Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Towards a general theory of extremes for observables of chaotic dynamical systems

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the cho- sen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan–Yorke dimension of the attractor. Preliminary numer- ical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.

On chaotic behavior of a fixed offshore structure

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On Non-ideal and Chaotic Energy Harvester Behavior

In this paper, we deal with the research of a proposed mathematical model of energy harvesting, including nonlinearities in the piezoelectric coupling and a non-ideal force of excitation. We showed using numerical simulations to analysis of the dynamic responses that, the power harvested was influenced by the nonlinear vibrations of the structure, as well as by the influence of the non-linearities in the piezoelectric coupling. We concluded through of the numerical results that the limited energy source was interacting with the system. Thus, the increasing of the voltage in DC motor led the system produce a good power response, especially in high-energy orbits in the resonance region, but the Sommerfeld effect occurs in the system and a chaotic behavior was found in the post-resonance region. So the power harvested along the time decreases because occurs loses of energy due the interaction between energy source and structure. Keeping the energy harvested constant over time is essential to make possible the use of energy harvesting systems in real applications. To achieve this objective, we applied a control technique in order to stabilize the chaotic system in a periodic stable orbit. We announced that the results were satisfactory and the control maintained the system in a stable condition. © 2012 Foundation for Scientific Research and Technological Innovation.

Effective synchronization of a class of chua's chaotic systems using an exponential feedback coupling

A robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method. © 2013 Patrick Louodop et al.

Nonlinear control in an electromechanical transducer with chaotic behaviour

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Rebuilding a Better Response

What is one thing in the world that we have little control over? Mother Nature. We as humans have tried to alter our natural environment countless times, and she has fought back twice as strong, leaving trails of devastation behind. The number of natural disasters has drastically increased, especially in the Southeast Asian region. The aftermath of a tsunami has left a large number of people homeless and lives forever changed. The current recovery process is chaotic and leaves affected individuals stranded without the means of rebuilding for long periods of time. This thesis aims to re-evaluate the recovery relief procedures and provide a better means of rebuilding their lives and community.

Egfr Activating Mutations And Their Association With Response To Platinum-doublet Chemotherapy In Brazilian Non-small Cell Lung Cancer Patients.

The aim of the study was to analyze the frequency of epidermal growth factor receptor (EGFR) mutations in Brazilian non-small cell lung cancer patients and to correlate these mutations with response to benefit of platinum-based chemotherapy in non-small cell lung cancer (NSCLC). Our cohort consisted of prospective patients with NSCLCs who received chemotherapy (platinum derivates plus paclitaxel) at the [UNICAMP], Brazil. EGFR exons 18-21 were analyzed in tumor-derived DNA. Fifty patients were included in the study (25 with adenocarcinoma). EGFR mutations were identified in 6/50 (12 %) NSCLCs and in 6/25 (24 %) adenocarcinomas; representing the frequency of EGFR mutations in a mostly self-reported White (82.0 %) southeastern Brazilian population of NSCLCs. Patients with NSCLCs harboring EGFR exon 19 deletions or the exon 21 L858R mutation were found to have a higher chance of response to platinum-paclitaxel (OR 9.67 [95 % CI 1.03-90.41], p = 0.047). We report the frequency of EGFR activating mutations in a typical southeastern Brazilian population with NSCLC, which are similar to that of other countries with Western European ethnicity. EGFR mutations seem to be predictive of a response to platinum-paclitaxel, and additional studies are needed to confirm or refute this relationship.

Impaired Compensatory Beta-cell Function And Growth In Response To High-fat Diet In Ldl Receptor Knockout Mice.

In this study, we investigated the effect of low density lipoprotein receptor (LDLr) deficiency on gap junctional connexin 36 (Cx36) islet content and on the functional and growth response of pancreatic beta-cells in C57BL/6 mice fed a high-fat (HF) diet. After 60 days on regular or HF diet, the metabolic state and morphometric islet parameters of wild-type (WT) and LDLr-/- mice were assessed. HF diet-fed WT animals became obese and hypercholesterolaemic as well as hyperglycaemic, hyperinsulinaemic, glucose intolerant and insulin resistant, characterizing them as prediabetic. Also they showed a significant decrease in beta-cell secretory response to glucose. Overall, LDLr-/- mice displayed greater susceptibility to HF diet as judged by their marked cholesterolaemia, intolerance to glucose and pronounced decrease in glucose-stimulated insulin secretion. HF diet induced similarly in WT and LDLr-/- mice, a significant decrease in Cx36 beta-cell content as revealed by immunoblotting. Prediabetic WT mice displayed marked increase in beta-cell mass mainly due to beta-cell hypertrophy/replication. Nevertheless, HF diet-fed LDLr-/- mice showed no significant changes in beta-cell mass, but lower islet-duct association (neogenesis) and higher beta-cell apoptosis index were seen as compared to controls. The higher metabolic susceptibility to HF diet of LDLr-/- mice may be explained by a deficiency in insulin secretory response to glucose associated with lack of compensatory beta-cell expansion.

