Expedition in Data and Harmonic Analysis on Graphs

The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian eigenvalues and eigenvectors. We extend these results and prove that the translation operator to the i’th node is invertible if and only if all eigenvectors are nonzero on the i’th node. Because of this dependency on the support of eigenvectors we study the characteristic set of Laplacian eigenvectors. We prove that the Fiedler vector of a planar graph cannot vanish on large neighborhoods and then explicitly construct a family of non-planar graphs that do exhibit this property. We then prove original results in modern analysis on graphs. We extend results on spectral graph wavelets to create vertex-dyanamic spectral graph wavelets whose support depends on both scale and translation parameters. We prove that Spielman’s Twice-Ramanujan graph sparsifying algorithm cannot outperform his conjectured optimal sparsification constant. Finally, we present numerical results on graph conditioning, in which edges of a graph are rescaled to best approximate the complete graph and reduce average commute time.

Comprendre l’interaction entre la douleur et le système moteur : une étude novatrice combinant la stimulation magnétique transcrânienne et l’électroencéphalographie

Résumé : L’interaction entre la douleur et le système moteur est bien connue en clinique et en réadaptation. Il est sans surprise que la douleur est un phénomène considérablement invalidant, affectant la qualité de vie de ceux et celles qui en souffrent. Toutefois, les bases neurophysiologiques qui sous-tendent cette interaction demeurent, encore aujourd’hui, mal comprises. Le but de la présente étude était de mieux comprendre les mécanismes corticaux impliqués dans l’interaction entre la douleur et le système moteur. Pour ce faire, une douleur expérimentale a été induite à l’aide d’une crème à base de capsaïcine au niveau de l’avant-bras gauche des participants. L'effet de la douleur sur la force des projections corticospinales ainsi que sur l’activité cérébrale a été mesuré à l’aide de la stimulation magnétique transcrânienne (TMS) et de l’électroencéphalographie (EEG), respectivement. L’analyse des données EEG a permis de révéler qu'en présence de douleur aiguë, il y a une augmentation de l’activité cérébrale au niveau du cuneus central (fréquence têta), du cortex dorsolatéral préfrontal gauche (fréquence alpha) ainsi que du cuneus gauche et de l'insula droite (toutes deux fréquence bêta), lorsque comparée à la condition initiale (sans douleur). Également, les analyses démontrent une augmentation de l'activité du cortex moteur primaire droit en présence de douleur, mais seulement chez les participants qui présentaient simultanément une diminution de leur force de projections corticales (mesurée avec la TMS t=4,45, p<0,05). Ces participants ont également montré une plus grande connectivité entre M1 et le cuneus que les participants dont la douleur n’a pas affecté la force des projections corticospinales (t=3,58, p<0,05). Ces résultats suggèrent qu’une douleur expérimentale induit, chez certains individus, une altération au niveau des forces de projections corticomotrices. Les connexions entre M1 et le cuneus seraient possiblement impliquées dans la survenue de ces changements corticomoteurs.

A lower bound for the energy of symmetric matrices and graphs

The energy of a symmetric matrix is the sum of the absolute values of its eigenvalues. We introduce a lower bound for the energy of a symmetric partitioned matrix into blocks. This bound is related to the spectrum of its quotient matrix. Furthermore, we study necessary conditions for the equality. Applications to the energy of the generalized composition of a family of arbitrary graphs are obtained. A lower bound for the energy of a graph with a bridge is given. Some computational experiments are presented in order to show that, in some cases, the obtained lower bound is incomparable with the well known lower bound $2\sqrt{m}$, where $m$ is the number of edges of the graph.

Social buffering of fear in zebrafish

Tese de Doutoramento em Biologia Comportamental apresentada ao ISPA - Instituto Universitário

On the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surface

We develop a method based on spectral graph theory to approximate the eigenvalues and eigenfunctions of the Laplace-Beltrami operator of a compact riemannian manifold -- The method is applied to a closed hyperbolic surface of genus two -- The results obtained agree with the ones obtained by other authors by different methods, and they serve as experimental evidence supporting the conjectured fact that the generic eigenfunctions belonging to the first nonzero eigenvalue of a closed hyperbolic surface of arbitrary genus are Morse functions having the least possible total number of critical points among all Morse functions admitted by such manifolds

The influence of environmental distraction on cognitive abilities in ADL performance after frontal brain injured.

