Modeling the Emergence of Circadian Rhythms in a Clock Neuron Network

Circadian rhythms in pacemaker cells persist for weeks in constant darkness, while in other types of cells the molecular oscillations that underlie circadian rhythms damp rapidly under the same conditions. Although much progress has been made in understanding the biochemical and cellular basis of circadian rhythms, the mechanisms leading to damped or self-sustained oscillations remain largely unknown. There exist many mathematical models that reproduce the circadian rhythms in the case of a single cell of the Drosophila fly. However, not much is known about the mechanisms leading to coherent circadian oscillation in clock neuron networks. In this work we have implemented a model for a network of interacting clock neurons to describe the emergence (or damping) of circadian rhythms in Drosophila fly, in the absence of zeitgebers. Our model consists of an array of pacemakers that interact through the modulation of some parameters by a network feedback. The individual pacemakers are described by a well-known biochemical model for circadian oscillation, to which we have added degradation of PER protein by light and multiplicative noise. The network feedback is the PER protein level averaged over the whole network. In particular, we have investigated the effect of modulation of the parameters associated with (i) the control of net entrance of PER into the nucleus and (ii) the non-photic degradation of PER. Our results indicate that the modulation of PER entrance into the nucleus allows the synchronization of clock neurons, leading to coherent circadian oscillations under constant dark condition. On the other hand, the modulation of non-photic degradation cannot reset the phases of individual clocks subjected to intrinsic biochemical noise.

Enhancing weak signal transmission through a feedforward network

The ability to transmit and amplify weak signals is fundamental to signal processing of artificial devices in engineering. Using a multilayer feedforward network of coupled double-well oscillators as well as Fitzhugh-Nagumo oscillators, we here investigate the conditions under which a weak signal received by the first layer can be transmitted through the network with or without amplitude attenuation. We find that the coupling strength and the nodes' states of the first layer act as two-state switches, which determine whether the transmission is significantly enhanced or exponentially decreased. We hope this finding is useful for designing artificial signal amplifiers.

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

SYNCHRONIZATION OF CHAOS AND THE TRANSITION TO WAVE TURBULENCE

We investigated the transition to wave turbulence in a spatially extended three-wave interacting model, where a spatially homogeneous state undergoing chaotic dynamics undergoes spatial mode excitation. The transition to this weakly turbulent state can be regarded as the loss of synchronization of chaos of mode oscillators describing the spatial dynamics.

Period determination in the food-entrainable and methamphetamine-sensitive circadian oscillator(s)

Daily rhythmic processes are coordinated by circadian clocks, which are present in numerous central and peripheral tissues. In mammals, two circadian clocks, the food-entrainable oscillator (FEO) and methamphetamine-sensitive circadian oscillator (MASCO), are "black box" mysteries because their anatomical loci are unknown and their outputs are not expressed under normal physiological conditions. In the current study, the investigation of the timekeeping mechanisms of the FEO and MASCO in mice with disruption of all three paralogs of the canonical clock gene, Period, revealed unique and convergent findings. We found that both the MASCO and FEO in Per1(-/-)/Per2(-/-)/Per3(-/-) mice are circadian oscillators with unusually short (similar to 21 h) periods. These data demonstrate that the canonical Period genes are involved in period determination in the FEO and MASCO, and computational modeling supports the hypothesis that the FEO and MASCO use the same timekeeping mechanism or are the same circadian oscillator. Finally, these studies identify Per1(-/-)/Per2(-/-)/Per3(-/-) mice as a unique tool critical to the search for the elusive anatomical location(s) of the FEO and MASCO.

Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations

An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.

Intrinsic organization of the suprachiasmatic nucleus in the capuchin monkey

The suprachiasmatic nucleus (SCN), which is the main circadian biological clock in mammals, is composed of multiple cells that function individually as independent oscillators to express the self-sustained mRNA and protein rhythms of the so-called clock genes. Knowledge regarding the presence and localization of the proteins and neuroactive substances of the SCN are essential for understanding this nucleus and for its successful manipulation. Although there have been advances in the investigation of the intrinsic organization of the SCN in rodents, little information is available in diurnal species, especially in primates. This study, which explores the pattern of expression and localization of PER2 protein in the SCN of capuchin monkey, evaluates aspects of the circadian system that are common to both primates and rodents. Here, we showed that PER2 protein immunoreactivity is higher during the light phase. Additionally, the complex organization of cells that express vasopressin, vasoactive intestinal polypeptide, neuron-specific nuclear protein, calbindin and calretinin in the SCN, as demonstrated by their immunoreactivity, reveals an intricate network that may be related to the similarities and differences reported between rodents and primates in the literature.

