Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Signal processing of physiological signals for automated assessment of stress in computer users

The need to provide computers with the ability to distinguish the affective state of their users is a major requirement for the practical implementation of affective computing concepts. This dissertation proposes the application of signal processing methods on physiological signals to extract from them features that can be processed by learning pattern recognition systems to provide cues about a person's affective state. In particular, combining physiological information sensed from a user's left hand in a non-invasive way with the pupil diameter information from an eye-tracking system may provide a computer with an awareness of its user's affective responses in the course of human-computer interactions. In this study an integrated hardware-software setup was developed to achieve automatic assessment of the affective status of a computer user. A computer-based "Paced Stroop Test" was designed as a stimulus to elicit emotional stress in the subject during the experiment. Four signals: the Galvanic Skin Response (GSR), the Blood Volume Pulse (BVP), the Skin Temperature (ST) and the Pupil Diameter (PD), were monitored and analyzed to differentiate affective states in the user. Several signal processing techniques were applied on the collected signals to extract their most relevant features. These features were analyzed with learning classification systems, to accomplish the affective state identification. Three learning algorithms: Naïve Bayes, Decision Tree and Support Vector Machine were applied to this identification process and their levels of classification accuracy were compared. The results achieved indicate that the physiological signals monitored do, in fact, have a strong correlation with the changes in the emotional states of the experimental subjects. These results also revealed that the inclusion of pupil diameter information significantly improved the performance of the emotion recognition system. ^

Endocrine regulation of dynamic communication signals in gymnotiform fish

Communication signals are shaped by the opposing selection pressures imposed by predators and mates. A dynamic signal might serve as an adaptive compromise between an inconspicuous signal that evades predators and an extravagant signal preferred by females. Such a signal has been described in the gymnotiform electric fish, Brachyhypopomus gauderio, which produces a sexually dimorphic electric organ discharge (EOD). The EOD varies on a circadian rhythm and in response to social cues. This signal plasticity is mediated by the slow action of androgens and rapid action of melanocortins. My dissertation research tested the hypotheses that (1) signal plasticity is related to sociality levels in gymnotiform species, and (2) differences in signal plasticity are regulated by differential sensitivity to androgen and melanocortin hormones. To assess the breadth of dynamic signaling within the order Gymnotiformes, I sampled 13 species from the five gymnotiform families. I recorded EODs to observe spontaneous signal oscillations after which I injected melanocortin hormones, saline control, or presented the fish with a conspecific. I showed that through the co-option of the ancient melanocortin pathway, gymnotiforms dynamically regulate EOD amplitude, spectral frequency, both, or neither. To investigate whether observed EOD plasticities are related to species-specific sociality I tested four species; two territorial, highly aggressive species, Gymnotus carapo and Apteronotus leptorhynchus, a highly gregarious species, Eigenmannia cf. virescens , and an intermediate short-lived species with a fluid social system, Brachyhypopomus gauderio. I examined the relationship between the androgens testosterone and 11-ketotestosterone, the melanocortin α-MSH, and their roles in regulating EOD waveform. I implanted all fish with androgen and blank silicone implants, and injected with α-MSH before and at the peak of implant effect. I found that waveforms of the most territorial and aggressive species were insensitive to hormone treatments; maintaining a static, stereotyped signal that preserves encoding of individual identity. Species with a fluid social system were most responsive to hormone treatments, exhibiting signals that reflect immediate condition and reproductive state. In conclusion, variation in gymnotiform signal plasticity is hormonally regulated and seems to reflect species-specific sociality.

Assessment of the Spatial and Temporal Distribution of Functional Connectivity in Resting-State BOLD fMRI

Recent research into resting-state functional magnetic resonance imaging (fMRI) has shown that the brain is very active during rest. This thesis work utilizes blood oxygenation level dependent (BOLD) signals to investigate the spatial and temporal functional network information found within resting-state data, and aims to investigate the feasibility of extracting functional connectivity networks using different methods as well as the dynamic variability within some of the methods. Furthermore, this work looks into producing valid networks using a sparsely-sampled sub-set of the original data.

In this work we utilize four main methods: independent component analysis (ICA), principal component analysis (PCA), correlation, and a point-processing technique. Each method comes with unique assumptions, as well as strengths and limitations into exploring how the resting state components interact in space and time.

