Temporal task allocation in periodic environments. An approach based on synchronization

In this paper, we study a robot swarm that has to perform task allocation in an environment that features periodic properties. In this environment, tasks appear in different areas following periodic temporal patterns. The swarm has to reallocate its workforce periodically, performing a temporal task allocation that must be synchronized with the environment to be effective. We tackle temporal task allocation using methods and concepts that we borrow from the signal processing literature. In particular, we propose a distributed temporal task allocation algorithm that synchronizes robots of the swarm with the environment and with each other. In this algorithm, robots use only local information and a simple visual communication protocol based on light blinking. Our results show that a robot swarm that uses the proposed temporal task allocation algorithm performs considerably more tasks than a swarm that uses a greedy algorithm.

Influence of crowds in the dynamic characteristics of a structure

The interest for modelling of human actions acting on structures has been recurrent since the first accidents on suspension bridges in the nineteenth century like Broughton (1831) in the U.K. or Angers (1850) in France. Stadiums, gymnasiums are other type of structure where the human induced vibration is very important. In these structures appear particular phenomenon like the interaction person-structure (lock-in), the person-person synchronization, and the influence of the mass and damping of the people in the structure behaviour. This work focuses on the latter topic. The dynamic characteristic of a structure can be changed due to the presence of people on it. In order to evaluate these property modifications several testing have been carried out on a structure designed to be a gymnasium. For the test an electro-dynamic shaker was installed in a fixed point of the gym slab and different groups of people were located around the shaker. In each test the number of people was changed and also their posture (standing and sitting). Test data were analyzed and processed to verify modifications in the structure behaviour.

Modifications in the Dynamic Properties of a Structure due to Human Actions

The interest for modelling of human actions acting on structures has been recurrent since the first accidents on suspension bridges in the nineteenth century such as Broughton (1831) in the U.K. or Angers (1850) in France. Stadiums, gymnasiums are other types of structure where human induced vibration is very important. In these structures a particular phenomenon appears such as the interaction personstructure (lock-in), the person-person synchronization, and the influence of the mass and damping of the people in the structural behaviour. This paper focuses on the latter topic. In order to evaluate these property modifications several tests have been carried out on a stand-alone building. For the test an electro-dynamic shaker was installed at a fixed point of the gym slab and different groups of people were located around the shaker. The dynamic characteristics of the structure without people inside have been calculated by two methods: using a three-dimensional finite element model of the building and by operational modal analysis. These calculated experimental and numerical values are the reference values used to evaluate the modifications in the dynamic properties of the structure.

Multimodal integration of functional and structural brain connectivity. An application to the characterization of Mild Cognitive Impairment

