Topographic time-frequency decomposition of the EEG

Frequency-transformed EEG resting data has been widely used to describe normal and abnormal brain functional states as function of the spectral power in different frequency bands. This has yielded a series of clinically relevant findings. However, by transforming the EEG into the frequency domain, the initially excellent time resolution of time-domain EEG is lost. The topographic time-frequency decomposition is a novel computerized EEG analysis method that combines previously available techniques from time-domain spatial EEG analysis and time-frequency decomposition of single-channel time series. It yields a new, physiologically and statistically plausible topographic time-frequency representation of human multichannel EEG. The original EEG is accounted by the coefficients of a large set of user defined EEG like time-series, which are optimized for maximal spatial smoothness and minimal norm. These coefficients are then reduced to a small number of model scalp field configurations, which vary in intensity as a function of time and frequency. The result is thus a small number of EEG field configurations, each with a corresponding time-frequency (Wigner) plot. The method has several advantages: It does not assume that the data is composed of orthogonal elements, it does not assume stationarity, it produces topographical maps and it allows to include user-defined, specific EEG elements, such as spike and wave patterns. After a formal introduction of the method, several examples are given, which include artificial data and multichannel EEG during different physiological and pathological conditions.

Soil characteristics and decomposition of organic matter on Anchorage, Signy and Falkland Islands

Antarctic terrestrial ecosystems have poorly developed soils and currently experience one of the greatest rates of climate warming on the globe. We investigated the responsiveness of organic matter decomposition in Maritime Antarctic terrestrial ecosystems to climate change, using two study sites in the Antarctic Peninsula region (Anchorage Island, 67°S; Signy Island, 61°S), and contrasted the responses found with those at the cool temperate Falkland Islands (52°S). Our approach consisted of two complementary methods: (1) Laboratory measurements of decomposition at different temperatures (2, 6 and 10 °C) of plant material and soil organic matter from all three locations. (2) Field measurements at all three locations on the decomposition of soil organic matter, plant material and cellulose, both under natural conditions and under experimental warming (about 0.8 °C) achieved using open top chambers. Higher temperatures led to higher organic matter breakdown in the laboratory studies, indicating that decomposition in Maritime Antarctic terrestrial ecosystems is likely to increase with increasing soil temperatures. However, both laboratory and field studies showed that decomposition was more strongly influenced by local substratum characteristics (especially soil N availability) and plant functional type composition than by large-scale temperature differences. The very small responsiveness of organic matter decomposition in the field (experimental temperature increase <1 °C) compared with the laboratory (experimental increases of 4 or 8 °C) shows that substantial warming is required before significant effects can be detected.

Strong Connectivity in Directed Hypergraphs and its Application to the Atomic Decomposition of Ontologies

