Dans cette thèse, nous utilisons un ensemble d'outils avancés de mathématiques et de méthodes de traitement du signal pour aborder trois problèmes importants en neuroscience: la détection de potentiels d'action (spikes), leur tri, et le codage neuronal. A partir d'enregistrements invasifs de l'activité de neurones, nous avons d'abord abordé la question de la détection de spikes. Les instants d'occurrence des spikes apparaissent (comme des irrégularités) de manière explicite dans les dérivées distributionnelles du signal neuronal. Le problème est alors posé en termes de détection et estimation conjointe de ces instants d'occurrence. En utilisant le calcul opérationnel, qui fournit un cadre commode pour manipuler des Dirac, nous caractérisons le temps d'occurrence d'un spike par une formule explicite. Après la détection nous abordons le problème du tri de spikes. Nous avons développé un algorithme simple pour des enregistrements multi-canaux. Il utilise une application itérative de l'algorithme ICA et une technique de déflation dans deux boucles imbriquées. Dans chaque itération de la boucle externe, l'activité d'un neurone est ciblée, puis isolée et ensuite élaguée des enregistrements. La boucle interne met en œuvre une séquence d'applications de ICA et de détection afin de supprimer tout ce qui ne relève pas du neurone cible. Enfin, nous menons une discussion sur les propriétés du code neuronal. Nous examinons l'hypothèse d'un code reposant sur un alphabet fini. Cette hypothèse correspond à un schéma de modulation PPM qui est déjà suggéré par le codage temporel et la présence de jitter.

This thesis contributes to the empirical literature on how firms meet exceptional financing needs in relation to “investment spikes” or years with unusually large investment activities. In the earlier part of the thesis, I show that the financing of investment during an investment spike is very different from that at other times. I have done this using data for publicly traded US firms over the period 1988 to 2007 and a filtering procedure suggested by Bond et al. (2006). Specifically, external finance, in particular debt finance, is very important in financing investment in years categorized as investment spikes, confirming the findings of Mayer and Sussman (2005). In addition, it has been found that firms with smaller size, lower profitability, more future growth opportunities, fewer tangible assets and more R&D spending tend to use more equity finance in relation to large investment requirements. I also propose the use of the Markov-switching filter to identify investment spikes. In implementing the Markov-switching filter, I apply a first-order two-state Markov-switching mean model to the investment rates de-trended using Hodrick and Prescott's (1997) filter. A Gibbs-sampling procedure is used to produce the marginal posterior distributions of unobserved state variables and model parameters. Among other advantages, this filter allows us to identify multi-year investment spikes. I show that two-year investment spikes identified by the Markov-switching filter are financed quite similarly to single-year investment spikes and that main findings are robust to calendar-time-dependent clustering of investment spikes generated by macroeconomic shocks. In the later part of the thesis, I find there is a positive effect of share liquidity on the propensity to raise debt finance. Using a sample of firm-year observations identified as investment spikes, I find that firms with more liquid shares tend to rely more heavily on debt to finance investment spikes. This result is robust to a control for the effects of firm size and other firm characteristics, the use of various leverage measures, and the use of a whole sample with investment spike characteristics. Another important finding is that firms with more liquid shares tend to have higher target leverage ratios. One interpretation of these results is that information spillovers from the presence of more informative share prices allow firms with more liquid shares to borrow on more favourable terms in normal times, as well as to obtain additional debt finance at lower costs when taking advantage of unusually large investment opportunities.

Epilepsy is a neurological disease causing seizures in its victims and affects approximately 50 million people worldwide. Successful treatment is dependent upon correct identification of the origin of the seizures within the brain. To achieve this, electroencephalograms (EEGs) are used to measure a patient’s brainwaves. This EEG data must be manually analyzed to identify interictal spikes that emanate from the afflicted region of the brain. This process can take a neurologist more than a week and a half per patient. This thesis presents a method to extract and process the interictal spikes in a patient, and use them to reduce the amount of data for a neurologist to manually analyze. The effectiveness of multiple neural network implementations is compared, and a data reduction of 3-4 orders of magnitude, or upwards of 99%, is achieved.