La investigación para el conocimiento del cerebro es una ciencia joven, su inicio se remonta a Santiago Ramón y Cajal en 1888. Desde esta fecha a nuestro tiempo la neurociencia ha avanzado mucho en el desarrollo de técnicas que permiten su estudio. Desde la neurociencia cognitiva hoy se explican muchos modelos que nos permiten acercar a nuestro entendimiento a capacidades cognitivas complejas. Aun así hablamos de una ciencia casi en pañales que tiene un lago recorrido por delante. Una de las claves del éxito en los estudios de la función cerebral ha sido convertirse en una disciplina que combina conocimientos de diversas áreas: de la física, de las matemáticas, de la estadística y de la psicología. Esta es la razón por la que a lo largo de este trabajo se entremezclan conceptos de diferentes campos con el objetivo de avanzar en el conocimiento de un tema tan complejo como el que nos ocupa: el entendimiento de la mente humana. Concretamente, esta tesis ha estado dirigida a la integración multimodal de la magnetoencefalografía (MEG) y la resonancia magnética ponderada en difusión (dMRI). Estas técnicas son sensibles, respectivamente, a los campos magnéticos emitidos por las corrientes neuronales, y a la microestructura de la materia blanca cerebral. A lo largo de este trabajo hemos visto que la combinación de estas técnicas permiten descubrir sinergias estructurofuncionales en el procesamiento de la información en el cerebro sano y en el curso de patologías neurológicas. Más específicamente en este trabajo se ha estudiado la relación entre la conectividad funcional y estructural y en cómo fusionarlas. Para ello, se ha cuantificado la conectividad funcional mediante el estudio de la sincronización de fase o la correlación de amplitudes entre series temporales, de esta forma se ha conseguido un índice que mide la similitud entre grupos neuronales o regiones cerebrales. Adicionalmente, la cuantificación de la conectividad estructural a partir de imágenes de resonancia magnética ponderadas en difusión, ha permitido hallar índices de la integridad de materia blanca o de la fuerza de las conexiones estructurales entre regiones. Estas medidas fueron combinadas en los capítulos 3, 4 y 5 de este trabajo siguiendo tres aproximaciones que iban desde el nivel más bajo al más alto de integración. Finalmente se utilizó la información fusionada de MEG y dMRI para la caracterización de grupos de sujetos con deterioro cognitivo leve, la detección de esta patología resulta relevante en la identificación precoz de la enfermedad de Alzheimer. Esta tesis está dividida en seis capítulos. En el capítulos 1 se establece un contexto para la introducción de la connectómica dentro de los campos de la neuroimagen y la neurociencia. Posteriormente en este capítulo se describen los objetivos de la tesis, y los objetivos específicos de cada una de las publicaciones científicas que resultaron de este trabajo. En el capítulo 2 se describen los métodos para cada técnica que fue empleada: conectividad estructural, conectividad funcional en resting state, redes cerebrales complejas y teoría de grafos y finalmente se describe la condición de deterioro cognitivo leve y el estado actual en la búsqueda de nuevos biomarcadores diagnósticos. En los capítulos 3, 4 y 5 se han incluido los artículos científicos que fueron producidos a lo largo de esta tesis. Estos han sido incluidos en el formato de la revista en que fueron publicados, estando divididos en introducción, materiales y métodos, resultados y discusión. Todos los métodos que fueron empleados en los artículos están descritos en el capítulo 2 de la tesis. Finalmente, en el capítulo 6 se concluyen los resultados generales de la tesis y se discuten de forma específica los resultados de cada artículo. ABSTRACT In this thesis I apply concepts from mathematics, physics and statistics to the neurosciences. This field benefits from the collaborative work of multidisciplinary teams where physicians, psychologists, engineers and other specialists fight for a common well: the understanding of the brain. Research on this field is still in its early years, being its birth attributed to the neuronal theory of Santiago Ramo´n y Cajal in 1888. In more than one hundred years only a very little percentage of the brain functioning has been discovered, and still much more needs to be explored. Isolated techniques aim at unraveling the system that supports our cognition, nevertheless in order to provide solid evidence in such a field multimodal techniques have arisen, with them we will be able to improve current knowledge about human cognition. Here we focus on the multimodal integration of magnetoencephalography (MEG) and diffusion weighted magnetic resonance imaging. These techniques are sensitive to the magnetic fields emitted by the neuronal currents and to the white matter microstructure, respectively. The combination of such techniques could bring up evidences about structural-functional synergies in the brain information processing and which part of this synergy fails in specific neurological pathologies. In particular, we are interested in the relationship between functional and structural connectivity, and how two integrate this information. We quantify the functional connectivity by studying the phase synchronization or the amplitude correlation between time series obtained by MEG, and so we get an index indicating similarity between neuronal entities, i.e. brain regions. In addition we quantify structural connectivity by performing diffusion tensor estimation from the diffusion weighted images, thus obtaining an indicator of the integrity of the white matter or, if preferred, the strength of the structural connections between regions. These quantifications are then combined following three different approaches, from the lowest to the highest level of integration, in chapters 3, 4 and 5. We finally apply the fused information to the characterization or prediction of mild cognitive impairment, a clinical entity which is considered as an early step in the continuum pathological process of dementia. The dissertation is divided in six chapters. In chapter 1 I introduce connectomics within the fields of neuroimaging and neuroscience. Later in this chapter we describe the objectives of this thesis, and the specific objectives of each of the scientific publications that were produced as result of this work. In chapter 2 I describe the methods for each of the techniques that were employed, namely structural connectivity, resting state functional connectivity, complex brain networks and graph theory, and finally, I describe the clinical condition of mild cognitive impairment and the current state of the art in the search for early biomarkers. In chapters 3, 4 and 5 I have included the scientific publications that were generated along this work. They have been included in in their original format and they contain introduction, materials and methods, results and discussion. All methods that were employed in these papers have been described in chapter 2. Finally, in chapter 6 I summarize all the results from this thesis, both locally for each of the scientific publications and globally for the whole work.

