Topological Perspective Research Articles

Modeling an electric power microgrid by model predictive control for analyzing its characteristics from reliability, controllability and topological perspectives

Microgrids can be a key solution for integrating renewable and distributed energy resources. This article analyzes microgrids’ characteristics adopting model predictive control. We study the microgrid performance under two operation modes: grid-connected and stand-alone. For each mode, we consider different faulty scenarios, and by dynamic simulations, we investigate the importance of the microgrid components from different perspectives: topological, reliability and controllability. This analysis enables evaluation of the microgrid performance and quantification of the importance of each component with respect to the different perspectives considered. The findings provide information for the design and operation of a microgrid, seeking the right balance of multiple characteristics.

Winding numbers of nodal points in Fe-based superconductors

We analyze the nodal points in multi-orbital Fe-based superconductors from a topological perspective. We consider the $s^{+-}$ gap structure with accidental nodes, and the $d$-wave gap with nodes along the symmetry directions. In both cases, the nodal points can be moved by varying an external parameter, e.g., a degree of inter-pocket pairing. Eventually, the nodes merge and annihilate via a Lifshitz-type transition. We discuss the Lifshitz transition in Fe-based superconductors from a topological point of view. We show, both analytically and numerically, that the merging nodal points have winding numbers of opposite sign. This is consistent with the general reasoning that the total winding number is a conserved quantity in the Lifshitz transition.

Editorial: The orderly city. Dispositio and Forma Urbis

Anche gli scritti di questo numero 32 di FAmagazine (sezione Teoria della international call for paper 2015), che riguardano il concetto vitruviano di dispositio in relazione alla forma della città e ad una strategia insediativa, non possono fare a meno di cavalcare l'onda lunga che oscilla tra astrazione e figurazione e, ancor più lunga, tra formale e informale. Lo stesso Le Corbusier riconosceva il valore strutturale “profondo” e astratto della pianta, definendola “un'austera astrazione” e “un'algebrizzazione arida”.

A detailed hydrogen bonding analysis on the compositions of H2SO4/HNO3/H2O ternary systems: A computational study

Hydrogen bonding properties of H2SO4/HNO3/H2O ternary molecular clusters have been studied by means of structural, energetic, topological, and spectroscopic perspectives. The roles of the hydrogen bonds in the formation of these clusters are considered according to the molecule positions (proton donor or proton acceptor) in the clusters. 33 stable conformers were identified on the potential energy surface. The global minimum one was obtained when HNO3 donates a proton to H2SO4, however, the cooperativity effect contribution was found to be significant for the cluster where HNO3 acts as a proton donor to an H2O molecule.

Multiple perspective vulnerability analysis of the power network

To understand the vulnerability of the power network from multiple perspectives, multi-angle and multi-dimensional vulnerability analysis as well as community based vulnerability analysis are proposed in this paper. Taking into account of central China power grid as an example, correlation analysis of different vulnerability models is discussed. Then, vulnerabilities produced by different vulnerability metrics under the given vulnerability models and failure scenarios are analyzed. At last, applying the community detecting approach, critical areas of central China power grid are identified, Vulnerable and robust communities on both topological and functional perspective are acquired and analyzed. The approach introduced in this paper can be used to help decision makers develop optimal protection strategies. It will be also useful to give a multiple vulnerability analysis of the other infrastructure systems.

Understanding and forecasting lifecycle events in information cascades

Most social network sites allow users to reshare a piece of information posted by a user. As time progresses, the cascade of reshares grows, eventually saturating after a certain time period. While previous studies have focused heavily on one aspect of the cascade phenomenon, specifically predicting when the cascade would go viral, in this paper, we take a more holistic approach by analyzing the occurrence of two events within the cascade lifecycle - the period of maximum growth in terms of surge in reshares and the period where the cascade starts declining in adoption. We address the challenges in identifying these periods and then proceed to make a comparative analysis of these periods from the perspective of network topology. We study the effect of several node-centric structural measures on the reshare responses using Granger causality which helps us quantify the significance of the network measures and understand the extent to which the network topology impacts the growth dynamics. This evaluation is performed on a dataset of 7407 cascades extracted from the Weibo social network. Using our causality framework, we found that an entropy measure based on nodal degree causally affects the occurrence of these events in 93.95% of cascades. Surprisingly, this outperformed clustering coefficient and PageRank which we hypothesized would be more indicative of the growth dynamics based on earlier studies. We also extend the Granger-causality Vector Autoregression (VAR) model to forecast the times at which the events occur in the cascade lifecycle.

