons as potential protein folding modules across a set of 38 abundant and conserved protein families. Taking advantage of genomic exon-intron organization and extensive protein sequence data, we explore exon boundary conservation and assess the foldon-like behavior of exons using energy landscape theoretic measurements. We found deviations in the exon size distribution from exponential decay indicating selection in evolution. We show that when taken together there is a pronounced tendency to independent foldability for segments corresponding to the more conserved exons, supporting the idea of exon-foldon correspondence. While 45% of the families follow this general trend when analyzed individually, there are some families for which other stronger functional determinants, such as preserving frustrated active sites, may be acting. We further develop a systematic partitioning of protein domains using exon boundary hotspots, showing that minimal common exons correspond with uninterrupted alpha and/or beta elements for the majority of the families but not for all of them.

An algebraic global linelet preconditioner for incompressible flow solvers

Given the wide range of scales present in fluid dynamics, highly anisotropic meshes are often employed to resolve boundary layer flow at high Reynolds numbers. However, such meshes result in distorted elements, which can deteriorate the convergence of the preconditioned conjugate gradient solver (PCG) used to solve the discrete pressure equations. To address this issue, the Linelet Preconditioner is commonly used to accelerate the convergence rate of the PCG by building line segments (linelets) along the direction of the strongest couplings and applying a specific operation to each linelet. Under the current state of the art, linelets are constrained to operate independently within each domain partition. In these scenarios, PCG convergence was observed to deteriorate when the number of domain partitions is increased. This work proposes a communication step to be integrated into the preconditioning step, enabling different linelets to exchange information. The proposed method is observed to improve the convergence rate of linear systems with high stiffness due to highly stretched elements. Also, an algorithm is developed to generate the preconditioning matrix by purely algebraic considerations, in contrast to the usual approach of building linelets based on geometrical considerations. Furthermore, since the current approach is agnostic to the domain partition, it does not impose any constraint on the domain decomposition. Hence, the proposed method is a robust preconditioner with a numerical performance almost independent of the quality of the domain decomposition, providing a way for a more balanced load distribution.

Domain partition leads to a manifold increase of heat transport in Rayleigh–Bénard convection at low Prandtl number

Results of an exploratory numerical study of Rayleigh–Bénard convection of a low-Pr fluid in a cylinder with a vertical partition are reported. It is shown that a partition may lead to a many-fold increase in the rate of convection heat transfer. The effect is associated with the formation of coherent hot and cold streams separated by the partition. The heat transfer enhancement is particularly strong in tall cylinders and requires that the partition penetrates into the thermal boundary layers near the top and bottom walls.

H3K9 methylation regulates heterochromatin silencing through incoherent feedforward loops.

Histone H3 lysine-9 methylation (H3K9me) is a hallmark of the condensed and transcriptionally silent heterochromatin. It remains unclear how H3K9me controls transcription silencing and how cells delimit H3K9me domains to avoid silencing essential genes. Here, using Arabidopsis genetic systems that induce H3K9me2 in genes and transposons de novo, we show that H3K9me2 accumulation paradoxically also causes the deposition of the euchromatic mark H3K36me3 by a SET domain methyltransferase, ASHH3. ASHH3-induced H3K36me3 confers anti-silencing by preventing the demethylation of H3K4me1 by LDL2, which mediates transcriptional silencing downstream of H3K9me2. These results demonstrate that H3K9me2 not only facilitates but orchestrates silencing by actuating antagonistic silencing and anti-silencing pathways, providing insights into the molecular basis underlying proper partitioning of chromatin domains and the creation of metastable epigenetic variation.

