Labyrinth chaos: Revisiting the elegant, chaotic, and hyperchaotic walks

Labyrinth chaos was discovered by Otto Rössler and René Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, we celebrate their discovery by considering a single labyrinth walks system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behaviour, reminiscent of chimera-like states, a peculiar synchronisation phenomenon. We discuss the properties of the single labyrinth walks system and review the ability of coupled labyrinth chaos systems to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories, what amounts to elegant, hyperchaotic walks. Finally, we discuss further implications in relation to the labyrinth walks system by showing that even though it is volume-preserving, it is not force-conservative

Hyperchaos & labyrinth chaos: revisiting Thomas-Rössler systems

We consider a multidimensional extension of Thomas-R ̈ossler systems, that was inspired by Ren ́e Thomas’ earlier work on biological feedback circuits, and we report on our first results that shows its ability to sustain spatio- temporal behaviour reminiscent of chimera states. The novelty here is that its underlying mechanism is based on “chaotic walks” discovered by Ren ́e Thomas during the course of his investigations on what he called Labyrinth Chaos. We briefly review the main properties of these systems and their chaotic and hyperchaotic dynamics and discuss the simplest way of coupling, necessary for this spatio-temporal behaviour that allows the emergence of complex dynamical behaviours. We also recall Ren ́e Thomas’ memorable influence and interaction with the authors as we dedicate this work to his memory

Weak Chaos and the "Melting Transition" in a Confined Microplasma System

We present results demonstrating the occurrence of changes in the collective dynamics of a Hamiltonian system which describes a confined microplasma characterized by long--range Coulomb interactions. In its lower energy regime, we first detect macroscopically, the transition from a "crystalline--like" to a "liquid--like" behavior, which we call the "melting transition". We then proceed to study this transition using a microscopic chaos indicator called the \emph{Smaller Alignment Index} (SALI), which utilizes two deviation vectors in the tangent dynamics of the flow and is nearly constant for ordered (quasi--periodic) orbits, while it decays exponentially to zero for chaotic orbits as $\exp(-(\lambda_{1}-\lambda_{2})t)$, where $\lambda_{1}>\lambda_{2}>0$ are the two largest Lyapunov exponents. During the "melting phase", SALI exhibits a peculiar, stair--like decay to zero, reminiscent of "sticky" orbits of Hamiltonian systems near the boundaries of resonance islands. This alerts us to the importance of the $\Delta\lambda=\lambda_{1}-\lambda_{2}$ variations in that regime and helps us identify the energy range over which "melting" occurs as a multi--stage diffusion process through weakly chaotic layers in the phase space of the microplasma. Additional evidence supporting further the above findings is given by examining the $GALI_{k}$ indices, which generalize SALI (=$GALI_{2}$) to the case of $k>2$ deviation vectors and depend on the complete spectrum of Lyapunov exponents of the tangent flow about the reference orbit.Comment: 21 pages, 7 figures, submitted at PR

Mild versus conventional ovarian stimulation for poor responders undergoing IVF/ICSI

Background/Aim: Mild stimulation protocols have been implemented to be offered to subfertile patients who respond poorly to ovarian stimulation. We aimed to compare the efficacy of mild versus conventional gonadotropin-releasing hormone (GnRH)-Agonist and antagonist protocols in poor responders undergoing in vitro fertilization/intra-cytoplasmic sperm injection (IVF/ICSI) cycles. Patients and Methods: A total of 58 poorlyresponding patients were divided into two groups: mild group (n=33), receiving clomiphene citrate 100 mg and 0.25 mg of cetrorelix with 150 IU of gonadotrophins daily; conventional group (n=25), undergoing the long GnRHagonist or-Antagonist protocols. The primary outcome was the number of cumulus oocyte complexes (COCs) retrieved. Results: A lower number of COCs [median (range)=1 (0-4) vs. 3 (0-8.4), p<0.001] was retrieved in the mild stimulation compared to the conventional group. Secondary outcomes favored the conventional group, whereas live birth (9.1% vs. 12%), clinical pregnancy (12.1% vs. 20%) and miscarriage rate (40% vs. 40%) were similar in the two groups. Conclusion: Mild ovarian stimulation is inferior to conventional regimes when applied to poor responders undergoing IVF/ICSI, in terms of the numbers of retrieved COCs

Transvaginal ovarian trauma, poor responders and improvement of success rates in IVF: Anecdotal data and a hypothesis

