Related papers: Symmetry Reduction for the Local Mu-Calculus
For families of Hamiltonians defined by parts that are local, the most general definition of a symmetry algebra is the commutant algebra, i.e., the algebra of operators that commute with each local part. Thinking about symmetry algebras as…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
In recent years there has been interest in the theory of local computation over probabilistic Bayesian graphical models. In this paper, local computation over Bayes linear belief networks is shown to be amenable to a similar approach.…
Calibration is commonly evaluated by comparing model confidence with its empirical correctness, implicitly treating reliability as a function of the confidence score alone. However, this view can hide substantial structure: models may be…
Local smoothing testing that is based on multivariate nonparametric regression estimation is one of the main model checking methodologies in the literature. However, relevant tests suffer from the typical curse of dimensionality resulting…
The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
Local network community detection aims to find a single community in a large network, while inspecting only a small part of that network around a given seed node. This is much cheaper than finding all communities in a network. Most methods…
Urban science has largely relied on universal models, rendering the heterogeneous and locally specific nature of cities effectively invisible. Here we introduce a topological framework that defines and detects localities in human mobility…
Matrix product states (MPS) are a standard tensor-network representation for ground states of one-dimensional quantum many-body systems, and they underpin widely used simulation tools such as DMRG. However, while quantum model checking has…
The multipartite nonlocality provides deep insights into the fundamental feature of quantum mechanics and guarantees different degrees of cryptography security for potential applications in the quantum internet. Verifying multipartite…
Community structure is of paramount importance for the understanding of complex networks. Consequently, there is a tremendous effort in order to develop efficient community detection algorithms. Unfortunately, the issue of a fair assessment…
Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes a subset C_i of the qubits. We say that the rho_i are ``consistent'' if there exists some global state…
Simulating large quantum circuits on hardware with limited qubit counts is often attempted through methods like circuit knitting, which typically incur sample costs that grow exponentially with the number of connections cut. In this work,…
Data coding as a building block of several image processing algorithms has been received great attention recently. Indeed, the importance of the locality assumption in coding approaches is studied in numerous works and several methods are…
Symmetry plays a crucial role in understanding the properties of mathematical structures and optimization problems. Recent work has explored this phenomenon in the context of neural networks, where the loss function is invariant under…
Suppose the data consist of a set $S$ of points $x_j, 1 \leq j \leq J$, distributed in a bounded domain $D \subset R^N$, where $N$ and $J$ are large numbers. In this paper an algorithm is proposed for checking whether there exists a…
Fully automated verification of concurrent programs is a difficult problem, primarily because of state explosion: the exponential growth of a program state space with the number of its concurrently active components. It is natural to apply…
Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with…
Image representations (artificial or biological) are often compared in terms of their global geometric structure; however, representations with similar global structure can have strikingly different local geometries. Here, we propose a…