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Formal Verification of Temporal Properties for Parametrized Concurrent Programs and Concurrent Data Structures

Los tipos de datos concurrentes son implementaciones concurrentes de las abstracciones de datos clásicas, con la diferencia de que han sido específicamente diseñados para aprovechar el gran paralelismo disponible en las modernas arquitecturas multiprocesador y multinúcleo. La correcta manipulación de los tipos de datos concurrentes resulta esencial para demostrar la completa corrección de los sistemas de software que los utilizan. Una de las mayores dificultades a la hora de diseñar y verificar tipos de datos concurrentes surge de la necesidad de tener que razonar acerca de un número arbitrario de procesos que invocan estos tipos de datos de manera concurrente. Esto requiere considerar sistemas parametrizados. En este trabajo estudiamos la verificación formal de propiedades temporales de sistemas concurrentes parametrizados, poniendo especial énfasis en programas que manipulan estructuras de datos concurrentes. La principal dificultad a la hora de razonar acerca de sistemas concurrentes parametrizados proviene de la interacción entre el gran nivel de concurrencia que éstos poseen y la necesidad de razonar al mismo tiempo acerca de la memoria dinámica. La verificación de sistemas parametrizados resulta en sí un problema desafiante debido a que requiere razonar acerca de estructuras de datos complejas que son accedidas y modificadas por un numero ilimitado de procesos que manipulan de manera simultánea el contenido de la memoria dinámica empleando métodos de sincronización poco estructurados. En este trabajo, presentamos un marco formal basado en métodos deductivos capaz de ocuparse de la verificación de propiedades de safety y liveness de sistemas concurrentes parametrizados que manejan estructuras de datos complejas. Nuestro marco formal incluye reglas de prueba y técnicas especialmente adaptadas para sistemas parametrizados, las cuales trabajan en colaboración con procedimientos de decisión especialmente diseñados para analizar complejas estructuras de datos concurrentes. Un aspecto novedoso de nuestro marco formal es que efectúa una clara diferenciación entre el análisis del flujo de control del programa y el análisis de los datos que se manejan. El flujo de control del programa se analiza utilizando reglas de prueba y técnicas de verificación deductivas especialmente diseñadas para lidiar con sistemas parametrizados. Comenzando a partir de un programa concurrente y la especificación de una propiedad temporal, nuestras técnicas deductivas son capaces de generar un conjunto finito de condiciones de verificación cuya validez implican la satisfacción de dicha especificación temporal por parte de cualquier sistema, sin importar el número de procesos que formen parte del sistema. Las condiciones de verificación generadas se corresponden con los datos manipulados. Estudiamos el diseño de procedimientos de decisión especializados capaces de lidiar con estas condiciones de verificación de manera completamente automática. Investigamos teorías decidibles capaces de describir propiedades de tipos de datos complejos que manipulan punteros, tales como implementaciones imperativas de pilas, colas, listas y skiplists. Para cada una de estas teorías presentamos un procedimiento de decisión y una implementación práctica construida sobre SMT solvers. Estos procedimientos de decisión son finalmente utilizados para verificar de manera automática las condiciones de verificación generadas por nuestras técnicas de verificación parametrizada. Para concluir, demostramos como utilizando nuestro marco formal es posible probar no solo propiedades de safety sino además de liveness en algunas versiones de protocolos de exclusión mutua y programas que manipulan estructuras de datos concurrentes. El enfoque que presentamos en este trabajo resulta ser muy general y puede ser aplicado para verificar un amplio rango de tipos de datos concurrentes similares. Abstract Concurrent data types are concurrent implementations of classical data abstractions, specifically designed to exploit the great deal of parallelism available in modern multiprocessor and multi-core architectures. The correct manipulation of concurrent data types is essential for the overall correctness of the software system built using them. A major difficulty in designing and verifying concurrent data types arises by the need to reason about any number of threads invoking the data type simultaneously, which requires considering parametrized systems. In this work we study the formal verification of temporal properties of parametrized concurrent systems, with a special focus on programs that manipulate concurrent data structures. The main difficulty to reason about concurrent parametrized systems comes from the combination of their inherently high concurrency and the manipulation of dynamic memory. This parametrized verification problem is very challenging, because it requires to reason about complex concurrent data structures being accessed and modified by threads which simultaneously manipulate the heap using unstructured synchronization methods. In this work, we present a formal framework based on deductive methods which is capable of dealing with the verification of safety and liveness properties of concurrent parametrized systems that manipulate complex data structures. Our framework includes special proof rules and techniques adapted for parametrized systems which work in collaboration with specialized decision procedures for complex data structures. A novel aspect of our framework is that it cleanly differentiates the analysis of the program control flow from the analysis of the data being manipulated. The program control flow is analyzed using deductive proof rules and verification techniques specifically designed for coping with parametrized systems. Starting from a concurrent program and a temporal specification, our techniques generate a finite collection of verification conditions whose validity entails the satisfaction of the temporal specification by any client system, in spite of the number of threads. The verification conditions correspond to the data manipulation. We study the design of specialized decision procedures to deal with these verification conditions fully automatically. We investigate decidable theories capable of describing rich properties of complex pointer based data types such as stacks, queues, lists and skiplists. For each of these theories we present a decision procedure, and its practical implementation on top of existing SMT solvers. These decision procedures are ultimately used for automatically verifying the verification conditions generated by our specialized parametrized verification techniques. Finally, we show how using our framework it is possible to prove not only safety but also liveness properties of concurrent versions of some mutual exclusion protocols and programs that manipulate concurrent data structures. The approach we present in this work is very general, and can be applied to verify a wide range of similar concurrent data types.

