Topological Computation Research Articles

Analysis of power losses in multilevel pulse-width modulation inverters

The paper describes the types of multilevel pulse-width modulation, as well as methods for obtaining control signals for the inverter power switches for each of the types. The dependence of the harmonic composition of the output voltage of the inverter on the number of levels and the switching frequency of the keys of each level is analyzed. By modeling, the dependences of the transistor junction temperature on the number of voltage levels, switching frequency and load power are determined. The power switching system of an inverter with phase-shifted pulse-width modulation in high-frequency mode is analyzed, the dependence of switching losses on inductance is investigated. The ways of solving or improving the control systems of the conductivity losses of the converter flowing through the primary winding of a high-frequency transformer during the free-running period are formulated. The importance of this direction for the technological development of the economy, where efficiency improvements can lower individual utility bills, create jobs, and help stabilize electricity prices and volatility is shown. The most important stage of inverter design is called structural synthesis stage – the choice of topology and modulation algorithm that will ensure the greatest efficiency of the device. In addition, since the efficiency and reliability of inverters depend on the efficiency and reliability of secondary electricity consumers, the task of optimizing inverter circuits is a cornerstone for the effective development of technology and economy. The maximum dynamic power loss at a PWM frequency of 1 kHz reaches only 80 watts compared to the static power loss value of 800 watts

Novel computational mathematical algorithms for structural optimization using graph-theoretical methods

PurposeThe purpose is to reduce round-off errors in numerical simulations. In the numerical simulation, different kinds of errors may be created during analysis. Round-off error is one of the sources of errors. In numerical analysis, sometimes handling numerical errors is challenging. However, by applying appropriate algorithms, these errors are manageable and can be reduced. In this study, five novel topological algorithms were proposed in setting up a structural flexibility matrix, and five different examples were used in applying the proposed algorithms. In doing so round-off errors were reduced remarkably.Design/methodology/approachFive new algorithms were proposed in order to optimize the conditioning of structural matrices. Along with decreasing the size and duration of analyses, minimizing analytical errors is a critical factor in the optimal computer analysis of skeletal structures. Appropriate matrices with a greater number of zeros (sparse), a well structure and a well condition are advantageous for this objective. As a result, a problem of optimization with various goals will be addressed. This study seeks to minimize analytical errors such as rounding errors in skeletal structural flexibility matrixes via the use of more consistent and appropriate mathematical methods. These errors become more pronounced in particular designs with ill-suited flexibility matrixes; structures with varying stiffness are a frequent example of this. Due to the usage of weak elements, the flexibility matrix has a large number of non-diagonal terms, resulting in analytical errors. In numerical analysis, the ill-condition of a matrix may be resolved by moving or substituting rows; this study examined the definition and execution of these modifications prior to creating the flexibility matrix. Simple topological and algebraic features have been mostly utilized in this study to find fundamental cycle bases with particular characteristics. In conclusion, appropriately conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.Findings(1) Five new algorithms were proposed in order to optimize the conditioning of structural flexibility matrices. (2) A JAVA programming language was written for all five algorithms and a friendly GUI software tool is developed to visualize sub-optimal cycle bases. (3) Topological and algebraic features of the structures were utilized in this study.Research limitations/implicationsThis is a multi-objective optimization problem which means that sparsity and well conditioning of a matrix cannot be optimized simultaneously. In conclusion, well-conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.Practical implicationsEngineers always finding mathematical modeling of real-world problems and make them as simple as possible. In doing so, lots of errors will be created and these errors could cause the mathematical models useless. Applying decent algorithms could make the mathematical model as precise as possible.Social implicationsErrors in numerical simulations should reduce due to the fact that they are toxic for real-world applications and problems.Originality/valueThis is an original research. This paper proposes five novel topological mathematical algorithms in order to optimize the structural flexibility matrix.

