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A diabatic potential energy matrix (DPEM) for the two lowest states of BeH 2 + has been constructed using the combined-hyperbolic-inverse-power-representation (CHIPR) method. By imposing symmetry constraints on the coefficients of polynomials, the complete nuclear permutation inversion symmetry is correctly preserved in the CHIPR functional form. The symmetrized CHIPR functional form is then used in the diabatization by ansatz procedure. The ab initio energies are reproduced with satisfactory accuracy. In addition, the CHIPR-based DPEM also reproduces the local topology of a conical intersection. Future work will focus on a complete four-state diabatic representation with emphasis on the long-range interactions and spin–orbit couplings, which will enable accurate quantum scattering calculations for the Be+(2P) + H2 → BeH+(X1Σ+) + H(2S) reaction. [ABSTRACT FROM AUTHOR]

We report the topology-mediated modulation of a twisted domain wall speed in a thick perpendicularly magnetized system. By exploiting the topological robustness of the direction of the Bloch wall component in the twisted domain wall, we show that the domain wall speed either increases or decreases depending on whether the transverse magnetic field is parallel or antiparallel to the Bloch wall component. The decrease in the speed is maintained until the antiparallel transverse reaches ∼0.3 T, indicating that the twisted domain wall can offer wide controllability supported by the topological robustness which involves an injection of a Bloch point. We also demonstrate that the transverse magnetic field suppresses the Walker breakdown, allowing high mobility domain wall motion for a wide range of perpendicular driving fields. [ABSTRACT FROM AUTHOR]

Topological regulation of DNA by topoisomerases in cells is very crucial for life. We propose a coarse-grained model to study the catenation process of double-stranded DNA (dsDNA) rings regulated by topoisomerase II (TOP2) and provide a computational method to characterize the topological structures of the Olympic gels obtained. The function of TOP2 in the catenation of dsDNA rings is implicitly fulfilled by operating the length of a stretchable catch bond in the dsDNA ring. After the catenation reaction of initially noncatenated dsDNA rings in the solution, the Olympic gel is obtained and the interlocked topology of the dsDNA rings can be characterized by a computational method derived from the HOMFLY polynomial, based on which the catenation degree and the complexity of catenation are quantified. Detailed dependence of the catenation degree and the complexity of the catenated topology on key parameters, including the size of the transient broken gap and the duration time of the break on the dsDNA ring during operation by TOP2, the initial molar ratio of TOP2 to the dsDNA rings, and the reaction temperature, has been investigated. [ABSTRACT FROM AUTHOR]

Non-Hermiticity alone can trigger topological phase transition in physical systems. Here, we construct different unit cells in an acoustic Su Schrieffer Heeger chain with different distributions of onsite losses. We theoretically and numerically investigate the different edge modes that can occur at the domain walls of different finite chains. Three types of edge modes are identified. The first type comes from the topology of the unit cells. The second type comes from the local Parity symmetry at the interface, which are cavity modes. The third one comes from the Parity-Time symmetric domain wall. The robustness against coupling disorder is then examined, confirming the robustness of the topologically protected modes. The evolution with increasing disorder of the interface modes due to the Parity-Time symmetric domain wall is singular as they appear first as more robust than the cavity modes before diverging. These results show the ability of the onsite losses ingredient to control wavefields. [ABSTRACT FROM AUTHOR]

It is shown that micromagnetic and atomistic spin dynamics simulations can use multiple graphical processing units (GPUs) not only to reduce computation time but also to allow for a larger simulation size than is possible on a single GPU. While interactions that depend on neighboring spins, such as exchange interactions, may be implemented efficiently by transferring data between GPUs using halo regions or direct memory accesses, implementing the long-range demagnetizing interaction is the main difficulty in achieving good performance scaling, where the data transfer rate between GPUs is a significant bottleneck. A multi-GPU convolution algorithm is developed here, which relies on single-GPU FFTs executed in parallel. It is shown that even for micromagnetic simulations where the demagnetizing interaction computation time dominates, good performance scaling may be achieved, with speedup factors up to 1.8, 2.5, and 3.1, for two, three, and four GPUs, respectively. The code developed here can be used for any number of GPUs in parallel, with performance scaling strongly dependent on the inter-GPU data transfer rate and connection topology. This is further improved in micromagnetic simulations, which include a spin transport solver, obtaining speedup factors up to 1.96, 2.8, and 3.7, for two, three, and four GPUs, respectively. The best case scenario is obtained for atomistic simulations, where the demagnetizing interaction is implemented with spin-averaged cells. Using a single workstation with four GPUs, it is shown that atomistic spin dynamics simulations with up to 1 × 109 spins and atomistic Monte Carlo simulations with up to 2 × 109 spins are possible, with near-ideal performance scaling. [ABSTRACT FROM AUTHOR]

The electric polarizability and the spread of the total position tensors are used to characterize the metallic vs insulator nature of large (finite) systems. Finite clusters are usually treated within the open boundary condition formalism. This introduces border effects, which prevent a fast convergence to the thermodynamic limit and can be eliminated within the formalism of periodic boundary conditions. Recently, we introduced an original approach to periodic boundary conditions, named Clifford boundary conditions. It considers a finite fragment extracted from a periodic system and the modification of its topology into that of a Clifford torus. The quantity representing the position is modified in order to fulfill the system periodicity. In this work, we apply the formalism of Clifford boundary conditions to the case of carbon nanotubes, whose treatment results in a particularly simple zigzag geometry. Indeed, we demonstrate that at the Hückel level, these nanotubes, either finite or periodic, are formally equivalent to a collection of non-interacting dimerized linear chains, thus simplifying their treatment. This equivalence is used to describe some nanotube properties as the sum of the contributions of the independent chains and to identify the origin of peculiar behaviors (such as conductivity). Indeed, if the number of hexagons along the circumference is a multiple of three, a metallic behavior is found, namely a divergence of both the (per electron) polarizability and total position spread of at least one linear chain. These results are in agreement with those in the literature from tight-binding calculations. [ABSTRACT FROM AUTHOR]

