Mathematical Graph Research Articles

Planform: an application and database of graph-encoded planarian regenerative experiments

Understanding the mechanisms governing the regeneration capabilities of many organisms is a fundamental interest in biology and medicine. An ever-increasing number of manipulation and molecular experiments are attempting to discover a comprehensive model for regeneration, with the planarian flatworm being one of the most important model species. Despite much effort, no comprehensive, constructive, mechanistic models exist yet, and it is now clear that computational tools are needed to mine this huge dataset. However, until now, there is no database of regenerative experiments, and the current genotype-phenotype ontologies and databases are based on textual descriptions, which are not understandable by computers. To overcome these difficulties, we present here Planform (Planarian formalization), a manually curated database and software tool for planarian regenerative experiments, based on a mathematical graph formalism. The database contains more than a thousand experiments from the main publications in the planarian literature. The software tool provides the user with a graphical interface to easily interact with and mine the database. The presented system is a valuable resource for the regeneration community and, more importantly, will pave the way for the application of novel artificial intelligence tools to extract knowledge from this dataset. The database and software tool are freely available at http://planform.daniel-lobo.com.

Graph and heuristic based topology optimization of crash loaded structures

For the efficient development of new structural concepts, it is necessary to perform an optimization of the mechanical properties of profile cross-sections taking into account all relevant load cases. Especially for crash load cases, there currently exists no established method for the conceptual design and topology optimization. The main problems are the complicated deformation conditions in the crash, the huge number of design variables, the existence of simulative and physical bifurcation points and the costly determination of sensitivity information. For the application area of developing profile cross-sections, the method presented in this paper attempts to overcome these shortfalls. It has been developed for the combined topology, shape and sizing optimization taking into account all relevant crash load cases. For this a flexible description of the structure's profile cross-section via mathematical graphs is used. Modifications of the structure's topology are performed with heuristics (rules), which are based on expert knowledge, whereas the automatically generated shape und sizing parameters of the structure are optimized with mathematic optimization algorithms.

Modeling spatial decisions with graph theory: logging roads and forest fragmentation in the Brazilian Amazon

This article addresses the spatial decision-making of loggers and implications for forest fragmentation in the Amazon basin. It provides a behavioral explanation for fragmentation by modeling how loggers build road networks, typically abandoned upon removal of hardwoods. Logging road networks provide access to land, and the settlers who take advantage of them clear fields and pastures that accentuate their spatial signatures. In shaping agricultural activities, these networks organize emergent patterns of forest fragmentation, even though the loggers move elsewhere. The goal of the article is to explicate how loggers shape their road networks, in order to theoretically explain an important type of forest fragmentation found in the Amazon basin, particularly in Brazil. This is accomplished by adapting graph theory to represent the spatial decision-making of loggers, and by implementing computational algorithms that build graphs interpretable as logging road networks. The economic behavior of loggers is conceptualized as a profit maximization problem, and translated into spatial decision-making by establishing a formal correspondence between mathematical graphs and road networks. New computational approaches, adapted from operations research, are used to construct graphs and simulate spatial decision-making as a function of discount rates, land tenure, and topographic constraints. The algorithms employed bracket a range of behavioral settings appropriate for areas of terras de volutas, public lands that have not been set aside for environmental protection, indigenous peoples, or colonization. The simulation target sites are located in or near so-called Terra do Meio, once a major logging frontier in the lower Amazon Basin. Simulation networks are compared to empirical ones identified by remote sensing and then used to draw inferences about factors influencing the spatial behavior of loggers. Results overall suggest that Amazonia's logging road networks induce more fragmentation than necessary to access fixed quantities of wood. The paper concludes by considering implications of the approach and findings for Brazil's move to a system of concession logging.

Peaked and Smooth Solitons forK*(4,1)Equation

This paper is contributed to explore all possible single peak solutions for theK*(4,1)equationut=uxu2+2α(uuxxx+2uxuxx). Our procedure shows that theK*(4,1)equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestallimξ→±∞u=A≠0or possesses compacton solutions only whenlimξ→±∞u=A=0. We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of theK*(4,1)equation.