Universal behavior of the Shannon mutual information of critical quantum chains

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q = 2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.

Mathematical models of cognitive processes

The research activity carried out during the PhD course was focused on the development of mathematical models of some cognitive processes and their validation by means of data present in literature, with a double aim: i) to achieve a better interpretation and explanation of the great amount of data obtained on these processes from different methodologies (electrophysiological recordings on animals, neuropsychological, psychophysical and neuroimaging studies in humans), ii) to exploit model predictions and results to guide future research and experiments. In particular, the research activity has been focused on two different projects: 1) the first one concerns the development of neural oscillators networks, in order to investigate the mechanisms of synchronization of the neural oscillatory activity during cognitive processes, such as object recognition, memory, language, attention; 2) the second one concerns the mathematical modelling of multisensory integration processes (e.g. visual-acoustic), which occur in several cortical and subcortical regions (in particular in a subcortical structure named Superior Colliculus (SC)), and which are fundamental for orienting motor and attentive responses to external world stimuli. This activity has been realized in collaboration with the Center for Studies and Researches in Cognitive Neuroscience of the University of Bologna (in Cesena) and the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA). PART 1. Objects representation in a number of cognitive functions, like perception and recognition, foresees distribute processes in different cortical areas. One of the main neurophysiological question concerns how the correlation between these disparate areas is realized, in order to succeed in grouping together the characteristics of the same object (binding problem) and in maintaining segregated the properties belonging to different objects simultaneously present (segmentation problem). Different theories have been proposed to address these questions (Barlow, 1972). One of the most influential theory is the so called “assembly coding”, postulated by Singer (2003), according to which 1) an object is well described by a few fundamental properties, processing in different and distributed cortical areas; 2) the recognition of the object would be realized by means of the simultaneously activation of the cortical areas representing its different features; 3) groups of properties belonging to different objects would be kept separated in the time domain. In Chapter 1.1 and in Chapter 1.2 we present two neural network models for object recognition, based on the “assembly coding” hypothesis. These models are networks of Wilson-Cowan oscillators which exploit: i) two high-level “Gestalt Rules” (the similarity and previous knowledge rules), to realize the functional link between elements of different cortical areas representing properties of the same object (binding problem); 2) the synchronization of the neural oscillatory activity in the γ-band (30-100Hz), to segregate in time the representations of different objects simultaneously present (segmentation problem). These models are able to recognize and reconstruct multiple simultaneous external objects, even in difficult case (some wrong or lacking features, shared features, superimposed noise). In Chapter 1.3 the previous models are extended to realize a semantic memory, in which sensory-motor representations of objects are linked with words. To this aim, the network, previously developed, devoted to the representation of objects as a collection of sensory-motor features, is reciprocally linked with a second network devoted to the representation of words (lexical network) Synapses linking the two networks are trained via a time-dependent Hebbian rule, during a training period in which individual objects are presented together with the corresponding words. Simulation results demonstrate that, during the retrieval phase, the network can deal with the simultaneous presence of objects (from sensory-motor inputs) and words (from linguistic inputs), can correctly associate objects with words and segment objects even in the presence of incomplete information. Moreover, the network can realize some semantic links among words representing objects with some shared features. These results support the idea that semantic memory can be described as an integrated process, whose content is retrieved by the co-activation of different multimodal regions. In perspective, extended versions of this model may be used to test conceptual theories, and to provide a quantitative assessment of existing data (for instance concerning patients with neural deficits). PART 2. The ability of the brain to integrate information from different sensory channels is fundamental to perception of the external world (Stein et al, 1993). It is well documented that a number of extraprimary areas have neurons capable of such a task; one of the best known of these is the superior colliculus (SC). This midbrain structure receives auditory, visual and somatosensory inputs from different subcortical and cortical areas, and is involved in the control of orientation to external events (Wallace et al, 1993). SC neurons respond to each of these sensory inputs separately, but is also capable of integrating them (Stein et al, 1993) so that the response to the combined multisensory stimuli is greater than that to the individual component stimuli (enhancement). This enhancement is proportionately greater if the modality-specific paired stimuli are weaker (the principle of inverse effectiveness). Several studies have shown that the capability of SC neurons to engage in multisensory integration requires inputs from cortex; primarily the anterior ectosylvian sulcus (AES), but also the rostral lateral suprasylvian sulcus (rLS). If these cortical inputs are deactivated the response of SC neurons to cross-modal stimulation is no different from that evoked by the most effective of its individual component stimuli (Jiang et al 2001). This phenomenon can be better understood through mathematical models. The use of mathematical models and neural networks can place the mass of data that has been accumulated about this phenomenon and its underlying circuitry into a coherent theoretical structure. In Chapter 2.1 a simple neural network model of this structure is presented; this model is able to reproduce a large number of SC behaviours like multisensory enhancement, multisensory and unisensory depression, inverse effectiveness. In Chapter 2.2 this model was improved by incorporating more neurophysiological knowledge about the neural circuitry underlying SC multisensory integration, in order to suggest possible physiological mechanisms through which it is effected. This endeavour was realized in collaboration with Professor B.E. Stein and Doctor B. Rowland during the 6 months-period spent at the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA), within the Marco Polo Project. The model includes four distinct unisensory areas that are devoted to a topological representation of external stimuli. Two of them represent subregions of the AES (i.e., FAES, an auditory area, and AEV, a visual area) and send descending inputs to the ipsilateral SC; the other two represent subcortical areas (one auditory and one visual) projecting ascending inputs to the same SC. Different competitive mechanisms, realized by means of population of interneurons, are used in the model to reproduce the different behaviour of SC neurons in conditions of cortical activation and deactivation. The model, with a single set of parameters, is able to mimic the behaviour of SC multisensory neurons in response to very different stimulus conditions (multisensory enhancement, inverse effectiveness, within- and cross-modal suppression of spatially disparate stimuli), with cortex functional and cortex deactivated, and with a particular type of membrane receptors (NMDA receptors) active or inhibited. All these results agree with the data reported in Jiang et al. (2001) and in Binns and Salt (1996). The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain the fundamental aspects of multisensory integration, and provides a biologically plausible hypothesis about the underlying circuitry.