Self-assembly of chiral particles with an L-shape is explored by Monte-Carlo computer simulations in two spatial dimensions. For sufficiently high packing densities in confinement, a carpet-like texture emerges due to the interlocking of L-shaped particles, resembling a distorted smectic liquid crystalline layer pattern. From the positions of either of the two axes of the particles, two different types of layers can be extracted, which form distinct but complementary entangled networks. These coarse-grained network structures are then analyzed from a topological point of view. We propose a global charge conservation law by using an analogy to uniaxial smectics and show that the individual network topology can be steered by both confinement and particle geometry. Our topological analysis provides a general classification framework for applications to other intertwined dual networks. [ABSTRACT FROM AUTHOR]

Recent work [Mirth et al., J. Chem. Phys. 154, 114114 (2021)] has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in 3 N-dimensions. This includes information about all transition paths between local minima (connected by critical points of index ≥ 1) and allows for differentiation of energy landscapes that may appear similar when considering only the lowest energy pathways (as tracked by other representations, such as disconnectivity graphs, using index 1 critical points). Using the additive nature of the conformational potential energy landscape of n-alkanes, it became apparent that some topological features—such as the number of sublevelset persistence bars—could be proven. This work expands the notion of predictable energy landscape topology to any additive intramolecular energy function on a product space, including the number of sublevelset persistent bars as well as the birth and death times of these topological features. This amounts to a rigorous methodology to predict the relative energies of all topological features of the conformational energy landscape in 3N dimensions (without the need for dimensionality reduction). This approach is demonstrated for branched alkanes of varying complexity and connectivity patterns. More generally, this result explains how the sublevelset persistent homology of an additive energy landscape can be computed from the individual terms comprising that landscape. [ABSTRACT FROM AUTHOR]

The inertia of trapping and detrapping of nonequilibrium charge carriers affects the electrochemical and transport properties of both bulk and nanoscopic structures in a very peculiar way. An emerging memory response with hysteresis in the current–voltage response and its eventual multiple crossing, produced by this universally available ingredient, are signatures of this process. Here, we deliver a microscopic and analytical solution for these behaviors, understood as the modulation of the topology of the current–voltage loops. Memory emergence thus becomes a characterization tool for intrinsic features that affect the electronic transport of solids such as the nature and number of trapping sites, intrinsic symmetry constraints, and natural relaxation time scales. This method is also able to reduce the seeming complexity of frequency-dependent electrochemical impedance and cyclic voltammetry observable for a variety of systems to a combination of simple microscopic ingredients. [ABSTRACT FROM AUTHOR]

We study the image of SU (n) under the diagonal product map. Using only elementary tools of linear algebra, analysis and general topology, we find the analytical formula for the boundary of this image and find all special unitary matrices whose diagonal product lies on that boundary. [ABSTRACT FROM AUTHOR]

In this paper we characterize hyperbolic cosine transforms of (positive) Borel measures ν in terms of exponential convexity (Bernstein's terminology). The case of compactly supported measures ν is also considered. All of this is then applied to (bounded) composition operators C T , ρ : f ↦ f ∘ T on L 2 (R κ , μ ρ) with affine symbols T = A + a , where d μ ρ (x) = ρ (x) d x , ρ (x) = ψ (‖ x ‖) − 1 , ψ is a continuous positive real valued function and ‖ ⋅ ‖ is the Euclidean norm on R κ. The main result states that the map R κ ∋ a ↦ C I + a , ρ is continuous in the strong operator topology and has cosubnormal values if and only if ψ is the hyperbolic cosine transform of a compactly supported Borel measure (I is the identity transformation). The case of affine symbols T that are not translations is also discussed. [ABSTRACT FROM AUTHOR]

Maintaining the stability of ecological communities is critical for conservation, yet we lack a clear understanding of what attributes of metacommunity structure control stability. Some theories suggest that greater dispersal promotes metacommunity stability by stabilizing local populations, while others suggest that dispersal synchronizes fluctuations across patches and leads to global instability. These effects of dispersal on stability may be mediated by metacommunity structure: the number of patches, the pattern of connections across patches, and levels of spatiotemporal correlation in the environment. Thus, we need theory to investigate metacommunity dynamics under different spatial structures and ecological scenarios. Here, we use simulations to investigate whether stability is primarily affected by connectivity, including dispersal rate and topology of connectivity network, or by mechanisms related to the number of patches. We find that in competitive metacommunities with environmental stochasticity, network topology has little effect on stability on the metacommunity scale even while it could change spatial diversity patterns. In contrast, the number of connected patches is the dominant factor promoting stability through averaging stochastic fluctuations across more patches, rather than due to more habitat heterogeneity per se. These results broaden our understanding of how metacommunity structure changes metacommunity stability, which is relevant for designing effective conservation strategies. [ABSTRACT FROM AUTHOR]

Summary: Multilevel inverters (MLIs) have recently drawn the huge attention of industry and academia since they are becoming a viable technology for a variety of applications. However, the risk of failure of the converter increases with the increasing number of component count for applications involving heavy duty and continuous operation. In this context, an asymmetrical source configured FT‐MLI (fault tolerant‐MLI) topology is investigated and developed with less number of device count and having the ability to withstand both OC (open‐circuit) and SC (short‐circuit) switch faults on single and multiple switches. The proposed architecture maintains the same output voltage levels and power in both pre‐ and post‐fault operations. In addition, a switching method is developed to reduce the capacitors' size by minimizing the voltage ripple. Furthermore, without the need for an external circuit, the voltage across the capacitors remains balanced in both pre‐ and post‐fault operations. The simulation and experimental results are provided to demonstrate the effectiveness of the proposed asymmetrical FT‐MLI topology. Finally, a comparison of the proposed topology with the existing MLI topologies is shown to emphasize the benefits of the proposed system. [ABSTRACT FROM AUTHOR]