Fault-Tolerant Topology of Agricultural Wireless Sensor Networks Based on a Double Price Function

Wireless sensor networks (WSN) enable the acquisition of multisource environmental data and crop states in precision agriculture. However, the complex agricultural environment causes the WSN topology to change frequently and link connection probability is difficult to predict. In order to improve the utilization of network resources and balance the network energy consumption, this paper studies an agricultural fault-tolerant topology construction method based on the potential game and cut vertex detection. Considering the connectivity redundancy, node lifetime, and residual energy, a fault-tolerant topology algorithm for agricultural WSN based on a double price function is designed. The network is clustered according to the node location and residual energy to form a single-hop effective cluster. Based on the network cluster, the price function is constructed in order to reduce energy consumption and balance network energy efficiency. The initial transmit power set supporting inter-cluster communication is obtained by potential game theory. While preserving the game characteristics of topology, the redundant links are eliminated and the transmit power is adjusted by a cut vertex detection algorithm to realize the construction of a 2-connected cluster head network. Simulation results show that the network topology constructed by the studied algorithm can balance the energy consumption and prolong the network lifetime effectively.

Revealing key lncRNAs in cytogenetically normal acute myeloid leukemia by reconstruction of the lncRNA\u2013miRNA\u2013mRNA network

Cytogenetically normal acute myeloid leukemia (CN-AML) is a heterogeneous disease with different prognoses. Researches on prognostic biomarkers and therapy targets of CN-AML are still ongoing. Instead of protein-coding genes, more and more researches were focused on the non-coding RNAs especially long non-coding RNAs (lncRNAs) which may play an important role in the development of AML. Although a large number of lncRNAs have been found, our knowledge of their functions and pathological process is still in its infancy. The purpose of this research is to identify the key lncRNAs and explore their functions in CN-AML by reconstructing the lncRNA–miRNA–mRNA network based on the competitive endogenous RNA (ceRNA) theory. We reconstructed a global triple network based on the ceRNA theory using the data from National Center for Biotechnology Information Gene Expression Omnibus and published literature. According to the topological algorithm, we identified the key lncRNAs which had both the higher node degrees and the higher numbers of lncRNA–miRNA pairs and total pairs in the ceRNA network. Meanwhile, Gene Ontology (GO) and pathway analysis were performed using databases such as DAVID, KOBAS and Cytoscape plug-in ClueGO respectively. The lncRNA–miRNA–mRNA network was composed of 90 lncRNAs,33mRNAs,26 miRNAs and 259 edges in the lncRNA upregulated group, and 18 lncRNAs,11 mRNAs,6 miRNAs and 45 edges in the lncRNA downregulated group. The functional assay showed that 53 pathways and 108 GO terms were enriched. Three lncRNAs (XIST, TUG1, GABPB1-AS1) could possibly be selected as key lncRNAs which may play an important role in the development of CN-AML. Particularly, GABPB1-AS1 was highly expressed in CN-AML by both bioinformatic analysis and experimental verification in AML cell line (THP-1) with quantitative real‐time polymerase chain reaction. In addition, GABPB1-AS1 was also negatively correlated with overall survival of AML patients. The lncRNA–miRNA–mRNA network revealed key lncRNAs and their functions in CN-AML. Particularly, lncRNA GABPB1-AS1 was firstly proposed in AML. We believe that GABPB1-AS1 is expected to become a candidate prognostic biomarker or a potential therapeutic target.

Earth Imagery Segmentation on Terrain Surface with Limited Training Labels: A Semi-supervised Approach based on Physics-Guided Graph Co-Training

Given earth imagery with spectral features on a terrain surface, this paper studies surface segmentation based on both explanatory features and surface topology. The problem is important in many spatial and spatiotemporal applications such as flood extent mapping in hydrology. The problem is uniquely challenging for several reasons: first, the size of earth imagery on a terrain surface is often much larger than the input of popular deep convolutional neural networks; second, there exists topological structure dependency between pixel classes on the surface, and such dependency can follow an unknown and non-linear distribution; third, there are often limited training labels. Existing methods for earth imagery segmentation often divide the imagery into patches and consider the elevation as an additional feature channel. These methods do not fully incorporate the spatial topological structural constraint within and across surface patches and thus often show poor results, especially when training labels are limited. Existing methods on semi-supervised and unsupervised learning for earth imagery often focus on learning representation without explicitly incorporating surface topology. In contrast, we propose a novel framework that explicitly models the topological skeleton of a terrain surface with a contour tree from computational topology, which is guided by the physical constraint (e.g., water flow direction on terrains). Our framework consists of two neural networks: a convolutional neural network (CNN) to learn spatial contextual features on a 2D image grid, and a graph neural network (GNN) to learn the statistical distribution of physics-guided spatial topological dependency on the contour tree. The two models are co-trained via variational EM. Evaluations on the real-world flood mapping datasets show that the proposed models outperform baseline methods in classification accuracy, especially when training labels are limited.

