We have generated sets of the problem instances obtained by using different pseudo-random methods to generate the graphs. The order and the size of an instances were generated randomly using function random() within the respective ranges. Each new edge was added in between two yet non-adjacent vertices randomly until the corresponding size was attained. This dataset is an extension of the Random Graph dataset available at https://data.mendeley.com/datasets/rr5bkj6dw5/8.

Question Paper Solutions of chapter Graphs and Trees of Discrete Mathematics, 4th Semester , Information Technology

In this article (motivated by question on existence of finite-memory algorithm to determine connectedness of a graph) we explore a non-standard approach to finding upper bounds for maximum hitting time for random walks on finite undirected graphs.We prove specific (and in some cases, exact) upper bounds for maximum hitting time for random walks on undirected graphs formulated as functions of the number of graph’s edges. Among them, the theorem that states that the maximum hitting time for symmetric random walk on connected graph with n edges is less than or equal to n2.We also consider asymmetric random walks on trees and connected graphs to find upper bounds for hitting time as simple functions of n and , where is a simple measure of walk’s asymmetry (or bias).

This dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.

We have generated sets of the problem instances obtained by using different pseudo-random methods to generate the graphs. The order and the size of an instances were generated randomly using function random() within the respective ranges. Each new edge was added in between two yet non-adjacent vertices randomly until the corresponding size was attained.

This dataset is about book series and is filtered where the books is Problems from the discrete to the continuous : probability, number theory, graph theory, and combinatorics, featuring 10 columns including authors, average publication date, book publishers, book series, and books. The preview is ordered by number of books (descending).

Code used to simulate a hybrid computing platform (CPUs + GPUs) to test several online algorithms (that discover the task graph as it is unveiled) and to compare them to the classical HEFT offline scheduler.

This data release includes water-quality data collected at 38 sites in central and eastern Massachusetts from April 2018 through May 2019 by the U.S. Geological Survey to support the implementation of site-dependent aluminum criteria for Massachusetts waters. Samples of effluent and receiving surface waters were collected monthly at four wastewater-treatment facilities (WWTFs) and seven water-treatment facilities (WTFs) (see SWQ_data_and_instantaneous_CMC_CCC_values.txt). The measured properties and constituents include pH, hardness, and filtered (dissolved) organic carbon, which are required inputs to the U.S. Environmental Protection Agency's Aluminum Criteria Calculator version 2.0. Outputs from the Aluminum Criteria Calculator are also provided in that file; these outputs consist of acute (Criterion Maximum Concentration, CMC) and chronic (Criterion Continuous Concentration, CCC) instantaneous water-quality values for total recoverable aluminum, calculated for monthly samples at selected ambient sites near each of the 11 facilities. Quality-control data from blank, replicate, and spike samples are provided (see SWQ_QC_data.txt). In addition to data tables, the data release includes time-series graphs of the discrete water-quality data (see SWQ_plot_discrete_all.zip). For pH, time-series graphs also are provided showing pH from the discrete monthly water-quality samples as well as near-continuous pH measured at one surface-water site at each facility (see SWQ_plot_contin_discrete_pH.zip). The near-continuous pH data, along with all of the discrete water-quality data except the quality-control data, are also available online from the U.S. Geological Survey's National Water Information System (NWIS) database (https://nwis.waterdata.usgs.gov/nwis).

Experimental data can broadly be divided in discrete or continuous data. Continuous data are obtained from measurements that are performed as a function of another quantitative variable, e.g., time, length, concentration, or wavelength. The results from these types of experiments are often used to generate plots that visualize the measured variable on a continuous, quantitative scale. To simplify state-of-the-art data visualization and annotation of data from such experiments, an open-source tool was created with R/shiny that does not require coding skills to operate it. The freely available web app accepts wide (spreadsheet) and tidy data and offers a range of options to normalize the data. The data from individual objects can be shown in 3 different ways: (1) lines with unique colors, (2) small multiples, and (3) heatmap-style display. Next to this, the mean can be displayed with a 95% confidence interval for the visual comparison of different conditions. Several color-blind-friendly palettes are available to label the data and/or statistics. The plots can be annotated with graphical features and/or text to indicate any perturbations that are relevant. All user-defined settings can be stored for reproducibility of the data visualization. The app is dubbed PlotTwist and runs locally or online: https://huygens.science.uva.nl/PlotTwist

This repository contains raw data generated for use in Rumpf and Kaul 2021 (referenced below), and includes sets of files for defining transit networks as well as raw data tables generated by the solution algorithm. See the included README for an in-depth explanation of each data set.

The main focus of the study was to develop and test a public transit design model for improving equity of access to social services throughout a city. The main case study was based on the Chicago Transit Authority network, with the goal of making minor alterations to the bus fleet assignments in order to improve equity of access to primary health care facilities. A small-scale artificial network was also generated for use in sensitivity analysis.

The data sets in this repository include network files used by our hybrid tabu search/simulated annealing solution algorithm in order to solve the social access maximization problem (see the GitHub repository referenced below). Also included are the raw data tables from the CTA and artificial network trial sets.

The results of this study indicate that it is indeed possible to significantly increase social service access levels in the least advantaged areas of a community while still guaranteeing that transit service remains near its current level. While improving the access in some areas does require that other areas lose some access, the gains are generally much greater than the losses. Moreover, the losses tend to occur in the areas that already enjoy the greatest levels of access, with the net result being a more even distribution of accessibility levels throughout the city.