Background: Previous studies have reported errors in Activities of Daily Living (ADL) under the presence of distracting objects in dementia and brain injury patients. However, little is known about which distractor-target objects relation might be more harmful for performance. Method: We compared the ADL execution in frontal brain injured patients and control participants under two conditions: One in which target objects were mixed with distractor objects that constituted an alternative semantically related but non-required task (contextual condition) and another in which target objects were mixed with related but isolated distractors that did not constituted a coherent task (non-contextual condition). We separately analyzed ADL commission errors (repetitions, substitutions, objects manipulations, failures in sequence, extra actions) and omissions. In addition, the participants were evaluated with a neuropsychological protocol including a very specific executive functions task (Selective attention, Stimulus-Stimulus and Stimulus-Response conflict). Results: We found that frontal patients produced more commission errors compared to control participants, but only under the contextual condition. No between groups significant differences were found in omissions in both conditions or commission errors in non-contextual conditions. Scores in the Stimulus-Response conflict was significantly correlated with commission errors in the contextual condition. Conclusion: The presence of different non-target objects in ADL performance could require different cognitive process. Contextual ADL conditions required a higher level of executive functions, especially at the level of response (Stimulus-Response conflict). Application to Practice: Occupational therapists should control the presence of objects related to the target task according to the intervention objectives with the patients.

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

Hyperactivations frontales en mémoire de travail dans le trouble cognitif léger

Des études récentes ont rapporté que les individus âgés avec un trouble cognitif léger (TCL) ont de plus grandes activations en lien avec la réalisation d’une tâche cognitive que des personnes âgées saines. Des auteurs ont proposé que ces hyperactivations pourraient refléter des processus de plasticité cérébrale compensatoires ayant lieu pendant la phase précoce de la maladie d’Alzheimer. Des processus de compensations fonctionnelles pourraient émerger en réponse à une perte d’intégrité structurelle dans les régions du cerveau normalement requises pour compléter une tâche. Dans ce mémoire, j’ai évalué cette hypothèse chez des personnes avec TCL en faisant appel à une tâche de mémoire de travail comportant plusieurs niveaux de difficulté ainsi qu’aux techniques d’imagerie par résonnance magnétique (IRM) structurelle et fonctionnelle. Des analyses de régression multiples ont été utilisées afin d’identifier les régions cérébrales dont l’activité variait en fonction de l’intégrité neuronale telle que définie par le volume de l’hippocampe. Les valeurs estimées des paramètres du signal de ces régions furent ensuite extraites afin de procéder à des analyses corrélationnelles sur la performance ainsi que sur le volume de différentes structures cérébrales. Les résultats indiquent des hyperactivations dans les régions frontales droites chez les participants TCL souffrant d’une plus grande atteinte neuronale. De plus, le niveau d’activation est négativement corrélé au volume de structures frontales et pariétales. Ces résultats indique la présence d’une hyperactivation compensatoire dans la phase du TCL associée à la réalisation d’une tâche de mémoire de travail.

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.

Adaptive edge analytics for distributed networked control of water systems

Over the last decade, there has been a trend where water utility companies aim to make water distribution networks more intelligent in order to improve their quality of service, reduce water waste, minimize maintenance costs etc., by incorporating IoT technologies. Current state of the art solutions use expensive power hungry deployments to monitor and transmit water network states periodically in order to detect anomalous behaviors such as water leakage and bursts. However, more than 97% of water network assets are remote away from power and are often in geographically remote underpopulated areas, facts that make current approaches unsuitable for next generation more dynamic adaptive water networks. Battery-driven wireless sensor/actuator based solutions are theoretically the perfect choice to support next generation water distribution. In this paper, we present an end-to-end water leak localization system, which exploits edge processing and enables the use of battery-driven sensor nodes. Our system combines a lightweight edge anomaly detection algorithm based on compression rates and an efficient localization algorithm based on graph theory. The edge anomaly detection and localization elements of the systems produce a timely and accurate localization result and reduce the communication by 99% compared to the traditional periodic communication. We evaluated our schemes by deploying non-intrusive sensors measuring vibrational data on a real-world water test rig that have had controlled leakage and burst scenarios implemented.