Behavioural Modelling of Lips Seal Made with Polytetrafluoroethylene Enriched by Glass Fibers

Polytetrafluoroethylene reinforced with glass fibers is a composite material widely used in industry mainly for the manufacture of seals at the level of the rotary shafts of vehicles and stationary floor machines such as turbines and compressors. However, due to elastic and viscous-plastic properties of this material, it wears quickly under the influence of some external parameters during operation. There are therefore material loss, increased clearance and loss of sealing. This work summarises a series of tests carried out with this material in order to analyse the variation of the friction coefficient due to the roughness of the work piece brought into contact with the PTFE, the linear velocity of contact between them and material yield strength. To do this analysis, we used the method of unconventional design of experiments to model the behaviour of material and consequently make decisions to reduce this wear. The results are shown and deeply analysed in the following text as a polynomial mathematical model, graphs, contours and response surfaces illustrating the holding of this material under the effect of the three parameters mentioned above. The previous PTFE samples enriched with chopped glass fibers are not subjected to axially force this time, contrary to the force applied radially. The advantage of this method is the relative linear velocity at the contact sample-disc and the applied pressure remains constant. Under the action of the weight “P” applied on the sample, it comes into friction with the rotating disc whose roughness changes from experience to another; it is expressed by the values of Ra. Tangential friction force appears at the point of contact and is equilibrated by measured force Fm on the lever. The calculation of the moment relative bench axis caused by 2 forces gives the coefficient of friction. Knowing the values of frictional force Ft by calculation and the weight P, we determine then the friction coefficient.

Kinesthetic Learning Applied to Mathematics Using Kinect

Mathematics is one of the main courses in education, learning the basics of this area is essential for any student. But along time Teachers have found several factors that takes the pupil attention away. Here is where Kinesthetic Learning have proven to be a determinant factor on learning this courses, with the inclusion of mechanical, and virtual devices is possible to extend the pupil knowledge, minimize distraction and gain focus on difficult topics and practices. In the past years, technology have become an important part of the educational system in many countries, in most cases the school or university requires the student to bring a laptop or mobile device to school, but in most cases this devices becomes the main distraction. The purpose of this research is to demonstrate that kinesthetic learning offer a new experience in education, allowing better understanding of mathematical concepts, graphs and formulas and allow the student to take action in the learning process. Trying to find a viable way to implement the kinesthetic learning, several test where held containing elements of augmented reality, the results of this demonstrate that AR provides a huge boost on the learning curve but is limited by the “marker” and the amount of movement, here is where Kinect comes in. With this capacity the Kinect makes a perfect hardware piece for Kinesthetic learning, now the main objective is to develop a set of tools involving augmented reality and virtual reality for the understanding and learning of mathematics for College students.

GraphML specializations to codify ancestral recombinant graphs

Software which simulates, infers, or analyzes ancestral recombination graphs (ARGs) faces the problem of communicating them. Existing formats omit information either about the location of recombinations along the chromosome or the position of recombinations relative to the branching topology. We present a specialization of GraphML, an XML-based standard for mathematical graphs, for communication of ARGs. The GraphML <node> type is specialized to contain the node type, time, recombination location, and name. The GraphML <edge> type is specialized to contain the ancestral material passed along that edge. This approach, which we call ArgML, retains all information in the original ARG. Due to its use of established formats ArgML can be parsed, checked and displayed by existing software.