Los hipergrafos dirigidos se han empleado en problemas relacionados con lógica proposicional, bases de datos relacionales, linguística computacional y aprendizaje automático. Los hipergrafos dirigidos han sido también utilizados como alternativa a los grafos (bipartitos) dirigidos para facilitar el estudio de las interacciones entre componentes de sistemas complejos que no pueden ser fácilmente modelados usando exclusivamente relaciones binarias. En este contexto, este tipo de representación es conocida como hiper-redes. Un hipergrafo dirigido es una generalización de un grafo dirigido especialmente adecuado para la representación de relaciones de muchos a muchos. Mientras que una arista en un grafo dirigido define una relación entre dos de sus nodos, una hiperarista en un hipergrafo dirigido define una relación entre dos conjuntos de sus nodos. La conexión fuerte es una relación de equivalencia que divide el conjunto de nodos de un hipergrafo dirigido en particiones y cada partición define una clase de equivalencia conocida como componente fuertemente conexo. El estudio de los componentes fuertemente conexos de un hipergrafo dirigido puede ayudar a conseguir una mejor comprensión de la estructura de este tipo de hipergrafos cuando su tamaño es considerable. En el caso de grafo dirigidos, existen algoritmos muy eficientes para el cálculo de los componentes fuertemente conexos en grafos de gran tamaño. Gracias a estos algoritmos, se ha podido averiguar que la estructura de la WWW tiene forma de “pajarita”, donde más del 70% del los nodos están distribuidos en tres grandes conjuntos y uno de ellos es un componente fuertemente conexo. Este tipo de estructura ha sido también observada en redes complejas en otras áreas como la biología. Estudios de naturaleza similar no han podido ser realizados en hipergrafos dirigidos porque no existe algoritmos capaces de calcular los componentes fuertemente conexos de este tipo de hipergrafos. En esta tesis doctoral, hemos investigado como calcular los componentes fuertemente conexos de un hipergrafo dirigido. En concreto, hemos desarrollado dos algoritmos para este problema y hemos determinado que son correctos y cuál es su complejidad computacional. Ambos algoritmos han sido evaluados empíricamente para comparar sus tiempos de ejecución. Para la evaluación, hemos producido una selección de hipergrafos dirigidos generados de forma aleatoria inspirados en modelos muy conocidos de grafos aleatorios como Erdos-Renyi, Newman-Watts-Strogatz and Barabasi-Albert. Varias optimizaciones para ambos algoritmos han sido implementadas y analizadas en la tesis. En concreto, colapsar los componentes fuertemente conexos del grafo dirigido que se puede construir eliminando ciertas hiperaristas complejas del hipergrafo dirigido original, mejora notablemente los tiempos de ejecucion de los algoritmos para varios de los hipergrafos utilizados en la evaluación. Aparte de los ejemplos de aplicación mencionados anteriormente, los hipergrafos dirigidos han sido también empleados en el área de representación de conocimiento. En concreto, este tipo de hipergrafos se han usado para el cálculo de módulos de ontologías. Una ontología puede ser definida como un conjunto de axiomas que especifican formalmente un conjunto de símbolos y sus relaciones, mientras que un modulo puede ser entendido como un subconjunto de axiomas de la ontología que recoge todo el conocimiento que almacena la ontología sobre un conjunto especifico de símbolos y sus relaciones. En la tesis nos hemos centrado solamente en módulos que han sido calculados usando la técnica de localidad sintáctica. Debido a que las ontologías pueden ser muy grandes, el cálculo de módulos puede facilitar las tareas de re-utilización y mantenimiento de dichas ontologías. Sin embargo, analizar todos los posibles módulos de una ontología es, en general, muy costoso porque el numero de módulos crece de forma exponencial con respecto al número de símbolos y de axiomas de la ontología. Afortunadamente, los axiomas de una ontología pueden ser divididos en particiones conocidas como átomos. Cada átomo representa un conjunto máximo de axiomas que siempre aparecen juntos en un modulo. La decomposición atómica de una ontología es definida como un grafo dirigido de tal forma que cada nodo del grafo corresponde con un átomo y cada arista define una dependencia entre una pareja de átomos. En esta tesis introducimos el concepto de“axiom dependency hypergraph” que generaliza el concepto de descomposición atómica de una ontología. Un modulo en una ontología correspondería con un componente conexo en este tipo de hipergrafos y un átomo de una ontología con un componente fuertemente conexo. Hemos adaptado la implementación de nuestros algoritmos para que funcionen también con axiom dependency hypergraphs y poder de esa forma calcular los átomos de una ontología. Para demostrar la viabilidad de esta idea, hemos incorporado nuestros algoritmos en una aplicación que hemos desarrollado para la extracción de módulos y la descomposición atómica de ontologías. A la aplicación la hemos llamado HyS y hemos estudiado sus tiempos de ejecución usando