TOP 10 journals in WoS-Stat.

Various datasets from the Bayesys repository.

Size: 6 groups of datasets with each up to 16 experimentally generated from the bayesian network with the number of observation 100,1000,…100000. Ground truth is given

Number of features: 6 - over 1000

Ground truth: Yes

Type of Graph: Directed graph

Six discrete BN case studies are used to generate data. The first three of them represent well-established examples from the BN structure learning literature, whereas the other three represent new cases and are based on recent BN real-world applications. Specifically,

• Asia: A small toy network for diagnosing patients at a clinic;

• Alarm: A medium-sized network based on an alarm message system for patient monitoring;

• Pathfinder: A very large network that was designed to assist surgical pathologists with the diagnosis of lymph-node diseases;

• Sports: A small BN that combines football team ratings with various team performance statistics to predict a series of match outcomes;

• ForMed: A large BN that captures the risk of violent reoffending of mentally ill prisoners, along with multiple interventions for managing this risk;

• Property: A medium BN that assesses investment decisions in the UK property market.

Data generated with noise:

Synthetic datasets - noise

Experiment No.	Experiment	Notes
1	N	No noise
2	M5	Missing data (5%)
3	M10	Missing data (10%)
4	I5	Incorrect data (5%)
5	I10	Incorrect data (10%)
6	S5	Merged states data (5%)
7	S10	Merged states data (10%)
8	L5	Latent confounders (5%)
9	L10	Latent confounders (10%)
10	cMI	M5 and I5
11	cMS	M5 and S5
12	cML	M5 and L5
13	cIS	I5 and S5
14	cIL	I5 and L5
15	cSL	S5 and L5
16	cMISL	M5, I5, S5 and L5

More information about the datasets is contained in the dataset_description.html files.

We propose a stochastic generative model to represent a directed graph constructed by citations among academic papers, where nodes and directed edges represent papers with discrete publication time and citations respectively. The proposed model assumes that a citation between two papers occurs with a probability based on the type of the citing paper, the importance of cited paper, and the difference between their publication times, like the existing models. We consider the out-degrees of citing paper as its type, because, for example, survey paper cites many papers. We approximate the importance of a cited paper by its in-degrees. In our model, we adopt three functions: a logistic function for illustrating the numbers of papers published in discrete time, an inverse Gaussian probability distribution function to express the aging effect based on the difference between publication times, and an exponential distribution (or a generalized Pareto distribution) for describing the out-degree distribution. We consider that our model is a more reasonable and appropriate stochastic model than other existing models and can perform complete simulations without using original data. In this paper, we first use the Web of Science database and see the features used in our model. By using the proposed model, we can generate simulated graphs and demonstrate that they are similar to the original data concerning the in- and out-degree distributions, and node triangle participation. In addition, we analyze two other citation networks derived from physics papers in the arXiv database and verify the effectiveness of the model.

In particular, MUTAG is a collection of nitroaromatic compounds and the goal is to predict their mutagenicity on Salmonella typhimurium. Input graphs are used to represent chemical compounds, where vertices stand for atoms and are labeled by the atom type (represented by one-hot encoding), while edges between vertices represent bonds between the corresponding atoms. It includes 188 samples of chemical compounds with 7 discrete node labels.

High-throughput technologies have led to the generation of an increasing amount of data in different areas of biology. Datasets capturing the cell’s response to its intra- and extra-cellular microenvironment allows such data to be incorporated as signed and directed graphs or influence networks. These prior knowledge networks (PKNs) represent our current knowledge of the causality of cellular signal transduction. New signalling data is often examined and interpreted in conjunction with PKNs. However, different biological contexts, such as cell type or disease states, may have distinct variants of signalling pathways, resulting in the misinterpretation of new data. The identification of inconsistencies between measured data and signalling topologies, as well as the training of PKNs using context specific datasets (PKN contextualization), are necessary conditions to construct reliable, predictive models, which are current challenges in the systems biology of cell signalling. Here we present PRUNET, a user-friendly software tool designed to address the contextualization of a PKNs to specific experimental conditions. As the input, the algorithm takes a PKN and the expression profile of two given stable steady states or cellular phenotypes. The PKN is iteratively pruned using an evolutionary algorithm to perform an optimization process. This optimization rests in a match between predicted attractors in a discrete logic model (Boolean) and a Booleanized representation of the phenotypes, within a population of alternative subnetworks that evolves iteratively. We validated the algorithm applying PRUNET to four biological examples and using the resulting contextualized networks to predict missing expression values and to simulate well-characterized perturbations. PRUNET constitutes a tool for the automatic curation of a PKN to make it suitable for describing biological processes under particular experimental conditions. The general applicability of the implemented algorithm makes PRUNET suitable for a variety of biological processes, for instance cellular reprogramming or transitions between healthy and disease states.

Dynamical properties relevant to ecological systems are gathered into patterns. The patterns are written in English and translated into CTL formulas. x and y are place-holders for state properties. (Adapted from [49]).

Data for graph (B) is given in a sheet containing an image identifier and fluorescence intensity measurements of LanA::GFP levels (y axis) in each genotype (x axis). (XLSX)

Double normalized data for FRAP plotted in graph (4F). Normalized mean fluorescence intensity values for each indicated replicate (y axis) were calculated using the easyFRAP web application [91] averaged and then plotted against time (x axis). Raw fluorescence values for each replicate are included on a separate sheet. (XLSX)