Production of microcellular foam based on PP/EPDM: The effects of processing parameters and nanoclay using response surface methodology

AbstractMicrocellular foam is a new class of material with superior properties due to smaller cell size and higher cell density compared to ordinary foams. In this work, microcellular foam of PP/EPDM/Organoclay with supercritical nitrogen as physical blowing agent was prepared via batch process. Experimental design was carried out according to Box-Behnken method and the effects of saturation pressure and foaming times as well as organoclay content on nucleation and final foam morphology were studied using response surface methodology (RSM). Three levels of saturation pressure, nanoclay content, and foaming time were chosen. The mathematical model and response surface graphs have been used to illustrate the relationship between considered parameters and foam properties. The results revealed that cell density and average cell diameter were affected by nanoclay content and pressure. Cell density was in the range of 109-1010 cell/cm3. Larger average cell sizes were observed as a result of increasing foaming time. Classic nucleation theory was used to study the nucleation mechanism. Nanoparticles acted as nucleating agents and changed nucleation mechanism from homogenous to heterogeneous by decreasing nucleating free energy. In order to find out nucleating energy reduction, gas-polymer-nanoparticle contact angle (Ө), was calculated by measuring surface and interfacial free energies of neat polymers and nanoparticle. In addition, nucleation efficiency of organoclay was estimated and the results showed that despite low nucleating efficiency, nucleation is dominated by presence of nanoclay.

Estimating landscape carrying capacity through maximum clique analysis

Habitat suitability (HS) maps are widely used tools in wildlife science and establish a link between wildlife populations and landscape pattern. Although HS maps spatially depict the distribution of optimal resources for a species, they do not reveal the population size a landscape is capable of supporting--information that is often crucial for decision makers and managers. We used a new approach, "maximum clique analysis," to demonstrate how HS maps for territorial species can be used to estimate the carrying capacity, N(k), of a given landscape. We estimated the N(k) of Ovenbirds (Seiurus aurocapillus) and bobcats (Lynx rufus) in an 1153-km2 study area in Vermont, USA. These two species were selected to highlight different approaches in building an HS map as well as computational challenges that can arise in a maximum clique analysis. We derived 30-m2 HS maps for each species via occupancy modeling (Ovenbird) and by resource utilization modeling (bobcats). For each species, we then identified all pixel locations on the map (points) that had sufficient resources in the surrounding area to maintain a home range (termed a "pseudo-home range"). These locations were converted to a mathematical graph, where any two points were linked if two pseudo-home ranges could exist on the landscape without violating territory boundaries. We used the program Cliquer to find the maximum clique of each graph. The resulting estimates of N(k) = 236 Ovenbirds and N(k) = 42 female bobcats were sensitive to different assumptions and model inputs. Estimates of N(k) via alternative, ad hoc methods were 1.4 to > 30 times greater than the maximum clique estimate, suggesting that the alternative results may be upwardly biased. The maximum clique analysis was computationally intensive but could handle problems with < 1500 total pseudo-home ranges (points). Given present computational constraints, it is best suited for species that occur in clustered distributions (where the problem can be broken into several, smaller problems), or for species with large home ranges relative to grid scale where resampling the points to a coarser resolution can reduce the problem to manageable proportions.

Geomorphic coupling and sediment connectivity in an alpine catchment — Exploring sediment cascades using graph theory

Through their relevance for sediment budgets and the sensitivity of geomorphic systems, geomorphic coupling and (sediment) connectivity represent important topics in geomorphology. Since the introduction of the systems perspective to physical geography by Chorley and Kennedy (1971), a catchment has been perceived as consisting of landscape elements (e.g. landforms, subcatchments) that are coupled by geomorphic processes through sediment transport. In this study, we present a novel application of mathematical graph theory to explore the network structure of coarse sediment pathways in a central alpine catchment. Numerical simulation models for rockfall, debris flows, and (hillslope and channel) fluvial processes are used to establish a spatially explicit graph model of sediment sources, pathways and sinks. The raster cells of a digital elevation model form the nodes of this graph, and simulated sediment trajectories represent the corresponding edges. Model results are validated by visual comparison with the field situation and aerial photos. The interaction of sediment pathways, i.e. where the deposits of a geomorphic process form the sources of another process, forms sediment cascades, represented by paths (a succession of edges) in the graph model. We show how this graph can be used to explore upslope (contributing area) and downslope (source to sink) functional connectivity by analysing its nodes, edges and paths. The analysis of the spatial distribution, composition and frequency of sediment cascades yields information on the relative importance of geomorphic processes and their interaction (however regardless of their transport capacity). In the study area, the analysis stresses the importance of mass movements and their interaction, e.g. the linkage of large rockfall source areas to debris flows that potentially enter the channel network. Moreover, it is shown that only a small percentage of the study area is coupled to the channel network which itself is longitudinally disconnected by natural and anthropogenic barriers. Besides the case study, we discuss the methodological framework and alternatives for node and edge representations of graph models in geomorphology. We conclude that graph theory provides an excellent methodological framework for the analysis of geomorphic systems, especially for the exploration of quantitative approaches towards sediment connectivity.

