A generalization of Ramsey theory for graphs /

Bibliography: p. 16.

Studies in graph algorithms : generation and labeling problems /

Thesis--Illinois.

A graph-structure transformation model for picture parsing,

"COO-2118-0031."

A switching theory for bilateral nets of threshold elements.

Issued also as thesis, University of Illinois.

A generalization of Ramsey theory for graphs /

Includes bibliographical references.

Graph analysis of verbal fluency test discriminate between patients with Alzheimer’s disease, Mild Cognitive Impairment and normal elderly controls

Verbal fluency is the ability to produce a satisfying sequence of spoken words during a given time interval. The core of verbal fluency lies in the capacity to manage the executive aspects of language. The standard scores of the semantic verbal fluency test are broadly used in the neuropsychological assessment of the elderly, and different analytical methods are likely to extract even more information from the data generated in this test. Graph theory, a mathematical approach to analyze relations between items, represents a promising tool to understand a variety of neuropsychological states. This study reports a graph analysis of data generated by the semantic verbal fluency test by cognitively healthy elderly (NC), patients with Mild Cognitive Impairment – subtypes amnestic(aMCI) and amnestic multiple domain (a+mdMCI) - and patients with Alzheimer’s disease (AD). Sequences of words were represented as a speech graph in which every word corresponded to a node and temporal links between words were represented by directed edges. To characterize the structure of the data we calculated 13 speech graph attributes (SGAs). The individuals were compared when divided in three (NC – MCI – AD) and four (NC – aMCI – a+mdMCI – AD) groups. When the three groups were compared, significant differences were found in the standard measure of correct words produced, and three SGA: diameter, average shortest path, and network density. SGA sorted the elderly groups with good specificity and sensitivity. When the four groups were compared, the groups differed significantly in network density, except between the two MCI subtypes and NC and aMCI. The diameter of the network and the average shortest path were significantly different between the NC and AD, and between aMCI and AD. SGA sorted the elderly in their groups with good specificity and sensitivity, performing better than the standard score of the task. These findings provide support for a new methodological frame to assess the strength of semantic memory through the verbal fluency task, with potential to amplify the predictive power of this test. Graph analysis is likely to become clinically relevant in neurology and psychiatry, and may be particularly useful for the differential diagnosis of the elderly.

Graph analysis of verbal fluency test discriminate between patients with Alzheimer’s disease, Mild Cognitive Impairment and normal elderly controls

Verbal fluency is the ability to produce a satisfying sequence of spoken words during a given time interval. The core of verbal fluency lies in the capacity to manage the executive aspects of language. The standard scores of the semantic verbal fluency test are broadly used in the neuropsychological assessment of the elderly, and different analytical methods are likely to extract even more information from the data generated in this test. Graph theory, a mathematical approach to analyze relations between items, represents a promising tool to understand a variety of neuropsychological states. This study reports a graph analysis of data generated by the semantic verbal fluency test by cognitively healthy elderly (NC), patients with Mild Cognitive Impairment – subtypes amnestic(aMCI) and amnestic multiple domain (a+mdMCI) - and patients with Alzheimer’s disease (AD). Sequences of words were represented as a speech graph in which every word corresponded to a node and temporal links between words were represented by directed edges. To characterize the structure of the data we calculated 13 speech graph attributes (SGAs). The individuals were compared when divided in three (NC – MCI – AD) and four (NC – aMCI – a+mdMCI – AD) groups. When the three groups were compared, significant differences were found in the standard measure of correct words produced, and three SGA: diameter, average shortest path, and network density. SGA sorted the elderly groups with good specificity and sensitivity. When the four groups were compared, the groups differed significantly in network density, except between the two MCI subtypes and NC and aMCI. The diameter of the network and the average shortest path were significantly different between the NC and AD, and between aMCI and AD. SGA sorted the elderly in their groups with good specificity and sensitivity, performing better than the standard score of the task. These findings provide support for a new methodological frame to assess the strength of semantic memory through the verbal fluency task, with potential to amplify the predictive power of this test. Graph analysis is likely to become clinically relevant in neurology and psychiatry, and may be particularly useful for the differential diagnosis of the elderly.

Network Construction and Graph Theoretical Analysis of Functional Language Networks in Pediatric Epilepsy