Efficient parallelization of a regional ocean model for the western Mediterranean Sea

This paper focuses on the parallelization of an ocean model applying current multicore processor-based cluster architectures to an irregular computational mesh. The aim is to maximize the efficiency of the computational resources used. To make the best use of the resources offered by these architectures, this parallelization has been addressed at all the hardware levels of modern supercomputers: firstly, exploiting the internal parallelism of the CPU through vectorization; secondly, taking advantage of the multiple cores of each node using OpenMP; and finally, using the cluster nodes to distribute the computational mesh, using MPI for communication within the nodes. The speedup obtained with each parallelization technique as well as the combined overall speedup have been measured for the western Mediterranean Sea for different cluster configurations, achieving a speedup factor of 73.3 using 256 processors. The results also show the efficiency achieved in the different cluster nodes and the advantages obtained by combining OpenMP and MPI versus using only OpenMP or MPI. Finally, the scalability of the model has been analysed by examining computation and communication times as well as the communication and synchronization overhead due to parallelization.

Automated wordlength optimization framework for multi-source statistical interval-based analysis of nonlinear systems with control-flow structures

El uso de aritmética de punto fijo es una opción de diseño muy extendida en sistemas con fuertes restricciones de área, consumo o rendimiento. Para producir implementaciones donde los costes se minimicen sin impactar negativamente en la precisión de los resultados debemos llevar a cabo una asignación cuidadosa de anchuras de palabra. Encontrar la combinación óptima de anchuras de palabra en coma fija para un sistema dado es un problema combinatorio NP-hard al que los diseñadores dedican entre el 25 y el 50 % del ciclo de diseño. Las plataformas hardware reconfigurables, como son las FPGAs, también se benefician de las ventajas que ofrece la aritmética de coma fija, ya que éstas compensan las frecuencias de reloj más bajas y el uso más ineficiente del hardware que hacen estas plataformas respecto a los ASICs. A medida que las FPGAs se popularizan para su uso en computación científica los diseños aumentan de tamaño y complejidad hasta llegar al punto en que no pueden ser manejados eficientemente por las técnicas actuales de modelado de señal y ruido de cuantificación y de optimización de anchura de palabra. En esta Tesis Doctoral exploramos distintos aspectos del problema de la cuantificación y presentamos nuevas metodologías para cada uno de ellos: Las técnicas basadas en extensiones de intervalos han permitido obtener modelos de propagación de señal y ruido de cuantificación muy precisos en sistemas con operaciones no lineales. Nosotros llevamos esta aproximación un paso más allá introduciendo elementos de Multi-Element Generalized Polynomial Chaos (ME-gPC) y combinándolos con una técnica moderna basada en Modified Affine Arithmetic (MAA) estadístico para así modelar sistemas que contienen estructuras de control de flujo. Nuestra metodología genera los distintos caminos de ejecución automáticamente, determina las regiones del dominio de entrada que ejercitarán cada uno de ellos y extrae los momentos estadísticos del sistema a partir de dichas soluciones parciales. Utilizamos esta técnica para estimar tanto el rango dinámico como el ruido de redondeo en sistemas con las ya mencionadas estructuras de control de flujo y mostramos la precisión de nuestra aproximación, que en determinados casos de uso con operadores no lineales llega a tener tan solo una desviación del 0.04% con respecto a los valores de referencia obtenidos mediante simulación. Un inconveniente conocido de las técnicas basadas en extensiones de intervalos es la explosión combinacional de términos a medida que el tamaño de los sistemas a estudiar crece, lo cual conlleva problemas de escalabilidad. Para afrontar este problema presen tamos una técnica de inyección de ruidos agrupados que hace grupos con las señales del sistema, introduce las fuentes de ruido para cada uno de los grupos por separado y finalmente combina los resultados de cada uno de ellos. De esta forma, el número de fuentes de ruido queda controlado en cada momento y, debido a ello, la explosión combinatoria se minimiza. También presentamos un algoritmo de particionado multi-vía destinado a minimizar la desviación de los resultados a causa de la pérdida de correlación entre términos de ruido con el objetivo de mantener los resultados tan precisos como sea posible. La presente Tesis Doctoral también aborda el desarrollo de metodologías de optimización de anchura de palabra basadas en simulaciones de Monte-Cario que se ejecuten en tiempos razonables. Para ello presentamos dos nuevas técnicas que exploran la reducción del tiempo de ejecución desde distintos ángulos: En primer lugar, el método interpolativo aplica un interpolador sencillo pero preciso para estimar la sensibilidad de cada señal, y que es usado después durante la etapa de optimización. En segundo lugar, el método incremental gira en torno al hecho de que, aunque es estrictamente necesario mantener un intervalo de confianza dado para los resultados finales de nuestra búsqueda, podemos emplear niveles de confianza más relajados, lo cual deriva en un menor número de pruebas por simulación, en las etapas iniciales de la búsqueda, cuando