una selección de ontologías muy conocidas del área biomédica, la mayoría disponibles en el portal de Internet NCBO. Los resultados de la evaluación muestran que los tiempos de ejecución de HyS son mucho mejores que las aplicaciones más rápidas conocidas. ABSTRACT Directed hypergraphs are an intuitive modelling formalism that have been used in problems related to propositional logic, relational databases, computational linguistic and machine learning. Directed hypergraphs are also presented as an alternative to directed (bipartite) graphs to facilitate the study of the interactions between components of complex systems that cannot naturally be modelled as binary relations. In this context, they are known as hyper-networks. A directed hypergraph is a generalization of a directed graph suitable for representing many-to-many relationships. While an edge in a directed graph defines a relation between two nodes of the graph, a hyperedge in a directed hypergraph defines a relation between two sets of nodes. Strong-connectivity is an equivalence relation that induces a partition of the set of nodes of a directed hypergraph into strongly-connected components. These components can be collapsed into single nodes. As result, the size of the original hypergraph can significantly be reduced if the strongly-connected components have many nodes. This approach might contribute to better understand how the nodes of a hypergraph are connected, in particular when the hypergraphs are large. In the case of directed graphs, there are efficient algorithms that can be used to compute the strongly-connected components of large graphs. For instance, it has been shown that the macroscopic structure of the World Wide Web can be represented as a “bow-tie” diagram where more than 70% of the nodes are distributed into three large sets and one of these sets is a large strongly-connected component. This particular structure has been also observed in complex networks in other fields such as, e.g., biology. Similar studies cannot be conducted in a directed hypergraph because there does not exist any algorithm for computing the strongly-connected components of the hypergraph. In this thesis, we investigate ways to compute the strongly-connected components of directed hypergraphs. We present two new algorithms and we show their correctness and computational complexity. One of these algorithms is inspired by Tarjan’s algorithm for directed graphs. The second algorithm follows a simple approach to compute the stronglyconnected components. This approach is based on the fact that two nodes of a graph that are strongly-connected can also reach the same nodes. In other words, the connected component of each node is the same. Both algorithms are empirically evaluated to compare their performances. To this end, we have produced a selection of random directed hypergraphs inspired by existent and well-known random graphs models like Erd˝os-Renyi and Newman-Watts-Strogatz. Besides the application examples that we mentioned earlier, directed hypergraphs have also been employed in the field of knowledge representation. In particular, they have been used to compute the modules of an ontology. An ontology is defined as a collection of axioms that provides a formal specification of a set of terms and their relationships; and a module is a subset of an ontology that completely captures the meaning of certain terms as defined in the ontology. In particular, we focus on the modules computed using the notion of syntactic locality. As ontologies can be very large, the computation of modules facilitates the reuse and maintenance of these ontologies. Analysing all modules of an ontology, however, is in general not feasible as the number of modules grows exponentially in the number of terms and axioms of the ontology. Nevertheless, the modules can succinctly be represented using the Atomic Decomposition of an ontology. Using this representation, an ontology can be partitioned into atoms, which are maximal sets of axioms that co-occur in every module. The Atomic Decomposition is then defined as a directed graph such that each node correspond to an atom and each edge represents a dependency relation between two atoms. In this thesis, we introduce the notion of an axiom dependency hypergraph which is a generalization of the atomic decomposition of an ontology. A module in the ontology corresponds to a connected component in the hypergraph, and the atoms of the ontology to the strongly-connected components. We apply our algorithms for directed hypergraphs to axiom dependency hypergraphs and in this manner, we compute the atoms of an ontology. To demonstrate the viability of this approach, we have implemented the algorithms in the application HyS which computes the modules of ontologies and calculate their atomic decomposition. In the thesis, we provide an experimental evaluation of HyS with a selection of large and prominent biomedical ontologies, most of which are available in the NCBO Bioportal. HyS outperforms state-of-the-art implementations in the tasks of extracting modules and computing the atomic decomposition of these ontologies.

