Simple one-electron invariants of molecular chirality

Pseudoscalar measures of electronic chirality for molecular systems are derived using the spectral moment theory applied to the frequency-dependent rotational susceptibility. In this scheme a one-electron chirality operator κ^ naturally emerges as a quantum counterpart of the triple scalar product, involving velocity, acceleration and second acceleration. Averaging κ^ over an electronic state vector gives rise to an additive chirality invariant (κ-index), considered as a quantitative measure of chirality. A simple computational technique for quick calculation of the κ-index is developed and various structural classes (cyclic hydrocarbons, cage-shaped systems, etc.) are studied. Reasonable behaviour of the chirality index is demonstrated. The chirality changes during the β-turn formation in Leu-Enkephalin is presented as a useful example of the chirality analysis for conformational transitions.

A Statistical Convergence Aplication for the Hopfield Networks

When Recurrent Neural Networks (RNN) are going to be used as Pattern Recognition systems, the problem to be considered is how to impose prescribed prototype vectors ξ^1,ξ^2,...,ξ^p as fixed points. The synaptic matrix W should be interpreted as a sort of sign correlation matrix of the prototypes, In the classical approach. The weak point in this approach, comes from the fact that it does not have the appropriate tools to deal efficiently with the correlation between the state vectors and the prototype vectors The capacity of the net is very poor because one can only know if one given vector is adequately correlated with the prototypes or not and we are not able to know what its exact correlation degree. The interest of our approach lies precisely in the fact that it provides these tools. In this paper, a geometrical vision of the dynamic of states is explained. A fixed point is viewed as a point in the Euclidean plane R2. The retrieving procedure is analyzed trough statistical frequency distribution of the prototypes. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented

On the Vertex Separation of Cactus Graphs

This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a \main theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.

On the Vertex Separation of Maximal Outerplanar Graphs

We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.

A New Approach for Eliminating the Spurious States in Recurrent Neural Networks

As is well known, the Convergence Theorem for the Recurrent Neural Networks, is based in Lyapunov ́s second method, which states that associated to any one given net state, there always exist a real number, in other words an element of the one dimensional Euclidean Space R, in such a way that when the state of the net changes then its associated real number decreases. In this paper we will introduce the two dimensional Euclidean space R2, as the space associated to the net, and we will define a pair of real numbers ( x, y ) , associated to any one given state of the net. We will prove that when the net change its state, then the product x ⋅ y will decrease. All the states whose projection over the energy field are placed on the same hyperbolic surface, will be considered as points with the same energy level. On the other hand we will prove that if the states are classified attended to their distances to the zero vector, only one pattern in each one of the different classes may be at the same energy level. The retrieving procedure is analyzed trough the projection of the states on that plane. The geometrical properties of the synaptic matrix W may be used for classifying the n-dimensional state- vector space in n classes. A pattern to be recognized is seen as a point belonging to one of these classes, and depending on the class the pattern to be retrieved belongs, different weight parameters are used. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented.

A Linear Time Algorithm for Computing Longest Paths in Cactus Graphs

ACM Computing Classification System (1998): G.2.2.

Developing multidimensional metrics for evaluating paediatric neurodevelopmental disorders

Healthy brain functioning depends on efficient communication of information between brain regions, forming complex networks. By quantifying synchronisation between brain regions, a functionally connected brain network can be articulated. In neurodevelopmental disorders, where diagnosis is based on measures of behaviour and tasks, a measure of the underlying biological mechanisms holds promise as a potential clinical tool. Graph theory provides a tool for investigating the neural correlates of neuropsychiatric disorders, where there is disruption of efficient communication within and between brain networks. This research aimed to use recent conceptualisation of graph theory, along with measures of behaviour and cognitive functioning, to increase understanding of the neurobiological risk factors of atypical development. Using magnetoencephalography to investigate frequency-specific temporal dynamics at rest, the research aimed to identify potential biological markers derived from sensor-level whole-brain functional connectivity. Whilst graph theory has proved valuable for insight into network efficiency, its application is hampered by two limitations. First, its measures have hardly been validated in MEG studies, and second, graph measures have been shown to depend on methodological assumptions that restrict direct network comparisons. The first experimental study (Chapter 3) addressed the first limitation by examining the reproducibility of graph-based functional connectivity and network parameters in healthy adult volunteers. Subsequent chapters addressed the second limitation through adapted minimum spanning tree (a network analysis approach that allows for unbiased group comparisons) along with graph network tools that had been shown in Chapter 3 to be highly reproducible. Network topologies were modelled in healthy development (Chapter 4), and atypical neurodevelopment (Chapters 5 and 6). The results provided support to the proposition that measures of network organisation, derived from sensor-space MEG data, offer insights helping to unravel the biological basis of typical brain maturation and neurodevelopmental conditions, with the possibility of future clinical utility.

