Topological Problems Research Articles

Aclarubicin Reduces the Nuclear Mobility of Human DNA Topoisomerase IIβ.

DNA topoisomerase II (TOP2) is an enzyme that resolves DNA topological problems arising in various nuclear processes, such as transcription. Aclarubicin, a member of the anthracyclines, is known to prevent the association of TOP2 with DNA, inhibiting the early step of TOP2 catalytic reactions. During our research on the subnuclear distribution of human TOP2B, we found that aclarubicin affects the mobility of TOP2B in the nucleus. FRAP analysis demonstrated that aclarubicin decreased the nuclear mobility of EGFP-tagged TOP2B in a concentration-dependent manner. Aclarubicin exerted its inhibitory effects independently of TOP2B enzymatic activities: TOP2B mutants defective for either ATPase or topoisomerase activity also exhibited reduced nuclear mobility in the presence of aclarubicin. Immunofluorescence analysis showed that aclarubicin antagonized the induction of DNA damage by etoposide. Although the prevention of the TOP2-DNA association is generally considered a primary action of aclarubicin in TOP2 inhibition, our findings highlight a previously unanticipated effect of aclarubicin on TOP2B in the cellular environment.

Reinforcement topology optimization considering the dynamic instability

AbstractThe present study develops a new topology optimization scheme considering the dynamic instability caused by the unsymmetrical properties of system. From a mathematical point of view, the left and right eigenvectors of asymmetric system are observed with the complex eigenvalues. With the dynamic instability, the magnitudes of structural responses are increasing with respect to time and this phenomenon causes many engineering issues. As the dynamic instability is one of the serious problems, the suppression is desired from an engineering point of view. To systematically reduce this dynamic instability, the present study develops a new topology optimization scheme for the reinforcement design. To overcome the numerical difficulties of the mode conversion and the highly nonlinear behavior, this research proposes the summation of the first several complex eigenvalues. To show the issues of the dynamic instability and the validity of the present approach, several topological reinforcement problems are solved.

Problems on [formula omitted]

This is an update on, and expansion of, our paper Open problems on βω in the book Open Problems in Topology.

Finite-time formation trajectory tracking control for unmanned underwater vehicles with time delays and Markov-switch topology

ABSTRACT The formation trajectory tracking control strategy of unmanned underwater vehicles is proposed for communication time delay and communication topology random switching. The methods ensure that formation systems are finite-time bounded under discrete time. Firstly, based on the consistency theory and the exact feedback linearised dynamics model of unmanned underwater vehicle, a control strategy is proposed for discrete formation system with communication time delay. Secondly, a cooperative control method is designed for communication problems of Markovian switching topology and time delay. Then, definition of finite-time bounded and linear matrix inequality technique are applied to sufficient conditions of system stability for the above problem. Finally, the formation motion of discrete unmanned underwater vehicle system in three-dimensional space is simulated, fully demonstrating the feasibility of the method.

A topological network connectivity design problem based on spectral analysis

How to improve network connectivity and which parts of the network are vulnerable are critical issues. We begin by defining an equal distribution problem, in which supplies are distributed equally to all nodes in the network. We then derive a topological network connectivity measure from the convergence speed, which is the second minimum eigenvalue of a Laplacian network matrix. Based on the equal distribution problem, we propose a method for identifying critical links for network connectivity using the derivative of the second minimum eigenvalue. Furthermore, we develop a network design problem that maximizes topological connectivity within a budget creating strengthening network links. The problem is convex programming, and the solution is global. Furthermore, it can be converted into an identical semidefinite programming problem, which requires less computational effort. Finally, we test the developed problems on road networks in the Japanese prefectures of Ishikawa and Toyama to determine their applicability and validity.

Highly sensitive mapping of in vitro type II topoisomerase DNA cleavage sites with SHAN-seq.

