Disagreement between correlations of quantum mechanics and stochastic electrodynamics in the damped parametric oscillator

Intracavity and external third order correlations in the damped nondegenerate parametric oscillator are calculated for quantum mechanics and stochastic electrodynamics (SED), a semiclassical theory. The two theories yield greatly different results, with the correlations of quantum mechanics being cubic in the system's nonlinear coupling constant and those of SED being linear in the same constant. In particular, differences between the two theories are present in at least a mesoscopic regime. They also exist when realistic damping is included. Such differences illustrate distinctions between quantum mechanics and a hidden variable theory for continuous variables.

The damped and coherently-driven Jaynes-Cummings model

We investigate the influence of a single-mode cavity on the Autler-Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler-Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom-cavity coupling strength g and the cavity damping K. For an increasing g and/or decreasing K the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double -dressing' model.

Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

Quadrature generators based on ring oscillators and shift registers

Quadrature oscillators are key elements in modern radio frequency (RF) transceivers and very useful nowadays in wireless communications, since they can provide: low quadrature error, low phase-noise, and wide tuning range (useful to cover several bands). RC oscillators can be fully integrated without the need of external components (external high Q-inductors), optimizing area, cost, and power consumption. The conventional structure of ring oscillator offers poor frequency stability and phasenoise, low quality factor (Q), and besides being vulnerable to process, voltage and temperature (PVT) variations, its performance degrades as the frequency of operation increases. This thesis is devoted to quadrature oscillators and presents a detailed comparative study of ring oscillator and shift register (SR) approaches. It is shown that in SRs both phase-noise and phase error are reduced, while ring oscillators have the advantage of occupying less area and less consumption due to the reduced number of components in the circuit. Thus, although ring oscillators are more suitable for biomedical applications, SRs are more appropriate for wireless applications, especially when specification requirements are more stringent and demanding. The first architecture studied consists in a simple CMOS ring oscillator employing an odd number of static single-ended inverters as delay cells. Subsequently, the quadrature 4-stage ring oscillator concept is shown and post-layout simulations are presented. The 3 and 4-phase single-frequency local oscillator (LO) generators employing SRs are presented, the latter with 50% and 25% duty-cycles. The circuits operate at 600 MHz and 900 MHz, and were designed in a 130 nm standard CMOS technology with a voltage supply of 1.2 V.

Analysis and design of sinusoidal quadrature RC-oscillators

Modern telecommunication equipment requires components that operate in many different frequency bands and support multiple communication standards, to cope with the growing demand for higher data rate. Also, a growing number of standards are adopting the use of spectrum efficient digital modulations, such as quadrature amplitude modulation (QAM) and orthogonal frequency division multiplexing (OFDM). These modulation schemes require accurate quadrature oscillators, which makes the quadrature oscillator a key block in modern radio frequency (RF) transceivers. The wide tuning range characteristics of inductorless quadrature oscillators make them natural candidates, despite their higher phase noise, in comparison with LC-oscillators. This thesis presents a detailed study of inductorless sinusoidal quadrature oscillators. Three quadrature oscillators are investigated: the active coupling RC-oscillator, the novel capacitive coupling RCoscillator, and the two-integrator oscillator. The thesis includes a detailed analysis of the Van der Pol oscillator (VDPO). This is used as a base model oscillator for the analysis of the coupled oscillators. Hence, the three oscillators are approximated by the VDPO. From the nonlinear Van der Pol equations, the oscillators’ key parameters are obtained. It is analysed first the case without component mismatches and then the case with mismatches. The research is focused on determining the impact of the components’ mismatches on the oscillator key parameters: frequency, amplitude-, and quadrature-errors. Furthermore, the minimization of the errors by adjusting the circuit parameters is addressed. A novel quadrature RC-oscillator using capacitive coupling is proposed. The advantages of using the capacitive coupling are that it is noiseless, requires a small area, and has low power dissipation. The equations of the oscillation amplitude, frequency, quadrature-error, and amplitude mismatch are derived. The theoretical results are confirmed by simulation and by measurement of two prototypes fabricated in 130 nm standard complementary metal-oxide-semiconductor (CMOS) technology. The measurements reveal that the power increase due to the coupling is marginal, leading to a figure-of-merit of -154.8 dBc/Hz. These results are consistent with the noiseless feature of this coupling and are comparable to those of the best state-of-the-art RC-oscillators, in the GHz range, but with the lowest power consumption (about 9 mW). The results for the three oscillators show that the amplitude- and the quadrature-errors are proportional to the component mismatches and inversely proportional to the coupling strength. Thus, increasing the coupling strength decreases both the amplitude- and quadrature-errors. With proper coupling strength, a quadrature error below 1° and amplitude imbalance below 1% are obtained. Furthermore, the simulations show that increasing the coupling strength reduces the phase noise. Hence, there is no trade-off between phase noise and quadrature error. In the twointegrator oscillator study, it was found that the quadrature error can be eliminated by adjusting the transconductances to compensate the capacitance mismatch. However, to obtain outputs in perfect quadrature one must allow some amplitude error.