Overexpression Of Ucp1 In Tobacco Induces Mitochondrial Biogenesis And Amplifies A Broad Stress Response.

Uncoupling protein one (UCP1) is a mitochondrial inner membrane protein capable of uncoupling the electrochemical gradient from adenosine-5'-triphosphate (ATP) synthesis, dissipating energy as heat. UCP1 plays a central role in nonshivering thermogenesis in the brown adipose tissue (BAT) of hibernating animals and small rodents. A UCP1 ortholog also occurs in plants, and aside from its role in uncoupling respiration from ATP synthesis, thereby wasting energy, it plays a beneficial role in the plant response to several abiotic stresses, possibly by decreasing the production of reactive oxygen species (ROS) and regulating cellular redox homeostasis. However, the molecular mechanisms by which UCP1 is associated with stress tolerance remain unknown. Here, we report that the overexpression of UCP1 increases mitochondrial biogenesis, increases the uncoupled respiration of isolated mitochondria, and decreases cellular ATP concentration. We observed that the overexpression of UCP1 alters mitochondrial bioenergetics and modulates mitochondrial-nuclear communication, inducing the upregulation of hundreds of nuclear- and mitochondrial-encoded mitochondrial proteins. Electron microscopy analysis showed that these metabolic changes were associated with alterations in mitochondrial number, area and morphology. Surprisingly, UCP1 overexpression also induces the upregulation of hundreds of stress-responsive genes, including some involved in the antioxidant defense system, such as superoxide dismutase (SOD), glutathione peroxidase (GPX) and glutathione-S-transferase (GST). As a consequence of the increased UCP1 activity and increased expression of oxidative stress-responsive genes, the UCP1-overexpressing plants showed reduced ROS accumulation. These beneficial metabolic effects may be responsible for the better performance of UCP1-overexpressing lines in low pH, high salt, high osmolarity, low temperature, and oxidative stress conditions. Overexpression of UCP1 in the mitochondrial inner membrane induced increased uncoupling respiration, decreased ROS accumulation under abiotic stresses, and diminished cellular ATP content. These events may have triggered the expression of mitochondrial and stress-responsive genes in a coordinated manner. Because these metabolic alterations did not impair plant growth and development, UCP1 overexpression can potentially be used to create crops better adapted to abiotic stress conditions.

Genetic Predictors Of Long-term Response To Growth Hormone (gh) Therapy In Children With Gh Deficiency And Turner Syndrome: The Influence Of A Socs2 Polymorphism.

There is great interindividual variability in the response to GH therapy. Ascertaining genetic factors can improve the accuracy of growth response predictions. Suppressor of cytokine signaling (SOCS)-2 is an intracellular negative regulator of GH receptor (GHR) signaling. The objective of the study was to assess the influence of a SOCS2 polymorphism (rs3782415) and its interactive effect with GHR exon 3 and -202 A/C IGFBP3 (rs2854744) polymorphisms on adult height of patients treated with recombinant human GH (rhGH). Genotypes were correlated with adult height data of 65 Turner syndrome (TS) and 47 GH deficiency (GHD) patients treated with rhGH, by multiple linear regressions. Generalized multifactor dimensionality reduction was used to evaluate gene-gene interactions. Baseline clinical data were indistinguishable among patients with different genotypes. Adult height SD scores of patients with at least one SOCS2 single-nucleotide polymorphism rs3782415-C were 0.7 higher than those homozygous for the T allele (P < .001). SOCS2 (P = .003), GHR-exon 3 (P= .016) and -202 A/C IGFBP3 (P = .013) polymorphisms, together with clinical factors accounted for 58% of the variability in adult height and 82% of the total height SD score gain. Patients harboring any two negative genotypes in these three different loci (homozygosity for SOCS2 T allele; the GHR exon 3 full-length allele and/or the -202C-IGFBP3 allele) were more likely to achieve an adult height at the lower quartile (odds ratio of 13.3; 95% confidence interval of 3.2-54.2, P = .0001). The SOCS2 polymorphism (rs3782415) has an influence on the adult height of children with TS and GHD after long-term rhGH therapy. Polymorphisms located in GHR, IGFBP3, and SOCS2 loci have an influence on the growth outcomes of TS and GHD patients treated with rhGH. The use of these genetic markers could identify among rhGH-treated patients those who are genetically predisposed to have less favorable outcomes.

