Folded network and structural transition in molten tin

The fundamental relationships between the structure and properties of liquids are far from being well understood. For instance, the structural origins of many liquid anomalies still remain unclear, but liquid-liquid transitions (LLT) are believed to hold a key. However, experimental demonstrations of LLTs have been rather challenging. Here, we report experimental and theoretical evidence of a second-order-like LLT in molten tin, one which favors a percolating covalent bond network at high temperatures. The observed structural transition originates from the fluctuating metallic/covalent behavior of atomic bonding, and consequently a new paradigm of liquid structure emerges. The liquid structure, described in the form of a folded network, bridges two well-established structural models for disordered systems, i.e., the random packing of hard-spheres and a continuous random network, offering a large structural midground for liquids and glasses. Our findings provide an unparalleled physical picture of the atomic arrangement for a plethora of liquids, shedding light on the thermodynamic and dynamic anomalies of liquids but also entailing far-reaching implications for studying liquid polyamorphism and dynamical transitions in liquids.

Analysis of epidemic propagation using mean field theory on signed graphs

Over the past few decades, the study of epidemic propagation has caught widespread attention from many areas. The field of graphs contains a wide body of research, yet only a few studies explore epidemic propagation’s dynamics in “signed” networks. Motivated by this problem, in this paper we propose a new epidemic propagation model for signed networks, denoted as S-SIS. To explain our analysis, we utilized the mean field theory to demonstrate the theoretical results. When we compare epidemic propagation through negative links to those only having positive links, we find that a higher proportion of infected nodes actually spreads at a relatively small infection rate. It is also found that when the infection rate is higher than a certain value, the overall spreading in a signed network begins showing signs of suppression. Finally, in order to verify our findings, we apply the S-SIS model on Erdös–Rényi random network and scale-free network, and the simulation results is well consist with the theoretical analysis.

Identification of patterns for space-time event networks

This paper provides new tools for analyzing spatio-temporal event networks. We build time series of directed event networks for a set of spatial distances, and based on scan-statistics, the spatial distance that generates the strongest change of event network connections is chosen. In addition, we propose an empirical random network event generator to detect significant motifs throughout time. This generator preserves the spatial configuration but randomizes the order of the occurrence of events. To prevent the large number of links from masking the count of motifs, we propose using standardized counts of motifs at each time slot. Our methodology is able to detect interaction radius in space, build time series of networks, and describe changes in its topology over time, by means of identification of different types of motifs that allows for the understanding of the spatio-temporal dynamics of the phenomena. We illustrate our methodology by analyzing thefts occurred in Medellín (Colombia) between the years 2003 and 2015.

DEVELOPMENT OF STATISTICALLY AVERAGED MODELS OF DEFORMATION OF MATERIALS WITH RANDOM NETWORK STRUCTURE OF DIFFERENTLY ORIENTED FIBERS

The paper describes the developed statistically averaged models of deformation of materials with a random network structure of differently oriented fibers. New methods of stress-strain analysis and micromacromechanical models of material deformation in the volume of bodies made of material with a network structure taking into account structural and physical nonlinearities have been created. These models are based on the micromechanics of network structures at the level of statistical sets of their chains. The novelty of approaches, models, methods and results is the creation of theoretical foundations for the analysis of the deformation of non-traditional network materials. Nonlinear mathematical models of material deformation in the form of a chaotic network structure of one-dimensional fragments are proposed, which are constructed involving fundamentally new approaches to the description of physical and mechanical properties at the micro level of statistical sets of fiber chains and spatial homogenization of their macroproperties. Compared to traditional models, they more adequately model the features of material deformation in the form of spatial chaotic and ordered network structures, as they do not involve a number of additional non-physical hypotheses. This creates fundamentally new opportunities not only for analyzing the properties of such materials, but also when creating new ones with specified properties. Using the created methods, models and research tools, the basis for solving a number of model and applied problems has been created. The nature of deformation of non-traditional materials with a network structure of one-dimensional elements is determined. The macro-properties of these materials are established on the basis of the developed micromechanical models, variational formulations and averaging methods. Keywords: stress-strain state, network structures, contact interaction, finite element method, contact pressure, machine parts, variational formulation