Development of spatial integration depends on top-down and interhemispheric connections that can be perturbed in migraine: a DCM analysis.

In humans, spatial integration develops slowly, continuing through childhood into adolescence. On the assumption that this protracted course depends on the formation of networks with slowly developing top-down connections, we compared effective connectivity in the visual cortex between 13 children (age 7-13) and 14 adults (age 21-42) using a passive perceptual task. The subjects were scanned while viewing bilateral gratings, which either obeyed Gestalt grouping rules [colinear gratings (CG)] or violated them [non-colinear gratings (NG)]. The regions of interest for dynamic causal modeling were determined from activations in functional MRI contrasts stimuli > background and CG > NG. They were symmetrically located in V1 and V3v areas of both hemispheres. We studied a common model, which contained reciprocal intrinsic and modulatory connections between these regions. An analysis of effective connectivity showed that top-down modulatory effects generated at an extrastriate level and interhemispheric modulatory effects between primary visual areas (all inhibitory) are significantly weaker in children than in adults, suggesting that the formation of feedback and interhemispheric effective connections continues into adolescence. These results are consistent with a model in which spatial integration at an extrastriate level results in top-down messages to the primary visual areas, where they are supplemented by lateral (interhemispheric) messages, making perceptual encoding more efficient and less redundant. Abnormal formation of top-down inhibitory connections can lead to the reduction of habituation observed in migraine patients.

Robust synchronization of coupled circadian and cell cycle oscillators in single mammalian cells.

Circadian cycles and cell cycles are two fundamental periodic processes with a period in the range of 1 day. Consequently, coupling between such cycles can lead to synchronization. Here, we estimated the mutual interactions between the two oscillators by time-lapse imaging of single mammalian NIH3T3 fibroblasts during several days. The analysis of thousands of circadian cycles in dividing cells clearly indicated that both oscillators tick in a 1:1 mode-locked state, with cell divisions occurring tightly 5 h before the peak in circadian Rev-Erbα-YFP reporter expression. In principle, such synchrony may be caused by either unidirectional or bidirectional coupling. While gating of cell division by the circadian cycle has been most studied, our data combined with stochastic modeling unambiguously show that the reverse coupling is predominant in NIH3T3 cells. Moreover, temperature, genetic, and pharmacological perturbations showed that the two interacting cellular oscillators adopt a synchronized state that is highly robust over a wide range of parameters. These findings have implications for circadian function in proliferative tissues, including epidermis, immune cells, and cancer.

Network-guided analysis of genes with altered somatic copy number and gene expression reveals pathways commonly perturbed in metastatic melanoma.

