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.

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).

The scale and complexity of relational data in critical domains like chemistry, neuroscience, and social media has ignited interest in graph neural networks as performant, expressive, flexible frameworks for solving problems specified over graphs. However, this performance comes at the cost of interpretability: the behavior of a typical neural network is, at best, a mystery. Graph grammars, in contrast, provide a symbolic, discrete, rule-based formalism for describing transformations between graphs. While profoundly interpretable, they are mired in the inductive biases and restrictive assumptions common to many traditional approaches to graph modeling.

This dissertation tries to diminish the discrepancy between graph neural networks and graph grammars. The first contribution introduces Dynamic Vertex Replacement Grammars as a way of modeling temporal graph datasets with graph grammars. The second contribution proposes an analytically-invertible normalizing flow network that learns prototypical probability distributions as intrinsic explanations for its behavior. The third contribution shows how the attention mechanism in graph neural networks induces grammars that can act as generative post hoc explainers.

This supports the thesis that discrete rules and continuous distributions are jointly critical to the future of machine learning.

In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. We show that a network model with discrete unobserved link heterogeneity and binary (or discrete) covariates corresponds to a stochastic blockmodel (SBM). We develop a spectral estimator for the effect of covariates on link probabilities, exploiting the correspondence of SBMs and generalized random dot product graphs (GRDPG). We show that computing our estimator is much faster than standard variational expectation–maximization algorithms and scales well for large networks. Monte Carlo experiments suggest that the estimator performs well under different data generating processes. Our application to Facebook data shows evidence of homophily in gender, role and campus-residence, while allowing us to discover unobserved communities. Finally, we establish asymptotic normality of our estimators.

BACKGROUND:Chaos Game Representation (CGR) is an iterated function that bijectively maps discrete sequences into a continuous domain. As a result, discrete sequences can be object of statistical and topological analyses otherwise reserved to numerical systems. Characteristically, CGR coordinates of substrings sharing an L-long suffix will be located within 2-L distance of each other. In the two decades since its original proposal, CGR has been generalized beyond its original focus on genomic sequences and has been successfully applied to a wide range of problems in bioinformatics. This report explores the possibility that it can be further extended to approach algorithms that rely on discrete, graph-based representations. RESULTS:The exploratory analysis described here consisted of selecting foundational string problems and refactoring them using CGR-based algorithms. We found that CGR can take the role of suffix trees and emulate sophisticated string algorithms, efficiently solving exact and approximate string matching problems such as finding all palindromes and tandem repeats, and matching with mismatches. The common feature of these problems is that they use longest common extension (LCE) queries as subtasks of their procedures, which we show to have a constant time solution with CGR. Additionally, we show that CGR can be used as a rolling hash function within the Rabin-Karp algorithm. CONCLUSIONS:The analysis of biological sequences relies on algorithmic foundations facing mounting challenges, both logistic (performance) and analytical (lack of unifying mathematical framework). CGR is found to provide the latter and to promise the former: graph-based data structures for sequence analysis operations are entailed by numerical-based data structures produced by CGR maps, providing a unifying analytical framework for a diversity of pattern matching problems.

Frictional pressure loss measurements are reported for two-phase air-water flow in a 4.55 cm diameter inclined pipe. The data are presented as graphs of shear-or frictional velocity against total velocity and show as discrete curves depending on the superficial liquid velocity. The frictional pressure loss is shown to be dependent on the flow regime present in the flow conduit. In general the separated flow regimes seem to be the preferred mode of transport as far as frictional pressure loss is concerned. Further the frictional pressure loss for pipes inclined one or two degrees from the horizontal is much higher than for the horizontal case.

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.

Business process event data modeled as labeled property graphs

Data Format
-----------

The dataset comprises one labeled property graph in two different file formats.

#1) Neo4j .dump format

A 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 format

A .zip file containing a .graphml file of the entire graph


Data 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 nodes

The 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/2005.14552


Data Contents
-------------

neo4j-bpic19-2021-02-17 (.dump|.graphml.zip)

An integrated graph describing the raw event data of the entire BPI Challenge 2019 dataset.
van Dongen, B.F. (Boudewijn) (2019): BPI Challenge 2019. 4TU.ResearchData. Collection. https://doi.org/10.4121/uuid:d06aff4b-79f0-45e6-8ec8-e19730c248f1

This data originated from a large multinational company operating from The Netherlands in the area of coatings and paints and we ask participants to investigate the purchase order handling process for some of its 60 subsidiaries. In particular, the process owner has compliance questions. In the data, each purchase order (or purchase document) contains one or more line items. For each line item, there are roughly four types of flows in the data: (1) 3-way matching, invoice after goods receipt: For these items, the value of the goods receipt message should be matched against the value of an invoice receipt message and the value put during creation of the item (indicated by both the GR-based flag and the Goods Receipt flags set to true). (2) 3-way matching, invoice before goods receipt: Purchase Items that do require a goods receipt message, while they do not require GR-based invoicing (indicated by the GR-based IV flag set to false and the Goods Receipt flags set to true). For such purchase items, invoices can be entered before the goods are receipt, but they are blocked until goods are received. This unblocking can be done by a user, or by a batch process at regular intervals. Invoices should only be cleared if goods are received and the value matches with the invoice and the value at creation of the item. (3) 2-way matching (no goods receipt needed): For these items, the value of the invoice should match the value at creation (in full or partially until PO value is consumed), but there is no separate goods receipt message required (indicated by both the GR-based flag and the Goods Receipt flags set to false). (4)Consignment: For these items, there are no invoices on PO level as this is handled fully in a separate process. Here we see GR indicator is set to true but the GR IV flag is set to false and also we know by item type (consignment) that we do not expect an invoice against this item. Unfortunately, the complexity of the data goes further than just this division in four categories. For each purchase item, there can be many goods receipt messages and corresponding invoices which are subsequently paid. Consider for example the process of paying rent. There is a Purchase Document with one item for paying rent, but a total of 12 goods receipt messages with (cleared) invoices with a value equal to 1/12 of the total amount. For logistical services, there may even be hundreds of goods receipt messages for one line item. Overall, for each line item, the amounts of the line item, the goods receipt messages (if applicable) and the invoices have to match for the process to be compliant. Of course, the log is anonymized, but some semantics are left in the data, for example: The resources are split between batch users and normal users indicated by their name. The batch users are automated processes executed by different systems. The normal users refer to human actors in the process. The monetary values of each event are anonymized from the original data using a linear translation respecting 0, i.e. addition of multiple invoices for a single item should still lead to the original item worth (although there may be small rounding errors for numerical reasons). Company, vendor, system and document names and IDs are anonymized in a consistent way throughout the log. The company has the key, so any result can be translated by them to business insights about real customers and real purchase documents.

The case ID is a combination of the purchase document and the purchase item. There is a total of 76,349 purchase documents containing in total 251,734 items, i.e. there are 251,734 cases. In these cases, there are 1,595,923 events relating to 42 activities performed by 627 users (607 human users and 20 batch users). Sometimes the user field is empty, or NONE, which indicates no user was recorded in the source system. For each purchase item (or case) the following attributes are recorded: concept:name: A combination of the purchase document id and the item id, Purchasing Document: The purchasing document ID, Item: The item ID, Item Type: The type of the item, GR-Based Inv. Verif.: Flag indicating if GR-based invoicing is required (see above), Goods Receipt: Flag indicating if 3-way matching is required (see above), Source: The source system of this item, Doc. Category name: The name of the category of the purchasing document, Company: The subsidiary of the company from where the purchase originated, Spend classification text: A text explaining the class of purchase item, Spend area text: A text explaining the area for the purchase item, Sub spend area text: Another text explaining the area for the purchase item, Vendor: The vendor to which the purchase document was sent, Name: The name of the vendor, Document Type: The document type, Item Category: The category as explained above (3-way with GR-based invoicing, 3-way without, 2-way, consignment).

The data contains the following entities and their events

- PO - Purchase Order documents handled at a large multinational company operating from The Netherlands
- POItem - an item in a Purchase Order document describing a specific item to be purchased
- Resource - the user or worker handling the document or a specific item
- Vendor - the external organization from which an item is to be purchased

Data Size
---------

BPIC19, nodes: 1926651, relationships: 15082099

The largest available cellular level connectivity map, of a 0.1 mm sample of the mouse retina Inner Plexiform Layer, was analysed using network models and visualized using spectral graph layouts and observed cell coordinates. This allows key nodes in the network to be identified with retinal neurons. Their strongest synaptic links can trace pathways in the network, elucidating possible circuits. Modular decomposition of the network, by sampling signal flows over nodes and links using the InfoMap method, shows discrete modules of cone bipolar cells that form a tiled mosaic in the retinal plane. The highest flow nodes, calculated by InfoMap, proved to be the most useful landmarks for elucidating possible circuits. Their dominant links to high flow amacrine cells reveal possible circuits linking bipolar through to ganglion cells and show an Off-On discrimination between the Left-Right sections of the sample. Circuits suggested by this analysis confirm known roles for some cells and point to roles for others.

Describing patterns of connectivity among organs is essential for identifying anatomical homologies among taxa. It is also critical for revealing morphogenetic processes and the associated constraints that control the morphological diversification of clades. This is particularly relevant for studies of organisms with skeletons made of discrete elements such as arthropods, vertebrates, and echinoderms. Nonetheless, relatively few studies devoted to morphological disparity have considered connectivity patterns as a level of morphological organization or developed comparative frameworks with proper tools. Here, we analyze connectivity patterns among apical plates in Atelostomata, the most diversified clade among irregular echinoids. The clade comprises approximately 1600 fossil and Recent species (e.g., 25% of post-Paleozoic species of echinoids) and shows high levels of morphological disparity. Plate connectivity patterns were analyzed using tools and statistics of graph theory. To describe and explore the diversity of connectivity patterns among plates, we symbolized each pattern as a graph in which plates are coded as nodes that are connected pairwise by edges. We then generated a comparative framework as a morphospace of connections, in which the disparity of plate patterns observed in nature was mapped and analyzed. Main results show that apical plate patterns are both highly disparate between and within atelostomate groups and limited in number; overall, they also constitute small, compact, and simple structures compared to possible random patterns. Main traits of the evolution of apical plate patterns reveal the existence of strong morphogenetic constraints that are phylogenetically determined. In contrast, evolutionary radiations within atelostomates were accompanied by a clear increase in disparity, suggesting a release of some constraints at the origin of clades.

Temporal exponential-family random graph models (TERGMs) are a flexible class of models for network ties that change over time. Separable TERGMs (STERGMs) are a subclass of TERGMs in which the dynamics of tie formation and dissolution can be separated within each discrete time step and may depend on different factors. The Carnegie et al. approximation improves estimation efficiency for a subclass of STERGMs, allowing them to be reliably estimated from inexpensive cross-sectional study designs. This approximation adapts to cross-sectional data by attempting to construct a STERGM with two specific properties: a cross-sectional equilibrium distribution defined by an exponential-family random graph model (ERGM) for the network structure, and geometric tie duration distributions defined by constant hazards for tie dissolution. In this article we focus on approaches for improving the behavior of the Carnegie et al. approximation and increasing its scope of application. We begin with Carnegie et al.’s observation that the exact result is tractable when the ERGM is dyad-independent, and then show that taking the sparse limit of the exact result leads to a different approximation than the one they presented. We show that the new approximation outperforms theirs for sparse, dyad-independent models, and observe that the errors tend to increase with the strength of dependence for dyad-dependent models. We then develop theoretical results in the dyad-dependent case, showing that when the ERGM is allowed to have arbitrary dyad-dependent terms and some dyad-dependent constraints, both the old and new approximations are asymptotically exact as the size of the STERGM time step goes to zero. We note that the continuous-time limit of the discrete-time approximations has the desired cross-sectional equilibrium distribution and exponential tie duration distributions with the desired means. We show that our results extend to hypergraphs, and we propose an extension of the Carnegie et al. framework to dissolution hazards that depend on tie age. Supplementary materials for this article are available online.

This statistic shows the inequality of income distribution in China from 2005 to 2023 based on the Gini Index. In 2023, China reached a score of ************ points. The Gini Index is a statistical measure that is used to represent unequal distributions, e.g. income distribution. It can take any value between 1 and 100 points (or 0 and 1). The closer the value is to 100 the greater is the inequality. 40 or 0.4 is the warning level set by the United Nations. The Gini Index for South Korea had ranged at about **** in 2022. Income distribution in China The Gini coefficient is used to measure the income inequality of a country. The United States, the World Bank, the US Central Intelligence Agency, and the Organization for Economic Co-operation and Development all provide their own measurement of the Gini coefficient, varying in data collection and survey methods. According to the United Nations Development Programme, countries with the largest income inequality based on the Gini index are mainly located in Africa and Latin America, with South Africa displaying the world's highest value in 2022. The world's most equal countries, on the contrary, are situated mostly in Europe. The United States' Gini for household income has increased by around ten percent since 1990, to **** in 2023. Development of inequality in China Growing inequality counts as one of the biggest social, economic, and political challenges to many countries, especially emerging markets. Over the last 20 years, China has become one of the world's largest economies. As parts of the society have become more and more affluent, the country's Gini coefficient has also grown sharply over the last decades. As shown by the graph at hand, China's Gini coefficient ranged at a level higher than the warning line for increasing risk of social unrest over the last decade. However, the situation has slightly improved since 2008, when the Gini coefficient had reached the highest value of recent times.

Overview

This is a synthetic volcano deformation dataset accompanying the publication of Graph Neural Network based elastic deformation emulators for magmatic reservoirs of complex geometries, on the journal Volcanica. Synthetic, quasi-static deformation is computed for magma chambers of various geometries, parameterized as spheroids or superpositions of spherical harmonics. Surface deformation is computed using the boundary element method (BEM) of Nikkhoo & Walter (2015). Please reference our paper for details of computational methods.

The dataset contains 50,000 realizations of magma chamber geometries/orientations/centroid depths and associated deformation fields. Surface deformation fields are sampled at discrete locations, with a uniform random distribution within [Lh x Lh], and a distribution that concentrates near the chamber (at radial distances, r = 10^(-3 random number) * Lh/2). Note this dataset contains only a small fraction of the total dataset. In total, 824,393 realizations of magma chambers were used to train our emulators. For accessing the complete training data set, please contact the authors.

Each .mat file contains the deformation field associated with a single chamber geometry. Use visData.m to visualize chamber geometry and associated surface displacement. Each file contains two MATLAB structures, "input" and "output".

Naming of each zip file

The numbers after the underscore, N:M, indicate that this file contains N of the M total chamber realizations for this particular setup.

sph_20AspRatios_1e4:151211.zip: deformation corresponding to spheroidal magma chambers parameterized by aspect ratios.

sh_complex_1e4:152283.zip: deformation corresponding to chamber geometry produced by superposition of spherical harmonic modes.

sh_mode_approx_1e4:138380.zip: deformation corresponding to chamber geometries corresponding to individual spherical harmonic modes, combined with a spherical mode (the spherical mode prevents chamber surfaces from having zero radii locally)

sh_spheroid_approx1e4:202272.zip: deformation corresponding to chambers approximating spheroids, but parameterized by spherical harmonics.

sh_spheroid_perturb_1e4:180247.zip: same as above, but with additional random perturbations parameterized in spherical harmonics.

Variables in each file

Input contains the following fields:

dp2mu: pressure change to shear modulus ratio.

dx, dy, dz: the coordinates of chamber centroid [meters]

mu: dimensionless crustal shear modulus (always set to 1)

nu: crustal Poisson's ratio (always set to 0.25)

Ns: number of points on the surface where displacements are computed

Lh, Lv: horizontal and vertical dimensions of the model domain [meters]. Lh is determined such that at the edge of the model domain, the displacement magnitude is below 10 percent of the maximum. Lv = Lh/2 + abs(dz)

for the spheroids -----------------------------------------------------------------------------------------------------------

the input files contain

asp: aspect ratio of chamber (length of the semi-major axis divided by that of the semi-minor axis)

ra, rb: semi-major, -minor, axis length [meters]

thetax, thetay, thetaz: counterclockwise rotation angles with regard to x, y, z axis [degrees]. thetax = [0, 90] degrees, thetay = 0 degrees, thetaz = 360 degrees.

for the general geometries--------------------------------------------------------------------------------------------------

the input files contain

ls, ms, fs: degree, order, coefficients of spherical harmonic modes. Spherical harmonics are sampled up to degree 5. fs is a complex vector of coefficients such that the resulting shape is real.

normF: normalization factor applied to the shape parameterized by ls, ms, fs, such that the shape as a maximum radius of unity.

rmax: scale factor to scale the spherical harmonics parameterized shape to real dimensions [meters].

=============================================================================================

Output contains the following fields,

X, Y, Z: coordinates of points where displacement vectors are computed [meters]

Ux, Uy, Uz: displacements in x, y, z directions [meters]

P, T: coordinates [meters] of vertices for the triangular mesh used in BEM calculation, and the connectivity matrix

C: coordinates [meters] of the center of each triangular element

that, dhat, nhat: unit vectors for orthogonal coordinate systems local to each triangular element. that ("t-hat") extends from vertex one to vertex two, nhat is outward normal, and dhat = cross (nhat, that).

Reference:

1. Nikkhoo, M., & Walter, T. R. (2015). Triangular dislocation: an analytical, artefact-free solution. Geophysical Journal International, 201(2), 1119-1141.

We show that ordering vertices of a graph subject to some objective function is a difficult task.

Debt-To-Assets-Ratio Time Series for Alpha and Omega Semiconductor Ltd. Alpha and Omega Semiconductor Limited designs, develops, and supplies power semiconductor products for computing, consumer electronics, communication, and industrial applications in Hong Kong, China, South Korea, the United States, and internationally. It offers power discrete products, including metal-oxide-semiconductor field-effect transistors (MOSFET), SRFETs, XSFET, electrostatic discharge, protected MOSFETs, high and mid-voltage MOSFETs, and insulated gate bipolar transistors for use in smart phone chargers, battery packs, notebooks, desktop and servers, data centers, base stations, graphics card, game boxes, TVs, AC adapters, power supplies, motor control, power tools, E-vehicles, white goods and industrial motor drives, UPS systems, solar inverters, and industrial welding. The company also provides power ICs that deliver power, as well as control and regulate the power management variables, such as the flow of current and level of voltage. Its power ICs are used in flat panel displays, TVs, notebooks, graphic cards, servers, DVD/Blu-Ray players, set-top boxes, and networking equipment. In addition, the company offers transient voltage protection products, analog switches, and electromagnetic interference filters for notebooks, desktop PCs, tablets, flat panel displays, TVs, smart phones, and portable electronic devices. Alpha and Omega Semiconductor Limited was incorporated in 2000 and is headquartered in Sunnyvale, California.

IntroductionMarkov chains are a powerful tool for modeling systems in various scientific domains, including queueing theory. These models are characterized by their ability to maintain complexity at a low level due to a property known as the Markov property, which enables the connection between states and transition probabilities. The transition matrices of Markov chains are represented by graphs, which show the properties and characteristics that help analyze the underlying processes.MethodThe graph representing the transition matrix of a Markov chain is formed from the transition state diagram, with weights representing the mean transition rates. A probability space is thus created, containing all the spanning trees of the graph that end up in the states of the Markov chain (anti-arborescences). A successive examination of the graph’s vertices is initiated to form monomials as products of the weights of the edges forming the symbolic solution.ResultsA general algorithm that commences with the Markov chain transition matrix as an input element and forms the state transition diagram. Subsequently, each vertex within the graph is examined, followed by a rearrangement of the vertices according to a depth-first search strategy. In the context of an inverted graph, implementing a suitable algorithm for forming spanning trees, such as the Gabow and Myers algorithm, is imperative. This algorithm is applied sequentially, resulting in the formation of monomials, polynomials for each vertex, and, ultimately, the set of polynomials of the graph. Utilizing these polynomials facilitates the calculation of the stationary probabilities of the Markov chain and the performance metrics.DiscussionThe proposed method provides a positive response to the inquiry regarding the feasibility of expressing the performance metrics of a system modeled by a Markov chain through closed-form equations. The study further posits that these specific equations are of considerable magnitude. The intricacy of their formulation enables their implementation in smaller systems, which can serve as building blocks for other methodologies. The correlation between Markov chains and graphs has the potential to catalyze novel research directions in both discrete mathematics and artificial intelligence.

This is the data used in the experiment of the paper published in the following conference:Arinik, N. & Figueiredo, R., & Labatut, V. (2020). Multiple partitioning of multiplex signed networks: Application to European parliament votes. Social Networks, 60, 83-102.URL https://doi.org/10.1016/j.socnet.2019.02.001The code source is accessible here: https://github.com/CompNet/MultiNetVotesFor more than a decade, graphs have been used to model the voting behavior taking place in parliaments. However, the methods described in the literature suffer from several limitations. The two main ones are that 1) they rely on some temporal integration of the raw data, which causes some information loss; and/or 2) they identify groups of antagonistic voters, but not the context associated with their occurrence. In this article, we propose a novel method taking advantage of multiplex signed graphs to solve both these issues. It consists in first partitioning separately each layer, before grouping these partitions by similarity. We show the interest of our approach by applying it to a European Parliament dataset. Particularly, we study the voting behavior of French and Italian MEPs on "Agriculture and Rural Development" (AGRI) during the 2012-13 legislative year.# RAW INPUT FILESThe 'itsyourparliament' folder contains all raw input files for further data processing. This is the same raw data that can be found in our previous Figshare repository: https://doi.org/10.6084/m9.figshare.5785833The folder structure is as follows:* itsyourparliament/** domains: There are 28 domain files. Each file corresponds to a domain (such as Agriculture, Economy, etc.) and contains corresponding vote identifiers and their "itsyourparliament.eu" links.** meps: There 870 Members of Parliament (MEP) files. Each file contains the MEP information (such as name, country, address, etc.)** votes: There are 7513 vote files. Each file contains the votes expressed by MEPs# ROLLCALL NETWORKSThis folder contains two separate zip files regarding rollcall networks:- rollcall-networks: This folder contains only the rollcall networks that are used in the article. - all-rollcall-networks: For those who are interested in other countries or domains, we make available all rollcall networks that we can extract from raw data.Note that these rollcall networks constitute the layers of the input signed multplex network, as illustrated in Figure 1 of the article. Note also that we consider three vote types in our network extraction process: FOR, AGAINST and ABSTAIN.# ROLLCALL PARTITIONSNote that MEPs who voted similarly are connected together by positive links, and are connected by negative links to MEPs that voted differently from them. MEPs who did not vote at all (ABSENT) are isolates (nodes without anyneighbor). We identify the factions of similarly voting MEPs in the graph by solving the Correlation Clustering problem (CC).The rollcall partitions correspond to voting patterns, as illustrated in Figure 1 of the article.# ROLLCALL CLUSTERINGThis folder contains the results of Steps 3 and 4 of our workflow (see Figure 1 in the article). The structure of this folder is as follows:|_ votetypes=FAA/: 'FAA' means we consider three vote types in our analysis: FOR, AGAINST and ABSTAIN. |_ F.purity-k=2-sil=SILHOUETTE_SCORE |_ clu=CLUSTER_NO/ |_ network: It corresponds to the network created through the similarity network-based approach, as explained in Section 4.4 of the article. |_ partition: It corresponds to the characteristic voting pattern, as explained in Section 4.4 of the article.

Public transportation like trains, buses, and light-rail vehicles can transport more people than commuter cars while taking up minimal space on roadways. While public transportation systems are highly effective in areas with high population density in the United States, they are definitively underused. In order to increase the number of people using public transportation, public transportation must improve. One of the most common and cost-effective methods of public transit is the city bus. The time a bus takes to complete its route is heavily dependent on the amount of traffic in a given area and road signals. Researchers have applied optimization techniques to bus routes where most of these algorithms have focused on either graph based methods or genetic algorithms, since a bus route is discrete problem. We have developed two models. The first is a continuous model of a city block, which allows us to apply gradient-based methods of optimization to the bus route problem. The second being a discrete graph like the ones performed previously to compare results. This paper reports on how continuous and discrete models can find an optimal route that changes when different traffic conditions are present. The model is presented and shown to work in naive cases, through standard Manhattan square blocks. The results are shown to find the optimal path for a city bus traveling between two points within a city grid and a full path.

The current model for Okazaki fragment maturation in bacteria invokes RNA cleavage by RNase H, followed by strand displacement synthesis and 5′ RNA flap removal by DNA polymerase I (Pol I). RNA removal by Pol I is thought to occur through the 5′-3′ flap endo/exonuclease (FEN) domain, located in the N-terminus of the protein. In addition to Pol I, many bacteria encode a second, Pol I-independent FEN. The contribution of Pol I and Pol I-independent FENs to DNA replication and genome stability remains unclear. In this work we purified Bacillus subtilis Pol I and FEN, then assayed these proteins on a variety of RNA-DNA hybrid and DNA-only substrates. We found that FEN is far more active than Pol I on nicked double-flap, 5′ single flap, and nicked RNA-DNA hybrid substrates. We show that the 5′ nuclease activity of B. subtilis Pol I is feeble, even during DNA synthesis when a 5′ flapped substrate is formed modeling an Okazaki fragment intermediate. Examination of Pol I and FEN on DNA-only substrates shows that FEN is more active than Pol I on most substrates tested. Further experiments show that ΔpolA phenotypes are completely rescued by expressing the C-terminal polymerase domain while expression of the N-terminal 5′ nuclease domain fails to complement ΔpolA. Cells lacking FEN (ΔfenA) show a phenotype in conjunction with an RNase HIII defect, providing genetic evidence for the involvement of FEN in Okazaki fragment processing. With these results, we propose a model where cells remove RNA primers using FEN while upstream Okazaki fragments are extended through synthesis by Pol I. Our model resembles Okazaki fragment processing in eukaryotes, where Pol δ catalyzes strand displacement synthesis followed by 5′ flap cleavage using FEN-1. Together our work highlights the conservation of ordered steps for Okazaki fragment processing in cells ranging from bacteria to human.

For each of the six queries we show: (1) its pattern type and CTL formula, (2) its translation into English, (3) ☑ the scenario selection (i.e. control valuations) for which the associated model-checking output of the query is yes, (4) an English interpretation of this scenario selection.