A Naturalistic Assessment of the Organization of Children’s Memories Predicts Cognitive Functioning and Reading Ability

To explore the relationship between memory and early school performance, we used graph theory to investigate memory reports from 76 children aged 6–8 years. The reports comprised autobiographical memories of events days to years past, and memories of novel images reported immediately after encoding. We also measured intelligence quotient (IQ) and theory of mind (ToM). Reading and Mathematics were assessed before classes began (December 2013), around the time of report collection (June 2014), and at the end of the academic year (December 2014). IQ and ToM correlated positively with word diversity and word-to-word connectivity, and negatively with word recurrence. Connectivity correlated positively with Reading in June 2014 as well as December 2014, even after adjusting for IQ and ToM. To our knowledge, this is the first study demonstrating a link between the structure of children’s memories and their cognitive or academic performance.

A Naturalistic Assessment of the Organization of Children’s Memories Predicts Cognitive Functioning and Reading Ability

To explore the relationship between memory and early school performance, we used graph theory to investigate memory reports from 76 children aged 6–8 years. The reports comprised autobiographical memories of events days to years past, and memories of novel images reported immediately after encoding. We also measured intelligence quotient (IQ) and theory of mind (ToM). Reading and Mathematics were assessed before classes began (December 2013), around the time of report collection (June 2014), and at the end of the academic year (December 2014). IQ and ToM correlated positively with word diversity and word-to-word connectivity, and negatively with word recurrence. Connectivity correlated positively with Reading in June 2014 as well as December 2014, even after adjusting for IQ and ToM. To our knowledge, this is the first study demonstrating a link between the structure of children’s memories and their cognitive or academic performance.

Petri Net Siphon Analysis and Network Centrality Measures for Identifying Combination Therapies in Signaling Pathways

Aberrant behavior of biological signaling pathways has been implicated in diseases such as cancers. Therapies have been developed to target proteins in these networks in the hope of curing the illness or bringing about remission. However, identifying targets for drug inhibition that exhibit good therapeutic index has proven to be challenging since signaling pathways have a large number of components and many interconnections such as feedback, crosstalk, and divergence. Unfortunately, some characteristics of these pathways such as redundancy, feedback, and drug resistance reduce the efficacy of single drug target therapy and necessitate the employment of more than one drug to target multiple nodes in the system. However, choosing multiple targets with high therapeutic index poses more challenges since the combinatorial search space could be huge. To cope with the complexity of these systems, computational tools such as ordinary differential equations have been used to successfully model some of these pathways. Regrettably, for building these models, experimentally-measured initial concentrations of the components and rates of reactions are needed which are difficult to obtain, and in very large networks, they may not be available at the moment. Fortunately, there exist other modeling tools, though not as powerful as ordinary differential equations, which do not need the rates and initial conditions to model signaling pathways. Petri net and graph theory are among these tools. In this thesis, we introduce a methodology based on Petri net siphon analysis and graph network centrality measures for identifying prospective targets for single and multiple drug therapies. In this methodology, first, potential targets are identified in the Petri net model of a signaling pathway using siphon analysis. Then, the graph-theoretic centrality measures are employed to prioritize the candidate targets. Also, an algorithm is developed to check whether the candidate targets are able to disable the intended outputs in the graph model of the system or not. We implement structural and dynamical models of ErbB1-Ras-MAPK pathways and use them to assess and evaluate this methodology. The identified drug-targets, single and multiple, correspond to clinically relevant drugs. Overall, the results suggest that this methodology, using siphons and centrality measures, shows promise in identifying and ranking drugs. Since this methodology only uses the structural information of the signaling pathways and does not need initial conditions and dynamical rates, it can be utilized in larger networks.

A Study of Some Centrality Measures in Graphs

Centrality is in fact one of the fundamental notions in graph theory which has established its close connection with various other areas like Social networks, Flow networks, Facility location problems etc. Even though a plethora of centrality measures have been introduced from time to time, according to the changing demands, the term is not well defined and we can only give some common qualities that a centrality measure is expected to have. Nodes with high centrality scores are often more likely to be very powerful, indispensable, influential, easy propagators of information, significant in maintaining the cohesion of the group and are easily susceptible to anything that disseminate in the network.

