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arXiv2018

The Inherent Instability of Disordered Systems

The Multiscale Law of Requisite Variety is a scientific law relating, at each scale, the variation in an environment to the variation in internal state that is necessary for effective response by a system. While this law has been used to describe the effectiveness of systems in self-regulation, the consequences for failure have not been formalized. Here we use this law to consider the internal dynamics of an unstructured system, and its response to a structured environment. We find that, due to its inability to respond, a completely unstructured system is inherently unstable to the formation of structure. And in general, any system without structure above a certain scale is unable to withstand structure arising above that scale. To describe complicated internal dynamics, we develop a characterization of multiscale changes in a system. This characterization is motivated by Shannon information theoretic ideas of noise, but considers structured information. We then relate our findings to political anarchism showing that society requires some organizing processes, even if there is no traditional government or hierarchies. We also formulate our findings as an inverse second law of thermodynamics; while closed systems collapse into disorder, systems open to a structured environment spontaneously generate order.

physics.soc-ph↗

arXiv2018

Robust Exceptional Points in Disordered Systems

We construct a theory to introduce the concept of topologically robust exceptional points (EP). Starting from an ordered system with $N$ elements, we find the necessary condition to have the highest order exceptional point, namely $N^\text{th}$ order EP. Using symmetry considerations, we show an EP associated with an order system is very sensitive to the disorder. Specifically, if the EP associated with the ordered system occurs at the fixed degree of non-Hermiticity $γ_{EP}$, the disordered system will not have EP at the same $γ_{PT}$ which puts an obstacle in front of the observation and applications of EPs. To overcome this challenge, by incorporating an asymmetric coupling we propose a disordered system that has a robust EP which is extended all over the space. While our approach can be easily realized in electronic circuits and acoustics, we propose a simple experimentally feasible photonic system to realize our robust EP. Our results will open a new direction to search for topologically robust extended states (as opposed to topological localized states) and find considerable applications in direct observation of EPs, realizing topological sensors and designing robust devices for metrology.

physics.optics↗

arXiv2018

Hyperuniformity and generalized fluctuations at Jamming

The suppression of density fluctuations at different length scales is the hallmark of hyperuniformity. However, its existence and significance in jammed solids is still a matter of debate. We explore the presence of this hidden order in a manybody interacting model known to exhibit a rigidity transition, and find that in contrary to exisiting speculations, density fluctuations in the rigid phase are only suppressed up to a finite lengthscale. This length scale grows and diverges at the critical point of the rigidity transition, such that the system is hyperuniform in the fluid phase. This suggests that hyperuniformity is a feature generically absent in jammed solids. Surprisingly, corresponding fluctuations in geometrical properties of the model are found to be strongly suppressed over an even greater but still finite lengthscale, indicating that the system self organizes in preference to suppress geometrical fluctuations at the expense of incurring density fluctuations.

cond-mat.stat-mech↗

arXiv2018

Urban scaling of football followership on Twitter

Social sciences have an important challenge today to take advantage of new research opportunities provided by large amounts of data generated by online social networks. Because of its marketing value, sports clubs are also motivated in creating and maintaining a stable audience in social media. In this paper, we analyze followers of prominent footballs clubs on Twitter by obtaining their home locations. We then measure how city size is connected to the number of followers using the theory of urban scaling. The results show that the scaling exponents of club followers depend on the income of a country. These findings could be used to understand the structure and potential growth areas of global football audiences.

cs.SI↗

arXiv2018

Topological Origins of Flexibility and Internal Stress in Sodium Aluminosilicate Glasses

In the framework of topological constraint theory, network glasses are classified as flexible, stressed--rigid, or isostatic if the number of atomic constraints is smaller, larger, or equal to the number of atomic degrees of freedom. Here, based on molecular dynamics simulations, we show that sodium aluminosilicate glasses exhibit a flexible-to-stressed--rigid transition driven by their composition. This transition manifests itself by a loss of atomic mobility and an onset of internal atomic stress. Importantly, we find that the flexible-to-rigid (i.e., loss of internal flexibility) and unstressed-to-stressed transitions (i.e., onset of internal stress) do not occur at the same composition. This suggests that the isostatic state (i.e., rigid but unstressed) is achieved within a window rather than at a threshold composition.