Dynamical measurements with quartz resonators

Dynamische Messungen mit Quarzresonatoren Die Resonanzfrequenz von Quarzoszillatoren liegt im MHz-Bereich. Die Resonanzen haben hohe Gueten und sind somit empfindlich auf kleine Aenderungen an der Resonatoroberflaeche. 1. Es wurde ein Aufbau entwickelt, um Reibung bei hohen Oberflaechengeschwindigkeiten zu messen (v = 1 m/s). Bei Annaeherung einer Kugel steigen Resonanzfrequenz sowie -breite des Schwingquarzes an. Für groeßere Normalkraefte entsteht ein elastischer Kontakt, der die Frequenzerhoehung erklaert. Kurz vor Eintreten dieses Kontaktes durchlaeuft die Daempfung ein Maximum, das charakteristisch ist für das Auftreten von Reibung. Bei Erhoehung der Schichtdicke (0,4-2,5 nm) einer Schmiermittelbeschichtung (Perfluoropolyether) verringern sich sowohl die Hoehe als auch die Breite dieses Maximums. Es verschwindet mit vollstaendiger Belegung mit einer Monolage (ca. 2 nm). Dies wird durch einen intermittierenden Kontakt der beiden Oberflaechen erklaert. 2. Die Schwingquarzoberfläche wurde mit Polymerbuersten verschiedener Schichtdicken (12-230 nm) beschichtet. Der Loesungsmittelgehalt in diesen Filmen variiert mit dem Dampfdruck der umgebenden Toluolatmosphaere. Bei Trocknung durchlaufen die Filme einen loesungsmittelinduzierten Glasuebergang. Die Sorptionskurven (Loesungsmittelgehalt gegen Dampfdruck) zeigen eine Knick beim Glasuebergang, ihre Ableitungen dagegen eine Stufe. Fuer duenner werdende Schichten verschiebt sich diese Stufe zu niedrigerem Dampfdruck sowie geringerem Loesungsmittelgehalt. Außerdem wird sie breiter und ihre Hoehe nimmt ab.

