Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

Photodimerization of coumarin in aqueous and micellar media

The photochemical and photophysical processes of many organic compounds are a function of the environment in which they are present. In this connection we have chosen to investigate the environmental perturbations on the photodimerization of coumarin,l and the results of our study in aqueous and micellar media are presented in this paper. Coumarin has historically been the subject of intense photochemical and spectroscopic interest, mainly as a consequence of its importance in biological systems. Coumarin has been chosen for our investigation as its fascinating photochemical behavior has been fairly well explored,2 and therefore the environmental influence, which is the subject of our concern, would be easily understandable.

M. bovis BCG induced expression of COX-2 involves nitric oxide-dependent and -independent signaling pathways

In a multifaceted immunity to mycobacterial infection, induced expression of cyclooxygenase-2 (COX-2) by Mycobacterium bovis bacillus Calmette-Guerin (BCG) may act as an important influencing factor for the effective host immunity. We here demonstrate that M. bovis BCG-triggered TLR2-dependent signaling leads to COX-2 and PGE2 expression in vitro in macrophages and in vivo in mice. Further, the presence of PGE2 could be demonstrated in sera or cerebrospinal fluid of tuberculosis patients. The induced COX-2 expression in macrophages is dependent on NF-kappa B activation, which is mediated by inducible NO synthase (iNOS)/NO-dependent participation of the members of Notch1-PI-3K signaling cascades as well as iNOS-independent activation of ERK1/2 and p38 MAPKs. Inhibition of iNOS activity abrogated the M. bovis BCG ability to trigger the generation of Notch1 intracellular domain (NICD), a marker for Notch1 signaling activation, as well as activation of the PI-3K signaling cascade. On the contrary, treatment of macrophages with 3-morpholinosydnonimine, a NO donor, resulted in a rapid increase in generation of NICD, activation of PI-3K pathway, as well as the expression of COX-2. Stable expression of NICD in RAW 264.7 macrophages resulted in augmented expression of COX-2. Further, signaling perturbations suggested the involvement of the cross-talk of Notch1 with members with the PI-3K signaling cascade. These results implicate the dichotomous nature of TLR2 signaling during M. bovis BCG-triggered expression of COX-2. In this perspective, we propose the involvement of iNOS/NO as one of the obligatory, early, proximal signaling events during M. bovis BCG-induced COX-2 expression in macrophages.

Flux balance analysis of biological systems: applications and challenges

Systems level modelling and simulations of biological processes are proving to be invaluable in obtaining a quantitative and dynamic perspective of various aspects of cellular function. In particular, constraint-based analyses of metabolic networks have gained considerable popularity for simulating cellular metabolism, of which flux balance analysis (FBA), is most widely used. Unlike mechanistic simulations that depend on accurate kinetic data, which are scarcely available, FBA is based on the principle of conservation of mass in a network, which utilizes the stoichiometric matrix and a biologically relevant objective function to identify optimal reaction flux distributions. FBA has been used to analyse genome-scale reconstructions of several organisms; it has also been used to analyse the effect of perturbations, such as gene deletions or drug inhibitions in silico. This article reviews the usefulness of FBA as a tool for gaining biological insights, advances in methodology enabling integration of regulatory information and thermodynamic constraints, and finally addresses the challenges that lie ahead. Various use scenarios and biological insights obtained from FBA, and applications in fields such metabolic engineering and drug target identification, are also discussed. Genome-scale constraint-based models have an immense potential for building and testing hypotheses, as well as to guide experimentation.

The Alpha-Method Direct Transcription In Path Constrained Dynamic Optimization

Numerically discretized dynamic optimization problems having active inequality and equality path constraints that along with the dynamics induce locally high index differential algebraic equations often cause the optimizer to fail in convergence or to produce degraded control solutions. In many applications, regularization of the numerically discretized problem in direct transcription schemes by perturbing the high index path constraints helps the optimizer to converge to usefulm control solutions. For complex engineering problems with many constraints it is often difficult to find effective nondegenerat perturbations that produce useful solutions in some neighborhood of the correct solution. In this paper we describe a numerical discretization that regularizes the numerically consistent discretized dynamics and does not perturb the path constraints. For all values of the regularization parameter the discretization remains numerically consistent with the dynamics and the path constraints specified in the, original problem. The regularization is quanti. able in terms of time step size in the mesh and the regularization parameter. For full regularized systems the scheme converges linearly in time step size.The method is illustrated with examples.