We present surface and structural models of a swarm of dm-scale subparallel faults exposed in a ∼2000 m2 glaciated outcrop near Franz Josef Glacier, in the Southern Alps of New Zealand. These structures are inferred to have slipped at ∼20 km depth in the hanging-wall Alpine Schist of the Alpine Fault under conditions that were variably brittle to ductile as the Pacific Plate was tilted and uplifted. Using field mapping, real-time kinematic GPS and digital images from a remotely piloted aircraft system, we have created a digital surface model of the outcrop and orthophotographs at a ground resolution of ∼1 cm to map compositional layering in the metasediments and the array of brittle-ductile faults displacing them. In order of decreasing relative age (and average thickness), displaced markers in the schist include primary psammite and pelite beds, quartz veins, and a deformational foliation. The surface models have been used to create 2-D transects and a 3-D model where faults are projected down-dip, to determine the connectivity, topology and intersection types of the fault swarm. Lithological variations, particularly the interface between pelitic and psammitic schist, were a primary control on the topology of the fault network and the spacing between faults. [ABSTRACT FROM AUTHOR]

• The attainment of the native structure of membrane proteins within biological membranes has been revealed as a dynamic and intricate process. • Foundational concepts like hydrophobicity and the positive inside rule offer a framework for comprehending insertion dynamics and determining topology. • Various techniques, including reporter fusions and biophysical assays, can be employed to experimentally ascertain the insertion properties and topology of membrane proteins. • The integration of topology prediction with deep learning 3D structure prediction models proves highly complementary, expanding our understanding of the membrane protein universe. Membrane proteins play pivotal roles in a wide array of cellular processes and constitute approximately a quarter of the protein-coding genes across all organisms. Despite their ubiquity and biological significance, our understanding of these proteins remains notably less comprehensive compared to their soluble counterparts. This disparity in knowledge can be attributed, in part, to the inherent challenges associated with employing specialized techniques for the investigation of membrane protein insertion and topology. This review will center on a discussion of molecular biology methodologies and computational prediction tools designed to elucidate the insertion and topology of helical membrane proteins. [ABSTRACT FROM AUTHOR]

We prove that, given a finitely generated subgroup H of a free group F , the following questions are decidable: is H closed (dense) in F for the pro-(met)abelian topology? Is the closure of H in F for the pro-(met)abelian topology finitely generated? We show also that if the latter question has a positive answer, then we can effectively construct a basis for the closure, and the closure has decidable membership problem in any case. Moreover, it is decidable whether H is closed for the pro- $\mathbf {V}$ topology when $\mathbf {V}$ is an equational pseudovariety of finite groups, such as the pseudovariety $\mathbf {S}_k$ of all finite solvable groups with derived length $\leq k$. We also connect the pro-abelian topology with the topologies defined by abelian groups of bounded exponent. [ABSTRACT FROM AUTHOR]

We propose conditioning field initialization for neural network-based topology optimization. In this work, we focus on (1) improving upon existing neural network-based topology optimization and (2) demonstrating that using a prior initial field on the unoptimized domain, the efficiency of neural network-based topology optimization can be further improved. Our approach consists of a topology neural network that is trained on a case by case basis to represent the geometry for a single topology optimization problem. It takes in domain coordinates as input to represent the density at each coordinate where the topology is represented by a continuous density field. The displacement is solved through a finite element solver. We employ the strain energy field calculated on the initial design domain as an additional conditioning field input to the neural network throughout the optimization. Running the same number of iterations, our method converges to a lower compliance. To reach the same compliance, our method takes fewer iterations. The addition of the strain energy field input improves the convergence speed compared to standalone neural network-based topology optimization. [ABSTRACT FROM AUTHOR]

This article studies the practical fixed‐time average consensus problem of general linear multi‐agent systems under switching topologies. First, a distributed fixed‐time consensus control protocol based on dynamic event‐triggered mechanism is designed by using the local information exchange between neighboring agents. The protocol introduces an internal dynamic variable and the triggering condition changes in real time based on the dynamic variable obtained online, which can significantly reduce the number of triggering events and effectively decrease the energy consumption of the multi‐agent system. Then, the sufficient conditions for the multi‐agent system to solve the practical fixed‐time average consensus problem are given, and it is proved that there is no Zeno behavior in the system. Furthermore, a self‐triggered control scheme is proposed such that the neighboring agents communicate with each other only when one of them is triggered. In other words, this scheme does not require continuous communication between neighboring agents and thus reduces communication cost of the system. Finally, the simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Let $f_0$ and $f_1$ be two homogeneous polynomials of degree d in three complex variables $z_1,z_2,z_3$. We show that the Lê–Yomdin surface singularities defined by $g_0:=f_0+z_i^{d+m}$ and $g_1:=f_1+z_i^{d+m}$ have the same abstract topology, the same monodromy zeta-function, the same $\mu ^*$ -invariant, but lie in distinct path-connected components of the $\mu ^*$ -constant stratum if their projective tangent cones (defined by $f_0$ and $f_1$ , respectively) make a Zariski pair of curves in $\mathbb {P}^2$ , the singularities of which are Newton non-degenerate. In this case, we say that $V(g_0):=g_0^{-1}(0)$ and $V(g_1):=g_1^{-1}(0)$ make a $\mu ^*$ -Zariski pair of surface singularities. Being such a pair is a necessary condition for the germs $V(g_0)$ and $V(g_1)$ to have distinct embedded topologies. [ABSTRACT FROM AUTHOR]