cond-mat.mtrl-sci↗

arXiv2018

Spectral peculiarity and criticality of the human connectome

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our analysis indicates several new peculiar features of the human connectome. We found that the spectral density of human connectome has the maximal deviation from the spectral density of the randomized network compared to all other organisms. For many animals except human structural peculiarities of connectomes are well reproduced in the network evolution induced by the preference of 3-cycles formation. To get the reliable fit , we discovered the crucial role of the conservation of local clusterization in human connectome evolution. We investigated for the first time the level spacing distribution in the spectrum of human connectome graph Laplacian. It turns out that the spectral statistics of human connectome corresponds exactly to the critical regime familiar in the condensed matter physics which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides the strong support for the much debated statement of the brain criticality.

q-bio.NC↗

arXiv2018

Statistical models of neural activity, criticality, and Zipf's law

In this overview, we discuss the connections between the observations of critical dynamics in neuronal networks and the maximum entropy models that are often used as statistical models of neural activity, focusing in particular on the relation between "statistical" and "dynamical" criticality. We present examples of systems that are critical in one way, but not in the other, exemplifying thus the difference of the two concepts. We then discuss the emergence of Zipf laws in neural activity, verifying their presence in retinal activity under a number of different conditions. In the second part of the chapter we review connections between statistical criticality and the structure of the parameter space, as described by Fisher information. We note that the model-based signature of criticality, namely the divergence of specific heat, emerges independently of the dataset studied; we suggest this is compatible with previous theoretical findings.

q-bio.NC↗

arXiv2018

Deep optical neural network by living tumour brain cells

The new era of artificial intelligence demands large-scale ultrafast hardware for machine learning. Optical artificial neural networks process classical and quantum information at the speed of light, and are compatible with silicon technology, but lack scalability and need expensive manufacturing of many computational layers. New paradigms, as reservoir computing and the extreme learning machine, suggest that disordered and biological materials may realize artificial neural networks with thousands of computational nodes trained only at the input and at the readout. Here we employ biological complex systems, i.e., living three-dimensional tumour brain models, and demonstrate a random neural network (RNN) trained to detect tumour morphodynamics via image transmission. The RNN, with the tumour spheroid as a three-dimensional deep computational reservoir, performs programmed optical functions and detects cancer morphodynamics from laser-induced hyperthermia inaccessible by optical imaging. Moreover, the RNN quantifies the effect of chemotherapy inhibiting tumour growth. We realize a non-invasive smart probe for cytotoxicity assay, which is at least one order of magnitude more sensitive with respect to conventional imaging. Our random and hybrid photonic/living system is a novel artificial machine for computing and for the real-time investigation of tumour dynamics.

physics.med-ph↗

arXiv2018

Kinetic modelling of competition and depletion of shared miRNAs by competing endogenous RNAs

Non-conding RNAs play a key role in the post-transcriptional regulation of mRNA translation and turnover in eukaryotes. miRNAs, in particular, interact with their target RNAs through protein-mediated, sequence-specific binding, giving rise to extended and highly heterogeneous miRNA-RNA interaction networks. Within such networks, competition to bind miRNAs can generate an effective positive coupling between their targets. Competing endogenous RNAs (ceRNAs) can in turn regulate each other through miRNA-mediated crosstalk. Albeit potentially weak, ceRNA interactions can occur both dynamically, affecting e.g. the regulatory clock, and at stationarity, in which case ceRNA networks as a whole can be implicated in the composition of the cell's proteome. Many features of ceRNA interactions, including the conditions under which they become significant, can be unraveled by mathematical and in silico models. We review the understanding of the ceRNA effect obtained within such frameworks, focusing on the methods employed to quantify it, its role in the processing of gene expression noise, and how network topology can determine its reach.