Advanced signal and receiver design for next generation OFDM systems

This thesis deal with the design of advanced OFDM systems. Both waveform and receiver design have been treated. The main scope of the Thesis is to study, create, and propose, ideas and novel design solutions able to cope with the weaknesses and crucial aspects of modern OFDM systems. Starting from the the transmitter side, the problem represented by low resilience to non-linear distortion has been assessed. A novel technique that considerably reduces the Peak-to-Average Power Ratio (PAPR) yielding a quasi constant signal envelope in the time domain (PAPR close to 1 dB) has been proposed.The proposed technique, named Rotation Invariant Subcarrier Mapping (RISM),is a novel scheme for subcarriers data mapping,where the symbols belonging to the modulation alphabet are not anchored, but maintain some degrees of freedom. In other words, a bit tuple is not mapped on a single point, rather it is mapped onto a geometrical locus, which is totally or partially rotation invariant. The final positions of the transmitted complex symbols are chosen by an iterative optimization process in order to minimize the PAPR of the resulting OFDM symbol. Numerical results confirm that RISM makes OFDM usable even in severe non-linear channels. Another well known problem which has been tackled is the vulnerability to synchronization errors. Indeed in OFDM system an accurate recovery of carrier frequency and symbol timing is crucial for the proper demodulation of the received packets. In general, timing and frequency synchronization is performed in two separate phases called PRE-FFT and POST-FFT synchronization. Regarding the PRE-FFT phase, a novel joint symbol timing and carrier frequency synchronization algorithm has been presented. The proposed algorithm is characterized by a very low hardware complexity, and, at the same time, it guarantees very good performance in in both AWGN and multipath channels. Regarding the POST-FFT phase, a novel approach for both pilot structure and receiver design has been presented. In particular, a novel pilot pattern has been introduced in order to minimize the occurrence of overlaps between two pattern shifted replicas. This allows to replace conventional pilots with nulls in the frequency domain, introducing the so called Silent Pilots. As a result, the optimal receiver turns out to be very robust against severe Rayleigh fading multipath and characterized by low complexity. Performance of this approach has been analytically and numerically evaluated. Comparing the proposed approach with state of the art alternatives, in both AWGN and multipath fading channels, considerable performance improvements have been obtained. The crucial problem of channel estimation has been thoroughly investigated, with particular emphasis on the decimation of the Channel Impulse Response (CIR) through the selection of the Most Significant Samples (MSSs). In this contest our contribution is twofold, from the theoretical side, we derived lower bounds on the estimation mean-square error (MSE) performance for any MSS selection strategy,from the receiver design we proposed novel MSS selection strategies which have been shown to approach these MSE lower bounds, and outperformed the state-of-the-art alternatives. Finally, the possibility of using of Single Carrier Frequency Division Multiple Access (SC-FDMA) in the Broadband Satellite Return Channel has been assessed. Notably, SC-FDMA is able to improve the physical layer spectral efficiency with respect to single carrier systems, which have been used so far in the Return Channel Satellite (RCS) standards. However, it requires a strict synchronization and it is also sensitive to phase noise of local radio frequency oscillators. For this reason, an effective pilot tone arrangement within the SC-FDMA frame, and a novel Joint Multi-User (JMU) estimation method for the SC-FDMA, has been proposed. As shown by numerical results, the proposed scheme manages to satisfy strict synchronization requirements and to guarantee a proper demodulation of the received signal.

Stochastische Modelle für nichtlineare Antwortfunktionen in ungeordneten Systemen

In dieser Arbeit werden nichtlineare Experimente zur Untersuchung der Dynamik in amorphen Festkörpern im Rahmen von Modellrechnungen diskutiert. Die Experimente beschäftigen sich mit der Frage nach dynamischen Heterogenitäten, worunter man das Vorliegen dynamischer Prozesse auf unterschiedlichen Zeitskalen versteht. Ist es möglich, gezielt 'langsame' oder 'schnelle' Dynamik in der Probe nachzuweisen, so ist die Existenz von dynamischen Heterogenitäten gezeigt. Ziel der Experimente sind deshalb sogenannte frequenzselektive Anregungen des Systems. In den beiden diskutierten Experimenten, zum einen nichtresonantes Lochbrennen, zum anderen ein ähnliches Experiment, das auf dem dynamischen Kerreffekt beruht, werden nichtlineare Antwortfunktionen gemessen. Um eine Probe in frequenzselektiver Weise anzuregen, werden zunächst einer oder mehrere Zyklen eines oszillierenden elektrischen Feldes an die Probe angelegt. Die Experimente werden zunächst im Terahertz-Bereich untersucht. Auf dieser Zeitskala findet man phonon-ähnliche kollektive Schwingungen in Gläsern. Diese Schwingungen werden durch (anharmonische) Brownsche Oszillatoren beschrieben. Der zentrale Befund der Modellrechnungen ist, daß eine frequenzselektive Anregung im Terahertz-Bereich möglich ist. Ein Nachweis dynamischer Heterogenitäten im Terahertz-Bereich ist somit durch beide Experimente möglich. Anschliessend wird das vorgestellte Kerreffekt-Experiment im Bereich wesentlich kleinerer Frequenzen diskutiert. Die langsame Reorientierungsdynamik in unterkühlten Flüssigkeiten wird dabei durch ein Rotationsdiffusionsmodell beschrieben. Es werden zum einen ein heterogenes und zum anderen ein homogenes Szenario zugrundegelegt. Es stellt sich heraus, daß wie beim Lochbrennen eine Unterscheidung durch das Experiment möglich ist. Das Kerreffekt-Experiment wird somit als eine relativ einfache Alternative zur Technik des nichtresonanten Lochbrennens vorgeschlagen.