REST-for-Physics, a ROOT-based framework for event oriented data analysis and combined Monte Carlo response

The REST-for-Physics (Rare Event Searches Toolkit for Physics) framework is a ROOT-based solution providing the means to process and analyze experimental or Monte Carlo event data. Special care has been taken to the traceability of the code and the validation of the results produced within the framework, together with the connectivity between code and stored data, registered through specific version metadata members.The framework development was originally motivated to cover the needs of Rare Event Searches experiments (experiments looking for phenomena having extremely low occurrence probability, like dark matter or neutrino interactions or rare nuclear decays). The framework components naturally implement tools to address the challenges in these kinds of experiments. The integration of a detector physics response, the implementation of signal processing routines, or topological algorithms for physical event identification are some examples. Despite this specialization, the framework was conceived thinking in scalability. Other event-oriented applications could benefit from the data processing routines and/or metadata description implemented in REST, being the generic framework tools completely decoupled from dedicated libraries.REST-for-Physics is a consolidated piece of software already serving the needs of different physics experiments - using gaseous Time Projection Chambers (TPCs) as detection technology - for detector data analysis and characterization, as well as generic R&D. Even though REST has been exploited mainly with gaseous TPCs, the code could be easily applied or adapted to other detector technologies. We present in this work an overview of REST-for-Physics, providing a broad perspective to the infrastructure and organization of the project as a whole. The framework and its different components will be described in the text.

Reconstructing linearly embedded graphs: A first step to stratified space learning

<p style='text-indent:20px;'>In this paper, we consider the simplest class of stratified spaces – linearly embedded graphs. We present an algorithm that learns the abstract structure of an embedded graph and models the specific embedding from a point cloud sampled from it. We use tools and inspiration from computational geometry, algebraic topology, and topological data analysis and prove the correctness of the identified abstract structure under assumptions on the embedding. The algorithm is implemented in the Julia package Skyler, which we used for the numerical simulations in this paper.</p>

Neuroevolution of Augmenting Topologies for Artificial Evolution: A Case Study of Kinesis of Creature in the Various Mediums

The motivation of the present study is to evolve virtual creatures in a diverse simulated 3D environment. The proposed scheme is based on the artificial evolution using the Neuro Evolution of Augmenting Topologies (NEAT) algorithm to educe a neural network that controls the muscle forces of the artificial creatures. The morphologies of the creatures are established using the Genetic Algorithm (GA) method based on the distance metrics fitness function. The concept of damaging crossover of neural networks and genetic language for the morphology of creatures has been considered in the morphologies of the artificial creature. Creatures with certain morphological traits consume a large time to optimize their kinetics, thus they are placed in a separate species to limit the search. The simulation results in the significant kinetics of artificial creatures (2-5 limbs) in virtual mediums with varying dynamic and static coefficients of friction (0.0-4.0). The motion of artificial creatures in the simulated medium was determined at different angles and demonstrated in the 3D space.

Efficient Local Level Set Algorithm Combined with Bidirectional Evolutionary Criterion Using Discrete Variables and its Appliance to Topology and Shape Optimization

Many level set methods (LSMs) have been used for topology and shape optimization. An efficient topology optimization algorithm is proposed by combining a new bi-directional evolutionary criterion (BEC) with the local LSM (LLSM). The BEC is established using multiple discrete variables (DVs) and introduced into the bi-directional evolutionary structural optimization (BESO) method so that the DV-BESO method obtained can be applied to topology optimization. The LLSM is used instead of the global LSM due to its high efficiency. In the LLSM, the computational efficiency can be further improved by solving a distance regularized equation without the re-initialization procedure. Two benchmarks show the high efficiency of this proposed combined algorithm for topology and shape optimization.

Formation of machine learning features based on computational topology methods

Formation of machine learning features based on computational topology methods

A Survey on the High Performance Computation of Persistent Homology

Persistent Homology is a computational method of data mining in the field of Topological Data Analysis. Large-scale data analysis with persistent homology is computationally expensive and memory intensive. The performance of persistent homology has been rigorously studied to optimize data encoding and intermediate data structures for high-performance computation. This paper provides an application-centric survey of the High-Performance Computation of Persistent Homology. Computational topology concepts are reviewed and detailed for a broad data science and engineering audience.