Configuration and Operation Optimization for Industrial Steam Power System Sustainable Retrofit Considering Renewable Energy Integration

AbstractRenewable energy integration and operational optimization are crucial in energy sustainability and decarbonization, especially for industrial steam power systems (SPS). This study establishes an SPS superstructure that integrates wind, solar, and biomass energy. A mixed‐integer nonlinear programming (MINLP) model is developed to determine an optimal retrofit strategy that minimizes the life cycle cost, which includes carbon emission cost and energy cost. To solve this high‐dimensional complex optimization problem, a multistage strategy fusion differential evolution algorithm with dynamic partitioning of the SVM feasible domain (SVM‐MS‐DE) is developed. The results from the optimal strategy demonstrate a 9.02% reduction in the system's total cost and a 9.64% decrease in carbon emission through the incorporation of wind and solar energy. Additionally, the sensitivity analysis on biomass ratio, carbon emission price, energy demand, and carbon emission limits reveal that the region can contribute significantly to renewable energy initiatives. Several recommended policies are provided to encourage enterprises to move towards sustainable development.

Discrete Weber Inequalities and Related Maxwell Compactness for Hybrid Spaces over Polyhedral Partitions of Domains with General Topology

Discrete Weber Inequalities and Related Maxwell Compactness for Hybrid Spaces over Polyhedral Partitions of Domains with General Topology

A method for chromatin domain partitioning based on hypergraph clustering

For many years, multi-scale models of chromatin domains, such as A/B compartments, sub-compartments, topologically associated domains (TADs), sub-TADs, and loops have been popular. However, existing methods can only identify structures at a single scale and cannot partition multi-scale structures. In this paper, we proposed a method (TORNADOES) for chromatin domain partitioning based on hypergraph clustering. First, we use a density clustering algorithm to identify TADs at different scales based on Hi-C data with different resolutions. Then, by combining ChIP-seq data features and TAD results at different scales, we generate a hypergraph based on these TADs. Finally, we partition the chromatin domain structure at different scales, including A/B, A1, A2, B1, B2, and B3 based on the Laplacian matrix feature of the hypergraph. Similarity comparison experiments and ChIP-seq signal enrichment analysis are performed on the A/B region and sub-TAD levels, respectively, demonstrating that our method can identify chromatin domains with distinct features and provide a deeper understanding of the organizational patterns and functional differences in TADs at the genomic hierarchical structure. Comparative analysis of multiple cell line data shows that TORNADOES can better classify different numbers and types of compartments by changing the factors ChIP-seq data and clustering number used to characterize TAD compared to other methods. Source code for the TORNADOES method can be found at https://github.com/ghaiyan/TORNADOES.

Exploiting Domain Partition in Response Function-Based Dynamic Surrogate Modeling: A Continuous Crystallizer Study

Given the exponential rise in the amount of data requiring processing in all engineering fields, phenomenological models have become computationally cumbersome. For this reason, more efficient data-driven models have been recently used with the purpose of substantially reducing simulation computational times. However, especially in process engineering, the majority of the proposed surrogate models address steady-state problems, while poor studies refer to dynamic simulation modeling. For this reason, using a response function-based approach, a crystallization unit case study was set up in order to derive a dynamic data-driven model for crystal growth whose characteristic differential parameters are derived via Response Surface Methodology. In particular, multiple independent variables were considered, and a well-established sampling technique was exploited for sample generation. Then, different sample sizes were tested and compared in terms of accuracy indicators. Finally, the domain partition strategy was exploited in order to show its relevant impact on the final model accuracy. In conclusion, the outcome of this study proved that the proposed procedure is a suitable methodology for dynamic system metamodeling, as it shows good compliance and relevant improvement in terms of computational time. In terms of future research perspectives, testing the proposed procedure on different systems and in other research fields would allow for greater improvement and would, eventually, extend its validity.

