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.

The various performance criteria applied in this analysis include the probability of reaching the ultimate target, the costs, elapsed times and system vulnerability resulting from any intrusion. This Excel file contains all the logical, probabilistic and statistical data entered by a user, and required for the evaluation of the criteria. It also reports the results of all the computations.

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 Excel table contains a detailed example of a graph-theoretic model used in the specification of the physical topology and network of the modeled system.

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.

This thesis investigates the parameterized computational complexity of six classic graph problems lifted to a temporal setting. More specifically, we consider problems defined on temporal graphs, that is, a graph where the edge set may change over a discrete time interval, while the vertex set remains unchanged. Temporal graphs are well-suited to model dynamic data and hence they are naturally motivated in contexts where dynamic changes or time-dependent interactions play an important role, such as, for example, communication networks, social networks, or physical proximity networks. The most important selection criteria for our problems was that they are well-motivated in the context of dynamic data analysis. Since temporal graphs are mathematically more complex than static graphs, it is maybe not surprising that all problems we consider in this thesis are NP-hard. We focus on the development of exact algorithms, where our goal is to obtain fixed-parameter tractability results, and refined computational hardness reductions that either show NP-hardness for very restricted input instances or parameterized hardness with respect to “large” parameters. In the context of temporal graphs, we mostly consider structural parameters of the underlying graph, that is, the graph obtained by ignoring all time information. However, we also consider parameters of other types, such as ones trying to measure how fast the temporal graph changes over time. In the following we briefly discuss the problem setting and the main results. Restless Temporal Paths. A path in a temporal graph has to respect causality, or time, which means that the edges used by a temporal path have to appear at non-decreasing times. We investigate temporal paths that additionally have a maximum waiting time in every vertex of the temporal graph. Our main contributions are establishing NP-hardness for the problem of finding restless temporal paths even in very restricted cases, and showing W[1]-hardness with respect to the feedback vertex number of the underlying graph. Temporal Separators. A temporal separator is a vertex set that, when removed from the temporal graph, destroys all temporal paths between two dedicated vertices. Our contribution here is twofold: Firstly, we investigate the computational complexity of finding temporal separators in temporal unit interval graphs, a generalization of unit interval graphs to the temporal setting. We show that the problem is NP-hard on temporal unit interval graphs but we identify an additional restriction which makes the problem solvable in polynomial time. We use the latter result to develop a fixed-parameter algorithm with a “distance-to-triviality” parameterization. Secondly, we show that finding temporal separators that destroy all restless temporal paths is Σ-P-2-hard. Temporal Matchings. We introduce a model for matchings in temporal graphs, where, if two vertices are matched at some point in time, then they have to “recharge” afterwards, meaning that they cannot be matched again for a certain number of time steps. In our main result we employ temporal line graphs to show that finding matchings is NP-hard even on instances where the underlying graph is a path. Temporal Coloring. We lift the classic graph coloring problem to the temporal setting. In our model, every edge has to be colored properly (that is, the endpoints are colored differently) at least once in every time interval of a certain length. We show that this problem is NP-hard in very restricted cases, even if we only have two colors. We present simple exponential-time algorithms to solve this problem. As a main contribution, we show that these algorithms presumably cannot be improved significantly. Temporal Cliques and s-Plexes. We propose a model for temporal s-plexes that is a canonical generalization of an existing model for temporal cliques. Our main contribution is a fixed-parameter algorithm that enumerates all maximal temporal s-plexes in a given temporal graph, where we use a temporal adaptation of degeneracy as a parameter. Temporal Cluster Editing. We present a model for cluster editing in temporal graphs, where we want to edit all “layers” of a temporal graph into cluster graphs that are sufficiently similar. Our main contribution is a fixed-parameter algorithm with respect to the parameter “number of edge modifications” plus the “measure of similarity” of the resulting clusterings. We further show that there is an efficient preprocessing procedure that can provably reduce the size of the input instance to be independent of the number of vertices of the original input instance.