Hyperactivations frontales en mémoire de travail dans le trouble cognitif léger

Des études récentes ont rapporté que les individus âgés avec un trouble cognitif léger (TCL) ont de plus grandes activations en lien avec la réalisation d’une tâche cognitive que des personnes âgées saines. Des auteurs ont proposé que ces hyperactivations pourraient refléter des processus de plasticité cérébrale compensatoires ayant lieu pendant la phase précoce de la maladie d’Alzheimer. Des processus de compensations fonctionnelles pourraient émerger en réponse à une perte d’intégrité structurelle dans les régions du cerveau normalement requises pour compléter une tâche. Dans ce mémoire, j’ai évalué cette hypothèse chez des personnes avec TCL en faisant appel à une tâche de mémoire de travail comportant plusieurs niveaux de difficulté ainsi qu’aux techniques d’imagerie par résonnance magnétique (IRM) structurelle et fonctionnelle. Des analyses de régression multiples ont été utilisées afin d’identifier les régions cérébrales dont l’activité variait en fonction de l’intégrité neuronale telle que définie par le volume de l’hippocampe. Les valeurs estimées des paramètres du signal de ces régions furent ensuite extraites afin de procéder à des analyses corrélationnelles sur la performance ainsi que sur le volume de différentes structures cérébrales. Les résultats indiquent des hyperactivations dans les régions frontales droites chez les participants TCL souffrant d’une plus grande atteinte neuronale. De plus, le niveau d’activation est négativement corrélé au volume de structures frontales et pariétales. Ces résultats indique la présence d’une hyperactivation compensatoire dans la phase du TCL associée à la réalisation d’une tâche de mémoire de travail.

Diversity of LFPs Activated in Different Target Regions by a Common CA3 Input

Identifying the pathways contributing to local field potential (LFP) events and oscillations is essential to determine whether synchronous interregional patterns indicate functional connectivity. Here, we studied experimentally and numerically how different target structures receiving input from a common population shape their LFPs. We focused on the bilateral CA3 that sends gamma-paced excitatory packages to the bilateral CA1, the lateral septum, and itself (recurrent input). The CA3-specific contribution was isolated from multisite LFPs in target regions using spatial discrimination techniques. We found strong modulation of LFPs by target-specific features, including the morphology and population arrangement of cells, the timing of CA3 inputs, volume conduction from nearby targets, and co-activated inhibition. Jointly they greatly affect the LFP amplitude, profile, and frequency characteristics. For instance, ipsilateral (Schaffer) LFPs occluded contralateral ones, and septal LFPs arise mostly from remote sources while local contribution from CA3 input was minor. In the CA3 itself, gamma waves have dual origin from local networks: in-phase excitatory and nearly antiphase inhibitory. Also, waves may have different duration and varying phase in different targets. These results indicate that to explore the cellular basis of LFPs and the functional connectivity between structures, besides identifying the origin population/s, target modifiers should be considered.

Mathematics and fiber arts

Mathematics can be found all over the world, even in what could be considered an unrelated area, like fiber arts. In knitting, crochet, and counted-thread embroidery, we can find concepts of algebra, graph theory, number theory, geometry of transformations, and symmetry, as well as computer science. For example, many fiber art pieces embody notions related with groups of symmetry. In this work, we focus on two areas of Mathematics associated with knitting, crochet, and cross-stitch works – number theory and geometry of transformations.

Magnetic resonance spectroscopy in seizure disorders

Key points • The clinical aims of MR spectroscopy (MRS) in seizure disorders are to help identify, localize and characterize epileptogenic foci. • Lateralizing MRS abnormalities in temporal lobe epilepsy (TLE) may be used clinically in combination with structural and T2 MRI measurements together with other techniques such as EEG, PET and SPECT. • Characteristic metabolite abnormalities are decreased N-acetylaspartate (NAA) with increased choline (Cho) and myoinositol (mI) (short-echo time). • Contralateral metabolite abnormalities are frequently seen in TLE, but are of uncertain significance. • In extra-temporal epilepsy, metabolite abnormalities may be seen where MR imaging (MRI) is normal; but may not be sufficiently localized to be useful clinically. • MRS may help to characterize epileptogenic lesions visible on MRI (aggressive vs. indolent neoplastic, dysplasia). • Spectral editing techniques are required to evaluate specific epilepsy-relevant metabolites (e.g. -aminobutyric acid (GABA)), which may be useful in drug development and evaluation. • MRS with phosphorus (31P) and other nuclei probe metabolism of epilepsy, but are less useful clinically. • There is potential for assessing the of drug mode of action and efficacy through 13C carbon metabolite measurements, while changes in sodium homeostasis resulting from seizure activity may be detected with 23Na MRS.