Large-scale dynamic hydrofracturing, healing and fracture network characterization

Permeability of a rock is a dynamic property that varies spatially and temporally. Fractures provide the most efficient channels for fluid flow and thus directly contribute to the permeability of the system. Fractures usually form as a result of a combination of tectonic stresses, gravity (i.e. lithostatic pressure) and fluid pressures. High pressure gradients alone can cause fracturing, the process which is termed as hydrofracturing that can determine caprock (seal) stability or reservoir integrity. Fluids also transport mass and heat, and are responsible for the formation of veins by precipitating minerals within open fractures. Veining (healing) thus directly influences the rock’s permeability. Upon deformation these closed factures (veins) can refracture and the cycle starts again. This fracturing-healing-refacturing cycle is a fundamental part in studying the deformation dynamics and permeability evolution of rock systems. This is generally accompanied by fracture network characterization focusing on network topology that determines network connectivity. Fracture characterization allows to acquire quantitative and qualitative data on fractures and forms an important part of reservoir modeling. This thesis highlights the importance of fracture-healing and veins’ mechanical properties on the deformation dynamics. It shows that permeability varies spatially and temporally, and that healed systems (veined rocks) should not be treated as fractured systems (rocks without veins). Field observations also demonstrate the influence of contrasting mechanical properties, in addition to the complexities of vein microstructures that can form in low-porosity and permeability layered sequences. The thesis also presents graph theory as a characterization method to obtain statistical measures on evolving network connectivity. It also proposes what measures a good reservoir should have to exhibit potentially large permeability and robustness against healing. The results presented in the thesis can have applications for hydrocarbon and geothermal reservoir exploration, mining industry, underground waste disposal, CO2 injection or groundwater modeling.

Estudio y optimización de las infraestructuras de los carriles para bicicletas

La necesidad cotidiana de los ciudadanos de desplazarse para realizar diferentes actividades, sea cual fuere su naturaleza, se ha visto afectada en gran medida por los cambios producidos. Las ventajas generadas por la inclusión de la bicicleta como modo de transporte y la proliferación de su uso entre la ciudadanía son innumerables y se extienden tanto en el ámbito de la movilidad urbana como del desarrollo sostenible. En la actualidad, hay multitud de programas para la implantación, fomento o aumento de la participación ciudadana relacionado con la bicicleta en las ciudades. Pero en definitiva, todos y cada uno de estas iniciativas tienen la misma finalidad, crear una malla de vías cicladles eficaz y útil. Capaces de permitir el uso de la bicicleta en vías preferentes con unas garantías de seguridad altas, incorporando la bicicleta en el modelo de intermodalidad del transporte urbano. Con la progresiva implantación del carril bici, muchas personas han empezado a utilizarlas para moverse por la ciudad. Pero todo lo nuevo necesita un periodo de adaptación. Y, la realidad es que la red de viales destinados para estos vehículos está repleta de obstáculos para el ciclista. La actual situación ha llevado a cuestionar qué cantidad de kilómetros de carriles bici son necesarios para abastecer la demanda existente de este modo de transporte y, si las obras ejecutadas y proyectadas son las correctas y suficientes. En este trabajo se presenta una herramienta, basada en un modelo de programación matemática, para el diseño óptimo de una red destinada a los ciclistas. En concreto, el sistema determina una infraestructura para la bicicleta adaptada a las características de la red de carreteras existentes, con base en criterios de teoría de grafos ponderados. Como una aplicación del modelo propuesto, se ofrece el resultado de estos experimentos, obteniéndose un número de conclusiones útiles para la planificación y el diseño de redes de carriles bici desde una perspectiva social. Se realiza una aplicación de la metodología desarrollada para el caso real del municipio de Málaga (España). Por último se produce la validación del modelo de optimización presentado y la repercusión que tiene éste sobre el resultado final y la importancia o el peso del total de variables capaces de condicionar el resultado final de la red ciclista. Se obtiene, por tanto, una herramienta destinada a la mejora de la planificación, diseño y gestión de las diferentes infraestructuras para la bicicleta, con capacidad de interactuar con el modelo de red vial actual y con el resto de los modos de transportes existentes en el entramado urbano de las ciudades.

Detecting phase transitions in community structures using big data analysis of the engineering education research landscape: a European perspective

Comunicação apresentada na 44th SEFI Conference, 12-­15 September 2016, Tampere, Finland

WEAK ISOMETRIES OF HAMMING SPACES

In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean cube, that is, the binary Hamming space. We attempted to generalize some of their methods to the non-boolean case. The 4th chapter has our new results and is split into two major contributions. Our first contribution shows if n=p or p < n2, then every weak isometry of Hnq that preserves distance p is an isometry. Our second contribution gives a possible method to check if a weak isometry is an isometry using linear algebra and graph theory.