Type II topoisomerases (topos) are a ubiquitous and essential class of enzymes that form transient enzyme-bound double-stranded breaks on DNA called cleavage complexes. The location and frequency of these cleavage complexes on DNA is important for cellular function, genomic stabilityand a number of clinically important anticancer and antibacterial drugs, e.g. quinolones. We developed a simple high-accuracy end-sequencing (SHAN-seq) method to sensitively map type II topo cleavage complexes on DNA in vitro. Using SHAN-seq, we detected Escherichia coli gyrase and topoisomerase IV cleavage complexes at hundreds of sites on supercoiled pBR322 DNA, approximately one site every ten bp, with frequencies that varied by two-to-three orders of magnitude. These sites included previously identified sites and 20-50-fold more new sites. We show that the location and frequency of cleavage complexes at these sites are enzyme-specific and vary substantially in the presence of the quinolone, ciprofloxacin, but not with DNA supercoil chirality, i.e. negative versus positive supercoiling. SHAN-seq's exquisite sensitivity provides an unprecedented single-nucleotide resolution view of the distribution of gyrase and topoisomerase IV cleavage complexes on DNA. Moreover, the discovery that these enzymes can cleave DNA at orders of magnitude more sites than the relatively few previously known sites resolves the apparent paradox of how these enzymes resolve topological problems throughout the genome.

Mean Squared Error May Lead You Astray When Optimizing Your Inverse Design Methods

Abstract When performing time-intensive optimization tasks, such as those in Topology or Shape Optimization, researchers have turned to machine-learned (ML) Inverse Design methods i.e., predicting the optimized geometry from input conditions to replace or warm start traditional optimizers. Such methods are often optimized to reduce the Mean Squared Error (MSE) or Binary Cross-Entropy between the output and a training dataset of optimized designs. While convenient, we show that this choice may be myopic. Specifically, we compare two methods of optimizing the hyper-parameters of easily reproducible Machine Learning models including random forest (RF), k-nearest neighbors (KNN), and Deconvolutional Neural Network (DeCNN) model for predicting the three optimal topology problems. We show that under both direct Inverse Design and when warm starting further Topology Optimization (TO), using MSE metrics to tune hyper-parameters produces less performant models than directly evaluating the objective function, though both produce designs that are almost one order of magnitude better than using the common uniform initialization. We also illustrate how warm starting impacts both the convergence time, the type of solutions obtained during optimization, and the final designs. Overall, our initial results portend that researchers may need to revisit common choices for evaluating ID methods that subtly trade-off factors in how an ID method will actually be used. We hope our open-source dataset and evaluation environment will spur additional research in those directions.

A Reconfigurable Phase-Shifted Full-Bridge DC–DC Converter with Wide Range Output Voltage

This paper analyzes, designs and implements a reconfigurable phase-shifted full-bridge (PSFB) converter. It adopts the topology of the traditional PSFB converter and incorporates clamping circuits to solve some fundamental problems of conventional topology. In addition, auxiliary switches are employed for output reconfiguration, which allows expanding the output voltage range without compromising the system efficiency. Single pole double throw (SPDT) mechanical switches are used to realize series and parallel connections. In this paper, the characterization of the PSFB converter with clamping circuit and its design considerations are discussed. A 10 kW prototype with a power density of 0.485 W/cm3, 900 V input voltage and 400/800 V nominal output voltage was manufactured. The experimental results validated the analysis and confirmed the high conversion efficiency for a wide load range; an efficiency of 96.69% was obtained for the full load condition.

Progressive transfer learning for advancing machine learning-based reduced-order modeling

To maximize knowledge transfer and improve the data requirement for data-driven machine learning (ML) modeling, a progressive transfer learning for reduced-order modeling (p-ROM) framework is proposed. A key concept of p-ROM is to selectively transfer knowledge from previously trained ML models and effectively develop a new ML model(s) for unseen tasks by optimizing information gates in hidden layers. The p-ROM framework is designed to work with any type of data-driven ROMs. For demonstration purposes, we evaluate the p-ROM with specific Barlow Twins ROMs (p-BT-ROMs) to highlight how progress learning can apply to multiple topological and physical problems with an emphasis on a small training set regime. The proposed p-BT-ROM framework has been tested using multiple examples, including transport, flow, and solid mechanics, to illustrate the importance of progressive knowledge transfer and its impact on model accuracy with reduced training samples. In both similar and different topologies, p-BT-ROM achieves improved model accuracy with much less training data. For instance, p-BT-ROM with four-parent (i.e., pre-trained models) outperforms the no-parent counterpart trained on data nine times larger. The p-ROM framework is poised to significantly enhance the capabilities of ML-based ROM approaches for scientific and engineering applications by mitigating data scarcity through progressively transferring knowledge.

