Related papers: A scale-free network hidden in the collapsing poly…
We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically…
A regular lattice in which the sites can have long range connections at a distance l with a probabilty $P(l) \sim l^{-\delta}$, in addition to the short range nearest neighbour connections, shows small-world behaviour for $0 \le \delta <…
Every route of a transport network approaching equilibrium can be represented by a vector of Euclidean space which length quantifies its segregation from the rest of the graph. We have empirically observed that the distribution of lengths…
Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a number of complex networks, in which some are deterministic and others are random. Compared with deterministic networks, random…
We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
We consider the directed network (DN) of edge states on the surface of a cylinder of length L and circumference C. By mapping it to a ferromagnetic superspin chain, and using a scaling analysis, we show its equivalence to a one-dimensional…
We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…
Neural collapse is a highly symmetric geometric pattern of neural networks that emerges during the terminal phase of training, with profound implications on the generalization performance and robustness of the trained networks. To…
Atomic collapse can be observed in graphene because of its large "effective" fine structure constant, which enables this phenomenon to occur for an impurity charge as low as $Z_c\sim 1-2$. Here, we investigate the effect of the sublattice…
We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the particle jumping rate function $p(n)=n^\delta$. We show analytically…
The nature of the theta point for a polymer in two dimensions has long been debated, with a variety of candidates put forward for the critical exponents. This includes those derived by Duplantier and Saleur (DS) for an exactly solvable…
We investigate Bak-Sneppen coevolution models on scale-free networks with various degree exponents $\gamma$ including random networks. For $\gamma >3$, the critical fitness value $f_c$ approaches to a nonzero finite value in the limit $N…
We study the detailed mechanism of the failure of scale-free networks under intentional attacks. Although it is generally accepted that such networks are very sensitive to targeted attacks, we show that for a particular type of structure…
Depth completion, inferring dense depth maps from sparse measurements, is crucial for robust 3D perception. Although deep learning based methods have made tremendous progress in this problem, these models cannot generalize well across…
We use scale-free networks to study properties of the infected mass $M$ of the network during a spreading process as a function of the infection probability $q$ and the structural scaling exponent $\gamma$. We use the standard SIR model and…
Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…
We study the partitioning of cosolute particles in a thin film of a semi-flexible polymer network by a combination of coarse-grained (implicit-solvent) stochastic dynamics simulations and mean-field theory. We focus on a wide range of…
It has been recently argued that interacting self-avoiding walks (ISAW) of length $ \ell , $ in their low temperature phase (i.e. below the $ \Theta $-point) should have a partition function of the form: $$ Q_{\ell} \sim \mu^{ \ell}_ 0\mu^{…
We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions which are of fundamental interest in the theory of critical phenomena and have…