We consider a type of forced "Van Der Pol" oscillator where the forced function is periodic and oscillatory around the t-axis. This problem derived from an electrical model. The important issues here is that this circuits presents the spiking phenomena over a one time period and it has important applications in signal processing and digital communication. The three most important problems that we addressed here in this thesis are to compute the number of spikes a solution completes in one time period (it can be used to transform the analog signal into digital information), how the dynamics of the number of spikes change with respect to the parameters amplitude (k) and frequency (w), and when the coupled circuits synchronize (i.e., the driver and the respond are on synchronous). Sophisticated mathematical and numerical analysis has been developed that enable us to give a complete study of the problems above described.

Thesis (M. Sc.), Memorial University of Newfoundland, 1999. / Bibliography: p. 194-229.

abstract: Interictal spikes, together with seizures, have been recognized as the two hallmarks of epilepsy, a brain disorder that 1% of the world's population suffers from. Even though the presence of spikes in brain's electromagnetic activity has diagnostic value, their dynamics are still elusive. It was an objective of this dissertation to formulate a mathematical framework within which the dynamics of interictal spikes could be thoroughly investigated. A new epileptic spike detection algorithm was developed by employing data adaptive morphological filters. The performance of the spike detection algorithm was favorably compared with others in the literature. A novel spike spatial synchronization measure was developed and tested on coupled spiking neuron models. Application of this measure to individual epileptic spikes in EEG from patients with temporal lobe epilepsy revealed long-term trends of increase in synchronization between pairs of brain sites before seizures and desynchronization after seizures, in the same patient as well as across patients, thus supporting the hypothesis that seizures may occur to break (reset) the abnormal spike synchronization in the brain network. Furthermore, based on these results, a separate spatial analysis of spike rates was conducted that shed light onto conflicting results in the literature about variability of spike rate before and after seizure. The ability to automatically classify seizures into clinical and subclinical was a result of the above findings. A novel method for epileptogenic focus localization from interictal periods based on spike occurrences was also devised, combining concepts from graph theory, like eigenvector centrality, and the developed spike synchronization measure, and tested very favorably against the utilized gold rule in clinical practice for focus localization from seizures onset. Finally, in another application of resetting of brain dynamics at seizures, it was shown that it is possible to differentiate with a high accuracy between patients with epileptic seizures (ES) and patients with psychogenic nonepileptic seizures (PNES). The above studies of spike dynamics have elucidated many unknown aspects of ictogenesis and it is expected to significantly contribute to further understanding of the basic mechanisms that lead to seizures, the diagnosis and treatment of epilepsy. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012

The aim of this essay is to question and analyze problems surrounding the current research within the field of spikes.The latest breakout was in the early 50's,since then there haven't been any major research projects and no interpretation have been made.Not only does this  essay bring a contribution to the research of spikes but also question what has earlier been established through interpretations.The focus of this essay is on the spikes found on the island of Gotland in the Baltic sea,these are currently stored at the Museum of Gotland.What was the main area of use that these spikes had and in which context are they found? Although only 27 finds will be analyzed during this essay ,the goal is to get a greater understanding of the usage of these finds and how this will contribute to the archaelogical sites.

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The ocean influences global weather patterns, stores and transports heat, and supports entire ecosystems. An area of interest is the relationship between the observed backscattered power received by a surface-based marine radar and the ocean surface topography. Current methods for obtaining surface elevation maps involve either in situ devices, which only provide point measurements, or an interferometric radar, which can be costly. During the late 1990's and early 2000's a radar was built at UMass, called the Focused Phased Array Imaging Radar II (FOPAIR II), and deployed at a several locations. A method is discussed to determine a transfer function between displacement and backscattered power for each of the range bins used by the radar and evaluate it's accuracy by applying the transfer function to separate data sets. In addition, it is known that horizontal polarized (H-Pol) backscatter exhibits a very different characteristic than vertical polarization (V-Pol). The horizontal polarization data exhibits less echo power except for intermittent bright spots, colloquially called “sea spikes'', that only briefly occur. Determining if there is correlation between these bright returns and a characteristic of the of the surface topography is investigated.

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