A module of a graph G is a set of vertices that have the same set of neighbours outside. Modules of a graphs form a so-called partitive family and thereby can be represented by a unique tree MD(G), called the modular decomposition tree. Motivated by the central role of modules in numerous algorithmic graph theory questions, the problem of efficiently computing MD(G) has been investigated since the early 70's. To date the best algorithms run in linear time but are all rather complicated. By combining previous algorithmic paradigms developed for the problem, we are able to present a simpler linear-time that relies on very simple data-structures, namely slice decomposition and sequences of rooted ordered trees.
相關內容
We introduce the R package clrng which leverages the gpuR package and is able to generate random numbers in parallel on a Graphics Processing Unit (GPU) with the clRNG (OpenCL) library. Parallel processing with GPU's can speed up computationally intensive tasks, which when combined with R, it can largely improve R's downsides in terms of slow speed, memory usage and computation mode. clrng enables reproducible research by setting random initial seeds for streams on GPU and CPU, and can thus accelerate several types of statistical simulation and modelling. The random number generator in clrng guarantees independent parallel samples even when R is used interactively in an ad-hoc manner, with sessions being interrupted and restored. This package is portable and flexible, developers can use its random number generation kernel for various other purposes and applications.
The simulation hypothesis suggests that we live in a computer simulation. That notion has attracted significant scholarly and popular interest. This article explores the simulation hypothesis from a business perspective. Due to the lack of a name for a universe consistent with the simulation hypothesis, we propose the term simuverse. We argue that if we live in a simulation, there must be a business justification. Therefore, we ask: If we live in a simuverse, what is its business model? We identify and explore business model scenarios, such as simuverse as a project, service, or platform. We also explore business model pathways and risk management issues. The article contributes to the simulation hypothesis literature and is the first to provide a business model perspective on the simulation hypothesis. The article discusses theoretical and practical implications and identifies opportunities for future research related to sustainability, digital transformation, and Artificial Intelligence (AI).
We study a truncated two-dimensional moment problem in terms of the Stieltjes transform. The set of the solutions is described by the Schur step-by-step algorithm, which is based on the continued fraction expansion of the solution. In particular, the obtained results are applicable to the two-dimensional moment problem for atomic measures.
Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the coarse space used in the two-level method. The analysis of adaptive coarse spaces we present here is quite general since it applies to symmetric and non symmetric problems, to symmetric preconditioners such the additive Schwarz method (ASM) and to the non-symmetric preconditioner restricted additive Schwarz (RAS), as well as to exact or inexact subdomain solves. The coarse space is built by solving generalized eigenvalues in the subdomains and applying a well-chosen operator to the selected eigenvectors.
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like tree structure of minimum size in which the leaves in left-to-right order represent the input strings in the given order. Contrary to standard tries, the order in which the characters of a string are encountered can be different on different root-to-leaf paths. Dawson et al. [ACM Trans. Program. Lang. Syst. 18(5):528--563, 1996] gave an algorithm that solves the problem in time $O(n^2 m (n+m))$. In this paper, we present an improved algorithm with running-time $O(n^2m)$.
The continental plates of Earth are known to drift over a geophysical timescale, and their interactions have lead to some of the most spectacular geoformations of our planet while also causing natural disasters such as earthquakes and volcanic activity. Understanding the dynamics of interacting continental plates is thus significant. In this work, we present a fluid mechanical investigation of the plate motion, interaction, and dynamics. Through numerical experiments, we examine the coupling between a convective fluid and plates floating on top of it. With physical modeling, we show the coupling is both mechanical and thermal, leading to the thermal blanket effect: the floating plate is not only transported by the fluid flow beneath, it also prevents the heat from leaving the fluid, leading to a convective flow that further affects the plate motion. By adding several plates to such a coupled fluid-structure interaction, we also investigate how floating plates interact with each other and show that, under proper conditions, small plates can converge into a supercontinent.
Progress in the realm of quantum technologies is paving the way for a multitude of potential applications across different sectors. However, the reduced number of available quantum computers, their technical limitations and the high demand for their use are posing some problems for developers and researchers. Mainly, users trying to execute quantum circuits on these devices are usually facing long waiting times in the tasks queues. In this context, this work propose a technique to reduce waiting times and optimize quantum computers usage by scheduling circuits from different users into combined circuits that are executed at the same time. To validate this proposal, different widely known quantum algorithms have been selected and executed in combined circuits. The obtained results are then compared with the results of executing the same algorithms in an isolated way. This allowed us to measure the impact of the use of the scheduler. Among the obtained results, it has been possible to verify that the noise suffered by executing a combination of circuits through the proposed scheduler does not critically affect the outcomes.
An interesting case of the well-known Dataset Shift Problem is the classification of Electroencephalogram (EEG) signals in the context of Brain-Computer Interface (BCI). The non-stationarity of EEG signals can lead to poor generalisation performance in BCI classification systems used in different sessions, also from the same subject. In this paper, we start from the hypothesis that the Dataset Shift problem can be alleviated by exploiting suitable eXplainable Artificial Intelligence (XAI) methods to locate and transform the relevant characteristics of the input for the goal of classification. In particular, we focus on an experimental analysis of explanations produced by several XAI methods on an ML system trained on a typical EEG dataset for emotion recognition. Results show that many relevant components found by XAI methods are shared across the sessions and can be used to build a system able to generalise better. However, relevant components of the input signal also appear to be highly dependent on the input itself.
Inverse kinematics is an important and challenging problem in the operation of industrial manipulators. This study proposes a simple inverse kinematics calculation scheme for an industrial serial manipulator. The proposed technique can calculate appropriate values of the joint variables to realize the desired end-effector position and orientation while considering the motion costs of each joint. Two scalar functions are defined for the joint variables: one is to evaluate the end-effector position and orientation, whereas the other is to evaluate the motion efficiency of the joints. By combining the two scalar functions, the inverse kinematics calculation of the manipulator is formulated as a numerical optimization problem. Furthermore, a simple algorithm for solving the inverse kinematics via the aforementioned optimization is constructed on the basis of the simultaneous perturbation stochastic approximation with a norm-limited update vector (NLSPSA). The proposed scheme considers not only the accuracy of the position and orientation of the end-effector but also the efficiency of the robot movement. Therefore, it yields a practical result of the inverse problem. Moreover, the proposed algorithm is simple and easy to implement owing to the high calculation efficiency of NLSPSA. Finally, the effectiveness of the proposed method is verified through numerical examples using a redundant manipulator.
We propose a monotone approximation scheme for a class of fully nonlinear PDEs called G-equations. Such equations arise often in the characterization of G-distributed random variables in a sublinear expectation space. The proposed scheme is constructed recursively based on a piecewise constant approximation of the viscosity solution to the G-equation. We establish the convergence of the scheme and determine the convergence rate with an explicit error bound, using the comparison principles for both the scheme and the equation together with a mollification procedure. The first application is obtaining the convergence rate of Peng's robust central limit theorem with an explicit bound of Berry-Esseen type. The second application is an approximation scheme with its convergence rate for the Black-Scholes-Barenblatt equation.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191