Related papers: Diffusive Capture Process on Complex Networks
Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…
Recently, we have shown that if the $i$th node of the Barab\'{a}si-Albert (BA) network is characterized by the generalized degree $q_i(t)=k_i(t)t_i^\beta/m$, where $k_i(t)\sim t^\beta$ and $m$ are its degree at current time $t$ and at birth…
Topological properties of "scale-free" networks are investigated by determining their spectral dimensions $d_S$, which reflect a diffusion process in the corresponding graphs. Data bases for citation networks and metabolic networks together…
We study the implications of coupling Langmuir kinetics (LK) process with the dynamics of an extending lattice. The model that we consider couples dynamically extending exclusion process (DEEP) with the process of random attachment and…
Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes…
We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of…
It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects an ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
We study the critical behavior for percolation on inhomogeneous random networks on $n$ vertices, where the weights of the vertices follow a power-law distribution with exponent $\tau \in (2,3)$. Such networks, often referred to as…
We investigate a variety of statistical properties associated with the number of distinct degrees that exist in a typical network for various classes of networks. For a single realization of a network with N nodes that is drawn from an…
Many products and innovations become well-known and widely adopted through the social interactions of individuals in a population. The Bass diffusion model has been widely used to model the temporal evolution of adoption in such social…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…
A new dynamic latent space eigenmodel (LSM) is proposed for weighted temporal networks. The model accommodates integer-valued weights, excess of zeros, time-varying node positions (features), and time-varying network sparsity. The latent…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
We propose a novel model-selection method for dynamic networks. Our approach involves training a classifier on a large body of synthetic network data. The data is generated by simulating nine state-of-the-art random graph models for dynamic…
We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a…
We analyze a trapping reaction with a single penetrable trap, in a one dimensional lattice, where both species (particles and trap) are mobile and have a drift velocity. We obtain the density as seen from a reference system attached to the…
Many dynamical processes on real world networks display complex temporal patterns as, for instance, a fat-tailed distribution of inter-events times, leading to heterogeneous waiting times between events. In this work, we focus on…
Recently, there has been growing evidence that if the width and depth of a neural network are scaled toward the so-called rich feature learning limit (\mup and its depth extension), then some hyperparameters -- such as the learning rate --…
We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure…