Honey flows through fertile valleys : The cognitive and evolutionary foundations of paradise representations

The aim of the study is to explain how paradise beliefs are born from the viewpoint of mental functions of the human mind. The focus is on the observation that paradise beliefs across the world are mutually more similar than dissimilar. By using recent theories and results from the cognitive and evolutionary study of religion as well as from studies of environmental preferences, I suggest that this is because pan-human unconscious motivations, the architecture of mind, and the way the human mind processes information constrain the possible repertoire of paradise beliefs. The study is divided into two parts, theoretical and empirical. The arguments in the theoretical part are tested with data in the empirical part with two data sets. The first data set was collected using an Internet survey. The second data set was derived from literary sources. The first data test the assumption that intuitive conceptions of an environment of dreams generally follow the outlines set by evolved environmental preferences, but that they can be tweaked by modifying the presence of desirable elements. The second data test the assumption that familiarity is a dominant factor determining the content of paradise beliefs. The results of the study show that in addition to the widely studied belief in supernatural agents, belief in supernatural environments wells from the natural functioning of the human mind attesting the view that religious thinking and ideas are natural for human species and are produced by the same mental mechanisms as other cultural information. The results also help us to understand that the mental structures behind the belief in the supernatural have a wider scope than has been previously acknowledged.

Language change as an evolutionary process

In the thesis it is discussed in what ways concepts and methodology developed in evolutionary biology can be applied to the explanation and research of language change. The parallel nature of the mechanisms of biological evolution and language change is explored along with the history of the exchange of ideas between these two disciplines. Against this background computational methods developed in evolutionary biology are taken into consideration in terms of their applicability to the study of historical relationships between languages. Different phylogenetic methods are explained in common terminology, avoiding the technical language of statistics. The thesis is on one hand a synthesis of earlier scientific discussion, and on the other an attempt to map out the problems of earlier approaches in addition to finding new guidelines in the study of language change on their basis. Primarily literature about the connections between evolutionary biology and language change, along with research articles describing applications of phylogenetic methods into language change have been used as source material. The thesis starts out by describing the initial development of the disciplines of evolutionary biology and historical linguistics, a process which right from the beginning can be seen to have involved an exchange of ideas concerning the mechanisms of language change and biological evolution. The historical discussion lays the foundation for the handling of the generalised account of selection developed during the recent few decades. This account is aimed for creating a theoretical framework capable of explaining both biological evolution and cultural change as selection processes acting on self-replicating entities. This thesis focusses on the capacity of the generalised account of selection to describe language change as a process of this kind. In biology, the mechanisms of evolution are seen to form populations of genetically related organisms through time. One of the central questions explored in this thesis is whether selection theory makes it possible to picture languages are forming populations of a similar kind, and what a perspective like this can offer to the understanding of language in general. In historical linguistics, the comparative method and other, complementing methods have been traditionally used to study the development of languages from a common ancestral language. Computational, quantitative methods have not become widely used as part of the central methodology of historical linguistics. After the fading of a limited popularity enjoyed by the lexicostatistical method since the 1950s, only in the recent years have also the computational methods of phylogenetic inference used in evolutionary biology been applied to the study of early language history. In this thesis the possibilities offered by the traditional methodology of historical linguistics and the new phylogenetic methods are compared. The methods are approached through the ways in which they have been applied to the Indo-European languages, which is the most thoroughly investigated language family using both the traditional and the phylogenetic methods. The problems of these applications along with the optimal form of the linguistic data used in these methods are explored in the thesis. The mechanisms of biological evolution are seen in the thesis as parallel in a limited sense to the mechanisms of language change, however sufficiently so that the development of a generalised account of selection is deemed as possibly fruiful for understanding language change. These similarities are also seen to support the validity of using phylogenetic methods in the study of language history, although the use of linguistic data and the models of language change employed by these models are seen to await further development.

Automatic Lameness Detection in a Milking Robot : Instrumentation, measurement software, algorithms for data analysis and a neural network model

The aim of this thesis is to develop a fully automatic lameness detection system that operates in a milking robot. The instrumentation, measurement software, algorithms for data analysis and a neural network model for lameness detection were developed. Automatic milking has become a common practice in dairy husbandry, and in the year 2006 about 4000 farms worldwide used over 6000 milking robots. There is a worldwide movement with the objective of fully automating every process from feeding to milking. Increase in automation is a consequence of increasing farm sizes, the demand for more efficient production and the growth of labour costs. As the level of automation increases, the time that the cattle keeper uses for monitoring animals often decreases. This has created a need for systems for automatically monitoring the health of farm animals. The popularity of milking robots also offers a new and unique possibility to monitor animals in a single confined space up to four times daily. Lameness is a crucial welfare issue in the modern dairy industry. Limb disorders cause serious welfare, health and economic problems especially in loose housing of cattle. Lameness causes losses in milk production and leads to early culling of animals. These costs could be reduced with early identification and treatment. At present, only a few methods for automatically detecting lameness have been developed, and the most common methods used for lameness detection and assessment are various visual locomotion scoring systems. The problem with locomotion scoring is that it needs experience to be conducted properly, it is labour intensive as an on-farm method and the results are subjective. A four balance system for measuring the leg load distribution of dairy cows during milking in order to detect lameness was developed and set up in the University of Helsinki Research farm Suitia. The leg weights of 73 cows were successfully recorded during almost 10,000 robotic milkings over a period of 5 months. The cows were locomotion scored weekly, and the lame cows were inspected clinically for hoof lesions. Unsuccessful measurements, caused by cows standing outside the balances, were removed from the data with a special algorithm, and the mean leg loads and the number of kicks during milking was calculated. In order to develop an expert system to automatically detect lameness cases, a model was needed. A probabilistic neural network (PNN) classifier model was chosen for the task. The data was divided in two parts and 5,074 measurements from 37 cows were used to train the model. The operation of the model was evaluated for its ability to detect lameness in the validating dataset, which had 4,868 measurements from 36 cows. The model was able to classify 96% of the measurements correctly as sound or lame cows, and 100% of the lameness cases in the validation data were identified. The number of measurements causing false alarms was 1.1%. The developed model has the potential to be used for on-farm decision support and can be used in a real-time lameness monitoring system.

The Significance of Wild Plants in the Evolutionary Ecology of Three Major Viruses Infecting Cultivated Sweetpotato in Uganda