todavía estamos lejos de las soluciones optimizadas. Mediante estas dos aproximaciones demostramos que podemos acelerar el tiempo de ejecución de los algoritmos clásicos de búsqueda voraz en factores de hasta x240 para problemas de tamaño pequeño/mediano. Finalmente, este libro presenta HOPLITE, una infraestructura de cuantificación automatizada, flexible y modular que incluye la implementación de las técnicas anteriores y se proporciona de forma pública. Su objetivo es ofrecer a desabolladores e investigadores un entorno común para prototipar y verificar nuevas metodologías de cuantificación de forma sencilla. Describimos el flujo de trabajo, justificamos las decisiones de diseño tomadas, explicamos su API pública y hacemos una demostración paso a paso de su funcionamiento. Además mostramos, a través de un ejemplo sencillo, la forma en que conectar nuevas extensiones a la herramienta con las interfaces ya existentes para poder así expandir y mejorar las capacidades de HOPLITE. ABSTRACT Using fixed-point arithmetic is one of the most common design choices for systems where area, power or throughput are heavily constrained. In order to produce implementations where the cost is minimized without negatively impacting the accuracy of the results, a careful assignment of word-lengths is required. The problem of finding the optimal combination of fixed-point word-lengths for a given system is a combinatorial NP-hard problem to which developers devote between 25 and 50% of the design-cycle time. Reconfigurable hardware platforms such as FPGAs also benefit of the advantages of fixed-point arithmetic, as it compensates for the slower clock frequencies and less efficient area utilization of the hardware platform with respect to ASICs. As FPGAs become commonly used for scientific computation, designs constantly grow larger and more complex, up to the point where they cannot be handled efficiently by current signal and quantization noise modelling and word-length optimization methodologies. In this Ph.D. Thesis we explore different aspects of the quantization problem and we present new methodologies for each of them: The techniques based on extensions of intervals have allowed to obtain accurate models of the signal and quantization noise propagation in systems with non-linear operations. We take this approach a step further by introducing elements of MultiElement Generalized Polynomial Chaos (ME-gPC) and combining them with an stateof- the-art Statistical Modified Affine Arithmetic (MAA) based methodology in order to model systems that contain control-flow structures. Our methodology produces the different execution paths automatically, determines the regions of the input domain that will exercise them, and extracts the system statistical moments from the partial results. We use this technique to estimate both the dynamic range and the round-off noise in systems with the aforementioned control-flow structures. We show the good accuracy of our approach, which in some case studies with non-linear operators shows a 0.04 % deviation respect to the simulation-based reference values. A known drawback of the techniques based on extensions of intervals is the combinatorial explosion of terms as the size of the targeted systems grows, which leads to scalability problems. To address this issue we present a clustered noise injection technique that groups the signals in the system, introduces the noise terms in each group independently and then combines the results at the end. In this way, the number of noise sources in the system at a given time is controlled and, because of this, the combinato rial explosion is minimized. We also present a multi-way partitioning algorithm aimed at minimizing the deviation of the results due to the loss of correlation between noise terms, in order to keep the results as accurate as possible. This Ph.D. Thesis also covers the development of methodologies for word-length optimization based on Monte-Carlo simulations in reasonable times. We do so by presenting two novel techniques that explore the reduction of the execution times approaching the problem in two different ways: First, the interpolative method applies a simple but precise interpolator to estimate the sensitivity of each signal, which is later used to guide the optimization effort. Second, the incremental method revolves on the fact that, although we strictly need to guarantee a certain confidence level in the simulations for the final results of the optimization process, we can do it with more relaxed levels, which in turn implies using a considerably smaller amount of samples, in the initial stages of the process, when we are still far from the optimized solution. Through these two approaches we demonstrate that the execution time of classical greedy techniques can be accelerated by factors of up to ×240 for small/medium sized problems. Finally, this book introduces HOPLITE, an automated, flexible and modular framework for quantization that includes the implementation of the previous techniques and is provided for public access. The aim is to offer a common ground for developers and researches for prototyping and verifying new techniques for system modelling and word-length optimization easily. We describe its work flow, justifying the taken design decisions, explain its public API and we do a step-by-step demonstration of its execution. We also show, through an example, the way new extensions to the flow should be connected to the existing interfaces in order to expand and improve the capabilities of HOPLITE.