Multi-group consensus of multi-agent systems subject to semi-Markov jump topologies against hybrid cyber-attacks

Multi-agent systems are widely used in practice. The existing results on the consensus of multi-agent systems mainly focus on the complete consensus, which can not deal with the situation of the system in the face of multiple tasks. In this paper, the multi-group consensus problem of multi-agent systems with semi-Markov jump topologies against hybrid cyber-attacks is studied. The purpose is to ensure that the multi-agent systems can achieve different consensus goals when they encounter hybrid cyber-attacks, and to solve the problem of time-varying communication topology between agents modeled by the semi-Markov process. Additionally, two types of cyber-attacks are taken into account in a single framework through two independent sets of Bernoulli sequences. Subsequently, a necessary condition is established to guide the system toward achieving the multi-group consensus objective. Lastly, a series of illustrative examples are presented to underscore the validity of the designed controller.

Genome-wide Mapping of Topoisomerase Binding Sites Suggests Topoisomerase 3α (TOP3A) as a Reader of Transcription-Replication Conflicts (TRC).

Both transcription and replication can take place simultaneously on the same DNA template, potentially leading to transcription-replication conflicts (TRCs) and topological problems. Here we asked which topoisomerase(s) is/are the best candidate(s) for sensing TRC. Genome-wide topoisomerase binding sites were mapped in parallel for all the nuclear topoisomerases (TOP1, TOP2A, TOP2B, TOP3A and TOP3B). To increase the signal to noise ratio (SNR), we used ectopic expression of those topoisomerases in H293 cells followed by a modified CUT&Tag method. Although each topoisomerase showed distinct binding patterns, all topoisomerase binding signals positively correlated with gene transcription. TOP3A binding signals were suppressed by DNA replication inhibition. This was also observed but to a lesser extent for TOP2A and TOP2B. Hence, we propose the involvement of TOP3A in sensing both head-on TRCs (HO-TRCs) and co-directional TRCs (CD-TRCs). In which case, the TOP3A signals appear concentrated within the promoters and first 20 kb regions of the 5' -end of genes, suggesting the prevalence of TRCs and the recruitment of TOP3A in the 5'-regions of transcribed and replicated genes.

Topology optimization for magnetic circuits with continuous adjoint method in 3D

PurposeThe purpose of this paper is to present a new approach to optimizing the design of 3D magnetic circuits. This approach is based on topology optimization, where derivative calculations are performed using the continuous adjoint method. Thus, the continuous adjoint method for magnetostatics has to be developed in 3D and has to be combined with penalization, filtering and homotopy approaches to provide an efficient optimization code.Design/methodology/approachTo provide this new topology optimization code, this study starts from 2D magnetostatic results to perform the sensitivity analysis, and this approach is extended to 3D. From this sensitivity analysis, the continuous adjoint method is derived to compute the gradient of an objective function of a 3D topological optimization design problem. From this result, this design problem is discretized and can then be solved by finite element software. Thus, by adding the solid isotropic material with penalization (SIMP) penalization approach and developing a homotopy-based optimization algorithm, an interesting means for designing 3D magnetic circuits is provided.FindingsIn this paper, the 3D continuous adjoint method for magnetostatic problems involving an objective least-squares function is presented. Based on 2D results, new theoretical results for developing sensitivity analysis in 3D taking into account different parameters including the ferromagnetic material, the current density and the magnetization are provided. Then, by discretizing, filtering and penalizing using SIMP approaches, a topology optimization code has been derived to address only the ferromagnetic material parameters. Based on this efficient gradient computation method, a homotopy-based optimization algorithm for solving large-scale 3D design problems is developed.Originality/valueIn this paper, an approach based on topology optimization to solve 3D magnetostatic design problems when an objective least-squares function is involved is proposed. This approach is based on the continuous adjoint method derived for 3D magnetostatic design problems. The effectiveness of this topology optimization code is demonstrated by solving the design of a 3D magnetic circuit with up to 100,000 design variables.

