Related papers: On reducing the complexity of matrix clocks
Matrix sensing has many real-world applications in science and engineering, such as system control, distance embedding, and computer vision. The goal of matrix sensing is to recover a matrix $A_\star \in \mathbb{R}^{n \times n}$, based on a…
Algorithms for the synchronisation of clocks across networks are both common and important within distributed systems. We here address not only the formal modelling of these algorithms, but also the formal verification of their behaviour.…
A fundamental description of time can be consistent not only with the usual monotonic behavior but also with a periodic physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact…
Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with $n$ labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game,…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Guarded recursion is a powerful modal approach to recursion that can be seen as an abstract form of step-indexing. It is currently used extensively in separation logic to model programming languages with advanced features by solving domain…
Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
We revisit the complexity of building, given a two-dimensional string of size $n$, an indexing structure that allows locating all $k$ occurrences of a two-dimensional pattern of size $m$. While a structure of size $\mathcal{O}(n)$ with…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
While the relationship of time and space is an established topic in traditional centralised complexity theory, this is not the case in distributed computing. We aim to remedy this by studying the time and space complexity of algorithms in a…
Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…
A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor…
Phase clocks are synchronization tools that implement a form of logical time in distributed systems. For systems tolerating transient faults by self-repair of damaged data, phase clocks can enable reasoning about the progress of distributed…
In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…
A recently discovered universal rank-based matrix method to extract trends from noisy time series is described in [1] but the formula for the output matrix elements, implemented there as an open-access supplement MATLAB computer code, is…
The {\it matrix-chain multiplication} problem is a classic problem that is widely taught to illustrate dynamic programming. The textbook solution runs in $\theta(n^3)$ time. However, there is a complex $O(n \log n)$-time method \cite{HU82},…
The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological…
The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…