Network Robustness Analysis Based on Maximum Flow

Network robustness is the ability of a network to maintain a certain level of structural integrity and its original functions after being attacked, and it is the key to whether the damaged network can continue to operate normally. We define two types of robustness evaluation indicators based on network maximum flow: flow capacity robustness, which assesses the ability of the network to resist attack, and flow recovery robustness, which assesses the ability to rebuild the network after an attack on the network. To verify the effectiveness of the robustness indicators proposed in this study, we simulate four typical networks and analyze their robustness, and the results show that a high-density random network is stronger than a low-density network in terms of connectivity and resilience; the growth rate parameter of scale-free network does not have a significant impact on robustness changes in most cases; the greater the average degree of a regular network, the greater the robustness; the robustness of small-world network increases with the increase in the average degree. In addition, there is a critical damage rate (when the node damage rate is less than this critical value, the damaged nodes and edges can almost be completely recovered) when examining flow recovery robustness, and the critical damage rate is around 20%. Flow capacity robustness and flow recovery robustness enrich the network structure indicator system and more comprehensively describe the structural stability of real networks.

Performance of reservoir computing in a random network of single-walled carbon nanotubes complexed with polyoxometalate

Molecular neuromorphic devices are composed of a random and extremely dense network of single-walled carbon nanotubes (SWNTs) complexed with polyoxometalate (POM). Such devices are expected to have the rudimentary ability of reservoir computing (RC), which utilizes signal response dynamics and a certain degree of network complexity. In this study, we performed RC using multiple signals collected from a SWNT/POM random network. The signals showed a nonlinear response with wide diversity originating from the network complexity. The performance of RC was evaluated for various tasks such as waveform reconstruction, a nonlinear autoregressive model, and memory capacity. The obtained results indicated its high capability as a nonlinear dynamical system, capable of information processing incorporated into edge computing in future technologies.

The physics of Empty Liquids: from Patchy particles to Water

Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures.

Wealth Inequality, Network Topology and Financial Instability

This paper asks if two, otherwise identical, economies were distinguished only by their distributions of wealth, are they equally stable in response to a random shock? A theoretical financial network model is proposed to understand the relationship between wealth inequality and financial crises. In a financial network, financial assets link individual asset and liability holders to form a web of economic connections. The total connectivity of an individual is described by their degree, and the overall distribution of connections in the network is imposed through a degree distribution--equivalent to the wealth distribution as incoming connections represent assets and outgoing connections liabilities. A network's topology varies with the level of wealth inequality and total wealth and together, simulations show, they determine network contagion in the event of a random negative income shock to some individual. Random network simulations, whereby each financial connection is randomly placed, reveal that increasing wealth inequality makes a wealthy network less stable--as measured by the share of individuals failing financially or the decline in financial asset values. These results suggest a unique architectural role for accumulated assets and their distribution in macro-financial stability.

Framework design for competitive marketing mechanism in Iraqi social media

Several organizations in Iraq manufacture similar commodities in this aggressive social trading. The objective of these organizations is diffusing information about their commodities publicly for popularity of the commodities in social media. More returns result in popular commodities and vice versa. The development of a framework incorporating two organizations engaging to broaden the information to the large media has been undertaken. The organizations first identified their initial seed points concurrently and then data was scattered as per the Independent Cascade Model (ICM). The major objective of the organizations is the identification of seed points for the diffusion of data to several points in social media. Significant is also how fast data diffusion can be done. Data effect will arise from either none, one or more nodes in a social interconnection. Evaluation is also accomplished on the number of fraction parts in various sections are affected by the different rates of data diffusion. The simulation result for suggested framework presented better outcomes result for random network 1 and random network 2 comparing with regular network. This framework is used a Hotellingframwork of competition.