A novel binomial strategy for simultaneous topology and size optimization of truss structures

The current work introduces a new probability-based regulatory mechanism for the simultaneous size and topology optimization of truss structures. The proposed mechanism, by leveraging the Boolean nature of the topological variables, attempts to forecast the behaviour of the search algorithm and emphasizes either topology or size actions to reduce the number of ineffective iterations. The importance of this task becomes more evident in further iterations since the optimal (or nearly optimal) structure topology is identified, and improper elimination of any member can result in infeasible mechanisms and lead to a waste of several iterations. To assess the effectiveness of the proposed auxiliary module, it is integrated with different optimization algorithms to solve distinct size and topology problems. The results demonstrate that this not only enhances the accuracy of the algorithms but also significantly reduces the required computational cost.

Solution of engineering design and truss topology problems with improved forensic-based investigation algorithm based on dynamic oppositional based learning

The forensic-based investigation (FBI) is a metaheuristic algorithm inspired by the criminal investigation process. The collaborative efforts of the investigation and pursuit teams demonstrate the FBI’s involvement during the exploitation and exploration phases. When choosing the promising population, the FBI algorithm’s population selection technique focuses on the same region. This research aims to propose a dynamic population selection method for the original FBI and thereby enhance its convergence performance. To achieve this objective, the FBI may employ dynamic oppositional learning (DOL), a dynamic version of the oppositional learning methodology, to dynamically navigate to local minima in various locations. Therefore, the proposed advanced method is named DOLFBI. The performance of DOLFBI on the CEC2019 and CEC2022 benchmark functions is evaluated by comparing it with several other popular metaheuristics in the literature. As a result, DOLFBI yielded the lowest fitness value in 18 of 22 benchmark problems. Furthermore, DOLFBI has shown promising results in solving real-world engineering problems. It can be argued that DOLFBI exhibits the best convergence performance in cantilever beam design, speed reducer, and tension/compression problems. DOLFBI is often utilized in truss engineering difficulties to determine the minimal weight. Its success is comparable to other competitive MAs in the literature. The Wilcoxon signed-rank and Friedman rank tests further confirmed the study’s stability. Convergence and trajectory analyses validate the superior convergence concept of the proposed method. When the proposed study is compared to essential and enhanced MAs, the results show that DOLFBI has a competitive framework for addressing complex optimization problems due to its robust convergence ability compared to other optimization techniques. As a result, DOLFBI is expected to achieve significant success in various optimization challenges, feature selection, and other complex engineering or real-world problems.

Complexity of Supersymmetric Systems and the Cohomology Problem

We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with N=2 supersymmetry and show that the problem remains QMA-complete. Our main motivation for studying this is the well-known fact that the ground state energy of a supersymmetric system is exactly zero if and only if a certain cohomology group is nontrivial. This opens the door to bringing the tools of Hamiltonian complexity to study the computational complexity of a large number of algorithmic problems that arise in homological algebra, including problems in algebraic topology, algebraic geometry, and group theory. We take the first steps in this direction by introducing the k-local Cohomology problem and showing that it is QMA1-hard and, for a large class of instances, is contained in QMA. We then consider the complexity of estimating normalized Betti numbers and show that this problem is hard for the quantum complexity class DQC1, and for a large class of instances is contained in BQP. In light of these results, we argue that it is natural to frame many of these homological problems in terms of finding ground states of supersymmetric fermionic systems. As an illustration of this perspective we discuss in some detail the model of Fendley, Schoutens, and de Boer consisting of hard-core fermions on a graph, whose ground state structure encodes l-dimensional holes in the independence complex of the graph. This offers a new perspective on existing quantum algorithms for topological data analysis and suggests new ones.