Correlation is perhaps the simplest technique. Using this technique, resting-state patterns can be identified based on how similar the time profile is to a seed region’s time profile. However, this method requires a seed region and can only identify one resting state network at a time. This simple correlation technique is able to reproduce the resting state network using subject data from one subject’s scan session as well as with 16 subjects.

Independent component analysis, the second technique, has established software programs that can be used to implement this technique. ICA can extract multiple components from a data set in a single analysis. The disadvantage is that the resting state networks it produces are all independent of each other, making the assumption that the spatial pattern of functional connectivity is the same across all the time points. ICA is successfully able to reproduce resting state connectivity patterns for both one subject and a 16 subject concatenated data set.

Using principal component analysis, the dimensionality of the data is compressed to find the directions in which the variance of the data is most significant. This method utilizes the same basic matrix math as ICA with a few important differences that will be outlined later in this text. Using this method, sometimes different functional connectivity patterns are identifiable but with a large amount of noise and variability.

To begin to investigate the dynamics of the functional connectivity, the correlation technique is used to compare the first and second halves of a scan session. Minor differences are discernable between the correlation results of the scan session halves. Further, a sliding window technique is implemented to study the correlation coefficients through different sizes of correlation windows throughout time. From this technique it is apparent that the correlation level with the seed region is not static throughout the scan length.

The last method introduced, a point processing method, is one of the more novel techniques because it does not require analysis of the continuous time points. Here, network information is extracted based on brief occurrences of high or low amplitude signals within a seed region. Because point processing utilizes less time points from the data, the statistical power of the results is lower. There are also larger variations in DMN patterns between subjects. In addition to boosted computational efficiency, the benefit of using a point-process method is that the patterns produced for different seed regions do not have to be independent of one another.

This work compares four unique methods of identifying functional connectivity patterns. ICA is a technique that is currently used by many scientists studying functional connectivity patterns. The PCA technique is not optimal for the level of noise and the distribution of the data sets. The correlation technique is simple and obtains good results, however a seed region is needed and the method assumes that the DMN regions is correlated throughout the entire scan. Looking at the more dynamic aspects of correlation changing patterns of correlation were evident. The last point-processing method produces a promising results of identifying functional connectivity networks using only low and high amplitude BOLD signals.

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

Modern Computational Chemistry Methods for Prediction of Ground- and Excited-State Properties in Open-Shell Systems

The main goal of the research presented in this work is to provide some important insights about computational modeling of open-shell species. Such projects are: the investigation of the size-extensivity error in Equation-of-Motion Coupled Cluster methods, the analysis of the Long-Range corrected scheme in predicting UV-Vis spectra of Cu(II) complexes with the 4-imidazole acetate and its ethylated derivative, and the exploration of the importance of choosing a proper basis set for the description of systems such as the lithium monoxide anion. The most significant findings of this research are: (i) The contribution of the left operator to the size-extensivity error of the CR-EOMCC(2,3) approach, (ii) The cause of d-d shifts when varying the range-separation parameter and the amount of the exact exchange arising from the imbalanced treatment of localized vs. delocalized orbitals via the "tuned" CAM-B3LYP* functional, (iii) The proper acidity trend of the first-row hydrides and their lithiated analogs that may be reversed if the basis sets are not correctly selected.

Applications of perceptual sparse representation (Spikegram) for copyright protection of audio signals