Driving developmental and evolutionary change: A systems biology view

Embryonic development is underpinned by ∼50 core processes that drive morphogenesis, growth, patterning and differentiation, and each is the functional output of a complex molecular network. Processes are thus the natural and parsimonious link between genotype and phenotype and the obvious focus for any discussion of biological change. Here, the implications of this approach are explored. One is that many features of developmental change can be modeled as mathematical graphs, or sets of connected triplets of the general form <noun><verb><noun>. In these, the verbs (edges) are the outputs of the processes that drive change and the nouns (nodes) are the time-dependent states of biological entities (from molecules to tissues). Such graphs help unpick the multi-level complexity of developmental phenomena and may help suggest new experiments. Another comes from analyzing the effect of mutation that lead to tinkering with the dynamic properties of these processes and to congenital abnormalities; if these changes are both inherited and advantageous, they become evolutionary modifications. In this context, protein networks often represents what classical evolutionary genetics sees as genes, and the realization that traits reflect the output processes of complex networks, particularly for growth, patterning and pigmentation, rather than anything simpler clarifies some problems that the evolutionary synthesis of the 1950s has found hard to solve. In the wider context, most processes are used many times in development and cooperate to produce tissue modules (bones, branching duct systems, muscles etc.). Their underlying generative networks can thus be thought of as genomic modules or subroutines.

A new ontology (structured hierarchy) of human developmental anatomy for the first 7 weeks (Carnegie stages 1–20)

This paper describes a new ontology of human developmental anatomy covering the first 49 days [Carnegie stages (CS)1-20], primarily structured around the parts of organ systems and their development. The ontology includes more than 2000 anatomical entities (AEs) that range from the whole embryo, through organ systems and organ parts down to simple or leaf tissues (groups of cells with the same morphological phenotype), as well as features such as cavities. Each AE has assigned to it a set of facts of the form <AE><relationship><parent>, with the relationships including starts_at and ends_at (CSs), part_of (there can be several parents) and is_a (this gives the type of tissue, from an organ system down to one of ~ 80 simple tissues predominantly composed of a single cell kind, which is also specified). Leaf tissues also have a develops_from link to its parent tissue. The ontology includes ~14 000 such facts, which are mainly from the literature and an earlier ontology of human developmental anatomy (EHDAA, now withdrawn). The relationships enable these facts to be integrated into a single, complex hierarchy (or mathematical graph) that was made and can be viewed in the OBO-Edit browser (oboedit.org). Each AE has an EHDAA2 ID that may be useful in an informatics context, while the ontology as a whole can be used for organizing databases of human development. It is also a knowledge resource: a user can trace the lineage of any tissue back to the egg, study the changes in cell phenotype that occur as a tissue develops, and use the structure to add further (e.g. molecular) information. The ontology may be downloaded from www.obofoundry.org. Queries and corrections should be sent to j.bard@ed.ac.uk.

Hexagrams by the mathematical graph of congruence.

Hexagrams by the mathematical graph of congruence.