Financial networks and interconnectedness in an advanced emerging market economy

Financial networks could become fragile during periods of economic and financial distress, since interconnectedness among participating firms could transmit and amplify adverse shocks. Relying on balance sheet data, complemented with information on interbank exposures, this paper analyses interconnectedness in an advanced emerging market economy, using two complementary approaches. The first approach focuses on the financial network topology, and finds that the financial system resembles a highly clustered small world network, with in and out-degrees, connectivity and exposures exhibiting a (double) heavy tail behaviour, which favours the formation of strong community structure and preferential attachment in the network. Bank size is Pareto distributed, and highly correlated with centrality. The second approach focuses on how the network topology contributes to the transmission of shocks by modelling default contagion, using balance sheet network analysis. It finds that direct counterparty credit exposure poses less risk to the banking system than fire sale losses triggered by liquidity shocks. Both approaches, either using a topological or induced system losses perspective, identify systemically important financial institutions (SIFIs) consistently by accounting for both macro and microprudential risk dimensions.

Lattice Homotopy Constraints on Phases of Quantum Magnets.

The Lieb-Schultz-Mattis (LSM) theorem and its extensions forbid trivial phases from arising in certain quantum magnets. Constraining infrared behavior with the ultraviolet data encoded in the microscopic lattice of spins, these theorems tie the absence of spontaneous symmetry breaking to the emergence of exotic phases like quantum spin liquids. In this work, we take a new topological perspective on these theorems, by arguing they originate from an obstruction to "trivializing" the lattice under smooth, symmetric deformations, which we call the "lattice homotopy problem." We conjecture that all LSM-like theorems for quantum magnets (many previously unknown) can be understood from lattice homotopy, which automatically incorporates the full spatial symmetry group of the lattice, including all its point-group symmetries. One consequence is that any spin-symmetric magnet with a half-integer moment on a site with even-order rotational symmetry must be a spin liquid. To substantiate the claim, we prove the conjecture in two dimensions for some physically relevant settings.

\u2018On the grammar of death\u2019: the construal of death and killing in Colombian newspapers

The aims of this paper are twofold. First, following Halliday’s 1998 paper ‘On the grammar of pain’, this study maps the lexicogrammatical resources available to Spanish speakers in the register of hard news to construe death and killing. Based primarily on a 250,000+ corpus of news reports of violent actions by illegal armed groups in the internal conflict from four major Colombian newspapers, it distinguishes between congruent and metaphorical construals of death, accounting for the different roles of the participants involved in these different types of constructions. In addition, it offers a topological perspective of the intersection of the more delicate distinction of process types and the system of Agency. The second objective is to apply these findings to contrast the construal of violence by the actors in the conflict, Marxist guerrillas and right wing paramilitaries. The results of the analysis show how the deployment of lexicogrammatical resources construes different semiotic spaces, highlighting the role of one group while diminishing the responsibility of the other.

Theoretical investigation of hydrogen bonding in the H2SO4⋯HNO3 system

Molecular clusters of two acidic species, H2SO4 and HNO3, were investigated using ab initio methods to observe intermolecular interactions. Geometric optimizations were conducted at the MP2 level using aug-cc-pVDZ and aug-cc-pVTZ basis sets. Eleven different stable geometries were detected on the intermolecular potential energy surface. Two main theories, atoms in molecules (AIM) and non-covalent interactions (NCI), were used to analyze the nature of hydrogen bonds in the H2SO4⋯HNO3 system. The results are discussed in terms of structural, energetic, spectroscopic and topological perspectives.

Knot contact homology, string topology, and the cord algebra

The conormal Lagrangian L K of a knot K in ℝ 3 is the submanifold of the cotangent bundle T * ℝ 3 consisting of covectors along K that annihilate tangent vectors to K. By intersecting with the unit cotangent bundle S * ℝ 3 , one obtains the unit conormal Λ K , and the Legendrian contact homology of Λ K is a knot invariant of K, known as knot contact homology. We define a version of string topology for strings in ℝ 3 ∪L K and prove that this is isomorphic in degree 0 to knot contact homology. The string topology perspective gives a topological derivation of the cord algebra (also isomorphic to degree 0 knot contact homology) and relates it to the knot group. Together with the isomorphism this gives a new proof that knot contact homology detects the unknot. Our techniques involve a detailed analysis of certain moduli spaces of holomorphic disks in T * ℝ 3 with boundary on ℝ 3 ∪L K .