A study on the application of teaching differential equations in higher mathematics based on visual network topology algorithm

A study on the application of teaching differential equations in higher mathematics based on visual network topology algorithm

Crystal structure of nyerereite: A possible messenger from the deep Earth

Abstract Carbonates in the system Na2CO3-CaCO3 are nowadays suggested as having a wide stability field at conditions of the mantle transition zone. Our structural analysis of nyerereite, which has limited stability fields at ambient conditions, and its similarities with already known carbonates that are stable at high-pressure conditions, allowed us to propose that nyerereite likely undergoes phase transitions at both high-pressure and high-temperature conditions. This supports the hypothesis that nyerereite takes part in carbon transportation from the mantle/deep crust toward the surface, with important implications for the deep carbon cycle associated with carbonatites. K-free nyerereite [Na2Ca(CO3)2] was synthesized both at hydrothermal conditions and from the melt. The structure of nyerereite was refined as a three-component twinned structure in the centrosymmetric Pbca space group with ratios of the three twinning components 0.221(3):0.287(3):0.492(3). Twinning at micro- and nano-level can introduce some minor structural deformations that influence the likely occurrence of the inversion center as one of the symmetry elements in the nyerereite structure. Based on the automated topological algorithms, we show that nyerereite has a unique crystal structure, not having analogs among the known structures, except for the structure with a similar composition K2Ca(CO3)2 fairchildite. A comparison between the centrosymmetric Pbca nyerereite structure and that of aragonite (CaCO3, Pmcn space group) reveals two main scenarios for the high-pressure form of Na2Ca(CO3)2: (1) poly-somatic relations as the interlayering of the high-pressure polymorph Na2CO3 and CaCO3-aragonite, and (2) high-pressure structure with ninefold-coordinated Na and Ca sites resembling that of aragonite. Our discussion heightens the interest in the high-pressure behavior of the nyerereite structure and strengthens the hypothesis about the possibility for nyerereite to be stable at high-pressure/high-temperature conditions.

Review of A Short Course in Computational Geometry and Topology by Herbert Edelsbrunner

Computational geometry and topology are huge branches of mathematics. Focussing on concepts that lead to computation is one strategy to provide a concrete conceptual basis for ideas that hold in a more general context. Indeed, this short book gives an introduction to a surprisingly broad range of ideas that can serve as a good introduction to geometry and topology (even broadly conceived) for undergraduates.

An Invulnerability Algorithm for Wireless Sensor Network's Topology Based on Distance and Energy

An Invulnerability Algorithm for Wireless Sensor Network's Topology Based on Distance and Energy

PCNA in Cervical Intraepithelial Neoplasia and Cervical Cancer: An Interaction Network Analysis of Differentially Expressed Genes

The investigation of differentially expressed genes (DEGs) and their interactome could provide valuable insights for the development of markers to optimize cervical intraepithelial neoplasia (CIN) screening and treatment. This study investigated patients with cervical disease to identify gene markers whose dysregulated expression and protein interaction interface were linked with CIN and cervical cancer (CC). Literature search of microarray datasets containing cervical epithelial samples was conducted in Gene Expression Omnibus and Pubmed/Medline from inception until March 2021. Retrieved DEGs were used to construct two protein-protein interaction (PPI) networks. Module DEGs that overlapped between CIN and CC samples, were ranked based on 11 topological algorithms. The highest-ranked hub gene was retrieved and its correlation with prognosis, tissue expression and tumor purity in patients with CC, was evaluated. Screening of the literature yielded 9 microarray datasets (GSE7803, GSE27678, GSE63514, GSE6791, GSE9750, GSE29570, GSE39001, GSE63678, GSE67522). Two PPI networks from CIN and CC samples were constructed and consisted of 1704 and 3748 DEGs along 21393 and 79828 interactions, respectively. Two gene clusters were retrieved in the CIN network and three in the CC network. Multi-algorithmic topological analysis revealed PCNA as the highest ranked hub gene between the two networks, both in terms of expression and interactions. Further analysis revealed that while PCNA was overexpressed in CC tissues, it was correlated with favorable prognosis (log-rank P=0.022, HR=0.58) and tumor purity (P=9.86 × 10-4, partial rho=0.197) in CC patients. This study identified that cervical PCNA exhibited multi-algorithmic topological significance among DEGs from CIN and CC samples. Overall, PCNA may serve as a potential gene marker of CIN progression. Experimental validation is necessary to examine its value in patients with cervical disease.