This paper presents the methodology and theoretical foundation of topology optimization (TO) Results Spaceframe Interpreter, an automatic TO results interpreter that generates a closely associated space frame consisting of welded structural tubing or rectangular bars. TO is a computational technique that uses a finite element (FE) formulation to identify the most weight-efficient structure within a design domain. Density-based TO results in structures that take organic forms and is usually a tedious and cumbersome process to generate a computer-aided-design (CAD) model to manufacture through conventional techniques. The optimal topology frequently resembles a space frame, which is well-known as being a rigid, lightweight structure. The methodology of the TO results interpreter leverages several techniques from volumetric image processing and has four primary processes. First, the results are obtained from commercial FE/TO software and mapped into a cubic grid of voxels. Second, junction locations are extracted and member connectivity that represents a frame is identified. Third, a sizing optimization is incorporated to determine appropriate sectional dimensions of the circular or rectangular space frame members. Fourth, the optimized space frame geometry is imported into a CAD design tool to automatically create a design model. The logic and are implemented within the frame extraction processes. The automated TO interpreter is designed to interact with commercial FE analysis and CAD systems. The interpreter is demonstrated on various spatial examples including aerospace and automotive applications. In each case, the welded space frame closely resembles the TO result, with nearly equivalent stiffness and mass. [ABSTRACT FROM AUTHOR]

The optical topology, which serves as a stable spatial electromagnetic structure, offers a new dimension for applications in the field of optical information processing, transmission, and storage. In recent years, there has been an increasing focus on these spatially structured light fields. By reversing the radiation of orthogonal dipole pairs, we propose an approach to generate Meron topologies within the focused light field while also investigating the evolution of the Meron structure along the longitudinal axis. Through introducing a dipole placed along the z -axis, we achieve precise positioning and fine adjustment of the topological center. The stability of Meron under a high numerical aperture objective lens (NA = 0.95) can be effectively demonstrated. [ABSTRACT FROM AUTHOR]

Topology optimization is an appealing technique for optimal layout of active controllers of structures. However, the existing methods are mainly restricted to deterministic excitations, and the optimal control law involved is determined by use of the classical optimal control (COC) method, in which the sensitivities of the gain matrix with respect to the design variables need to be determined by solving the Riccati sensitivity equation numerically. In this study, a reliability-based topology optimization framework is proposed for optimal layout of active controllers of structures under nonstationary random excitations. The optimization problem is formulated as the minimization of the failure probability of the structure subjected to a specified maximum number of controllers. To avoid solving the Riccati equation, an explicit optimal control (EOC) method is first employed to derive the closed-form optimal control law in terms of the position parameters of controllers. The statistical moments of the optimal control forces and structural responses under random excitations are then obtained explicitly by the operation rules of moments, and the first-passage dynamic reliability of the structure can be formulated using the level-crossing theory. On this basis, the sensitivities of the structural failure probability with respect to the position parameters of controllers can be derived analytically by the direct differential method. Finally, the explicit formulations of the response statistics and the relevant sensitivities are incorporated into a gradient-based method of moving asymptotes (MMA) for topology optimization of the layout of controllers in conjunction with the solid isotropic material with penalization (SIMP) technique. Two numerical examples are presented to demonstrate the feasibility of the proposed topology optimization framework. [ABSTRACT FROM AUTHOR]

A guanine‐rich oligonucleotide based on a human telomeric sequence but with the first three‐nucleotide intervening stretch replaced by a putative 15‐nucleotide hairpin‐forming sequence shows a pH‐dependent folding into different quadruplex‐duplex hybrids in a potassium containing buffer. At slightly acidic pH, the quadruplex domain adopts a chair‐type conformation. Upon increasing the pH, a transition with a midpoint close to neutral pH to a major and minor (3+1) hybrid topology with either a coaxially stacked or orthogonally oriented duplex stem‐loop occurs. NMR‐derived high‐resolution structures reveal that an adenine protonation is prerequisite for the formation of a non‐canonical base quartet, capping the outer G‐tetrad at the quadruplex‐duplex interface and stabilizing the antiparallel chair conformation in an acidic environment. Being directly associated with interactions at the quadruplex‐duplex interface, this unique pH‐dependent topological transition is fully reversible. Coupled with a conformation‐sensitive optical readout demonstrated as a proof of concept using the fluorescent dye thiazole orange, the present quadruplex‐duplex hybrid architecture represents a potentially valuable pH‐sensing system responsive in a physiological pH range of 7±1. [ABSTRACT FROM AUTHOR]

This paper investigates N-bipolar hypersoft topology (N-BHST), a novel extension of both the well-established N-hypersoft topology (N-HST) and hypersoft topology (HST). Deviating significantly from its precursor, the N-bipolar hypersoft (N-BHS) set, N-BHST introduces a multi-opinion approach to decision-making, augmenting robustness and adaptability. This innovative framework addresses identified limitations in N-bipolar soft topology (N-BST), especially in managing multi-argument approximate functions. The study analyzes various operators (closure, interior, exterior, and boundary) within the N-BHST framework, elucidating their interrelationships. Additionally, an examination is carried out on the enhancement of multi-criteria group decision-making (MCGDM) using N-BHST, setting it apart from existing models. A numerical example is presented to illustrate its application in real-world decision scenarios. [ABSTRACT FROM AUTHOR]