Network of 27 papers and 37 citation links related to "Analysis of radiation and corn borer data using discrete Poisson Xrama distribution".

Different graph types may differ in their suitability to support group comparisons, due to the underlying graph schemas. This study examined whether graph schemas are based on perceptual features (i.e., each graph type, e.g., bar or line graph, has its own graph schema) or common invariant structures (i.e., graph types share common schemas). Furthermore, it was of interest which graph type (bar, line, or pie) is optimal for comparing discrete groups. A switching paradigm was used in three experiments. Two graph types were examined at a time (Experiment 1: bar vs. line, Experiment 2: bar vs. pie, Experiment 3: line vs. pie). On each trial, participants received a data graph presenting the data from three groups and were to determine the numerical difference of group A and group B displayed in the graph. We scrutinized whether switching the type of graph from one trial to the next prolonged RTs. The slowing of RTs in switch trials in comparison to trials with only one graph type can indicate to what extent the graph schemas differ. As switch costs were observed in all pairings of graph types, none of the different pairs of graph types tested seems to fully share a common schema. Interestingly, there was tentative evidence for differences in switch costs among different pairings of graph types. Smaller switch costs in Experiment 1 suggested that the graph schemas of bar and line graphs overlap more strongly than those of bar graphs and pie graphs or line graphs and pie graphs. This implies that results were not in line with completely distinct schemas for different graph types either. Taken together, the pattern of results is consistent with a hierarchical view according to which a graph schema consists of parts shared for different graphs and parts that are specific for each graph type. Apart from investigating graph schemas, the study provided evidence for performance differences among graph types. We found that bar graphs yielded the fastest group comparisons compared to line graphs and pie graphs, suggesting that they are the most suitable when used to compare discrete groups.

Network of 31 papers and 48 citation links related to "NONLINEAR SAMPLED-DATA OBSERVER DESIGN VIA APPROXIMATE DISCRETE-TIME MODELS AND EMULATION".

Graph-theoretic approaches have relevant applications in landscape genetic analyses. When species form populations in discrete habitat patches, genetic graphs can be used i) to identify direct dispersal paths followed by propagules or ii) to quantify landscape effects on multigenerational gene flow. However, the influence of their construction parameters remains to be explored. Using a simulation approach, we constructed genetic graphs using several pruning methods (geographical distance thresholds, topological constraints, statistical inference) and genetic distances to weight graph links (FST, DPS, Euclidean genetic distances). We then compared the capacity of these different graphs to i) identify the precise topology of the dispersal network and ii) to infer landscape resistance to gene flow from the relationship between cost-distances and genetic distances. Although not always clear-cut, our results showed that methods based on geographical distance thresholds seem to better identif...

Graph Processor Unit Market Outlook

According to our latest research, the global Graph Processor Unit (GPU) market size reached USD 54.7 billion in 2024. The market is projected to expand at a robust CAGR of 15.3% during the forecast period, reaching a value of USD 161.3 billion by 2033. The primary growth factor driving this surge is the increasing adoption of GPUs across diverse applications such as artificial intelligence, gaming, and data centers, which are fueling unprecedented demand for high-performance computing solutions worldwide.

One of the key growth drivers for the Graph Processor Unit market is the exponential rise in artificial intelligence and machine learning workloads. As organizations across various industries embrace AI-driven analytics, deep learning, and neural networks, the need for parallel processing capabilities provided by GPUs has become essential. GPUs offer significant advantages over traditional CPUs in terms of processing massive datasets and running complex algorithms, making them the preferred choice for AI research, autonomous vehicles, and advanced robotics. The ongoing evolution of AI models, which require ever-increasing computational power, is expected to sustain the demand for high-performance GPUs well into the next decade.