q-bio.MN↗

arXiv2018

Theory of Shear Modulus in Glasses

We construct a linear response theory of applying shear deformations from boundary walls in the film geometry in Kubo's theoretical scheme. Our method is applicable to any solids and fluids. For glasses, we assume quasi-equilibrium around a fixed inherent state. Then, we obtain linear-response expressions for any variables including the stress and the particle displacements, even though the glass interior is elastically inhomogeneous. In particular, the shear modulus can be expressed in terms of the correlations between the interior stress and the forces from the walls. It can also be expressed in terms of the inter-particle correlations, as has been shown in the previous literature. Our stress relaxation function includes the effect of the boundary walls and can be used for inhomogeneous flow response. We show the presence of long-ranged, long-lived correlations among the fluctuations of the forces from the walls and the displacements of all the particles in the cell. We confirm these theoretical results numerically in a two-dimensional model glass. As an application, we describe propagation of transverse sounds after boundary wall motions using these time-correlation functions We also find resonant sound amplification when the frequency of an oscillatory shear approaches that of the first transverse sound mode.

cond-mat.soft↗

arXiv2018

Goos-Hänchen Shifts in Graphene-Based Linear Barrier

Using the energy spectrum of a system made of graphene subjected to a linear barrier potential, we study the Goos-Hänshen shifts. The calculation is done by first determining the corresponding phase shifts via the transmission and reflection probabilities. Numerical analysis shows that the Goos-Hänshen shifts depend strongly on the incident energy, barrier height and width, and vary positively or negatively under suitable conditions.

cond-mat.mes-hall↗

arXiv2019

Electronic conduction mechanisms in GeSe$_3$:Ag and Al$_2$O$_3$:Cu

In this paper, we discuss the atomistic structure of two conducting bridge computer memory materials, including Cu-doped alumina and silver-doped GeSe$_3$. We show that the Ag is rather uniformly distributed through the chalcogenide glass, whereas the Cu strongly clusters in the alumina material. The copper-oxide system conducts via extended state conduction through Cu atoms once the concentration becomes high enough to form connected Cu channels. What is more, the addition of Cu leads to extended states throughout the large alumina (host) optical gap. By contrast, Ag in the selenide host is not strongly conducting even if one imposes a very narrow nanowire geometry. All of these results are discussed using novel techniques for computing the conduction active parts of the network.

cond-mat.dis-nn↗

arXiv2019

Resonant Excitation of Oscillator with Randomly Shifted Levels

The problem of resonant excitation of a harmonic oscillator the energy levels of which are slightly shifted under the action of a random potential is solved. It is shown that, in this case, there exists a threshold magnitude of the exciting resonance field, below which the excitation is localized on lower levels, and above which the oscillator is indefinitely excited so that it is necessary to take into account dissipative processes. A method similar to that developed for the oscillator is applied to examine the localization of electrons in a wire with cross-section varying along its length. It is shown, in particular, that there is no localization if this variation is superlinear.

cond-mat.dis-nn↗

arXiv2019

Collective learning from individual experiences and information transfer during group foraging

Living in groups brings benefits to many animals, such as a protection against predators and an improved capacity for sensing and making decisions while searching for resources in uncertain environments. A body of studies has shown how collective behaviors within animal groups on the move can be useful for pooling information about the current state of the environment. The effects of interactions on collective motion have been mostly studied in models of agents with no memory. Thus, whether coordinated behaviors can emerge from individuals with memory and different foraging experiences is still poorly understood. By means of an agent based model, we quantify how individual memory and information fluxes can contribute to improving the foraging success of a group in complex environments. In this context, we define collective learning as a coordinated change of behavior within a group resulting from individual experiences and information transfer. We show that an initially scattered population of foragers visiting dispersed resources can gradually achieve cohesion and become selectively localized in space around the most salient resource sites. Coordination is lost when memory or information transfer among individuals is suppressed. The present modelling framework provides predictions for empirical studies of collective learning and could also find applications in swarm robotics and motivate new search algorithms based on reinforcement.