Covalent adaptable networks and vitrimers are novel polymers with dynamic reversible bond exchange reactions for crosslinks, enabling them to modulate their properties between those of thermoplastics and thermosets. They have been gathering interest as materials for their recycling and self-healing properties. In this review, we discuss different molecular simulation efforts that have been used over the last decade to investigate and understand the nanoscale and molecular behaviors of covalent adaptable networks and vitrimers. In particular, molecular dynamics, Monte Carlo, and a hybrid of molecular dynamics and Monte Carlo approaches have been used to model the dynamic bond exchange reaction, which is the main mechanism of interest since it controls both the mechanical and rheological behaviors. The molecular simulation techniques presented yield sufficient results to investigate the structure and dynamics as well as the mechanical and rheological responses of such dynamic networks. The benefits of each method have been highlighted. The use of other tools such as theoretical models and machine learning has been included. We noticed, amongst the most prominent results, that stress relaxes as the bond exchange reaction happens, and that at temperatures higher than the glass transition temperature, the self-healing properties are better since more bond BERs are observed. The lifetime of dynamic covalent crosslinks follows, at moderate to high temperatures, an Arrhenius-like temperature dependence. We note the modeling of certain properties like the melt viscosity with glass transition temperature and the topology freezing transition temperature according to a behavior ruled by either the Williams–Landel–Ferry equation or the Arrhenius equation. Discrepancies between the behavior in dissociative and associative covalent adaptable networks are discussed. We conclude by stating which material parameters and atomistic factors, at the nanoscale, have not yet been taken into account and are lacking in the current literature. [ABSTRACT FROM AUTHOR]

The performance consistency of an RF MEMS switch matrix is a crucial metric that directly impacts its operational lifespan. An improved crossbar-based RF MEMS switch matrix topology, SR-Crossbar, was investigated in this article. An optimized port configuration scheme was proposed for the RF MEMS switch matrix. Both the utilization probability of individual switch nodes and the path lengths in the switch matrix achieve their best consistency simultaneously under the proposed port configuration scheme. One significant advantage of this scheme lies in that it only adjusts the positions of the input and output ports, with the topology and individual switch nodes kept unchanged. This grants it a high level of generality and feasibility and also introduces an additional degree of freedom for optimizations. In this article, a universal utilization probability function of single nodes was constructed and an optimization objective function for the SR-Crossbar RF MEMS switch matrix was formulated, which provide a convenient approach to directly solving the optimized port configuration scheme for practical applications. Simulations to demonstrate the optimized dynamic and static consistencies were conducted. For an 8 × 8 SR-Crossbar switch matrix, the standard deviations of contact resistances of 128 units and losses of all 64 paths decreased from 1.00 and 0.42 to 0.51 and 0.23, respectively. These results aligned closely with theoretical calculations derived from the proposed model. [ABSTRACT FROM AUTHOR]

The effective capture and recovery of radioiodine species associated with nuclear fuel reprocessing is of significant importance in nuclear power plants. Porous materials have been proven to be one of the most effective adsorbents for the capture of radioiodine. In this work, we design and synthesize a series of conjugated microporous polymers (CMPs), namely, TPDA–TFPB CMP, TPDA–TATBA CMP, and TPDA–TECHO CMP, which are constructed based on a planar rectangular 4-connected organic monomer and three triangular 3-connected organic monomers, respectively. The resultant CMPs are characterized using various characterization techniques and used as effective adsorbents for iodine capture. Our experiments indicated that the CMPs exhibit excellent iodine adsorption capacities as high as 6.48, 6.25, and 6.37 g g−1 at 348 K and ambient pressure. The adsorption mechanism was further investigated and the strong chemical adsorption between the iodine and the imine/tertiary ammonia of the CMPs, 3D network structure with accessible hierarchical pores, uniform micromorphology, wide π-conjugated structure, and high-density Lewis-base sites synergistically contribute to their excellent iodine adsorption performance. Moreover, the CMPs demonstrated good recyclability. This work provides guidance for the construction of novel iodine adsorbent materials with high efficiency in the nuclear power field. [ABSTRACT FROM AUTHOR]

Isolated bidirectional DC–DC converters are becoming increasingly important in various applications, particularly in the electric vehicle sector, due to their ability to achieve bidirectional power flow and their safety features. This paper aims to review the switch strategies and topologies of isolated bidirectional DC–DC converters, with a specific focus on their applications in the field of electric vehicles. From the perspective of topology, PWM-type isolated bidirectional DC–DC converters, dual active bridge converters, and resonant-type isolated bidirectional DC–DC converters constitute the three main categories of these converters. The paper further examines the traditional switch strategies of these converters and discusses how specific switch technologies, such as single-phase shift, expanding-phase shift, double-phase shift, and triple-phase shift, can enhance the overall performance of isolated bidirectional DC–DC converters. The paper meticulously examines the characteristics of each topology and control scheme, as well as their typical use cases in practical applications. Particularly, the paper delves into the applications of isolated bidirectional DC–DC converters in the electric vehicle sector and draws conclusions regarding their potential and trends in future electric vehicle technology. [ABSTRACT FROM AUTHOR]

Highly connected molecular building blocks (MBBs) have been demonstrated to play a crucial role in reticular chemistry, particularly in predicting the topologies of metal–organic frameworks. Metal phosphonate clusters exhibit considerable advantages in constructing high-connectivity MBBs, owing to the multiple coordination modes offered by phosphonic ligands. Herein, four metal (M = CoII, MnII) phosphonocarboxylate frameworks (CoPCF-1,2 and MnPCF-1,2) were successfully prepared under solvothermal conditions by utilizing the phosphonocarboxylic ligand, 4′-phosphonobiphenyl-3,5-dicarboxylic acid (H4pbpdc), and their structural characterization was performed using single-crystal X-ray diffraction (SCXRD). The structures feature a duodenary nuclear M12(µ3-OH)2(CO2)12(PO3)6(DMF)6/(CH3COO)4.5 cluster, bearing resemblance to the well-known Wells–Dawson ion from polyoxometallate chemistry. It is the first time a Wells–Dawson type cage has served as an 18-connected molecular building block, forming two kinds of porous metal phosphonocarboxylate frameworks with novel (3,18)-connected gez and gea topologies. Their permanent porosities were confirmed through N2 adsorption studies. Notably, the MBB Co12 cluster-based CoPCF-1 shows a loss and recovery process of µ3-OH through single-crystal-to-single-crystal (SCSC) transformation. The magnetic properties of the four compounds exhibit antiferromagnetic behavior. [ABSTRACT FROM AUTHOR]

In the realm of evolutionary game theory, the majority of scenarios involve players with incomplete knowledge, specially regarding their opponents' actions and payoffs compounded by the ever‐shifting landscape of players' interactions. These dynamics present formidable challenges in both the analysis and optimization of game evolution. To address this, a novel model named the networked evolutionary game (NEG) is proposed based on incomplete information with switched topologies. This model captures situations where players possess limited insight into their opponents' benefits, yet make decisions based on their own payoffs while adapting to different networks and new players. To bridge the gap between incomplete and complete information games, R. Selten's transformation method is leveraged, a renowned approach that converts an incomplete information game into an interim agent game, thereby establishing the equivalence of pure Nash equilibria (NE) in both scenarios. Employing the semi‐tensor product (STP) of matrices, a powerful tool in logistic system, the evolution of the model is articulated through algebraic relationships. This enables to unravel the patterns of game evolution and identify the corresponding pure Nash equilibria. By introducing control players, strategically positioned within the game, optimized control is facilitated over the evolutionary trajectory, ultimately leading to convergence towards an optimal outcome. Finally, these concepts are illustrated with a practical example within the paper. [ABSTRACT FROM AUTHOR]

Let F be a free group of arbitrary rank and let H be a finitely generated subgroup of F. Given a pseudovariety V of finite groups, i.e. a class of finite groups closed under taking subgroups, quotients and finitary direct products, we endow F with its pro- V topology. Our main result states that it is decidable whether H is pro- Su dense, where Su ⊂ S denote respectively the pseudovarieties of all finite supersolvable groups and all finite solvable groups. Our motivation stems from the following open problem: is it decidable whether H is pro- S dense? [ABSTRACT FROM AUTHOR]

Naturally occurring polymeric structures often consist of 1D polymer chains intricately folded and entwined through non‐covalent bonds, adopting precise topologies crucial for their functionality. The exploration of crystalline 1D polymers through dynamic covalent chemistry (DCvC) and supramolecular interactions represents a novel approach for developing crystalline polymers. This study shows that sub‐angstrom differences in the counter‐ion size can lead to various helical covalent polymer (HCP) topologies, including a novel metal‐coordination HCP (m‐HCP) motif. Single‐crystal X‐ray diffraction (SCXRD) analysis of HCP−Na revealed that double helical pairs are formed by sodium ions coordinating to spiroborate linkages to form rectangular pores. The double helices are interpenetrated by the unreacted diols coordinating sodium ions. The reticulation of the m‐HCP structure was demonstrated by the successful synthesis of HCP−K. Finally, ion‐exchange studies were conducted to show the interconversion between HCP structures. This research illustrates how seemingly simple modifications, such as changes in counter‐ion size, can significantly influence the polymer topology and determine which supramolecular interactions dominate the crystal lattice. [ABSTRACT FROM AUTHOR]

Naturally occurring polymeric structures often consist of 1D polymer chains intricately folded and entwined through non‐covalent bonds, adopting precise topologies crucial for their functionality. The exploration of crystalline 1D polymers through dynamic covalent chemistry (DCvC) and supramolecular interactions represents a novel approach for developing crystalline polymers. This study shows that sub‐angstrom differences in the counter‐ion size can lead to various helical covalent polymer (HCP) topologies, including a novel metal‐coordination HCP (m‐HCP) motif. Single‐crystal X‐ray diffraction (SCXRD) analysis of HCP−Na revealed that double helical pairs are formed by sodium ions coordinating to spiroborate linkages to form rectangular pores. The double helices are interpenetrated by the unreacted diols coordinating sodium ions. The reticulation of the m‐HCP structure was demonstrated by the successful synthesis of HCP−K. Finally, ion‐exchange studies were conducted to show the interconversion between HCP structures. This research illustrates how seemingly simple modifications, such as changes in counter‐ion size, can significantly influence the polymer topology and determine which supramolecular interactions dominate the crystal lattice. [ABSTRACT FROM AUTHOR]

Despite the huge importance that the centrality metrics have in understanding the topology of a network, too little is known about the effects that small alterations in the topology of the input graph induce in the norm of the vector that stores the node centralities. If so, then it could be possible to avoid re-calculating the vector of centrality metrics if some minimal changes occur in the network topology, which would allow for significant computational savings. Hence, after formalising the notion of centrality, three of the most basic metrics were herein considered (i.e., Degree, Eigenvector, and Katz centrality). To perform the simulations, two probabilistic failure models were used to describe alterations in network topology: Uniform (i.e., all nodes can be independently deleted from the network with a fixed probability) and Best Connected (i.e., the probability a node is removed depends on its degree). Our analysis suggests that, in the case of degree, small variations in the topology of the input graph determine small variations in Degree centrality, independently of the topological features of the input graph; conversely, both Eigenvector and Katz centralities can be extremely sensitive to changes in the topology of the input graph. In other words, if the input graph has some specific features, even small changes in the topology of the input graph can have catastrophic effects on the Eigenvector or Katz centrality. [ABSTRACT FROM AUTHOR]

Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer the lattice structure of neutrosophic open sets of a neutrosophic topology generated via a neutrosophic relation and examine its different characteristics. Furthermore, we enlarge to this lattice structure the notions of ideals (respectively, filters) and characterize them with regard to the lattice operations. We end this work by studying the prime neutrosophic ideal and prime neutrosophic filter as interesting types of neutrosophic ideals and neutrosophic filters. [ABSTRACT FROM AUTHOR]

The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism. [ABSTRACT FROM AUTHOR]

In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine's notions of generalized closed sets and Maki's  Λ  sets. The methods used in this investigation are described in my previous work, where a unified concept of general closedness is presented. From a methodology point of view, the present concept is symmetric to the previous. In generalizing open subsets, one can use the two methods. According to the first one, the family of Levine's generalization is used as some base to build the family of closed subsets of the new topology. In the second method, the family of open subsets is extended, in the same way, as the family of closed subsets in the classic Levine's method. The results obtained in this general conception easily extend and imply well-known theorems of this area of investigation. In the literature on this issue, many versions of generalizations of  Λ -sets have been investigated. The tools used in this paper enabled us to prove that there exist at most 10 generalizations of these types, and we show the relationships between them in the graph. As a result, it turns out that some generalizations investigated in the literature are trivial. [ABSTRACT FROM AUTHOR]

Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of multicellular organisms. Tubular forms offer the advantage of a regulated internal milieu, and Fibonacci forms may offer packing efficiencies. The underlying mechanisms behind the cellular genesis of Fibonacci and tubular forms remain unknown. Methods: In a multicellular organism, cells adhere to form a macrostructure and to coordinate further replication. We propose and prove simple theorems connecting cell replication and adhesion to Fibonacci forms and simplicial topology. Results: We identify some cellular and molecular properties whereby the contact inhibition of replication by adhered cells may approximate Fibonacci growth patterns. We further identify how a component 2 → 3 cellular multiplication step may generate a multicellular structure with some properties of a two-simplex. Tracking the homotopy of a two-simplex to a circle and to a tube, we identify some molecular and cellular growth properties consistent with the morphogenesis of tubes. We further find that circular and tubular cellular aggregates may be combinatorially favored in multicellular adhesion over flat shapes. Conclusions: We propose a correspondence between the cellular and molecular mechanisms that generate Fibonacci cell counts and those that enable tubular forms. This implies molecular and cellular arrangements that are candidates for experimental testing and may provide guidance for the synthetic biology of hollow morphologies. [ABSTRACT FROM AUTHOR]

We present CharacterMixer, a system for blending two rigged 3D characters with different mesh and skeleton topologies while maintaining a rig throughout interpolation. CharacterMixer also enables interpolation during motion for such characters, a novel feature. Interpolation is an important shape editing operation, but prior methods have limitations when applied to rigged characters: they either ignore the rig (making interpolated characters no longer posable) or use a fixed rig and mesh topology. To handle different mesh topologies, CharacterMixer uses a signed distance field (SDF) representation of character shapes, with one SDF per bone. To handle different skeleton topologies, it computes a hierarchical correspondence between source and target character skeletons and interpolates the SDFs of corresponding bones. This correspondence also allows the creation of a single "unified skeleton" for posing and animating interpolated characters. We show that CharacterMixer produces qualitatively better interpolation results than two state‐of‐the‐art methods while preserving a rig throughout interpolation. Project page: https://seanxzhan.github.io/projects/CharacterMixer. [ABSTRACT FROM AUTHOR]

Shape‐conveying line drawings generated from 3D models normally create closed regions in image space. These lines and regions can be stylized to mimic various artistic styles, but for complex objects, the extracted topology is unnecessarily dense, leading to unappealing and unnatural results under stylization. Prior works typically simplify line drawings without considering the regions between them, and lines and regions are stylized separately, then composited together, resulting in unintended inconsistencies. We present a method for joint simplification of lines and regions simultaneously that penalizes large changes to region structure, while keeping regions closed. This feature enables region stylization that remains consistent with the outline curves and underlying 3D geometry. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing secure control for networked multi-agent systems (MASs) under Denial-of-Service (DoS) attacks. We propose a constructive design method based on the interaction topology. The MAS with a non-attack communication topology, modeled by quasi-Abelian Cayley graphs subject to DoS attacks, can be represented as a switched system. Using switching theory, we provide easily implementable sufficient conditions for the networked MAS to remain asymptotically stable despite DoS attacks. Our results are applicable to both continuous-time and discrete-time systems, as well as to discrete-time systems with variable steps or systems that combine discrete and continuous times. [ABSTRACT FROM AUTHOR]

The present study investigates topology for battery charging units (BCU) with simple design and power factor correction. It has a galvanic isolation between the grid and the battery, which is one of the law and standard requirements. The impulse transformer ensures galvanic isolation, which makes the topology suitable for onboard electric vehicles (EV) charging units (OBC). The study also presents a simulation model a simulation model with the help of which a simulation is conducted and a result is obtained. [ABSTRACT FROM AUTHOR]

This work presents an improved structure of a single-phase muti-input multilevel inverter (MIMLI) for distributed energy resources, which is capable of producing a nine-level output in symmetric mode and 21 levels in asymmetrical mode. The topology uses four DC sources and ten switches, with four switches being bidirectional and the remaining unidirectional. The operation of the circuit is analyzed in an asymmetrical mode, and switching signals are accomplished using the Nearest Level Control (NLC) PWM technique. Depending on the value of the DC sources used, the number of levels can vary. In this work, different DC source algorithms were also proposed, and the analysis of the inverter has been carried out considering the algorithms producing the maximum number of levels. The inverter was simulated in MATLAB/Simulink under steady state and dynamic conditions, achieving a 3.89% THD in output. The thermal analysis was conducted using PLECS software 4.1.2 to assess losses and efficiency. A laboratory prototype of the proposed topology was developed and tested, confirming its performance through simulation results and proving it economically viable for medium- and high-power applications. [ABSTRACT FROM AUTHOR]