Layer topology of smectic grain boundaries

ABSTRACT Grain boundaries in extremely confined colloidal smectics possess a topological fine structure with coexisting nematic and tetratic symmetry of the director field. An alternative way to approach the problem of smectic topology is via the layer structure, which is typically more accessible in experiments on molecular liquid crystals. Here, we consider exemplary density functional theory results for two-dimensional hard rods to illustrate how the concept of endpoint defects, which appear as tetratic disclinations of quarter charge in director topology, translates to smectic layer topology built around the networks formed by density maxima and minima. By doing so, we elaborate on further advantages of a topological concept evolving around the layer structure rather than the director field, such as providing insight in the structure of edge dislocations or virtual defects at the confining walls.

Fixed‐time Synchronization of Stochastic Kuramoto‐Oscillator Networks With Switching Topology Under Dynamic Event‐triggered Scheme

AbstractThis paper proposes a dynamic event‐triggered fixed‐time control scheme for the phase synchronization of Kuramoto networks with switching topology and stochastic coupling noise. To deal with the problems of switching topology and stochastic coupling noise, a multilayered control structure with a specially designed noise reduction layer is developed. The effectiveness is proved based on stochastic differential theory. To save communication resources and reduce control frequency, a dynamic event‐triggered mechanism is proposed. By introducing a dynamic variable into the triggering condition, the triggered instants are further reduced compared to the traditional static event‐triggered method. The synchronizing criteria and parameter conditions are established with stochastic Lyapunov stability theory. The analysis of Zeno behavior is also given. Finally, numerical simulation experiments are conducted to demonstrate the effectiveness of the proposed dynamic event‐triggered control scheme.

A Robust Networking Model With Quantum Evolution for Internet of Things

The Internet of Things (IoT), which includes massive energy-limited sensor nodes, has become the foundation of smart city. Improving the ability of network topology to resist node cascading failures, namely robustness, is the key for IoT to provide stable data-aware services for upper-layer applications. However, the robustness optimization problem of complex topology is an NP-hard problem and cannot be optimally solved in polynomial time. The existing researches try to find the approximate solution by heuristic algorithms, but there are problems of slow convergence and easy to fall into local optimum. Quantum computing has more diverse search spaces due to the existence of quantum superposition states, which can jump out of the local optimum. Therefore, this paper firstly combines quantum computing with topology robustness evolution, and proposes a robust networking model based on quantum evolution. By using the quantum encoding, we design a novel quantum measurement method to collapse quantum states towards a more robust network topology. The experimental results show that our model can jump out of the local optimum with fewer population individuals and achieve higher robustness.

Topology optimization of truss structures considering local buckling stability

This paper proposes the double-layer optimization algorithm to solve the truss topology problem with bar local buckling constraints. With this algorithm, the constraints on the local buckling are treated as linear functions of the optimized variables, which ensures efficient computation. In addition, two practical algorithms are proposed to solve the problems of the existence of transient hinges and the difficulty in matching the bar sections with standard sections. In addition, the topology optimization plug-in, named Topaz, is developed in this paper in the Rhino-Grasshopper parametric modeling platform to facilitate rapid model building. Finally, numerical examples show that the optimization results satisfy the requirements of strength, local buckling, and slenderness ratio of the bar, which demonstrates the effectiveness of the proposed algorithm.

New Insights in Smooth Occluding Contours for Nonphotorealistic Rendering.

Computing occluding contours is often a crucial step in stroke-based artistic 3-D stylization for movies, video games, and visualizations. However, many existing applications use only simple curve stylization techniques, such as thin black lines or hand-animated strokes. This is because sophisticated procedural stylization requires accurate curve topology, which has long been an unsolved research problem. This article describes a recent theoretical breakthrough in the topology problem. Specifically, the new theory points out that existing contour algorithms often generate curves that cannot have any valid visibility, and new algorithms show how to correct the problem. This article surveys classes of algorithms that can compute contours accurately and identifies new research opportunities.