Applications of Quantum Field Theory, From the Formal to the Phenomenological

Thesis (Ph.D.)--University of Washington, 2016-06

On decomposition of sub-linearised polynomials

We give a detailed exposition of the theory of decompositions of linearised polynomials, using a well-known connection with skew-polynomial rings with zero derivative. It is known that there is a one-to-one correspondence between decompositions of linearised polynomials and sub-linearised polynomials. This correspondence leads to a formula for the number of indecomposable sub-linearised polynomials of given degree over a finite field. We also show how to extend existing factorisation algorithms over skew-polynomial rings to decompose sub-linearised polynomials without asymptotic cost.

Solar thermal decomposition of desalination reject brine for carbon dioxide removal and neutralisation of ocean acidity

Desalination plants could become net absorbers (rather than net emitters) of CO2. Thermal decomposition of salts in desalination reject brine can yield MgO which, added to the ocean, would take up CO2 through conversion to bicarbonate. The process proposed here comprises dewatering of brine followed by decomposition in a solar receiver using a heliostat field.

Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

Let G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the isotropy subgroup at a point on such a variety is a parabolic subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the isotropy subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt.

Equivalence of quantum field theories related by the θ-exact Seiberg-Witten map

The equivalence of the noncommutative U(N) quantum field theories related by the θ-exact Seiberg-Witten maps is, in this paper, proven to all orders in the perturbation theory with respect to the coupling constant. We show that this holds for super Yang-Mills theories with N=0, 1, 2, 4 supersymmetry. A direct check of this equivalence relation is performed by computing the one-loop quantum corrections to the quadratic part of the effective action in the noncommutative U(1) gauge theory with N=0, 1, 2, 4 supersymmetry.

Thermal decomposition of mercerized linter cellulose and its acetates obtained from a homogeneous reaction

Cellulose acetates with different degrees of substitution (DS, from 0.6 to 1.9) were prepared from previously mercerized linter cellulose, in a homogeneous medium, using N,N-dimethylacetamide/lithium chloride as a solvent system. The influence of different degrees of substitution on the properties of cellulose acetates was investigated using thermogravimetric analyses (TGA). Quantitative methods were applied to the thermogravimetric curves in order to determine the apparent activation energy (Ea) related to the thermal decomposition of untreated and mercerized celluloses and cellulose acetates. Ea values were calculated using Broido's method and considering dynamic conditions. Ea values of 158 and 187 kJ mol-1 were obtained for untreated and mercerized cellulose, respectively. A previous study showed that C6OH is the most reactive site for acetylation, probably due to the steric hindrance of C2 and C3. The C6OH takes part in the first step of cellulose decomposition, leading to the formation of levoglucosan and, when it is changed to C6OCOCH3, the results indicate that the mechanism of thermal decomposition changes to one with a lower Ea. A linear correlation between Ea and the DS of the acetates prepared in the present work was identified.

Comparison of full-field electroretinogram in diabetic and non diabetic dogs with cataracts

Being the commonest ocular disorder, dense cataracts disable fundoscopic examination and the diagnosis of retinal disorders, which dogs may be predisposed. The aim of this study was to compare the electroretinographic responses recorded according to the International Society for Clinical Electrophysiology of Vision human protocol to evaluate retinal function of diabetic and non diabetic dogs, both presenting mature or hypermature cataracts. Full-field electroretinogram was recorded from 66 dogs, with ages varying from 6 to 15 years old allocated into two groups: (1) CG, non diabetic cataractous dogs, and (2) DG, diabetic cataractous dogs. Mean peak-to-peak amplitude (microvolts) and b-wave implicit time (milliseconds) were determined for each of the five standard full-field ERG responses (rod response, maximal response, oscillatory potentials, single-flash cone response and 30 Hz flicker). Comparing CG to DG, ERGs recorded from diabetic dogs presented lower amplitude and prolonged b-wave implicit time in all ERG responses. Prolonged b-wave implicit time was statistically significant (p< 0.05) at 30 Hz flicker (24.0 ms versus 22.4 ms). These data suggests full-field ERG is capable to record sensible alterations, such as flicker's implicit time, being useful to investigate retinal dysfunction in diabetic dogs.