Self-sufficient control of urate homeostasis in mice by a synthetic circuit

Synthetic biology has shown that the metabolic behavior of mammalian cells can be altered by genetic devices such as epigenetic and hysteretic switches, timers and oscillators, biocomputers, hormone systems and heterologous metabolic shunts. To explore the potential of such devices for therapeutic strategies, we designed a synthetic mammalian circuit to maintain uric acid homeostasis in the bloodstream, disturbance of which is associated with tumor lysis syndrome and gout. This synthetic device consists of a modified Deinococcus radiodurans-derived protein that senses uric acids levels and triggers dose-dependent derepression of a secretion-engineered Aspergillus flavus urate oxidase that eliminates uric acid. In urate oxidase-deficient mice, which develop acute hyperuricemia, the synthetic circuit decreased blood urate concentration to stable sub-pathologic levels in a dose-dependent manner and reduced uric acid crystal deposits in the kidney. Synthetic gene-network devices providing self-sufficient control of pathologic metabolites represent molecular prostheses, which may foster advances in future gene- and cell-based therapies.

Space-qualified laser system for the BepiColombo Laser Altimeter

The space-qualified design of a miniaturized laser for pulsed operation at a wavelength of 1064 nm and at repetition rates up to 10 Hz is presented. This laser consists of a pair of diode-laser pumped, actively q-switched Nd:YAG rod oscillators hermetically sealed and encapsulated in an environment of dry synthetic air. The system delivers at least 300 million laser pulses with 50 mJ energy and 5 ns pulse width (FWHM). It will be launched in 2017 aboard European Space Agency’s Mercury Planetary Orbiter as part of the BepiColombo Laser Altimeter, which, after a 6-years cruise, will start recording topographic data from orbital altitudes between 400 and 1500 km above Mercury’s surface.

ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. I. ATMOSPHERIC DYNAMICS VIA THE SHALLOW WATER SYSTEM

Within the context of exoplanetary atmospheres, we present a comprehensive linear analysis of forced, damped, magnetized shallow water systems, exploring the effects of dimensionality, geometry (Cartesian, pseudo-spherical, and spherical), rotation, magnetic tension, and hydrodynamic and magnetic sources of friction. Across a broad range of conditions, we find that the key governing equation for atmospheres and quantum harmonic oscillators are identical, even when forcing (stellar irradiation), sources of friction (molecular viscosity, Rayleigh drag, and magnetic drag), and magnetic tension are included. The global atmospheric structure is largely controlled by a single key parameter that involves the Rossby and Prandtl numbers. This near-universality breaks down when either molecular viscosity or magnetic drag acts non-uniformly across latitude or a poloidal magnetic field is present, suggesting that these effects will introduce qualitative changes to the familiar chevron-shaped feature witnessed in simulations of atmospheric circulation. We also find that hydrodynamic and magnetic sources of friction have dissimilar phase signatures and affect the flow in fundamentally different ways, implying that using Rayleigh drag to mimic magnetic drag is inaccurate. We exhaustively lay down the theoretical formalism (dispersion relations, governing equations, and time-dependent wave solutions) for a broad suite of models. In all situations, we derive the steady state of an atmosphere, which is relevant to interpreting infrared phase and eclipse maps of exoplanetary atmospheres. We elucidate a pinching effect that confines the atmospheric structure to be near the equator. Our suite of analytical models may be used to develop decisively physical intuition and as a reference point for three-dimensional magnetohydrodynamic simulations of atmospheric circulation.