D3: A Methodological Exploration of Domain Division, Modeling, and Balance in Multi-Domain Recommendations

To enhance the efficacy of multi-scenario services in industrial recommendation systems, the emergence of multi-domain recommendation has become prominent, which entails simultaneous modeling of all domains through a unified model, effectively capturing commonalities and differences among them. However, current methods rely on manual domain partitioning, which overlook the intricate domain relationships and the heterogeneity of different domains during joint optimization, hindering the integration of domain commonalities and differences. To address these challenges, this paper proposes a universal and flexible framework D3 aimed at optimizing the multi-domain recommendation pipeline from three key aspects. Firstly, an attention-based domain adaptation module is introduced to automatically identify and incorporate domain-sensitive features during training. Secondly, we propose a fusion gate module that enables the seamless integration of commonalities and diversities among domains, allowing for implicit characterization of intricate domain relationships. Lastly, we tackle the issue of joint optimization by deriving loss weights from two complementary viewpoints: domain complexity and domain specificity, alleviating inconsistencies among different domains during the training phase. Experiments on three public datasets demonstrate the effectiveness and superiority of our proposed framework. In addition, D3 has been implemented on a real-life, high-traffic internet platform catering to millions of users daily.

Gravimetric inversion based on model exploration with growing source bodies (Growth) in diverse earth science disciplines

<abstract> <p>Gravimetry is a discipline of geophysics that deals with observation and interpretation of the earth gravity field. The acquired gravity data serve the study of the earth interior, be it the deep or the near surface one, by means of the inferred subsurface structural density distribution. The subsurface density structure is resolved by solving the gravimetric inverse problem. Diverse methods and approaches exist for solving this non-unique and ill-posed inverse problem. Here, we focused on those methods that do not pre-constrain the number or geometries of the density sources. We reviewed the historical development and the basic principles of the Growth inversion methodology, which belong to the methods based on the growth of the model density structure throughout an iterative exploration process. The process was based on testing and filling the cells of a subsurface domain partition with density contrasts through an iterative mixed weighted adjustment procedure. The procedure iteratively minimized the data misfit residuals jointly with minimizing the total anomalous mass of the model, which facilitated obtaining compact meaningful source bodies of the solution. The applicability of the Growth inversion approach in structural geophysical studies, in geodynamic studies, and in near surface gravimetric studies was reviewed and illustrated. This work also presented the first application of the Growth inversion tool to near surface microgravimetric data with the goal of seeking very shallow cavities in archeological prospection and environmental geophysics.</p> </abstract>

Evaluation of the "Step-Ramp-Step" Protocol: Accurate Aerobic Exercise Prescription with Different Steps and Ramp Slopes.

To assess whether: i) a lower amplitude constant-load MOD is appropriate to determine the mean response time (MRT); ii) the method accurately corrects the dissociation in the V̇O 2 -PO relationship during ramp compared with constant-load exercise when using different ramp slopes. Eighteen participants (7 females) performed three SRS tests including: i) step-transitions into MOD from 20 to 50 W (MOD 50 ) and 80 W (MOD 80 ); and ii) slopes of 15, 30, and 45 W·min -1 . The V̇O 2 and PO at the gas exchange threshold (GET) and the corrected respiratory compensation point (RCP CORR ) were determined. Two to three 30-min constant-load trials evaluated the V̇O 2 and PO at the maximal metabolic steady state (MMSS). There were no differences in V̇O 2 at GET (1.97 ± 0.36, 1.99 ± 0.36, 1.95 ± 0.30 L·min -1 ), and RCP (2.81 ± 0.57, 2.86 ± 0.59, 2.84 ± 0.59) between 15, 30, and 45 W·min -1 ramps, respectively ( P > 0.05). The MRT in seconds was not affected by the amplitude of the MOD or the slope of the ramp (range 19 ± 10 s to 23 ± 20 s; P > 0.05). The mean PO at GET was not significantly affected by the amplitude of the MOD or the slope of the ramp (range 130 ± 30 W to 137 ± 30 W; P > 0.05). The PO at RCP CORR was similar for all conditions ((range 186 ± 43 W to 193 ± 47 W; P > 0.05). The SRS protocol accounts for the V̇O 2 MRT when using smaller amplitude steps, and for the V̇O 2 slow component when using different ramp slopes, allowing for accurate partitioning of the exercise intensity domains in a single test.