Comparison of the Effects of Electrical Field Stimulation and Low-Level Laser Therapy on Bone Loss in Spinal Cord-Injured Rats

Objective: This study investigated the effects of low-level laser therapy (LLLT) and electrical stimulation (ES) on bone loss in spinal cord-injured rats. Materials and Methods: Thirty-seven male Wistar rats were divided into four groups: standard control group (CG); spinal cord-injured control (SC); spinal cord-injured treated with laser (SCL; GaAlAs, 830 nm, CW, 30mW/cm, 250 J/cm(2)); and spinal cord-injured treated with electrical field stimulation (SCE; 1.5 MHz, 1: 4 duty cycles, 30 mW, 20 min). Biomechanical, densitometric, and morphometric analyses were performed. Results: SC rats showed a significant decrease in bone mass, biomechanical properties, and morphometric parameters (versus CG). SCE rats showed significantly higher values of inner diameter and internal and external areas of tibia diaphyses; and the SCL group showed a trend toward the same result (versus SC). No increase was found in either mechanical or densitometric parameters. Conclusion: We conclude that the mentioned treatments were able to initiate a positive bone-tissue response, maybe through stimulation of osteoblasts, which was able to determine the observed morphometric modifications. However, the evoked tissue response could not determine either biomechanical or densitometric modifications.

The metal content of bulge field stars from FLAMES-GIRAFFE spectra - I. Stellar parameters and iron abundances

Aims. We determine the iron distribution function (IDF) for bulge field stars, in three different fields along the Galactic minor axis and at latitudes b = -4 degrees, b = -6 degrees, and b = -12 degrees. A fourth field including NGC 6553 is also included in the discussion. Methods. About 800 bulge field K giants were observed with the GIRAFFE spectrograph of FLAMES@VLT at spectral resolution R similar to 20 000. Several of them were observed again with UVES at R similar to 45 000 to insure the accuracy of the measurements. The LTE abundance analysis yielded stellar parameters and iron abundances that allowed us to construct an IDF for the bulge that, for the first time, is based on high-resolution spectroscopy for each individual star. Results. The IDF derived here is centered on solar metallicity, and extends from [Fe/H] similar to -1.5 to [Fe/H] similar to + 0.5. The distribution is asymmetric, with a sharper cutoff on the high-metallicity side, and it is narrower than previously measured. A variation in the mean metallicity along the bulge minor axis is clearly between b = -4 degrees and b = -6 degrees ([Fe/H] decreasing similar to by 0.6 dex per kpc). The field at b = -12 degrees. is consistent with the presence of a gradient, but its quantification is complicated by the higher disk/bulge fraction in this field. Conclusions. Our findings support a scenario in which both infall and outflow were important during the bulge formation, and then suggest the presence of a radial gradient, which poses some challenges to the scenario in which the bulge would result solely from the vertical heating of the bar.

Dynamical breaking of gauge symmetry in supersymmetric quantum electrodynamics in three-dimensional spacetime

The dynamical breaking of gauge symmetry in the supersymmetric quantum electrodynamics in three-dimensional spacetime is studied at two-loop approximation. At this level, the effective superpotential is evaluated in a supersymmetric phase. At one-loop order, we observe a generation of the Chern-Simons term due to a parity violating term present in the classical action. At two-loop order, the scalar background superfield acquires a nonvanishing vacuum expectation value, generating a mass term A(alpha)A(alpha) through the Coleman-Weinberg mechanism. It is observed that the mass of gauge superfield is predominantly an effect of the topological Chern-Simons term.

Decomposition of complete tripartite graphs into gregarious 4-cycles

A 4-cycle in a tripartite graph with vertex partition {V-1, V-2, V-3} is said to be gregarious if it has at least one vertex in each V-i, 1 less than or equal to i less than or equal to 3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.