相关论文: Scaling laws for molecular communication

The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules…

We consider a basic stochastic particle system consisting of $N$ identical particles with isotropic $k$-particle synchronization, $k\geq 2$. In the limit when both number of particles $N$ and time $t=t(N)$ grow to infinity we study an…

Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to…

We consider the linear wave equation with the time-dependent scale-invariant damping and mass. We also treat the corresponding equation with the energy critical nonlinearity. Our aim is to show that the solution scatters to a modified…

In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the…

Molecular Communication (MC) is a communication strategy that uses molecules as carriers of information, and is widely used by biological cells. As an interdisciplinary topic, it has been studied by biologists, communication theorists and a…

Two-dimensional $CP^{N-1}$ models are investigated by Monte Carlo methods on the lattice, for values of $N$ ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length $\xi$.…

The mean square size of topologically interlocked molecules (TIMs) is presented as a linear combination of contributions from the backbone and subcomponents. Using scaling analyses and extensive molecular dynamics simulations of…

Multiple relaxation channels often arise in the dynamics of liquids where the momentum current associated to the particle-conservation law splits into distinct contributions. Examples are strongly confined liquids for which the currents in…

Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is…

We present a detailed study of soliton compression of ultra-short pulses based on phase-mismatched second-harmonic generation (\textit{i.e.}, the cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The single-cycle…

Capacity scaling laws are analyzed in an underwater acoustic network with $n$ regularly located nodes on a square. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of $n$. In the network, we…

We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…

We give trade-offs between classical communication, quantum communication, and entanglement for processing information in the Shannon-theoretic setting. We first prove a unit-resource capacity theorem that applies to the scenario where only…

Molecular communication emerges as a promising communication paradigm for nanotechnology. However, solid mathematical foundations for information-theoretic analysis of molecular communication have not yet been built. In particular, no one…

In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter we relax the assumption…

Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the…

For nano-scale communications, there must be cooperation and simultaneous communication between nano devices. To this end, in this paper we investigate two-way (a.k.a. bi-directional) molecular communications between nano devices. If…

We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range ($r^{-(1+\sigma)}$) interactions with $\sigma>0$, ``Energy-Scaling'' arguments predict a growth-law of the average domain size $L \sim…

Out-of-time-order correlators (OTOCs) can be used to probe how quickly a quantum system scrambles information when the initial conditions of the dynamics are changed. In sufficiently large quantum systems, one can extract from the OTOC the…