위상학적 관점의 선율 구조 분석 : 브람스와 레거의 클라리넷 소나타를 중심으로

위상학적 관점의 선율 구조 분석 : 브람스와 레거의 클라리넷 소나타를 중심으로

On weak topology for optimal control of switched nonlinear systems

Optimal control of switched systems is challenging in general due to the discrete nature of the switching control input. One of the most well-known approaches is the embedding based method which addresses this challenge by solving a relaxed optimization problem with only continuous inputs and then projecting the relaxed solution back to obtain a solution to the original problem. In this paper, we present a unified topology based framework for analyzing and designing various embedding based switched optimal control algorithms. The proposed framework views the embedding based approaches from a novel topological perspective as a change of topology over the optimization space. A general procedure of constructing different switched optimal control algorithms with guaranteed convergence to a stationary point is described. Numerical examples are also provided to illustrate the effectiveness of the proposed framework.

The Designated Convergence Rate Problems of Consensus or Flocking of Double-Integrator Agents With General Nonequal Velocity and Position Couplings: Further Results and Patterns of Convergence Rate Contours.

This paper considers the designated convergence rate (DCR) (or the designated convergence margin) problems of consensus or flocking of coupled double-integrator agents. The DCR problems are more valuable for systems design than just convergence or stability conditions. The system setting in this paper is general, i.e., the velocity coupling and position coupling (VCPC) between agents, respectively, are set to be general and nonequal (up to rescaling), together with distinct damping and stiffness gains for the VCPC, respectively. This paper has two primary contributions on consensus: 1) further necessary and sufficient conditions are established to guarantee the DCR problems of the system, which have enriched the previous results and 2) the patterns of the convergence rate contours for the DCR are characterized, in terms of the damping and stiffness gains, which are closely related to the characteristics of the spectra of the two Laplacian matrices of the VCPC. Additionally, this paper has a contribution on matrix theory, i.e., the sufficient conditions for the simultaneous upper-triangularization of two independent Laplacian matrices, particularly from an easily verifiable topological perspective on the corresponding digraphs of these Laplacian matrices.

Nominal energy optimisation method of constrained battery packs through the iteration of the series-parallel topology

Summary The design of a battery pack commonly deals with high performance goals and challenging constraints in terms of cost, volume or weight. One of the most crucial variables to maximise is the nominal energy, which depends on the number of discrete battery cells that can be allocated and their individual technical specifications. This work proposes a systematic method to optimise the nominal energy of a constrained battery pack from the perspective of the series-parallel topology. A mathematical and graphical characterisation is presented on how the main battery's variables are related to a topology bounded to discretisation procedures. It was theoretically found that the effects of rounding the values of the topology may lead to a considerable loss of potential nominal energy, a risk that increases linearly with the number of series. The behaviour of the battery is assessed under nominal conditions and under the event of a cell failure. The theoretical analysis suggests that the detrimental effects due to an open-circuit increase as the number of series increases, while it is the opposite in the case of a shorted cell. The method is satisfactorily implemented in the development of two different battery packs for solar competition cars with limiting regulations. The candidate topologies outperformed the nominal energy of topologies defined without the method in up to 5%. It was also found that selecting an energy-maximising topology is not always the most convenient choice, because other variables may be of interest and are dependent on the topology as well. The method is of great use to guide the topology definition process in early theoretical stages, which is usually a compromise between allocating as much cells as possible within constraints, and approaching other performance goals such as a given nominal voltage or capacity. Copyright © 2017 John Wiley & Sons, Ltd.

Latest Advances of LLC Converters in High Current, Fast Dynamic Response, and Wide Voltage Range Applications

LLC converter has been the simplest topology since long to achieve soft switching and overall the highest performance within small form factor at converter level. This paper discusses the latest advances of LLC converter from the perspective of topology and control. The technology ranges from high current, fast dynamic response to wide operational voltage range. The application mainly falls in the scope of server and data center, and may also cover telecom, PV, battery charging, etc.

Synthesis and crystal structures of three new lead(II) isonicotinoylhydrazone derivatives: Anion controlled nuclearity and dimensionality

Treatment of lead(II) acetate, Pb(CH3COO)2·3H2O, with an isonicotinoylhydrazone building block (HL) and in the presence of two different salts (NaN3 or NaClO4) as a source of auxiliary ligand, resulted in two novel coordination compounds, namely a discrete 0D complex [Pb4(μ3-L)(L)(μ-N3)(N3)][Pb(L)(N3)(MeOH)]·0.75MeOH (1) and a 2D coordination polymer [Pb(μ-L)(μ-CH3COO)Na(μ-ClO4)(MeOH)]n (2), respectively. A related reaction of Pb(NO3)2 with HL afforded a different product [Pb(μ-L)(NO3]n (3), which is a 1D coordination polymer. All compounds were isolated in good yields as air-stable solids and were fully characterized by elemental analysis, FTIR spectroscopy, single crystal X-ray diffraction, topological analysis, and theoretical calculations. An interesting feature of all structures 1–3 concerns the hemi-directional coordination of Pb(II) atoms and the observation of tetrel bonds [noncovalent Pb⋯N/O interactions], which were analyzed in detail by DFT calculations and Hirshfeld surface analysis. In fact, tetrel bonding interactions are responsible for the extension [0D→2D (in 1) or 1D→2D (in 3)] or reinforcement [(2D→2D (in 2)] of the crystal structures, thus giving rise to intricate 2D supramolecular layers. After simplification, these layers were analyzed and classified from the topological perspective, disclosing binodal 3,5-connected underlying nets with the same 3,5L24 topology in 1 and 2 but being constructed from structurally distinct components, and a binodal 3,6-connected net with the 3,5L60 topology in 3.