An assessment tool to improve rural groundwater access: Integrating hydrogeological modelling with socio-technical factors

Sustainable exploitation of groundwater resources for drinking water provision in rural communities in sub-Sahara Africa remains elusive due to the limited knowledge of these hydrogeological systems. This is exacerbated by poor maintenance of existing infrastructure, limited technical capacity, the socio-economic characteristics of the area and poor governance. Assessing the likelihood of a given individual user experiencing water shortage calls for an interdisciplinary approach. After a preliminary multifactorial analysis incorporating a range of variables from technical to societal, it was found that most of the overall risk of water shortage for an individual household could be attributed to three factors; (1) Proximity, specified as the distance to the closest supply well (determined by geographical parameters), (2) Availability of good quality water in the wells (determined by hydrogeological understanding and modelling), and (3) Sustainability (determined by socio-technical and socio-economic parameters). In the latter case, a distinction was made between hardware functionality- the water point's performance considering a sufficient yield and reliability through time- and software functionality, based on a combination of socioeconomic data from surveys and analysed using Multiple Factor Analysis (MFA). All three factors are eventually mapped onto indicators in the range of [0–1] and then represented in a Geographical Information System based on the partition of the entire spatial domain (e.g., counties, villages, and neighbourhoods). The three indicators are then combined in a final index based on the product of the three factors, thus mapping time-dependent overall risk and allowing the assessment of temporal risk-evolution scenarios. The methodology is applied to Kwale County, Kenya, where community handpumps and groundwater points comprise the main water supply system. Apart from mapping the present situation, the methodology is finally used to assess the impact of future climate scenarios.

An incremental singular value decomposition approach for large-scale spatially parallel & distributed but temporally serial data – applied to technical flows

The article presents a strategy and its algorithm to compile a simulation-accompanying, incremental Singular Value Decomposition (SVD) for time-evolving, spatially parallel discrete data sets. The framework addresses state-of-the-art PDE solvers for computational science and engineering applications. An important characteristic of such applications is that the spatial size of the data is often time-invariant and significantly exceeds the temporal size due to the large computational grid in 3D applications. Typical examples, which are also considered in this article, relate to results extracted from unsteady flow simulations. Herein, the flow data, which progresses over time, is frequently calculated spatially parallel based on domain decomposition strategies, which allow to parallelize the simulation on distributed memory machines following a Single Instruction Multiple Data (SIMD) concept.With a view to the memory-efficient reuse of (compressed) simulation results and their CPU time-saving, sufficiently accurate generation, the paper scrutinizes the efficiency of incremental/parallel SVD approaches for such simulation examples. To improve the computational efficiency, the introduction of a bunch matrix is proposed, which enables the aggregation of multiple time steps and SVD updates, and significantly increases the efficiency. The suggested strategy is verified and validated by simple 2D laminar single-phase flows and subsequently applied to more complex 2D and 3D turbulent two-phase flows. Emphasis is given to (a) the accuracy of SVD-based reconstruction, (b) the physical realizability of the reconstructed quantities, (c) the independence of domain partitioning, (d) an efficient snapshot bunching, and (e) related implementation aspects. In addition, the influence of lower and (adaptive) upper rank thresholds on the effort and accuracy is evaluated. A final application renders the practical benefits of the approach and refers to a merchant ship in head waves at Re = 1.4×107 and Fn = 0.26. The simulation involves 2880 processor cores and the related full-rank snapshot matrix has (108×104) entries. With a numerical overhead of O(10%), this snapshot matrix can be incrementally generated and compressed by O(95%). The compression is accompanied by only small errors in the integral force and local wave elevation of O(10−2%). This qualifies the method for an efficient subsequent data processing.