With the widespread use of new equipment such as distributed photovoltaics, distributed energy storage, electric vehicles, and distributed wind power, the control of low-voltage distribution networks (LVDNs) has become increasingly complex. Acquiring the most recent topological structure is essential for conducting accurate analysis and real-time control of LVDNs. The signal injection-based topology identification algorithm is favored for its speed and efficiency. This research introduces an innovative topology identification algorithm based on signal injection, specifically designed to address the challenges of incomplete and inaccurate identifications caused by the missing data in feature signal records (FSRs). Based on the correlations among FSRs at various devices, the algorithm introduces a dual-axis completion strategy—both vertical and horizontal—to effectively address missing data. Subsequently, an inclusion detection process is devised to process the completed FSRs, culminating in an accurate topology of LVDNs. Based on the study of actual LVDN data, the results indicate that the proposed algorithm markedly enhances the completeness and accuracy of topology identification. This advancement offers a robust solution tailored to accommodate the dynamic and swiftly changing topological configurations of LVDNs. [ABSTRACT FROM AUTHOR]

Conventional cooling channels used in die casting molds exhibit significant drawbacks, resulting in extended cooling times for cast parts. Issues such as the formation of dirt, limescale, and corrosion substantially diminish the thermal efficiency of these channels, leading to challenges in achieving uniform cooling and potential quality issues. In response to these challenges, this study proposes Topology Optimization as a novel approach. It involves designing cooling structures through Topology Optimization to replace traditional cooling channels, incorporating both Discrete and Gaussian boundary conditions to optimize thermal efficiency. Additionally, Structural Topology Optimization is employed to ensure structural integrity, preventing deformation or yielding under high loads during the die casting process. Numerical analysis revealed superior thermal performance compared to conventional channels, particularly when subjected to Discrete and Gaussian boundary conditions. Furthermore, the application of the latter establishes conformal cooling and minimizes temperature gradients in the casting, reducing casting defects such as shrinkage porosity. These findings highlight the efficacy of Topology Optimization in addressing the challenges of traditional cooling methods, with wide-ranging implications for manufacturing processes utilizing permanent molds for shaping materials. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of varying the part geometric complexity and 3D printing process setup on the resulting structural load bearing capacity of fiber composites. Three levels of geometric complexity are developed through 2.5D topology optimization, 3D topology optimization, and 3D topology optimization with directional material removal. The 3D topology optimization is performed with the SIMP method and accelerated by high-performance computing. The directional material removal is realized by incorporating the advection-diffusion partial differential equation-based filter to prevent interior void or undercut in certain directions. A set of 3D printing and mechanical performance tests are performed. It is interestingly found that, the printing direction affects significantly on the result performance and if subject to the uni direction, the load-bearing capacity increases from the 2.5D samples to the 3D samples with the increased complexity, but the load-bearing capacity further increases for the 3D simplified samples due to directional material removal. Hence, it is concluded that a restricted structural complexity is suitable for topology optimization of 3D-printed fiber composites, since large area cross-sections give more degrees of design freedom to the fiber path layout and also makes the inter-layer bond of the filaments firmer. [ABSTRACT FROM AUTHOR]

Topology optimization is one of the most flexible structural optimization methodologies. However, in exchange for its high level of design freedom, typical topology optimization cannot avoid multimodality, where multiple local optima exist. This study focuses on developing a gradient-free topology optimization framework to avoid being trapped in undesirable local optima. Its core is a data-driven multifidelity topology design (MFTD) method, in which the design candidates generated by solving low-fidelity topology optimization problems are updated through a deep generative model and high-fidelity evaluation. As its key component, the deep generative model compresses the original data into a low-dimensional manifold, i.e., the latent space, and randomly arranges new design candidates over the space. Although the original framework is gradient free, its randomness may lead to convergence variability and premature convergence. Inspired by a popular crossover operation of evolutionary algorithms (EAs), this study merges the data-driven MFTD framework and proposes a new crossover operation called latent crossover. We apply the proposed method to a maximum stress minimization problem in 2D structural mechanics. The results demonstrate that the latent crossover improves convergence stability compared to the original data-driven MFTD method. Furthermore, the optimized designs exhibit performance comparable to or better than that in conventional gradient-based topology optimization using the P-norm measure. [ABSTRACT FROM AUTHOR]

RNA transcripts play a crucial role as witnesses of gene expression health. Identifying disruptive short sequences in RNA transcription and regulation is essential for potentially treating diseases. Let us delve into the mathematical intricacies of these sequences. We have previously devised a mathematical approach for defining a "healthy" sequence. This sequence is characterized by having at most four distinct nucleotides (denoted as n t ≤ 4 ). It serves as the generator of a group denoted as f p . The desired properties of this sequence are as follows: f p should be close to a free group of rank n t − 1 , it must be aperiodic, and f p should not have isolated singularities within its S L 2 (C) character variety (specifically within the corresponding Groebner basis). Now, let us explore the concept of singularities. There are cubic surfaces associated with the character variety of a four-punctured sphere denoted as S 2 4 . When we encounter these singularities, we find ourselves dealing with some algebraic solutions of a dynamical second-order differential (and transcendental) equation known as the Painlevé VI Equation. In certain cases, S 2 4 degenerates, in the sense that two punctures collapse, resulting in a "wild" dynamics governed by the Painlevé equations of an index lower than VI. In our paper, we provide examples of these fascinating mathematical structures within the context of miRNAs. Specifically, we find a clear relationship between decorated character varieties of Painlevé equations and the character variety calculated from the seed of oncomirs. These findings should find many applications including cancer research and the investigation of neurodegenative diseases. [ABSTRACT FROM AUTHOR]