Chaque année, le piratage mondial de la musique coûte plusieurs milliards de dollars en pertes économiques, pertes d’emplois et pertes de gains des travailleurs ainsi que la perte de millions de dollars en recettes fiscales. La plupart du piratage de la musique est dû à la croissance rapide et à la facilité des technologies actuelles pour la copie, le partage, la manipulation et la distribution de données musicales [Domingo, 2015], [Siwek, 2007]. Le tatouage des signaux sonores a été proposé pour protéger les droit des auteurs et pour permettre la localisation des instants où le signal sonore a été falsifié. Dans cette thèse, nous proposons d’utiliser la représentation parcimonieuse bio-inspirée par graphe de décharges (spikegramme), pour concevoir une nouvelle méthode permettant la localisation de la falsification dans les signaux sonores. Aussi, une nouvelle méthode de protection du droit d’auteur. Finalement, une nouvelle attaque perceptuelle, en utilisant le spikegramme, pour attaquer des systèmes de tatouage sonore. Nous proposons tout d’abord une technique de localisation des falsifications (‘tampering’) des signaux sonores. Pour cela nous combinons une méthode à spectre étendu modifié (‘modified spread spectrum’, MSS) avec une représentation parcimonieuse. Nous utilisons une technique de poursuite perceptive adaptée (perceptual marching pursuit, PMP [Hossein Najaf-Zadeh, 2008]) pour générer une représentation parcimonieuse (spikegramme) du signal sonore d’entrée qui est invariante au décalage temporel [E. C. Smith, 2006] et qui prend en compte les phénomènes de masquage tels qu’ils sont observés en audition. Un code d’authentification est inséré à l’intérieur des coefficients de la représentation en spikegramme. Puis ceux-ci sont combinés aux seuils de masquage. Le signal tatoué est resynthétisé à partir des coefficients modifiés, et le signal ainsi obtenu est transmis au décodeur. Au décodeur, pour identifier un segment falsifié du signal sonore, les codes d’authentification de tous les segments intacts sont analysés. Si les codes ne peuvent être détectés correctement, on sait qu’alors le segment aura été falsifié. Nous proposons de tatouer selon le principe à spectre étendu (appelé MSS) afin d’obtenir une grande capacité en nombre de bits de tatouage introduits. Dans les situations où il y a désynchronisation entre le codeur et le décodeur, notre méthode permet quand même de détecter des pièces falsifiées. Par rapport à l’état de l’art, notre approche a le taux d’erreur le plus bas pour ce qui est de détecter les pièces falsifiées. Nous avons utilisé le test de l’opinion moyenne (‘MOS’) pour mesurer la qualité des systèmes tatoués. Nous évaluons la méthode de tatouage semi-fragile par le taux d’erreur (nombre de bits erronés divisé par tous les bits soumis) suite à plusieurs attaques. Les résultats confirment la supériorité de notre approche pour la localisation des pièces falsifiées dans les signaux sonores tout en préservant la qualité des signaux. Ensuite nous proposons une nouvelle technique pour la protection des signaux sonores. Cette technique est basée sur la représentation par spikegrammes des signaux sonores et utilise deux dictionnaires (TDA pour Two-Dictionary Approach). Le spikegramme est utilisé pour coder le signal hôte en utilisant un dictionnaire de filtres gammatones. Pour le tatouage, nous utilisons deux dictionnaires différents qui sont sélectionnés en fonction du bit d’entrée à tatouer et du contenu du signal. Notre approche trouve les gammatones appropriés (appelés noyaux de tatouage) sur la base de la valeur du bit à tatouer, et incorpore les bits de tatouage dans la phase des gammatones du tatouage. De plus, il est montré que la TDA est libre d’erreur dans le cas d’aucune situation d’attaque. Il est démontré que la décorrélation des noyaux de tatouage permet la conception d’une méthode de tatouage sonore très robuste. Les expériences ont montré la meilleure robustesse pour la méthode proposée lorsque le signal tatoué est corrompu par une compression MP3 à 32 kbits par seconde avec une charge utile de 56.5 bps par rapport à plusieurs techniques récentes. De plus nous avons étudié la robustesse du tatouage lorsque les nouveaux codec USAC (Unified Audion and Speech Coding) à 24kbps sont utilisés. La charge utile est alors comprise entre 5 et 15 bps. Finalement, nous utilisons les spikegrammes pour proposer trois nouvelles méthodes d’attaques. Nous les comparons aux méthodes récentes d’attaques telles que 32 kbps MP3 et 24 kbps USAC. Ces attaques comprennent l’attaque par PMP, l’attaque par bruit inaudible et l’attaque de remplacement parcimonieuse. Dans le cas de l’attaque par PMP, le signal de tatouage est représenté et resynthétisé avec un spikegramme. Dans le cas de l’attaque par bruit inaudible, celui-ci est généré et ajouté aux coefficients du spikegramme. Dans le cas de l’attaque de remplacement parcimonieuse, dans chaque segment du signal, les caractéristiques spectro-temporelles du signal (les décharges temporelles ;‘time spikes’) se trouvent en utilisant le spikegramme et les spikes temporelles et similaires sont remplacés par une autre. Pour comparer l’efficacité des attaques proposées, nous les comparons au décodeur du tatouage à spectre étendu. Il est démontré que l’attaque par remplacement parcimonieux réduit la corrélation normalisée du décodeur de spectre étendu avec un plus grand facteur par rapport à la situation où le décodeur de spectre étendu est attaqué par la transformation MP3 (32 kbps) et 24 kbps USAC.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.