Scale-free networks in complex systems

In the past few years, several studies have explored the topology of interactions in different complex systems. Areas of investigation span from biology to engineering, physics and the social sciences. Although having different microscopic dynamics, the results demonstrate that most systems under consideration tend to self-organize into structures that share common features. In particular, the networks of interaction are characterized by a power law distribution, $P(k)\sim k^{-\alpha}$, in the number of connections per node, $k$, over several orders of magnitude. Networks that fulfill this propriety of scale-invariance are referred to as ``scale-free''. In the present work we explore the implication of scale-free topologies in the antiferromagnetic (AF) Ising model and in a stochastic model of opinion formation. In the first case we show that the implicit disorder and frustration lead to a spin-glass phase transition not observed for the AF Ising model on standard lattices. We further illustrate that the opinion formation model produces a coherent, turbulent-like dynamics for a certain range of parameters. The influence, of random or targeted exclusion of nodes is studied.Comment: 9 pages, 4 figures. Proceeding to "SPIE International Symposium Microelectronics, MEMS, and Nanotechnology", 11-15 December 2005, Brisbane, Australi

Detection of hidden structures on all scales in amorphous materials and complex physical systems: basic notions and applications to networks, lattice systems, and glasses

Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate correlations between their constituents. For a detailed understanding, there is a need for tools that enable the detection of pertinent structures on all spatial and temporal scales. Towards this end, we suggest a new method by invoking ideas from network analysis and information theory. Our method efficiently identifies basic unit cells and topological defects in systems with low disorder and may analyze general amorphous structures to identify candidate natural structures where a clear definition of order is lacking. This general unbiased detection of physical structure does not require a guess as to which of the system properties should be deemed as important and may constitute a natural point of departure for further analysis. The method applies to both static and dynamic systems.Comment: (23 pages, 9 figures

A walk in the statistical mechanical formulation of neural networks

Neural networks are nowadays both powerful operational tools (e.g., for pattern recognition, data mining, error correction codes) and complex theoretical models on the focus of scientific investigation. As for the research branch, neural networks are handled and studied by psychologists, neurobiologists, engineers, mathematicians and theoretical physicists. In particular, in theoretical physics, the key instrument for the quantitative analysis of neural networks is statistical mechanics. From this perspective, here, we first review attractor networks: starting from ferromagnets and spin-glass models, we discuss the underlying philosophy and we recover the strand paved by Hopfield, Amit-Gutfreund-Sompolinky. One step forward, we highlight the structural equivalence between Hopfield networks (modeling retrieval) and Boltzmann machines (modeling learning), hence realizing a deep bridge linking two inseparable aspects of biological and robotic spontaneous cognition. As a sideline, in this walk we derive two alternative (with respect to the original Hebb proposal) ways to recover the Hebbian paradigm, stemming from ferromagnets and from spin-glasses, respectively. Further, as these notes are thought of for an Engineering audience, we highlight also the mappings between ferromagnets and operational amplifiers and between antiferromagnets and flip-flops (as neural networks -built by op-amp and flip-flops- are particular spin-glasses and the latter are indeed combinations of ferromagnets and antiferromagnets), hoping that such a bridge plays as a concrete prescription to capture the beauty of robotics from the statistical mechanical perspective.Comment: Contribute to the proceeding of the conference: NCTA 2014. Contains 12 pages,7 figure

Inversion of diffraction data for amorphous materials

The general and practical inversion of diffraction data-producing a computer model correctly representing the material explored - is an important unsolved problem for disordered materials. Such modeling should proceed by using our full knowledge base, both from experiment and theory. In this paper, we describe a robust method to jointly exploit the power of ab initio atomistic simulation along with the information carried by diffraction data. The method is applied to two very different systems: amorphous silicon and two compositions of a solid electrolyte memory material silver-doped GeSe3 . The technique is easy to implement, is faster and yields results much improved over conventional simulation methods for the materials explored. By direct calculation, we show that the method works for both poor and excellent glass forming materials. It offers a means to add a priori information in first principles modeling of materials, and represents a significant step toward the computational design of non-crystalline materials using accurate interatomic interactions and experimental information

Critical Networks Exhibit Maximal Information Diversity in Structure-Dynamics Relationships

Network structure strongly constrains the range of dynamic behaviors available to a complex system. These system dynamics can be classified based on their response to perturbations over time into two distinct regimes, ordered or chaotic, separated by a critical phase transition. Numerous studies have shown that the most complex dynamics arise near the critical regime. Here we use an information theoretic approach to study structure-dynamics relationships within a unified framework and how that these relationships are most diverse in the critical regime

Food Physical Chemistry and Biophysical Chemistry

Food Physical Chemistry is considered to be a branch of Food Chemistry^1,2^ concerned with the study of both physical and chemical interactions in foods in terms of physical and chemical principles applied to food systems, as well as the applications of physical/chemical techniques and instrumentation for the study of foods^3,4,5,6^. This field encompasses the "physiochemical principles of the reactions and conversions that occur during the manufacture, handling, and storage of foods"^7^. Two rapidly growing, related areas are Food Biotechnology and Food Biophysical Chemistry. 
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Quantum scale biomimicry of low dimensional growth: An unusual complex amorphous precursor route to TiO2 band confinement by shape adaptive biopolymer-like flexibility for energy applications

Crystallization via an amorphous pathway is often preferred by biologically driven processes enabling living species to better regulate activation energies to crystal formation that are intrinsically linked to shape and size of dynamically evolving morphologies. Templated ordering of 3-dimensional space around amorphous embedded non-equilibrium phases at heterogeneous polymer-metal interfaces signify important routes for the genesis of low-dimensional materials under stress-induced polymer confinement. We report the surface induced catalytic loss of P=O ligands to bond activated aromatization of C-C C=C and Ti=N resulting in confinement of porphyrin-TiO(2 )within polymer nanocages via particle attachment. Restricted growth nucleation of TiO2 to the quantum scale (˂= 2 nm) is synthetically assisted by nitrogen, phosphine and hydrocarbon polymer chemistry via self-assembly. Here, the amorphous arrest phase of TiO, is reminiscent of biogenic amorphous crystal growth patterns and polymer coordination has both a chemical and biomimetic significance arising from quantum scale confinement which is atomically challenging. The relative ease in adaptability of non-equilibrium phases renders host structures more shape compliant to congruent guests increasing the possibility of geometrical confinement. Here, we provide evidence for synthetic biomimicry akin to bio-polymerization mechanisms to steer disorder-to-order transitions via solvent plasticization-like behaviour. This challenges the rationale of quantum driven confinement processes by conventional processes. Further, we show the change in optoelectronic properties under quantum confinement is intrinsically related to size that affects their optical absorption band energy range in DSSC.This work was supported by the National Research Foundation of Korea (NRF) grant funded by Korea government (MEST) NRF-2012R1A1A2008196, NRF 2012R1A2A2A01047189, NRF 2017R1A2B4008801, 2016R1D1A1A02936936, (NRF-2018R1A4A1059976, NRF-2018R1A2A1A13078704) and NRF Basic Research Programme in Science and Engineering by the Ministry of Education (No. 2017R1D1A1B03036226) and by the INDO-KOREA JNC program of the National Research Foundation of Korea Grant No. 2017K1A3A1A68. We thank BMSI (A*STAR) and NSCC for support. SJF is funded by grant IAF25 PPH17/01/a0/009 funded by A* STAR/NRF/EDB. CSV is the founder of a spinoff biotech Sinopsee Therapeutics. The current work has no conflicting interests with the company. We would like to express our very great appreciation to Ms. Hyoseon Kim for her technical expertise during HRTEM imaging