In addition to AI adoption, the rapid expansion of the gaming industry continues to be a major catalyst for GPU market growth. The gaming sector, driven by the rise of immersive technologies such as virtual reality (VR) and augmented reality (AR), demands cutting-edge graphics processing capabilities. Game developers are leveraging the latest GPUs to deliver photorealistic visuals and seamless user experiences, which in turn drives consumer demand for advanced gaming hardware. Furthermore, the proliferation of eSports and online gaming platforms has created a robust ecosystem that continually pushes the boundaries of GPU innovation, ensuring sustained market expansion.

Another significant growth factor is the increasing deployment of GPUs in data centers and cloud computing environments. As enterprises migrate workloads to the cloud and demand scalable infrastructure for big data analytics, GPUs are being integrated into data center architectures to accelerate parallel processing and reduce latency. The emergence of GPU-as-a-Service (GPUaaS) models enables organizations to access high-performance computing resources on demand, further broadening the addressable market. Additionally, industries such as healthcare, automotive, and finance are leveraging GPU-powered solutions for advanced simulations, real-time analytics, and complex visualizations, amplifying the market’s growth trajectory.

From a regional perspective, Asia Pacific is emerging as the dominant force in the Graph Processor Unit market, driven by large-scale investments in technology infrastructure, a thriving gaming industry, and government initiatives promoting AI and digital transformation. North America follows closely, benefiting from a strong presence of leading GPU manufacturers, robust R&D activities, and early adoption of advanced technologies in sectors such as automotive, healthcare, and defense. Europe is also witnessing significant growth, particularly in automotive and industrial automation applications, while Latin America and the Middle East & Africa present promising opportunities as digitalization initiatives gain momentum. Regional dynamics are further shaped by evolving regulatory frameworks, trade policies, and cross-border collaborations that influence market access and competitive positioning.

Product Type Analysis

The Graph Processor Unit market is segmented by product type into Discrete GPU, Integrated GPU, and Hybrid GPU, each catering to distinct user requirements and application domains. Discrete GPUs are standalone graphics cards, offering superior performance and are widely used in gaming, professional visualization, and high-performance computing environments. These GPUs are favored by enthusiasts

Using the User Manual included in the research paper, and the Graph Design Example file as a reference, the user enters or saves all the vertices and edges needed to specify the model of the system topography.

Business process event data modeled as labeled property graphsData Format-----------The dataset comprises one labeled property graph in two different file formats.#1) Neo4j .dump formatA neo4j (https://neo4j.com) database dump that contains the entire graph and can be imported into a fresh neo4j database instance using the following command, see also the neo4j documentation: https://neo4j.com/docs//bin/neo4j-admin.(bat|sh) load --database=graph.db --from=The .dump was created with Neo4j v3.5.#2) .graphml formatA .zip file containing a .graphml file of the entire graphData Schema-----------The graph is a labeled property graph over business process event data. Each graph uses the following concepts:Event nodes - each event node describes a discrete event, i.e., an atomic observation described by attribute "Activity" that occurred at the given "timestamp":Entity nodes - each entity node describes an entity (e.g., an object or a user), it has an EntityType and an identifier (attribute "ID"):Log nodes - describes a collection of events that were recorded together, most graphs only contain one log node:Class nodes - each class node describes a type of observation that has been recorded, e.g., the different types of activities that can be observed, :Class nodes group events into sets of identical observations:CORR relationships - from :Event to :Entity nodes, describes whether an event is correlated to a specific entity; an event can be correlated to multiple entities:DF relationships - "directly-followed by" between two :Event nodes describes which event is directly-followed by which other event; both events in a :DF relationship must be correlated to the same entity node. All :DF relationships form a directed acyclic graph.:HAS relationship - from a :Log to an :Event node, describes which events had been recorded in which event log:OBSERVES relationship - from an :Event to a :Class node, describes to which event class an event belongs, i.e., which activity was observed in the graph:REL relationship - placeholder for any structural relationship between two :Entity nodesThe concepts a further defined in Stefan Esser, Dirk Fahland: Multi-Dimensional Event Data in Graph Databases. CoRR abs/2005.14552 (2020) https://arxiv.org/abs/2005.14552Data Contents-------------neo4j-bpic17-2021-02-17 (.dump|.graphml.zip)An integrated graph describing the raw event data of the entire BPI Challenge 2017 dataset. van Dongen, B.F. (Boudewijn) (2017): BPI Challenge 2017. 4TU.ResearchData. Collection. https://doi.org/10.4121/uuid:5f3067df-f10b-45da-b98b-86ae4c7a310bThis event log pertains to a loan application process of a Dutch financial institute. The data contains all applications filed trough an online system in 2016 and their subsequent events until February 1st 2017, 15:11. The company providing the data and the process under consideration is the same as doi:10.4121/uuid:3926db30-f712-4394-aebc-75976070e91f. However, the system supporting the process has changed in the meantime. In particular, the system now allows for multiple offers per application. These offers can be tracked through their IDs in the log.The data contains the following entities and their events- Application - a credit application document submitted by a customer to a Dutch financial institute- Offer - a loan offer document created by the institute and sent to the customer- Workflow - a logical grouping of activities by the case management system supporting workers at the financial institute to handle applications and offers- Case_R - a user or worker of the financial institute- Case_AO - a derived entity describing the reified relation between an offer and its related application- Case_AW - a derived entity describing the reified relation between the workflow and its related application- Case_WO - a derived entity describing the reified relation between an offer and its related workflowData Size---------BPIC17, nodes: 1425995, relationships: 10300197