The studies presented in this thesis contribute to the understanding of evolutionary ecology of three major viruses threatening cultivated sweetpotato (Ipomoea batatas Lam) in East Africa: Sweet potato feathery mottle virus (SPFMV; genus Potyvirus; Potyviridae), Sweet potato chlorotic stunt virus (SPCSV; genus Crinivirus; Closteroviridae) and Sweet potato mild mottle virus (SPMMV; genus Ipomovirus; Potyviridae). The viruses were serologically detected and the positive results confirmed by RT-PCR and sequencing. SPFMV was detected in 24 wild plant species of family Convolvulacea (genera Ipomoea, Lepistemon and Hewittia), of which 19 species were new natural hosts for SPFMV. SPMMV and SPCSV were detected in wild plants belonging to 21 and 12 species (genera Ipomoea, Lepistemon and Hewittia), respectively, all of which were previously unknown to be natural hosts of these viruses. SPFMV was the most abundant virus being detected in 17% of the plants, while SPMMV and SPCSV were detected in 9.8% and 5.4% of the assessed plants, respectively. Wild plants in Uganda were infected with the East African (EA), common (C), and the ordinary (O) strains, or co-infected with the EA and the C strain of SPFMV. The viruses and virus-like diseases were more frequent in the eastern agro-ecological zone than the western and central zones, which contrasted with known incidences of these viruses in sweetpotato crops, except for northern zone where incidences were lowest in wild plants as in sweetpotato. The NIb/CP junction in SPMMV was determined experimentally which facilitated CP-based phylogenetic and evolutionary analyses of SPMMV. Isolates of all the three viruses from wild plants were genetically similar to those found in cultivated sweetpotatoes in East Africa. There was no evidence of host-driven population genetic structures suggesting frequent transmission of these viruses between their wild and cultivated hosts. The p22 RNA silencing suppressor-encoding sequence was absent in a few SPCSV isolates, but regardless of this, SPCSV isolates incited sweet potato virus disease (SPVD) in sweetpotato plants co-infected with SPFMV, indicating that p22 is redundant for synergism between SCSV and SPFMV. Molecular evolutionary analysis revealed that isolates of strain EA of SPFMV that is largely restricted geographically in East Africa experience frequent recombination in comparison to isolates of strain C that is globally distributed. Moreover, non-homologous recombination events between strains EA and C were rare, despite frequent co-infections of these strains in wild plants, suggesting purifying selection against non-homologous recombinants between these strains or that such recombinants are mostly not infectious. Recombination was detected also in the 5 - and 3 -proximal regions of the SPMMV genome providing the first evidence of recombination in genus Ipomovirus, but no recombination events were detected in the characterized genomic regions of SPCSV. Strong purifying selection was implicated on evolution of majority of amino acids of the proteins encoded by the analyzed genomic regions of SPFMV, SPMMV and SPCSV. However, positive selection was predicted on 17 amino acids distributed over the whole the coat protein (CP) in the globally distributed strain C, as compared to only 4 amino acids in the multifunctional CP N-terminus (CP-NT) of strain EA largely restricted geographically to East Africa. A few amino acid sites in the N-terminus of SPMMV P1, the p7 protein and RNA silencing suppressor proteins p22 and RNase3 of SPCSV were also submitted to positive selection. Positively selected amino acids may constitute ligand-binding domains that determine interactions with plant host and/or insect vector factors. The P1 proteinase of SPMMV (genus Ipomovirus) seems to respond to needs of adaptation, which was not observed with the helper component proteinase (HC-Pro) of SPMMV, although the HC-Pro is responsible for many important molecular interactions in genus Potyvirus. Because the centre of origin of cultivated sweetpotato is in the Americas from where the crop was dispersed to other continents in recent history (except for the Australasia and South Pacific region), it would be expected that identical viruses and their strains occur worldwide, presuming virus dispersal with the host. Apparently, this seems not to be the case with SPMMV, the strain EA of SPFMV and the strain EA of SPCSV that are largely geographically confined in East Africa where they are predominant and occur both in natural and agro-ecosystems. The geographical distribution of plant viruses is constrained more by virus-vector relations than by virus-host interactions, which in accordance of the wide range of natural host species and the geographical confinement to East Africa suggest that these viruses existed in East African wild plants before the introduction of sweetpotato. Subsequently, these studies provide compelling evidence that East Africa constitutes a cradle of SPFMV strain EA, SPCSV strain EA, and SPMMV. Therefore, sweet potato virus disease (SPVD) in East Africa may be one of the examples of damaging virus diseases resulting from exchange of viruses between introduced crops and indigenous wild plant species. Keywords: Convolvulaceae, East Africa, epidemiology, evolution, genetic variability, Ipomoea, recombination, SPCSV, SPFMV, SPMMV, selection pressure, sweetpotato, wild plant species Author s Address: Arthur K. Tugume, Department of Agricultural Sciences, Faculty of Agriculture and Forestry, University of Helsinki, Latokartanonkaari 7, P.O Box 27, FIN-00014, Helsinki, Finland. Email: tugume.arthur@helsinki.fi Author s Present Address: Arthur K. Tugume, Department of Botany, Faculty of Science, Makerere University, P.O. Box 7062, Kampala, Uganda. Email: aktugume@botany.mak.ac.ug, tugumeka@yahoo.com

Discovering hidden structures in molecular data using a Bayesian partition model approach

Advancements in the analysis techniques have led to a rapid accumulation of biological data in databases. Such data often are in the form of sequences of observations, examples including DNA sequences and amino acid sequences of proteins. The scale and quality of the data give promises of answering various biologically relevant questions in more detail than what has been possible before. For example, one may wish to identify areas in an amino acid sequence, which are important for the function of the corresponding protein, or investigate how characteristics on the level of DNA sequence affect the adaptation of a bacterial species to its environment. Many of the interesting questions are intimately associated with the understanding of the evolutionary relationships among the items under consideration. The aim of this work is to develop novel statistical models and computational techniques to meet with the challenge of deriving meaning from the increasing amounts of data. Our main concern is on modeling the evolutionary relationships based on the observed molecular data. We operate within a Bayesian statistical framework, which allows a probabilistic quantification of the uncertainties related to a particular solution. As the basis of our modeling approach we utilize a partition model, which is used to describe the structure of data by appropriately dividing the data items into clusters of related items. Generalizations and modifications of the partition model are developed and applied to various problems. Large-scale data sets provide also a computational challenge. The models used to describe the data must be realistic enough to capture the essential features of the current modeling task but, at the same time, simple enough to make it possible to carry out the inference in practice. The partition model fulfills these two requirements. The problem-specific features can be taken into account by modifying the prior probability distributions of the model parameters. The computational efficiency stems from the ability to integrate out the parameters of the partition model analytically, which enables the use of efficient stochastic search algorithms.

Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

Cross-layer Assisted TCP Algorithms for Vertical Handoff

The ever expanding growth of the wireless access to the Internet in recent years has led to the proliferation of wireless and mobile devices to connect to the Internet. This has created the possibility of mobile devices equipped with multiple radio interfaces to connect to the Internet using any of several wireless access network technologies such as GPRS, WLAN and WiMAX in order to get the connectivity best suited for the application. These access networks are highly heterogeneous and they vary widely in their characteristics such as bandwidth, propagation delay and geographical coverage. The mechanism by which a mobile device switches between these access networks during an ongoing connection is referred to as vertical handoff and it often results in an abrupt and significant change in the access link characteristics. The most common Internet applications such as Web browsing and e-mail make use of the Transmission Control Protocol (TCP) as their transport protocol and the behaviour of TCP depends on the end-to-end path characteristics such as bandwidth and round-trip time (RTT). As the wireless access link is most likely the bottleneck of a TCP end-to-end path, the abrupt changes in the link characteristics due to a vertical handoff may affect TCP behaviour adversely degrading the performance of the application. The focus of this thesis is to study the effect of a vertical handoff on TCP behaviour and to propose algorithms that improve the handoff behaviour of TCP using cross-layer information about the changes in the access link characteristics. We begin this study by identifying the various problems of TCP due to a vertical handoff based on extensive simulation experiments. We use this study as a basis to develop cross-layer assisted TCP algorithms in handoff scenarios involving GPRS and WLAN access networks. We then extend the scope of the study by developing cross-layer assisted TCP algorithms in a broader context applicable to a wide range of bandwidth and delay changes during a handoff. And finally, the algorithms developed here are shown to be easily extendable to the multiple-TCP flow scenario. We evaluate the proposed algorithms by comparison with standard TCP (TCP SACK) and show that the proposed algorithms are effective in improving TCP behavior in vertical handoff involving a wide range of bandwidth and delay of the access networks. Our algorithms are easy to implement in real systems and they involve modifications to the TCP sender algorithm only. The proposed algorithms are conservative in nature and they do not adversely affect the performance of TCP in the absence of cross-layer information.

Problems and Algorithms for Sequence Segmentations

The analysis of sequential data is required in many diverse areas such as telecommunications, stock market analysis, and bioinformatics. A basic problem related to the analysis of sequential data is the sequence segmentation problem. A sequence segmentation is a partition of the sequence into a number of non-overlapping segments that cover all data points, such that each segment is as homogeneous as possible. This problem can be solved optimally using a standard dynamic programming algorithm. In the first part of the thesis, we present a new approximation algorithm for the sequence segmentation problem. This algorithm has smaller running time than the optimal dynamic programming algorithm, while it has bounded approximation ratio. The basic idea is to divide the input sequence into subsequences, solve the problem optimally in each subsequence, and then appropriately combine the solutions to the subproblems into one final solution. In the second part of the thesis, we study alternative segmentation models that are devised to better fit the data. More specifically, we focus on clustered segmentations and segmentations with rearrangements. While in the standard segmentation of a multidimensional sequence all dimensions share the same segment boundaries, in a clustered segmentation the multidimensional sequence is segmented in such a way that dimensions are allowed to form clusters. Each cluster of dimensions is then segmented separately. We formally define the problem of clustered segmentations and we experimentally show that segmenting sequences using this segmentation model, leads to solutions with smaller error for the same model cost. Segmentation with rearrangements is a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even to approximate. We devise effective algorithms for the proposed problem, combining ideas from dynamic programming and outlier detection algorithms in sequences. In the final part of the thesis, we discuss the problem of aggregating results of segmentation algorithms on the same set of data points. In this case, we are interested in producing a partitioning of the data that agrees as much as possible with the input partitions. We show that this problem can be solved optimally in polynomial time using dynamic programming. Furthermore, we show that not all data points are candidates for segment boundaries in the optimal solution.

