相关论文: Distributed Computation as Hierarchy

Concurrent computations resemble conversations. In a conversation, participants direct utterances at others and, as the conversation evolves, exploit the known common context to advance the conversation. Similarly, collaborating software…

Over the last two decades, the Latent Position Model (LPM) has become a prominent tool to obtain model-based visualizations of networks. However, the geometric structure of the LPM is inherently symmetric, in the sense that outgoing and…

Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still…

Distributed Software Development today is in its childhood and not too widespread as a method of developing software in the global IT Industry. In this context, Petrinets are a mathematical model for describing distributed systems…

Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…

Coded distributed computing (CDC) is a new technique proposed with the purpose of decreasing the intense data exchange required for parallelizing distributed computing systems. Under the famous MapReduce paradigm, this coded approach has…

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…

In computable topology, a represented space is called computably discrete if its equality predicate is semidecidable. While any such space is classically isomorphic to an initial segment of the natural numbers, the computable-isomorphism…

Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…

The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term…

Especially in lattice structured populations, homogeneous mixing represents an inadequate assumption. Various improvements upon the ordinary pair approximation based on a number of assumptions concerning the higher-order correlations have…

We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…

A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…

In edge computing deployments, where devices may be in close proximity to each other, these devices may offload similar computational tasks (i.e., tasks with similar input data for the same edge computing service or for services of the same…

We introduce a two-dimensional network model that realizes a higher-order topological phase (HOTP). We find that in the HOTP the bulk and boundaries of the system are gapped, and a total of 16 corner states are protected by the combination…

Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…

As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…

We present a new model for distributed shared memory systems, based on remote data accesses. Such features are offered by network interface cards that allow one-sided operations, remote direct memory access and OS bypass. This model leads…

In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…

Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…