This dissertation introduces a new approach for assessing the effects of pediatric epilepsy on the language connectome. Two novel data-driven network construction approaches are presented. These methods rely on connecting different brain regions using either extent or intensity of language related activations as identified by independent component analysis of fMRI data. An auditory description decision task (ADDT) paradigm was used to activate the language network for 29 patients and 30 controls recruited from three major pediatric hospitals. Empirical evaluations illustrated that pediatric epilepsy can cause, or is associated with, a network efficiency reduction. Patients showed a propensity to inefficiently employ the whole brain network to perform the ADDT language task; on the contrary, controls seemed to efficiently use smaller segregated network components to achieve the same task. To explain the causes of the decreased efficiency, graph theoretical analysis was carried out. The analysis revealed no substantial global network feature differences between the patient and control groups. It also showed that for both subject groups the language network exhibited small-world characteristics; however, the patient’s extent of activation network showed a tendency towards more random networks. It was also shown that the intensity of activation network displayed ipsilateral hub reorganization on the local level. The left hemispheric hubs displayed greater centrality values for patients, whereas the right hemispheric hubs displayed greater centrality values for controls. This hub hemispheric disparity was not correlated with a right atypical language laterality found in six patients. Finally it was shown that a multi-level unsupervised clustering scheme based on self-organizing maps, a type of artificial neural network, and k-means was able to fairly and blindly separate the subjects into their respective patient or control groups. The clustering was initiated using the local nodal centrality measurements only. Compared to the extent of activation network, the intensity of activation network clustering demonstrated better precision. This outcome supports the assertion that the local centrality differences presented by the intensity of activation network can be associated with focal epilepsy.

Simplicial Complexes From Graphs Toward Graph Persistence

Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph theory, we define the persistent block number and the persistent edge-block number.

User scheduling for low earth orbit multi-user multiple-input-multiple-output non-terrestrial network systems

In rural and isolated areas without cellular coverage, Satellite Communication (SatCom) is the best candidate to complement terrestrial coverage. However, the main challenge for future generations of wireless networks will be to meet the growing demand for new services while dealing with the scarcity of frequency spectrum. As a result, it is critical to investigate more efficient methods of utilizing the limited bandwidth; and resource sharing is likely the only choice. The research community’s focus has recently shifted towards the interference management and exploitation paradigm to meet the increasing data traffic demands. In the Downlink (DL) and Feedspace (FS), LEO satellites with an on-board antenna array can offer service to numerous User Terminals (UTs) (VSAT or Handhelds) on-ground in FFR schemes by using cutting-edge digital beamforming techniques. Considering this setup, the adoption of an effective user scheduling approach is a critical aspect given the unusually high density of User terminals on the ground as compared to the on-board available satellite antennas. In this context, one possibility is that of exploiting clustering algorithms for scheduling in LEO MU-MIMO systems in which several users within the same group are simultaneously served by the satellite via Space Division Multiplexing (SDM), and then these different user groups are served in different time slots via Time Division Multiplexing (TDM). This thesis addresses this problem by defining a user scheduling problem as an optimization problem and discusses several algorithms to solve it. In particular, focusing on the FS and user service link (i.e., DL) of a single MB-LEO satellite operating below 6 GHz, the user scheduling problem in the Frequency Division Duplex (FDD) mode is addressed. The proposed State-of-the-Art scheduling approaches are based on graph theory. The proposed solution offers high performance in terms of per-user capacity, Sum-rate capacity, SINR, and Spectral Efficiency.

Quantum Riemannian geometry on graphs for gauge field theory

In questo lavoro estendiamo concetti classici della geometria Riemanniana al fine di risolvere le equazioni di Maxwell sul gruppo delle permutazioni $S_3$. Cominciamo dando la strutture algebriche di base e la definizione di calcolo differenziale quantico con le principali proprietà. Generalizziamo poi concetti della geometria Riemanniana, quali la metrica e l'algebra esterna, al caso quantico. Tutto ciò viene poi applicato ai grafi dando la forma esplicita del calcolo differenziale quantico su $\mathbb{K}(V)$, della metrica e Laplaciano del secondo ordine e infine dell'algebra esterna. A questo punto, riscriviamo le equazioni di Maxwell in forma geometrica compatta usando gli operatori e concetti della geometria differenziale su varietà che abbiamo generalizzato in precedenza. In questo modo, considerando l'elettromagnetismo come teoria di gauge, possiamo risolvere le equazioni di Maxwell su gruppi finiti oltre che su varietà differenziabili. In particolare, noi le risolviamo su $S_3$.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Skewness, splitting number and vertex deletion of some toroidal meshes

The skewness sk(G) of a graph G = (V, E) is the smallest integer sk(G) >= 0 such that a planar graph can be obtained from G by the removal of sk(C) edges. The splitting number sp(G) of C is the smallest integer sp(G) >= 0 such that a planar graph can be obtained from G by sp(G) vertex splitting operations. The vertex deletion vd(G) of G is the smallest integer vd(G) >= 0 such that a planar graph can be obtained from G by the removal of vd(G) vertices. Regular toroidal meshes are popular topologies for the connection networks of SIMD parallel machines. The best known of these meshes is the rectangular toroidal mesh C(m) x C(n) for which is known the skewness, the splitting number and the vertex deletion. In this work we consider two related families: a triangulation Tc(m) x c(n) of C(m) x C(n) in the torus, and an hexagonal mesh Hc(m) x c(n), the dual of Tc(m) x c(n) in the torus. It is established that sp(Tc(m) x c(n)) = vd(Tc(m) x c(n) = sk(Hc(m) x c(n)) = sp(Hc(m) x c(n)) = vd(Hc(m) x c(n)) = min{m, n} and that sk(Tc(m) x c(n)) = 2 min {m, n}.