Generating probability distributions on intervals and spheres: Convex decomposition

This work studies the convexity of a class of positive definite probability measures with density functionsρ=cλ∑n=0∞g(n)Cnλwλ, that are generated through the interval characteristic sequences. We discuss when such measures supported in an interval are convex and demonstrate how convexity is preserved under multiplication by certain multipliers and under the intertwining product. A key message to be delivered from this work is: any integrable function f on the interval with a polynomial expansion that has relatively fast absolute convergence, can be decomposed into a non-unique pair of positive convex interval probabilities (f+,f−)∈Eλ′×Eλ′ up to normalization, in the sense that f=f+−f−, where Eλ′ is a class of convex functions. Consequently not only the study of an interval distribution is reduced to the study of the properties of class Eλ′, but also the discontinuous probabilistic Galerkin schemes can be simplified. As concrete examples the decomposition of polynomials and truncated normal distribution are computed and graphically illustrated. Such interval measures lead to localized spherical probability measures, and as a convex expression of probability measure is a Jensen type inequality for spherical random variables. Based on the spherical information entropy models, one dependent on the domain partition and the other not, we propose three minimization formulations for the probabilistic finite element method, including one that mixes the least-squares and entropy models.

Tighter Bounds on Transient Moments of Stochastic Chemical Systems

The use of approximate solution techniques for the Chemical Master Equation is a common practice for the analysis of stochastic chemical systems. Despite their widespread use, however, many such techniques rely on unverifiable assumptions and only a few provide mechanisms to control the approximation error quantitatively. Addressing this gap, Dowdy and Barton (J Chem Phys 149(7):074103, 2018) proposed an optimization-based technique for the computation of guaranteed bounds on the moment trajectories associated with stochastic chemical systems, thereby providing a general framework for rigorous uncertainty quantification. Here, we present an extension of this method. The key contribution is a new hierarchy of convex necessary moment conditions that build upon partitioning of the time domain. These conditions reflect the temporal causality that is inherent to the moment trajectories associated with stochastic processes described by the Chemical Master Equation and can be strengthened by simple refinement of the time domain partition. Analogous to the original method, these conditions generate a hierarchy of semidefinite programs that furnishes monotonically improving bounds on the trajectories of the moments and related statistics of stochastic chemical systems. Compared to its predecessor, the presented hierarchy produces bounds that are at least as tight and features new bound tightening mechanisms such as refinement of the time domain partition which often enable the computation of dramatically tighter bounds with lower computational cost. We analyze the properties of the presented hierarchy, discuss some aspects of its practical implementation and demonstrate its merits with several examples.

Spectral minimal partitions of unbounded metric graphs

We investigate the existence or non-existence of spectral minimal partitions of unbounded metric graphs, where the operator applied to each of the partition elements is a Schrödinger operator of the form -\Delta + V with suitable (electric) potential V , which is taken as a fixed, underlying function on the whole graph. We show that there is a strong link between spectral minimal partitions and infimal partition energies on the one hand, and the infimum \Sigma of the essential spectrum of the corresponding Schrödinger operator on the whole graph on the other. Namely, we show that for any k\in\mathbb{N} , the infimal energy among all admissible k -partitions is bounded from above by \Sigma , and if it is strictly below \Sigma , then a spectral minimal k -partition exists. We illustrate our results with several examples of existence and non-existence of minimal partitions of unbounded and infinite graphs, with and without potentials. The nature of the proofs, a key ingredient of which is a version of the characterization of the infimum of the essential spectrum known as Persson’s theorem for quantum graphs, strongly suggests that corresponding results should hold for Schrödinger operator-based partitions of unbounded domains in Euclidean space.

Formula omitted]-smooth planar parameterization of complex domains for isogeometric analysis

The construction of high-quality parameterizations for complex domains remains a significant challenge in isogeometric analysis. To address this issue, we propose a G1-smooth parameterization method for planar domains with arbitrary topology. Firstly, we generate a coarse decomposition of the given complex shape without internal singularities utilizing the extracted skeleton of the domain. We then perform a finer domain partition to obtain more accurate boundary representations. Both rectangular and triangular Bézier patches are employed to represent the geometry. Secondly, by imposing G1 continuity constraints on the adjacent patches, we construct an initial parameterization that is globally G1 continuous. Finally, we enhance the parameterization quality of each patch separately using the quasi-conformal mapping technique. Various examples are presented to justify the capability of the proposed method and to demonstrate its superiority over existing multi-patch parameterizations.