Related papers: A Sheaf-Theoretic Characterization of Tasks in Dis…
Performance evaluation of caching systems is an old and widely investigated research topic. The research community is once again actively working on this topic because the Internet is evolving towards new transfer modes, which envisage to…
Real-time scheduling and locking protocols are fundamental facilities to construct time-critical systems. For parallel real-time tasks, predictable locking protocols are required when concurrent sub-jobs mutually exclusive access to shared…
Distributed linearly separable computation is a fundamental problem in large-scale distributed systems, requiring the computation of linearly separable functions over different datasets across distributed workers. This paper studies a…
We introduce a new model for the task mapping problem to aid in the systematic design of algorithms for heterogeneous systems including, but not limited to, CPUs, GPUs and FPGAs. A special focus is set on the communication between the…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
Risks and potential benefits of distributing software development projects globally depend to a large extent on how to allocate work to different development sites and regions. Existing methods in task allocation are likely to omit the…
Cloud Computing is a paradigm of both parallel processing and distributed computing. It offers computing facilities as a utility service in pay as par use manner. Virtualization, self service provisioning, elasticity and pay per use are the…
Equipping graph neural networks with a convolution operation defined in terms of a cellular sheaf offers advantages for learning expressive representations of heterophilic graph data. The most flexible approach to constructing the sheaf is…
We study algorithms in the distributed message-passing model that produce secured output, for an input graph $G$. Specifically, each vertex computes its part in the output, the entire output is correct, but each vertex cannot discover the…
This work extends the theory of reciprocal diagrams in graphic statics to frameworks that are invariant under finite group actions by utilizing the homology and representation theory of cellular cosheaves, recent tools from applied…
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality…
We consider the problem of task allocation in a network of cyber-physical systems (CPSs). The network can have different states, and the tasks are of different types. The task arrival is stochastic and state-dependent. Every CPS is capable…
A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have…
Global protocol specifications are the starting point of top-down verification methodologies, and serve as a blueprint for synthesizing local specifications that guarantee the correctness of distributed implementations. In this work, we…
Distributed computing often gives rise to complex concurrent and interacting activities. In some cases several concurrent activities may be working together, i.e. cooperating, to solve a given problem; in other cases, the activities may be…
In this article, we revise Conway's Law from a mathematical point of view. By introducing a task graph, we first rigorously state Conway's Law based on the homomorphisms in graph theory for the software system and the organizations that…
We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are based on the sheaf Laplacian, a generalization of the graph…
Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…
A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize \v{C}ech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\mathbb{P}^n_M$, a projective…
In this note we present a work in progress whose main purpose is to establish a categorified version of sheaf theory. We present a notion of derived categorical sheaves, which is a categorified version of the notion of complexes of sheaves…