On the Kelvin-Helmholtz instability of structured plasma layers in the magnetosphere

The hydromagnetic Kelvin-Helmholtz (K-H) instability problem is studied for a three-layered system analytically by arriving at the marginal instability condition. As the magnetic field directions are taken to vary in the three regions, both the angle and finite thickness effects are seen on the instability criterion. When the relative flow speed of the plasmas on the two sides of the interfaces separating the inner and the surrounding layers is U < Uc, where Uc is the critical speed, the system is stable both for symmetric and asymmetric perturbations. However, unlike the case of the interface bounded by two semiinfinite media, Uc is no longer the minimum critical speed above which the system will be unstable for all wavenumbers; another critical speed U* > Uc is introduced due to the finiteness of the system. When Uc < U < U*, the instability can set in either through the symmetric or asymmetric mode, depending on the ratio of the plasma parameters and angle between the magnetic field directions across the boundaries. The instability arises for a finite range of wavenumbers, thus giving rise to the upper and lower cut-off frequencies for the spectra of hydromagnetic surface waves generated by the K-H instability mechanism. When U > U*, both the modes are unstable for short wavelengths. The results are finally used to explain some observational features of the dependence of hydromagnetic energy spectra in the magnetosphere on the interplanetary parameters.

Wild dog control impacts on calf wastage in extensive beef cattle enterprises

Wild dogs (Canis lupus dingo and hybrids) are routinely controlled to protect beef cattle from predation yet beef producers are sometimes ambivalent as to whether wild dogs are a significant problem or not. This paper reports the loss of calves between birth and weaning in pregnancy-tested herds located on two beef cattle properties in south-central and far north Queensland for up to 4 consecutive years. Comparisons of lactation failures (identified when dams that previously tested pregnant were found non-lactating at weaning) were made between adjoining test herds grazed in places with or without annual (or twice annual) wild dog poison baiting programs. No correlation between wild dog relative abundance and lactation failures was apparent. Calf loss was frequently higher (three in 7 site-years, 11–32%) in baited areas than in non-baited areas (9% in 1 of 7 site-years). Predation loss of calves (in either area) only occurred in seasons of below-average rainfall, but was not related to herd nutrition. These data suggest that controlling wild dogs to protect calves on extensive beef cattle enterprises is unnecessary in most years because wild dogs do not routinely prey on calves. In those seasons when wild dog predation might occur, baiting can be counter-productive. Baiting appears to produce perturbations that change the way surviving or re-colonising wild dog populations select and handle prey and/or how they interact with livestock.

Relaminarization in highly accelerated turbulent boundary layers

The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.

Effect of inclination on laminar film condensation

The effect of inclination on laminar film condensation over and under isothermal flat plates is investigated analytically. The complete set of Navier Stokes equations in two dimensions is considered. Analysed as a perturbation problem, the zero-order perturbation represents the boundary layer equations. First and second order perturbations are solved to bring about the leading edge effects. Corresponding velocity and temperature profiles are presented. The results show decrease in heat transfer with larger ∥inclinations∥ from the vertical. Comparison with experimental data of Gerstmann and Griffith indicates a closer agreement of the present results than the analytical results of the same authors.

Mesospheric temperature response to variations in geomagnetic activity

Temperature data collected over several years from rocket grenade and other experiments at Point Barrow (Alaska), Fort Churchill (Canada) and Wallops Island (Virginia) have been analysed to determine the effect of geomagnetic activity on the neutral temperature in the mesosphere and to study the latitudinal variation of this effect. An analysis carried out has revealed almost certainly significant correlations between the temperature and the geomagnetic indicies Kp and Ap at Fort Churchill and marginally significant correlations at Barrow and Wallops. This has also been substantiated by a linear regression analysis. The results indicate two types of interdependence between mesospheric temperature and geomagnetic field variations. The first type is the direct heating effect, during a geomagnetic disturbance, which has been observed in the present analysis with a time lag of 3–15 hr at the high latitudes and 36 hr at the middle latitudes. The magnitude of this heating effect has been found to decrease at the lower altitudes. The second type of interrelation which has been observed is temperature perturbations preceding geomagnetic field variations, both presumably caused by a disturbance in atmospheric circulation at these levels.

Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

The use of metabolomics to monitor simultaneous changes in metabolic variables following supramaximal low volume high intensity exercise

High Intensity Exercise (HIE) stimulates greater physiological remodeling when compared to workload matched low-moderate intensity exercise. This study utilized an untargeted metabolomics approach to examine the metabolic perturbations that occur following two workload matched supramaximal low volume HIE trials. In a randomized order, 7 untrained males completed two exercise protocols separated by one week; 1) HIE150%: 30 x 20s cycling at 150% VO2peak, 40s passive rest; 2) HIE300%: 30 x 10s cycling at 300% VO2peak, 50 s passive rest. Total exercise duration was 30 minutes for both trials. Blood samples were taken at rest, during and immediately following exercise and at 60 minutes post exercise. Gas chromatography-mass spectrometry (GC-MS) analysis of plasma identified 43 known metabolites of which 3 demonstrated significant fold changes (HIE300% compared to the HIE150% value) during exercise, 14 post exercise and 23 at the end of the recovery period. Significant changes in plasma metabolites relating to lipid metabolism [fatty acids: dodecanoate (p=0.042), hexadecanoate (p=0.001), octadecanoate (p=0.001)], total cholesterol (p=0.001), and glycolysis [lactate (p=0.018)] were observed following exercise and during the recovery period. The HIE300% protocol elicited greater metabolic changes relating to lipid metabolism and glycolysis when compared to HIE150% protocol. These changes were more pronounced throughout the recovery period rather than during the exercise bout itself. Data from the current study demonstrate the use of metabolomics to monitor intensity-dependent changes in multiple metabolic pathways following exercise. The small sample size indicates a need for further studies in a larger sample cohort to validate these findings.

Endoplasmic reticulum stress and cell death mechanisms in the cell model of Huntington’s disease

This thesis clarifies important molecular pathways that are activated during the cell death observed in Huntington’s disease. Huntington’s disease is one of the most common inherited neurodegenerative diseases, which is primarily inherited in an autosomal dominant manner. HD is caused by an expansion of CAG repeats in the first exon of the IT15 gene. IT15 encodes the production of a Huntington’s disease protein huntingtin. Mutation of the IT15 gene results in a long stretch of polyQ residues close to the amino-terminal region of huntingtin. Huntington’s disease is a fatal autosomal neurodegenerative disorder. Despite the current knowledge of HD, the precise mechanism behind the selective neuronal death, and how the disease propagates, still remains an enigma. The studies mainly focused on the control of endoplasmic reticulum (ER) stress triggered by the mutant huntingtin proteins. The ER is a delicate organelle having essential roles in protein folding and calcium regulation. Even the slightest perturbations on ER homeostasis are effective enough to trigger ER stress and its adaptation pathways, called unfolded protein response (UPR). UPR is essential for cellular homeostasis and it adapts ER to the changing environment and decreases ER stress. If adaptation processes fail and stress is excessive and prolonged; irreversible cell death pathways are engaged. The results showed that inhibition of ER stress with chemical agents are able to decrease cell death and formation of toxic cell aggregates caused by mutant huntingtin proteins. The study concentrated also to the NF-κB (nuclear factor-kappaB) pathway, which is activated during ER stress. NF-κB pathway is capable to regulate the levels of important cellular antioxidants. Cellular antioxidants provide a first line of defence against excess reactive oxygen species. Excess accumulation of reactive oxygen species and subsequent activation of oxidative stress damages motley of vital cellular processes and induce cell degeneration. Data showed that mutant huntingtin proteins downregulate the expression levels of NF-κB and vital antioxidants, which was followed by increased oxidative stress and cell death. Treatment with antioxidants and inhibition of oxidative stress were able to counteract these adverse effects. In addition, thesis connects ER stress caused by mutant huntingtin to the cytoprotective autophagy. Autophagy sustains cellular balance by degrading potentially toxic cell proteins and components observed in Huntington’s disease. The results revealed that cytoprotective autophagy is active at the early points (24h) of ER stress after expression of mutant huntingtin proteins. GADD34 (growth arrest and DNA damage-inducible gene 34), which is previously connected to the regulation of translation during cell stress, was shown to control the stimulation of autophagy. However, GADD34 and autophagy were downregulated at later time points (48h) during mutant huntingtin proteins induced ER stress, and subsequently cell survival decreased. Overexpression GADD34 enhanced autophagy and decreased cell death, indicating that GADD34 plays a critical role in cell protection. The thesis reveales new interesting data about the neuronal cell death pathways seen in Huntington’s disease, and how cell degeneration is partly counteracted by various therapeutic agents. Expression of mutant huntingtin proteins is shown to alter signaling events that control ER stress, oxidative stress and autophagy. Despite that Huntington’s disease is mainly an untreatable disorder; these findings offer potential targets and neuroprotective strategies in designing novel therapies for Huntington’s disease.