scholarly journals Higher-Order Networks

2021 ◽  
Author(s):  
Ginestra Bianconi
Keyword(s):  
Complex Systems ◽  
Network Topology ◽  
Simplicial Complexes ◽  
Higher Order ◽  
Topological Data Analysis ◽  
Mathematical Framework ◽  
Wide Range ◽  
Underlying Network ◽  
Many Body Interactions ◽  
Higher Order Networks

Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.

scholarly journals Hypergraph reconstruction from network data

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Jean-Gabriel Young ◽  
Giovanni Petri ◽  
Tiago P. Peixoto
Keyword(s):  
Complex Systems ◽  
Bayesian Approach ◽  
Higher Order ◽  
Statistical Evidence ◽  
Network Data ◽  
Fundamental Interactions ◽  
Wide Range ◽  
Principle Of Parsimony ◽  
Order Structures

AbstractNetworks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the fundamental interactions involve more than two entities at the same time. Pairwise representations nonetheless remain ubiquitous, because higher-order interactions are often not recorded explicitly in network data. Here, we introduce a Bayesian approach to reconstruct latent higher-order interactions from ordinary pairwise network data. Our method is based on the principle of parsimony and only includes higher-order structures when there is sufficient statistical evidence for them. We demonstrate its applicability to a wide range of datasets, both synthetic and empirical.

scholarly journals The Euler Characteristic and Topological Phase Transitions in Complex Systems

2019 ◽  
Author(s):  
Edgar Amorim ◽  
Rodrigo A. Moreira ◽  
Fernando A N Santos
Keyword(s):  
Phase Transitions ◽  
Complex Systems ◽  
Euler Characteristic ◽  
Biological Networks ◽  
Algebraic Topology ◽  
Similarity Measures ◽  
Topological Data Analysis ◽  
Topological Phase ◽  
Wide Range ◽  
Topological Phase Transitions

In this work, we use methods and concepts of applied algebraic topology to comprehensively explore topological phase transitions in complex systems. Topological phase transitions are characterized by the zeros of the Euler characteristic (EC) or by singularities of the Euler entropy and also indicate signal changes in the mean node curvature of networks. Here, we provide strong evidence that the zeros of the Euler characteristic can be interpreted as a complex network’s intrinsic fingerprint. We theoretically and empirically illustrate this across different biological networks: We first target our investigation to protein-protein interaction networks (PPIN). To do so, we used methods of topological data analysis to compute the Euler characteristic analytically, and the Betti numbers numerically as a function of the attachment probability for two variants of the Duplication Divergence model, namely the totally asymmetric model and the heterodimerization model. We contrast our theoretical results with experimental data freely available for gene co-expression networks (GCN) of Saccharomyces cerevisiae, also known as baker’s yeast, as well as of the nematode Caenorhabditis elegans. Supporting our theoretical expectations, we are able to detect topological phase transitions in both networks obtained according to different similarity measures. Later, we theoretically illustrate the emergence of topological phase transitions in three classical network models, namely the Watts-Strogratz model, the Random Geometric Graph, and the Barabasi-Albert model. Given the universality and wide use of those models across disciplines, our results indicate that topological phase transitions may permeate across a wide range of theoretical and empirical networks. Hereby, our paper reinforces the idea of using topological phase transitions to advance the understanding of complex systems more generally.

scholarly journals Higher-order simplicial synchronization of coupled topological signals

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Reza Ghorbanchian ◽  
Juan G. Restrepo ◽  
Joaquín J. Torres ◽  
Ginestra Bianconi
Keyword(s):  
Algebraic Topology ◽  
Network Models ◽  
Simplicial Complexes ◽  
Higher Order ◽  
Large Network ◽  
Underlying Network ◽  
Discontinuous Phase ◽  
Fully Connected ◽  
The Brain ◽  
Fully Connected Networks

AbstractSimplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of simplicial complexes. In particular we consider topological signals, i.e., dynamical signals defined on simplices of different dimension, here taken to be nodes and links for simplicity. We show that coupling between signals defined on nodes and links leads to explosive topological synchronization in which phases defined on nodes synchronize simultaneously to phases defined on links at a discontinuous phase transition. We study the model on real connectomes and on simplicial complexes and network models. Finally, we provide a comprehensive theoretical approach that captures this transition on fully connected networks and on random networks treated within the annealed approximation, establishing the conditions for observing a closed hysteresis loop in the large network limit.