Depreciation Time Series for Belden Inc. Belden Inc. provides connection solutions to bring data infrastructure into alignment to unlock new possibilities for its customers. It operates through two segments, Smart Infrastructure Solutions and Automation Solutions. The Smart Infrastructure Solutions segment offers copper cable and connectivity solutions, fiber cable and connectivity solutions, interconnect panels, racks and enclosures, and signal extension and matrix switching systems for use in local area networks, data centers, access control, 5G, fiber to the home, and building automation applications. It also provides power, cooling, and airflow management products for mission-critical data center operations; and end-to-end fiber and copper network systems. This segment serves commercial real estate, education, financial, stadiums and venues, military installations, and broadband and wireless service providers, as well as data centers, government, healthcare, and hospitality sectors. The Automation Solutions segment offers network infrastructure and digitization solutions; and products and solutions covering various aspects of data handling, including acquisition, transmission, orchestration, and management for applications in discrete automation, process automation, energy, and mass transit. It sells its products to distributors, end-users, installers, and original equipment manufacturers (OEMs). Belden Inc. operates in the Americas, Europe, the Middle East, Africa, and the Asia-Pacific. The company was formerly known as Belden CDT Inc. and changed its name to Belden Inc. in May 2007. Belden Inc. was founded in 1902 and is headquartered in Saint Louis, Missouri.

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.

The present article introduces the notion of smoothness of rhythm and proposes a unified method that transforms an arbitrary rhythm into a smooth one. The method employs a self-map Rav, discrete average map, on the space of rhythms of arbitrary length with a fixed number of onsets. It is shown that, for any rhythm a in the space, the iterations Ravk(a) become eventually periodic, and that the final cycle consists only of smooth rhythms. The discrete average map leads naturally to a finite directed graph, which visualizes the realm of smooth rhythms in the whole world of rhythms. This article has an Online Supplement, in which we give detailed proof of the main result.

Summary of network visualisation tools commonly used for the analysis of biological data.

Symbols used to describe our computational model known as a discrete Graph Dynamical System (GDS).

Summary of citation networks arXiv-HepTh and arXiv-HepPh.

In the previous version, the Hamiltonian was not explicitly derived, which confined the theoretical predictions to highly complex and currently inaccessible experimental regimes. This work reports an explicitly falsifiable (already today) discrete–quantum‐graph model of spacetime and noise in quantum processors. Continuum limits and recovery of field equations (ℓp→0) remain open for future work; our focus is on delivering real, quantitative falsifiability now.