Victorian statistical graphics and the iconography of Florence Nightingale's polar area graph

The popular iconic image of Florence Nightingale as the ‘Lady with the Lamp’, who administered acute nursing care to the casualties during the Crimean War, belies a more integrated approach to Nightingale's nursing, which was shaped by her use of evidence-based medicine, promulgated in her statistical reports, books and papers. This image thus undermines Nightingale's prodigious statistical work and her innovative statistical graphs that led to major health reforms in military and civilian hospitals, usually with the full support of the government. It was this empirically based strategy that enabled her to establish the necessary and essential nursing and hospital reforms, which modernized nursing in the mid- to late-Victorian period. This paper will examine the mathematical and statistical graphs that arose in the nineteenth century, which influenced Nightingale's use of statistical graphs. The iconography of her polar area graph, which was based on the mortality rates of British soldiers during the Crimean War, will also be assessed. It will be shown that Nightingale's role in promoting this graph helped to establish its iconic status, as did her introduction of new elements into the ordinary polar area graph.

An Insight into Calculus of Communicating System and Formalisms, for Bioinspired Logic Device Design using Computational Aspects of Protocells

In our current paper, we consider bio-inspired logic device modeling based on proto-cells, using process algebra based Efficient Symbolic Tools package(EST) and analyze a case study through simulation, to highlight the importance of bio-inspired computational platforms. As a promising inheritance, from systems biology and computational cell biology, synthetic biology uses a wide variety of mathematical descriptions including graph theory, boolean logic, ordinary, partial and stochastic differential equations. It is the solid feedback, between an accurate and realistic modeling of the subject, under investigation and the precise reproduction of the genetic or chemical design in the laboratory, that has recently granted synthetic biology a high-profile attention, in the scientific community. We explore here, how and why proto-cells, can provide a good basis, to model logical components, and how molecular modeling methods, allow to understand the physical mechanism of this process.

Determing the entanglement of quantum nonbinary graph states

Graph states are multipartite entangled states that correspond to mathematical graphs, where the vertices of the graph now play the role of quantum multilevel systems and edges represent interactions of the systems. Graph states are the basis of quantum error correction and one-way quantum computer. We systematically study the entanglement of non-binary graph states. Using iterative algorithm and entanglement bounds, we calculate the entanglement of all the ternary graph states up to nine vertices and parts of quaternary and quinary graph states modulo local unitary transformations and graph isomorphisms. The entanglement measure can be the geometric measure, the measure of relative entropy of entanglement or the measure of logarithmic robustness. We classify the graph states according to the entanglement values obtained. The closest product states obtained in the calculations are studied.

Network of the core: mapping and visualizing the core of scientific domains

In this article, we propose mapping and visualizing the core of scientific domains using social network analysis techniques derived from mathematical graph theory. In particular, the concept of Network of the Core is introduced which can be employed to visualize scientific domains by constructing a network among theoretical constructs, models, and concepts. A Network of the Core can be used to reveal hidden properties and structures of a research domain such as connectedness, centrality, density, structural equivalence, and cohesion, by modeling the casual relationship among theoretical constructs. Network of the Core concept can be used to explore the strengths and limitations of a research domain, and graphically and mathematically derive the number research hypotheses. The Network of the Core approach can be applied to any domain given that the investigator has a deep understanding of the area under consideration, a graphical or conceptual view (in the form of a network of association among the theoretical constructs and concepts) of the scientific domain can be obtained, and an underlying theory is available or can be constructed to support Network of the Core formation. Future research directions and several other issues related to the Network of the Core concept are also discussed.