Current Trends in Biotherapeutic Higher Order Structure Characterization by Irreversible Covalent Footprinting Mass Spectrometry

2019 ◽  
Vol 26 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Natalie K. Garcia ◽  
Galahad Deperalta ◽  
Aaron T. Wecksler
Keyword(s):  
Mass Spectrometry ◽  
Protein Structure ◽  
Protein Interactions ◽  
Quaternary Structure ◽  
Solvent Accessibility ◽  
Higher Order ◽  
Structure Characterization ◽  
Order Structure ◽  
Protein Footprinting ◽  
Wide Range

Background: Biotherapeutics, particularly monoclonal antibodies (mAbs), are a maturing class of drugs capable of treating a wide range of diseases. Therapeutic function and solutionstability are linked to the proper three-dimensional organization of the primary sequence into Higher Order Structure (HOS) as well as the timescales of protein motions (dynamics). Methods that directly monitor protein HOS and dynamics are important for mapping therapeutically relevant protein-protein interactions and assessing properly folded structures. Irreversible covalent protein footprinting Mass Spectrometry (MS) tools, such as site-specific amino acid labeling and hydroxyl radical footprinting are analytical techniques capable of monitoring the side chain solvent accessibility influenced by tertiary and quaternary structure. Here we discuss the methodology, examples of biotherapeutic applications, and the future directions of irreversible covalent protein footprinting MS in biotherapeutic research and development. Conclusion: Bottom-up mass spectrometry using irreversible labeling techniques provide valuable information for characterizing solution-phase protein structure. Examples range from epitope mapping and protein-ligand interactions, to probing challenging structures of membrane proteins. By paring these techniques with hydrogen-deuterium exchange, spectroscopic analysis, or static-phase structural data such as crystallography or electron microscopy, a comprehensive understanding of protein structure can be obtained.

scholarly journals Learning the best nanoscale heat engines through evolving network topology

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Yuto Ashida ◽  
Takahiro Sagawa
Keyword(s):  
Network Topology ◽  
Heat Engine ◽  
Search Space ◽  
Single Electron ◽  
Thermodynamic Efficiency ◽  
Full Potential ◽  
Thermal Systems ◽  
Nanoscale Systems ◽  
Heat Engines ◽  
Many Body Interactions

AbstractThe quest to identify the best heat engine has been at the center of science and technology. Considerable studies have so far revealed the potentials of nanoscale thermal machines to yield an enhanced thermodynamic efficiency in noninteracting regimes. However, the full benefit of many-body interactions is yet to be investigated; identifying the optimal interaction is a hard problem due to combinatorial explosion of the search space, which makes brute-force searches infeasible. We tackle this problem with developing a framework for reinforcement learning of network topology in interacting thermal systems. We find that the maximum possible values of the figure of merit and the power factor can be significantly enhanced by electron-electron interactions under nondegenerate single-electron levels with which, in the absence of interactions, the thermoelectric performance is quite low in general. This allows for an alternative strategy to design the best heat engines by optimizing interactions instead of single-electron levels. The versatility of the developed framework allows one to identify full potential of a broad range of nanoscale systems in terms of multiple objectives.

scholarly journals HONEM: Learning Embedding for Higher Order Networks

Big Data ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 255-269 ◽  
Author(s):  
Mandana Saebi ◽  
Giovanni Luca Ciampaglia ◽  
Lance M. Kaplan ◽  
Nitesh V. Chawla
Keyword(s):  
Higher Order ◽  
Higher Order Networks