Topological Characteristics of the Hong Kong Stock Market: A Test-based P-threshold Approach to Understanding Network Complexity

In this paper, we analyze the relationship among stock networks by focusing on the statistically reliable connectivity between financial time series, which accurately reflects the underlying pure stock structure. To do so, we firstly filter out the effect of market index on the correlations between paired stocks, and then take a t-test based P-threshold approach to lessening the complexity of the stock network based on the P values. We demonstrate the superiority of its performance in understanding network complexity by examining the Hong Kong stock market. By comparing with other filtering methods, we find that the P-threshold approach extracts purely and significantly correlated stock pairs, which reflect the well-defined hierarchical structure of the market. In analyzing the dynamic stock networks with fixed-size moving windows, our results show that three global financial crises, covered by the long-range time series, can be distinguishingly indicated from the network topological and evolutionary perspectives. In addition, we find that the assortativity coefficient can manifest the financial crises and therefore can serve as a good indicator of the financial market development.

Effects of the unit cell topology on the compression properties of porous Co-Cr scaffolds fabricated via selective laser melting

PurposeSelective laser melting (SLM) is an additive manufacturing process suitable for fabricating metal porous scaffolds. The unit cell topology is a significant factor that determines the mechanical property of porous scaffolds. Therefore, the purpose of this paper is to evaluate the effects of unit cell topology on the compression properties of porous Cobalt–chromium (Co-Cr) scaffolds fabricated by SLM using finite element (FE) and experimental measurement methods.Design/methodology/approachThe Co-Cr alloy porous scaffolds constructed in four different topologies, i.e. cubic close packed (CCP), face-centered cubic (FCC), body-centered cubic (BCC) and spherical hollow cubic (SHC), were designed and fabricated via SLM process. FE simulations and compression tests were performed to evaluate the effects of unit cell topology on the compression properties of SLM-processed porous scaffolds.FindingsThe Mises stress predicted by FE simulations showed that different unit cell topologies resulted in distinct stress distributions on the bearing struts of scaffolds, whereas the unit cell size directly determined the stress value. Comparisons on the stress results for four topologies showed that the FCC unit cell has the minimum stress concentration due to its inclined bearing struts and horizontal arms. Simulations and experiments both indicated that the compression modulus and strengths of FCC, BCC, SHC, CCP scaffolds with the same cell size presented in a descending order. These distinct compression behaviors were correlated with the corresponding mechanics response on bearing struts. Two failure mechanisms, cracking and collapse, were found through the results of compression tests, and the influence of topological designs on the failure was analyzed and discussed. Finally, the cell initial response of the SLM-processed Co-Cr scaffold was tested through the in vitro cell culture experiment.Originality/valueA focus and concern on the compression properties of SLM-processed porous scaffolds was presented from a new perspective of unit cell topology. It provides some new knowledge to the structure optimization of porous scaffolds for load-bearing bone implants.

Coordination Polymers with Intramolecular Fluorine-Involved Contacts in Two-Dimensional Sheet Windows

Six two-dimensional polymeric complexes of [Hg(L2-F)2]n, 1, [Hg(L2,5-F)2]n, 2, [Hg(L3-F)2]n, 3, [Hg(L2,3,4-F)2]n, 4, [Hg(L3,4,5-F)2]n, 5, and [Hg(L2,3,4,5-F)2]n, 6 and a discrete complex of [Hg(L2,6-F)2], 7, in which Ln-F ligands are N-(fluorinatedphenyl)-2-pyrazinecarboxamides carrying fluorine atoms on the different positions of phenyl ring, have been synthesized and characterized. The crystal structures from X-ray diffraction reveal that all polymeric complexes have similar two-dimensional (2D) sheet windows. From a topological perspective, each metal atom can be viewed as 4-connected nodes and Ln-F ligands can be considered as linkers in the formation of these 2D windows. Because of the flexibility of the ligand, fluorinated-phenyl rings as hanging groups in the windows are pointed toward the adjacent groups to generate different fluorine-involved intramolecular interactions. One of the common features in the crystal structures of these complexes is the presence of a strong tendency to form intramolec...