Cancer genomes frequently contain somatic copy number alterations (SCNA) that can significantly perturb the expression level of affected genes and thus disrupt pathways controlling normal growth. In melanoma, many studies have focussed on the copy number and gene expression levels of the BRAF, PTEN and MITF genes, but little has been done to identify new genes using these parameters at the genome-wide scale. Using karyotyping, SNP and CGH arrays, and RNA-seq, we have identified SCNA affecting gene expression ('SCNA-genes') in seven human metastatic melanoma cell lines. We showed that the combination of these techniques is useful to identify candidate genes potentially involved in tumorigenesis. Since few of these alterations were recurrent across our samples, we used a protein network-guided approach to determine whether any pathways were enriched in SCNA-genes in one or more samples. From this unbiased genome-wide analysis, we identified 28 significantly enriched pathway modules. Comparison with two large, independent melanoma SCNA datasets showed less than 10% overlap at the individual gene level, but network-guided analysis revealed 66% shared pathways, including all but three of the pathways identified in our data. Frequently altered pathways included WNT, cadherin signalling, angiogenesis and melanogenesis. Additionally, our results emphasize the potential of the EPHA3 and FRS2 gene products, involved in angiogenesis and migration, as possible therapeutic targets in melanoma. Our study demonstrates the utility of network-guided approaches, for both large and small datasets, to identify pathways recurrently perturbed in cancer.

Deletion of the RNA-binding proteins ZFP36L1 and ZFP36L2 leads to perturbed thymic development and T lymphoblastic leukemia.

ZFP36L1 and ZFP36L2 are RNA-binding proteins (RBPs) that interact with AU-rich elements in the 3' untranslated region of mRNA, which leads to mRNA degradation and translational repression. Here we show that mice that lacked ZFP36L1 and ZFP36L2 during thymopoiesis developed a T cell acute lymphoblastic leukemia (T-ALL) dependent on the oncogenic transcription factor Notch1. Before the onset of T-ALL, thymic development was perturbed, with accumulation of cells that had passed through the beta-selection checkpoint without first expressing the T cell antigen receptor beta-chain (TCRbeta). Notch1 expression was higher in untransformed thymocytes in the absence of ZFP36L1 and ZFP36L2. Both RBPs interacted with evolutionarily conserved AU-rich elements in the 3' untranslated region of Notch1 and suppressed its expression. Our data establish a role for ZFP36L1 and ZFP36L2 during thymocyte development and in the prevention of malignant transformation.

Harmonic oscillators driven by colored noise: crossovers, resonances and spectra

We study second-order properties of linear oscillators driven by exponentially correlated noise. We focus our attention on dynamical exponents and crossovers and also on resonance phenomena that appear when the driving noise is dichotomous. We also obtain the power spectrum and show its different behaviors according to the color of the noise.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

Networks of noisy oscillators with correlated degree and frequency dispersion

We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase oscillators that represent the node dynamics. Crucially in our work, the variability in the number of connections of the nodes is correlated with the width of the frequency distribution of the oscillators. By numerical simulations on Erdös-Rényi networks, where the frequencies of the oscillators are Gaussian distributed, we make the counterintuitive observation that an increase in the strength of the correlation is accompanied by an increase in the critical coupling strength for the onset of synchronization. We further observe that the critical coupling can solely depend on the average number of connections or even completely lose its dependence on the network connectivity. Only beyond this state, a weighted mean-field approximation breaks down. If noise is present, the correlations have to be stronger to yield similar observations.

Hepatic circadian clock oscillators and nuclear receptors integrate microbiome-derived signals.

The liver is a key organ of metabolic homeostasis with functions that oscillate in response to food intake. Although liver and gut microbiome crosstalk has been reported, microbiome-mediated effects on peripheral circadian clocks and their output genes are less well known. Here, we report that germ-free (GF) mice display altered daily oscillation of clock gene expression with a concomitant change in the expression of clock output regulators. Mice exposed to microbes typically exhibit characterized activities of nuclear receptors, some of which (PPARα, LXRβ) regulate specific liver gene expression networks, but these activities are profoundly changed in GF mice. These alterations in microbiome-sensitive gene expression patterns are associated with daily alterations in lipid, glucose, and xenobiotic metabolism, protein turnover, and redox balance, as revealed by hepatic metabolome analyses. Moreover, at the systemic level, daily changes in the abundance of biomarkers such as HDL cholesterol, free fatty acids, FGF21, bilirubin, and lactate depend on the microbiome. Altogether, our results indicate that the microbiome is required for integration of liver clock oscillations that tune output activators and their effectors, thereby regulating metabolic gene expression for optimal liver function.