Towards leveraging collective performance with the support of MPI 4.0 features in MPC

Persistent collective communications and communicator splitting according to the underlying hardware topology have recently been voted in the MPI standard. Persistent semantics contains an initialization phase called only once for a specific collective operation, with subsequent recurring invocations. This opens the door to many optimizations requiring heavy setup costs to improve collective performances. Communicator topological splitting offers a standard way to design topological algorithm through the use of sub-communicators mapped to hardware hierarchical levels. Setting these communicators might be too costly to be efficient on a single collective call. However, the persistent semantics allow to create these communicators once at initialization, and use them repeatedly in the multiple collective invocations to have an efficient algorithm.In this paper, we describe the implementation of these two new MPI features in the MPC framework. We first present a naïve and an optimized version of persistent collectives without topology knowledge. Then, after detailing the implementation of hardware topology splitting and the hierarchical levels supported in MPC, we showcase how these two features can be combined to produce efficient topology-aware persistent collective implementations. Experimental results show that the topology-aware algorithms built with these basic blocks offer good performances, independent of the MPI processes binding.

Optimal Design of a Synchronous Reluctance Motor Using a Genetic Topology Algorithm

The topology algorithm (TA) can effectively find an optimal solution by changing the material and shape of the design target without the limitation of design variables. In this paper, a genetic topology algorithm (GTA) is proposed for the design optimization of a synchronous reluctance motor (SynRM). By applying the stochastic algorithm (genetic algorithm (GA)) and the deterministic algorithm (ON-OFF method) to the design, the optimal shape can be found quickly and effectively. The GTA, which improves manufacturability by removing the aliasing that occurs in TA, was applied to the design of SynRM to search for the optimal model. After dividing the rotor into a reverse mesh grid, the optimal topology was searched for by GA and ON-OFF methods. Then, mechanical stability was verified through stress analysis, and additional performance improvement was obtained through the skew technique. The final design, which satisfies the minimum efficiency, required torque, and torque ripple was derived by applying the step-by-step design using GTA to the SynRM optimization.

Numerical Investigation of Discrepancies Between Two-Dimensional and Three-Dimensional Acoustic Metamaterials

In order to get insight information of the band structure of acoustic metamaterials (AMMs) in condensed matter, periodic lattice structures are analyzed using Bloch’s theorem. Typical approaches of the band structure computation methods, topology optimization, and tunable abilities cannot overcome the gap between the two-dimensional (2D) AMMs theoretical and three-dimensional (3D) specimens’ experimental data yet. In this work, the variation in the results of the band structure obtained from the 2D mathematical model computed with respect to the 3D experimental models, and related cause of the variation is explored. The band structures and mode shapes of the 2D AMMs, quasi-2D models, and 3D specimen models are followed to reveal the boundary conditions and source for the observed differences in band structures. The cause for the discrepancies is verified by using the finite element method (FEM) with corresponding boundary conditions. It is found that outcomes from computational data of the 2D AMMs model are diverted significantly by means of bandgap, band structure, and stress distribution in counterparts of the 3D specimen model. This approach can provide assistance for computing the band structure of 2D AMMs for practical applications.

Quantitative and interpretable order parameters for phase transitions from persistent homology

We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully-frustrated XY models. In particular, we use persistent homology, which computes the births and deaths of individual topological features as a coarse-graining scale or sublevel threshold is increased, to summarize multiscale and high-point correlations in a spin configuration. We employ vector representations of this information called persistence images to formulate and perform the statistical task of distinguishing phases. For the models we consider, a simple logistic regression on these images is sufficient to identify the phase transition. Interpretable order parameters are then read from the weights of the regression. This method suffices to identify magnetization, frustration, and vortex-antivortex structure as relevant features for phase transitions in our models. We also define "persistence" critical exponents and study how they are related to those critical exponents usually considered.