Phase transitions and memory effects in the dynamics of Boolean networks

The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and its constituent Boolean functions represent the system's quenched disorder and are sampled from a given distribution. The framework accommodates a variety of topologies and Boolean function distributions and can be used to study both the noisy and noiseless regimes; it enables one to calculate correlation functions at different times that are inaccessible via commonly used approximations. It is also used to determine conditions for the annealed approximation to be valid, explore phases of the system under different levels of noise and obtain results for models with strong memory effects, where existing approximations break down. Links between Boolean networks and general Boolean formulas are identified and results common to both system types are highlighted. © 2012 Copyright Taylor and Francis Group, LLC.

Slow-phase onset influence on waveform identification and foveation time measure in congenital nystagmus

Congenital nystagmus (CN) is an ocular-motor disorder characterised by involuntary, conjugated ocular oscillations and its pathogenesis is still under investigation. This kind of nystagmus is termed congenital (or infantile) since it could be present at birth or it can arise in the first months of life. Most of CN patients show a considerable decrease of their visual acuity: image fixation on the retina is disturbed by nystagmus continuous oscillations, mainly horizontal. However, the image of a given target can still be stable during short periods in which eye velocity slows down while the target image is placed onto the fovea (called foveation intervals). To quantify the extent of nystagmus, eye movement recording are routinely employed, allowing physicians to extract and analyse nystagmus main features such as waveform shape, amplitude and frequency. Using eye movement recording, it is also possible to compute estimated visual acuity predictors: analytical functions which estimates expected visual acuity using signal features such as foveation time and foveation position variability. Use of those functions extend the information from typical visual acuity measurement (e.g. Landolt C test) and could be a support for therapy planning or monitoring. This study focuses on detection of CN patients' waveform type and on foveation time measure. Specifically, it proposes a robust method to recognize cycles corresponding to the specific CN waveform in the eye movement pattern and, for those cycles, evaluate the exact signal tracts in which a subject foveates. About 40 eyemovement recordings, either infrared-oculographic or electrooculographic, were acquired from 16 CN subjects. Results suggest that the use of an adaptive threshold applied to the eye velocity signal could improve the estimation of slow phase start point. This can enhance foveation time computing and reduce influence of repositioning saccades and data noise on the waveform type identification.

Phase diagram and influence of defects in the double perovskites

The phase diagram of the double perovskites of the type Sr_(2-x)La_(x)FeMoO_(6) is analyzed, with and without disorder due to antisites. In addition to an homogeneous half metallic ferrimagnetic phase in the absence of doping and disorder, we find antiferromagnetic phases at large dopings, and other ferrimagnetic phases with lower saturation magnetization, in the presence of disorder.

Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.

We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Effective self-management strategies for bipolar disorder: a community-engaged Delphi consensus consultation study

BACKGROUND: Self-management represents an important complement to psychosocial treatments for bipolar disorder (BD), but research is limited. Specifically, little is known about self-management approaches for elevated mood states; this study investigated self-management strategies for: (1) maintaining balance in mood, and (2) stopping progression into hypomania/mania. METHODS: To identify the common components of BD self-management, Delphi Consensus Consultation methods were combined with a Community-Based Participatory Research (CBPR) approach across five study phases: (1) Qualitative dataset content analysis; (2) Academic/grey literature reviews; (3) Content analysis; (4) Two Delphi rounds (rating strategies on a 5-point Likert scale, Very Unhelpful-Very Helpful), and; (5) Quantitative analysis and interpretation. Participants were people with BD and healthcare providers. RESULTS: Phases 1 and 2 identified 262 and 3940 candidate strategies, respectively; 3709 were discarded as duplicates/unintelligible. The remaining 493 were assessed via Delphi methods in Phase 4: 101 people with BD and 52 healthcare providers participated in Round 1; 83 of the BD panel (82%) and 43 of the healthcare provider panel (83%) participated in Round 2-exploratory factor analysis (EFA) was conducted on Round 2 results. LIMITATIONS: EFA was underpowered and sample was not ethnically diverse, limiting generalizability. DISCUSSION: High concordance was observed in ratings of strategy effectiveness between the two panels. Future research could usefully investigate the provisional discovery here of underlying factors which link individual strategies. For example, 'maintaining hope' underpinned strategies for maintaining balance, and 'decreasing use of stimulants' underpinned strategies to interrupt hypo/manic ascent. There is merit in combining CBPR and Delphi methods.

C-reactive protein concentrations across the mood spectrum in bipolar disorder: a systematic review and meta-analysis

BACKGROUND: Inflammatory processes and neural-immune interactions have been implicated in the pathogenesis of psychiatric conditions, but studies in bipolar disorder are inconclusive so far. We aimed to investigate whether peripheral concentrations of C-reactive protein (CRP), an acute-phase response protein of inflammatory activity, are increased in bipolar disorder across the mood spectrum. METHODS: In this systematic review and meta-analysis, we searched MEDLINE, the Cochrane Library, Scopus, and Web of Knowledge from database inception to Aug 14, 2016, for studies that measured serum and plasma CRP concentrations in adult patients with bipolar disorder (as defined by DSM-IV-TR) and healthy controls. We extracted data from published reports. We did three between-group meta-analyses comparing CRP concentrations in patients in mania, depression, or euthymia, with those in healthy controls (cross-sectional studies), and two within-group meta-analyses comparing changes in CRP concentrations before and after treatment of an index manic or depressive episode (longitudinal studies). We used Hedges' adjusted g to calculate effect sizes and pooled results using random-effect models. We also did meta-regression analyses by mood state to investigate possible moderators of CRP concentrations. FINDINGS: We identified 27 studies representing 2161 patients with bipolar disorder and 81 932 healthy controls. Compared with healthy individuals, CRP concentrations were moderately increased in people with bipolar disorder during depression (g 0·67, 95% CI 0·23 to 1·11; p=0·003) and euthymia (0·65, 0·40 to 0·90; p<0·0001) and more substantially increased during mania (0·87, 0·58 to 1·15; p<0·0001). The extent of the increases in CRP concentrations in mania and depression was not related to symptom severity (p=0·256 for mania and p=0·626 for depression). CRP concentrations were moderately decreased after resolution of an index manic episode (-0·36, -0·66 to -0·05; p=0·022) and slightly decreased after resolution of an index depressive episode (-0·18, -0·30 to -0·07; p=0·002). INTERPRETATION: CRP concentrations are increased in bipolar disorder regardless of mood state, but are higher during mania than in depression and euthymia, suggesting an increased inflammatory burden in mania.

Condensed phase combustion travelling waves with sequential exothermic or endothermic reactions

The one-dimensional propagation of a combustion wave through a premixed solid fuel for two-stage kinetics is studied. We re-examine the analysis of a single reaction travelling-wave and extend it to the case of two-stage reactions. We derive an expression for the travelling wave speed in the limit of large activation energy for both reactions. The analysis shows that when both reactions are exothermic, the wave structure is similar to the single reaction case. However, when the second reaction is endothermic, the wave structure can be significantly different from single reaction case. In particular, as might be expected, a travelling wave does not necessarily exist in this case. We establish conditions in the limiting large activation energy limit for the non-existence, and for monotonicity of the temperature profile in the travelling wave.