The structure of ecological state transitions: Amplification, synchronization, and constraints in responses to environmental change

Effects of environmental change may be either amplified and facilitated, or constrained, by the network of state-changes in ecological systems. Network structure affects system response independently of the dynamics of the individual subsystems. Ecological responses were represented as state-and-transition models (STMs), and analyzed as mathematical graphs. Three metrics were applied that reflect: (1) the extent to which environmental change is amplified or filtered by state transitions; (2) network synchronizability and the rate of propagation of state changes; and (3) the extent of system structural constraints to the spatial propagation of state transitions. These were determined for seven archetypal graph structures representing common forms of connectivity in ecological networks, and linked to distinct modes of ecological change. Radiation-type structures are the least synchronized and most constrained patterns, with the most limited amplification, followed by other low-connectivity patterns such as those associated with monotonic succession. The maximum-connectivity rigid polygon structure (any state can transition to any other) has the strongest amplification and synchronization and least constraints. Structural constraints to change propagation are most sensitive to increasing numbers of transitions for a given number of states, and synchronization also increases at least linearly with the number of links. Amplification, however, does not increases as rapidly; as long as a graph is connected, increasing the number of links does not proportionally increase it. Because the more densely connected structures have much higher synchronization than other patterns, and fewer constraints on change propagation, environments characterized by these types of STMs may be prone to rapid, complex transitions in response to environmental changes. STMs for rangelands in two regions of Texas show that the rigid polygon structure is very common. If this phenomenon is more general, it suggests that relatively abrupt landscape reorganizations may be more likely than more orderly successions of change along environmental gradients. This analysis shows that identification of STMs and their network structure is useful for recognizing environments at higher risk for complex reorganization, and for identification of management actions to either retard or facilitate propagation of state changes.

A systems biology representation of developmental anatomy.

The formation of any tissue involves differentiation, cell dynamics and interactions with adjacent tissues. This paper suggests that the complexity of the system as a whole can be represented as a mathematical graph, that is, a set of connected triples of the general form [term] <relationship> [term]. Computationally, such graphs are widely used for modeling data; visually, they form hierarchies and networks. For morphogenesis, the triples are of the general structure <noun > <verb > <noun >, where nouns cover tissues, molecules and networks and verbs describe processes such as moves, differentiates, grows and apoptoses. The paper considers the general formalism of graphs, where graphs are already used in biology, and how developmental anatomy may be described using this format. Representing morphogenesis as a visual graph is complicated as the formalism has to incorporate tissue types, molecular signals, networks, dynamic processes and some aspects, at least, of tissue geometry. The formation of a capillary sprout is chosen as an example of how this complexity can be represented graphically, with colour used to distinguish tissues and molecules. There are three key benefits, beyond its compactness, in using the graph formalism of morphogenesis to complement experimentation. First, it emphasizes the distributed nature of causality in morphogenesis. Secondly, producing all the triples for the visual graph requires explicit formalization of each aspect of the process, and this, in turn, often exposes gaps in knowledge and so suggests new experiments. Thirdly, once the graph has been formalized, triples can be annotated with associated information or IDs (e.g. cell types, publications, gene-expression data) that link to external online resources that may be regularly updated. Such annotations allow the graph to be viewed as a self-maintaining review. The graph approach sees dynamic processes as the drivers of developmental momentum and, because the same processes are used many times during development, it seems appropriate to view them as modules and their underlying networks as genomic subroutines.

Dissociable Network Properties of Anesthetic State Transitions

It is still unknown whether anesthetic state transitions are continuous or binary. Mathematical graph theory is one method by which to assess whether brain networks change gradually or abruptly upon anesthetic induction and emergence. Twenty healthy males were anesthetized with an induction dose of propofol, with continuous measurement of 21-channel electroencephalogram at baseline, during anesthesia, and during recovery. From these electroencephalographic data a "genuine network" was reconstructed based on the surrogate data method. The effects of topologic structure and connection strength on information transfer through the network were measured independently across different states. Loss of consciousness was consistently associated with a disruption of network topology. However, recovery of consciousness was associated with complex patterns of altered connection strength after the initial topologic structure had slowly recovered. In one group of subjects, there was a precipitous increase of connection strength that was associated with reduced variability of emergence time. Analysis of regional effects on brain networks demonstrated that the parietal network was significantly disrupted, whereas the frontal network was minimally affected. By dissociating the effects of network structure and connection strength, both continuous and discrete elements of anesthetic state transitions were identified. The study also supports a critical role of parietal networks as a target of general anesthetics.