Comment On 'practical Advice For Avoidance Of Pain Associated With Insertion Of Intrauterine Contraceptives': Authors' Response.

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S-nitrosoglutathione (gsno) Is Cytotoxic To Intracellular Amastigotes And Promotes Healing Of Topically Treated Leishmania Major Or Leishmania Braziliensis Skin Lesions-authors' Response.

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Ki-1/57 And Cgi-55 Ectopic Expression Impact Cellular Pathways Involved In Proliferation And Stress Response Regulation.

Ki-1/57 (HABP4) and CGI-55 (SERBP1) are regulatory proteins and paralogs with 40.7% amino acid sequence identity and 67.4% similarity. Functionally, they have been implicated in the regulation of gene expression on both the transcriptional and mRNA metabolism levels. A link with tumorigenesis is suggested, since both paralogs show altered expression levels in tumor cells and the Ki-1/57 gene is found in a region of chromosome 9q that represents a haplotype for familiar colon cancer. However, the target genes regulated by Ki-1/57 and CGI-55 are unknown. Here, we analyzed the alterations of the global transcriptome profile after Ki-1/57 or CGI-55 overexpression in HEK293T cells by DNA microchip technology. We were able to identify 363 or 190 down-regulated and 50 or 27 up-regulated genes for Ki-1/57 and CGI-55, respectively, of which 20 were shared between both proteins. Expression levels of selected genes were confirmed by qRT-PCR both after protein overexpression and siRNA knockdown. The majority of the genes with altered expression were associated to proliferation, apoptosis and cell cycle control processes, prompting us to further explore these contexts experimentally. We observed that overexpression of Ki-1/57 or CGI-55 results in reduced cell proliferation, mainly due to a G1 phase arrest, whereas siRNA knockdown of CGI-55 caused an increase in proliferation. In the case of Ki-1/57 overexpression, we found protection from apoptosis after treatment with the ER-stress inducer thapsigargin. Together, our data give important new insights that may help to explain these proteins putative involvement in tumorigenic events.

Leaf-, Panel- And Latex-expressed Sequenced Tags From The Rubber Tree (hevea Brasiliensis) Under Cold-stressed And Suboptimal Growing Conditions: The Development Of Gene-targeted Functional Markers For Stress Response.

Hevea brasiliensis is a native species of the Amazon Basin of South America and the primary source of natural rubber worldwide. Due to the occurrence of South American Leaf Blight disease in this area, rubber plantations have been extended to suboptimal regions. Rubber tree breeding is time-consuming and expensive, but molecular markers can serve as a tool for early evaluation, thus reducing time and costs. In this work, we constructed six different cDNA libraries with the aim of developing gene-targeted molecular markers for the rubber tree. A total of 8,263 reads were assembled, generating 5,025 unigenes that were analyzed; 912 expressed sequence tags (ESTs) represented new transcripts, and two sequences were highly up-regulated by cold stress. These unigenes were scanned for microsatellite (SSR) regions and single nucleotide polymorphisms (SNPs). In total, 169 novel EST-SSR markers were developed; 138 loci were polymorphic in the rubber tree, and 98 % presented transferability to six other Hevea species. Locus duplication was observed in H. brasiliensis and other species. Additionally, 43 SNP markers in 13 sequences that showed similarity to proteins involved in stress response, latex biosynthesis and developmental processes were characterized. cDNA libraries are a rich source of SSR and SNP markers and enable the identification of new transcripts. The new markers developed here will be a valuable resource for linkage mapping, QTL identification and other studies in the rubber tree and can also be used to evaluate the genetic variability of other Hevea species, which are valuable assets in rubber tree breeding.