A Parallel HOFD Scheme for Direct Numerical Simulation of Turbulent Magnetically Driven Flows

2001 ◽  
Author(s):  
X. Ai ◽  
B. Q. Li
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Parallel Machines ◽  
Higher Order ◽  
Electrically Conducting ◽  
Wide Range ◽  
Order Scheme ◽  
Higher Order Scheme

Abstract Turbulent magnetically flows occur in a wide range of material processing systems involving electrically conducting melts. This paper presents a parallel higher order scheme for the direct numerical simulation of turbulent magnetically driven flows in induction channels. The numerical method is based on the higher order finite difference algorithm, which enjoys the spectral accuracy while minimizing the computational intensity. This, coupled with the parallel computing strategy, provides a very useful means to simulate turbulent flows. The higher order finite difference formulation of magnetically driven flow problems is described in this paper. The details of the parallel algorithm and its implementation for the simulations on parallel machines are discussed. The accuracy and numerical performance of the higher order finite difference scheme are assessed in comparison with the spectral method. The examples of turbulent magnetically driven flows in induction channels and pressure gradient driven flows in regular channels are given, and the computed results are compared with experimental measurements wherever possible.

scholarly journals Duality of Complex Systems Built from Higher-Order Elements

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Dalibor Biolek ◽  
Zdeněk Biolek ◽  
Viera Biolková
Keyword(s):  
Nonlinear Systems ◽  
Complex Systems ◽  
Higher Order ◽  
Duality Principle ◽  
Shift Type ◽  
Hardware Emulation ◽  
Classical Duality ◽  
Memristive Circuits ◽  
Circuit Elements

The duality of nonlinear systems built from higher-order two-terminal Chua’s elements and independent voltage and current sources is analyzed. Two different approaches are now being generalized for circuits with higher-order elements: the classical duality principle, hitherto restricted to circuits built from R-C-L elements, and Chua’s duality of memristive circuits. The so-called storeyed structure of fundamental elements is used as an integrating platform of both approaches. It is shown that the combination of associated flip-type and shift-type transformations of the circuit elements can generate dual networks with interesting features. The regularities of the duality can be used for modeling, hardware emulation, or synthesis of systems built from elements that are not commonly available, such as memristors, via classical dual elements.

scholarly journals Traits and values as predictors of the frequency of everyday behavior: Comparison between models and levels

2018 ◽  
Vol 40 (1) ◽  
pp. 133-153 ◽  
Author(s):  
Ewa Skimina ◽  
Jan Cieciuch ◽  
Włodzimierz Strus
Keyword(s):  
Personality Traits ◽  
Factor Model ◽  
Five Factor Model ◽  
Personal Values ◽  
Derived Categories ◽  
Higher Order ◽  
Behavioral Factors ◽  
Wide Range ◽  
Age Range ◽  
Hexaco Model

AbstractThe aims of this study were to compare (a) personality traits vs personal values, (b) Five-Factor Model (FFM) vs HEXACO model of personality traits, and (c) broad vs narrow personality constructs in terms of their relationship with the frequency of everyday behaviors. These relationships were analyzed at three organizational levels of self-reported behavior: (a) single behavioral acts, (b) behavioral components (empirically derived categories of similar behaviors), and (c) two higher-order factors. The study was conducted on a Polish sample (N = 532, age range 16–72). We found that (a) even the frequencies of single behavioral acts were related to various personality constructs instead of one narrow trait or value, (b) personality traits and personal values were comparable as predictors of a wide range of everyday behaviors, (c) HEXACO correlated with the frequency of behaviors slightly higher than FFM, and (d) narrow and broad personality constructs did not differ substantially as predictors of everyday behavior at the levels of acts and components, but at the level of higher-order behavioral factors, broad personality measures were better predictors than narrow ones.

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