Related papers: Counting Path Configurations in Parallel Diffusion
This paper proposes a parallel numerical algorithm to simulate the flow and the transport in a discrete fracture network taking into account the mass exchanges with the surrounding matrix. The discretization of the Darcy fluxes is based on…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
A new method ( PI-DFT ) which combines path integrals and density functional theory is proposed as a pathway to many fields of physics. Within path integral theory it is possible to construct particle densities without explicitly…
A non-Markovian counting process, the `generalized fractional Poisson process' (GFPP) introduced by Cahoy and Polito in 2013 is analyzed. The GFPP contains two index parameters $0<\beta\leq 1$, $\alpha >0$ and a time scale parameter.…
An integer adder for integers in the binary representation is one of the basic operations of any digital processor. For adding two integers of N bits each, the serial adder takes as many clock ticks. For achieving higher speeds, parallel…
We study the behavior of the activity of the parallel chip-firing upon increasing the number of chips on an Erd\H{o}s--R\'enyi random graph. We show that in various situations the resulting activity diagrams converge to a devil's staircase…
We present a theoretical framework for analyzing linear attention models through matrix-valued state space models (SSMs). Our approach, Parallel Flows, provides a perspective that systematically decouples temporal dynamics from…
Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…
Topological phases and topological phase transitions (TPT) are among the most fantastic phenomena in Nature. Here we show that injecting a current may lead to new topological phases, especially new gapless topological metallic phases with…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
Uncertainty calibration in pre-trained transformers is critical for their reliable deployment in risk-sensitive applications. Yet, most existing pre-trained transformers do not have a principled mechanism for uncertainty propagation through…
The rapid advancements in machine learning techniques have led to significant achievements in various real-world robotic tasks. These tasks heavily rely on fast and energy-efficient inference of deep neural network (DNN) models when…
We introduce and analyze different strategies for the parallel-in-time integration method PFASST to recover from hard faults and subsequent data loss. Since PFASST stores solutions at multiple time steps on different processors, information…
We introduce the diffusion and superposition distances as two metrics to compare signals supported in the nodes of a network. Both metrics consider the given vectors as initial temperature distributions and diffuse heat trough the edges of…
Over the last two decades, frameworks for distributed-memory parallel computation, such as MapReduce, Hadoop, Spark and Dryad, have gained significant popularity with the growing prevalence of large network datasets. The Massively Parallel…
Hierarchical cooperation has recently been shown to achieve better throughput scaling than classical multihop schemes under certain assumptions on the channel model in static wireless networks. However, the end-to-end delay of this scheme…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
Large deep learning models have demonstrated strong ability to solve many tasks across a wide range of applications. Those large models typically require training and inference to be distributed. Tensor parallelism is a common technique…
Addressing a quest by Gupta et al. [ICALP'14], we provide a first, comprehensive study of finding a short s-t path in the multistage graph model, referred to as the Multistage s-t Path problem. Herein, given a sequence of graphs over the…