Matrix Decomposition Methods for Data Mining : Computational Complexity and Algorithms

Matrix decompositions, where a given matrix is represented as a product of two other matrices, are regularly used in data mining. Most matrix decompositions have their roots in linear algebra, but the needs of data mining are not always those of linear algebra. In data mining one needs to have results that are interpretable -- and what is considered interpretable in data mining can be very different to what is considered interpretable in linear algebra. --- The purpose of this thesis is to study matrix decompositions that directly address the issue of interpretability. An example is a decomposition of binary matrices where the factor matrices are assumed to be binary and the matrix multiplication is Boolean. The restriction to binary factor matrices increases interpretability -- factor matrices are of the same type as the original matrix -- and allows the use of Boolean matrix multiplication, which is often more intuitive than normal matrix multiplication with binary matrices. Also several other decomposition methods are described, and the computational complexity of computing them is studied together with the hardness of approximating the related optimization problems. Based on these studies, algorithms for constructing the decompositions are proposed. Constructing the decompositions turns out to be computationally hard, and the proposed algorithms are mostly based on various heuristics. Nevertheless, the algorithms are shown to be capable of finding good results in empirical experiments conducted with both synthetic and real-world data.

Algorithms for 13C metabolic flux analysis

The metabolism of an organism consists of a network of biochemical reactions that transform small molecules, or metabolites, into others in order to produce energy and building blocks for essential macromolecules. The goal of metabolic flux analysis is to uncover the rates, or the fluxes, of those biochemical reactions. In a steady state, the sum of the fluxes that produce an internal metabolite is equal to the sum of the fluxes that consume the same molecule. Thus the steady state imposes linear balance constraints to the fluxes. In general, the balance constraints imposed by the steady state are not sufficient to uncover all the fluxes of a metabolic network. The fluxes through cycles and alternative pathways between the same source and target metabolites remain unknown. More information about the fluxes can be obtained from isotopic labelling experiments, where a cell population is fed with labelled nutrients, such as glucose that contains 13C atoms. Labels are then transferred by biochemical reactions to other metabolites. The relative abundances of different labelling patterns in internal metabolites depend on the fluxes of pathways producing them. Thus, the relative abundances of different labelling patterns contain information about the fluxes that cannot be uncovered from the balance constraints derived from the steady state. The field of research that estimates the fluxes utilizing the measured constraints to the relative abundances of different labelling patterns induced by 13C labelled nutrients is called 13C metabolic flux analysis. There exist two approaches of 13C metabolic flux analysis. In the optimization approach, a non-linear optimization task, where candidate fluxes are iteratively generated until they fit to the measured abundances of different labelling patterns, is constructed. In the direct approach, linear balance constraints given by the steady state are augmented with linear constraints derived from the abundances of different labelling patterns of metabolites. Thus, mathematically involved non-linear optimization methods that can get stuck to the local optima can be avoided. On the other hand, the direct approach may require more measurement data than the optimization approach to obtain the same flux information. Furthermore, the optimization framework can easily be applied regardless of the labelling measurement technology and with all network topologies. In this thesis we present a formal computational framework for direct 13C metabolic flux analysis. The aim of our study is to construct as many linear constraints to the fluxes from the 13C labelling measurements using only computational methods that avoid non-linear techniques and are independent from the type of measurement data, the labelling of external nutrients and the topology of the metabolic network. The presented framework is the first representative of the direct approach for 13C metabolic flux analysis that is free from restricting assumptions made about these parameters.In our framework, measurement data is first propagated from the measured metabolites to other metabolites. The propagation is facilitated by the flow analysis of metabolite fragments in the network. Then new linear constraints to the fluxes are derived from the propagated data by applying the techniques of linear algebra.Based on the results of the fragment flow analysis, we also present an experiment planning method that selects sets of metabolites whose relative abundances of different labelling patterns are most useful for 13C metabolic flux analysis. Furthermore, we give computational tools to process raw 13C labelling data produced by tandem mass spectrometry to a form suitable for 13C metabolic flux analysis.

Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.