Synchronization between prefrontal and posterior association cortex during human working memory

We measured coherence between the electroencephalogram at different scalp sites while human subjects performed delayed response tasks. The tasks required the retention of either verbalizable strings of characters or abstract line drawings. In both types of tasks, a significant enhancement in coherence in the θ range (4–7 Hz) was found between prefrontal and posterior electrodes during 4-s retention intervals. During 6-s perception intervals, far fewer increases in θ coherence were found. Also in other frequency bands, coherence increased; however, the patterns of enhancement made a relevance for working memory processes seem unlikely. Our results suggest that working memory involves synchronization between prefrontal and posterior association cortex by phase-locked, low frequency (4–7 Hz) brain activity.

Approximate solution for frequency synchronization in a finite-size Kuramoto model

Peer reviewed

Multistability, chaos, and random signal generation in semiconductor superlattices

Peer reviewed

Gamma rhythms and beta rhythms have different synchronization properties

Experimental and modeling efforts suggest that rhythms in the CA1 region of the hippocampus that are in the beta range (12–29 Hz) have a different dynamical structure than that of gamma (30–70 Hz). We use a simplified model to show that the different rhythms employ different dynamical mechanisms to synchronize, based on different ionic currents. The beta frequency is able to synchronize over long conduction delays (corresponding to signals traveling a significant distance in the brain) that apparently cannot be tolerated by gamma rhythms. The synchronization properties are consistent with data suggesting that gamma rhythms are used for relatively local computations whereas beta rhythms are used for higher level interactions involving more distant structures.

Information about movement direction obtained from synchronous activity of motor cortical neurons

Although neuronal synchronization has been shown to exist in primary motor cortex (MI), very little is known about its possible contribution to coding of movement. By using cross-correlation techniques from multi-neuron recordings in MI, we observed that activity of neurons commonly synchronized around the time of movement initiation. For some cell pairs, synchrony varied with direction in a manner not readily predicted by the firing of either neuron. Information theoretic analysis demonstrated quantitatively that synchrony provides information about movement direction beyond that expected by simple rate changes. Thus, MI neurons are not simply independent encoders of movement parameters but rather engage in mutual interactions that could potentially provide an additional coding dimension in cortex.

Experimentally determined chaotic phase synchronization in a neuronal system

Mathematical analysis of the subthreshold oscillatory properties of inferior olivary neurons in vitro indicates that the oscillation is nonlinear and supports low dimensional chaotic dynamics. This property leads to the generation of complex functional states that can be attained rapidly via phase coherence that conform to the category of “generalized synchronization.” Functionally, this translates into neuronal ensemble properties that can support maximum functional permissiveness and that rapidly can transform into robustly determined multicellular coherence.