q-bio.PE↗

arXiv2019

Dilute magnetism in graphene

The phase diagram of graphene decorated with magnetic adatoms distributed either on a single sublattice, or evenly over the two sublattices, is computed for adatom concentrations as low as $\sim1\%$. Within the framework of the $s$-$d$ interaction, we take into account disorder effects due to the random positioning of the adatoms and/or to the thermal fluctuations in the direction of magnetic moments. Despite the presence of disorder, the magnetic phases are shown to be stable down to the lowest concentration accessed here. This result agrees with several experimental observations where adatom decorated graphene has been shown to have a magnetic response. In particular, the present theory provides a qualitative understanding for the results of Hwang et al. [Sci. Rep. 6, 21460 (2016)], where a ferromagnetic phase has been found below $\sim30\,\text{K}$ for graphene decorated with S-atoms.

cond-mat.mes-hall↗

arXiv2019

Atomistic simulation of nearly defect-free models of amorphous silicon: An information-based approach

We present an information-based total-energy optimization method to produce nearly defect-free structural models of amorphous silicon. Using geometrical, structural and topological information from disordered tetrahedral networks, we have shown that it is possible to generate structural configurations of amorphous silicon, which are superior than the models obtained from conventional reverse Monte Carlo and molecular-dynamics simulations. The new data-driven hybrid approach presented here is capable of producing atomistic models with structural and electronic properties which are on a par with those obtained from the modified Wooten-Winer-Weaire (WWW) models of amorphous silicon. Structural, electronic and thermodynamic properties of the hybrid models are compared with the best dynamical models obtained from using machine-intelligence-based potentials and efficient classical molecular-dynamics simulations, reported in the recent literature. We have shown that, together with the WWW models, our hybrid models represent one of the best structural models so far produced by total-energy-based Monte Carlo methods in conjunction with experimental diffraction data and a few structural constraints.

cond-mat.dis-nn↗

arXiv2019

Generalisation dynamics of online learning in over-parameterised neural networks

Deep neural networks achieve stellar generalisation on a variety of problems, despite often being large enough to easily fit all their training data. Here we study the generalisation dynamics of two-layer neural networks in a teacher-student setup, where one network, the student, is trained using stochastic gradient descent (SGD) on data generated by another network, called the teacher. We show how for this problem, the dynamics of SGD are captured by a set of differential equations. In particular, we demonstrate analytically that the generalisation error of the student increases linearly with the network size, with other relevant parameters held constant. Our results indicate that achieving good generalisation in neural networks depends on the interplay of at least the algorithm, its learning rate, the model architecture, and the data set.

stat.ML↗

arXiv2019

Atomic-scale factors that control the rate capability of nanostructured amorphous Si for high-energy-density batteries

Nanostructured Si is the most promising high-capacity anode material to substantially increase the energy density of Li-ion batteries. Among the remaining challenges is its low rate capability as compared to conventional materials. To understand better what controls the diffusion of Li in the amorphous Li-Si alloy, we use a novel machine-learning potential trained on more than 40,000 ab-initio calculations and nanosecond-scale molecular dynamics simulations, to visualize for the first time the delithiation of entire LiSi nanoparticles. Our results show that the Si host is not static but undergoes a dynamic rearrangement from isolated atoms, to chains, and clusters, with the Li diffusion strongly governed by this Si rearrangement. We find that the Li diffusivity is highest when Si segregates into clusters, so that Li diffusion proceeds via hopping between the Si clusters. The average size of Si clusters and the concentration range over which Si clustering occurs can thus function as design criteria for the development of rate-improved anodes based on modified Si.

cond-mat.dis-nn↗