In this report, we propose an intervention capable of improving IVF outcomes in subfertile women with poor ovarian response. This intervention derives from anecdotal data and observations in our daily practice, but most importantly from trials on experimental models and subfertile women with Polycystic Ovarian Syndrome (PCOS). Our hypothesis suggests that transvaginal induction of trauma to the ovary in the cycle preceding IVF should benefit poor ovarian responders and their lowered pregnancy rates by increasing - at least - the number of retrieved oocytes during oocyte retrieval. Up-to-the minute data show that, via this means, there is a unique response of the ovarian surface epithelium and stroma to the induced trauma. The potential pathways of this beneficial response involve an improvement of the raised gonadotrophins to act either through the mechanical reduction of the size of the ovary or through alterations of the hormonal profile by lowering LH, inhibin and local androgen concentrations through hypothalamic-pituitary axis feedbacks, the induction of increased blood flow to the ovaries, a differentiated local immune reaction and a non-elucidated as yet role of reactive oxygen species. In this report, we also describe the technique and the associated possible negative points while we try to point out the needed research steps to ensure its efficiency before it enters daily clinical practice. © 2014 Elsevier Ltd

Aspirin for in vitro fertilisation

Background: Aspirin is used with the aim of optimising the chance of live birth in women undergoing assisted reproductive technology (ART), despite inconsistent evidence of its efficacy and safety (in terms of intraoperative bleeding during oocyte retrieval and risk of miscarriage). The most appropriate time to commence aspirin therapy and the length of treatment required are also still to be determined. This is the second update of the review first published in 2007. Objectives: To evaluate the effectiveness and safety of aspirin in women undergoing ART. Search methods: We searched the Cochrane Gynaecology and Fertility Group Trials Register, Cochrane Central Register of Controlled Trials (CENTRAL; 2016, Issue 4) in the Cochrane Library (searched 9 May 2016); the databases MEDLINE (1946 to 9 May 2016) and Embase (1974 to 9 May 2016); and trial registers (ClinicalTrials.gov and the World Health Organization International Clinical Trials Registry Platform search portal). We also examined the reference lists of all known primary studies and review articles, citation lists of relevant publications and abstracts of major scientific meetings, combined with the Cochrane Gynaecology and Fertility Group's search strategy. Selection criteria: Randomised controlled trials on aspirin for women undergoing ART. Data collection and analysis: Two review authors independently assessed trial eligibility and risk of bias and extracted the data. The primary review outcome was live birth. Secondary outcomes included clinical pregnancy, ongoing pregnancy, multiple pregnancy, miscarriage, and other complications associated with IVF/ICSI or with pregnancy and birth. We combined data to calculate risk ratios (RRs) (for dichotomous data) and mean differences (MDs) (for continuous data) and 95% confidence intervals (CIs). Statistical heterogeneity was assessed using the I2 statistic. We assessed the overall quality of the evidence for the main comparisons using GRADE methods. Main results: The search identified 13 trials as eligible for inclusion in the review, including a total of 2653 participants with a mean age of 35 years. Ten studies used a dose of 100 mg and three used 80 mg of aspirin per day. In most of them, aspirin was commenced immediately at the start of down-regulation, while the duration of treatment varied widely. Eight studies provided a placebo for the control group. There was no evidence of a difference between the aspirin group and the group receiving no treatment or placebo in rates of live birth (RR 0.91, 95% CI 0.72 to 1.15, 3 RCTs, n = 1053, I2 = 15%, moderate-quality evidence). In addition, clinical pregnancy rates were also similar for the two groups (RR 1.03, 95% CI 0.91 to 1.17, 10 RCTs, n = 2142, I2 = 27%, moderate-quality evidence); sensitivity analysis, excluding studies at high risk of bias, did not change the effect estimate. There was no evidence of a difference between groups in terms of multiple pregnancy as confirmed by ultrasound (RR 0.67, 95% CI 0.37 to 1.25, 2 RCTs, n = 656, I2 = 0%, low-quality evidence), miscarriage (RR 1.10, 95% CI 0.68 to 1.77, 5 RCTs, n = 1497, I2 = 0%, low-quality evidence), ectopic pregnancy (RR 1.86, 95% CI 0.75 to 4.63, 3 RCTs, n = 1135, I2 = 0%, very low quality evidence) or vaginal bleeding (RR 1.01, 95% CI 0.14 to 7.13, 1 RCT, n = 487, very low quality evidence). Data were lacking on other adverse effects. The overall quality of the evidence ranged from very low to moderate; limitations were poor reporting of study methods and suspected publication bias. Authors' conclusions: Currently there is no evidence in favour of routine use of aspirin in order to improve pregnancy rates for a general IVF population. This is based on available data from randomised controlled trials, where there is currently no evidence of an effect of aspirin on women undergoing ART, as there is no single outcome measure demonstrating a benefit with its use. Furthermore, current evidence does not exclude the possibility of adverse effects. © 2016 The Cochrane Collaboration. Published by John Wiley & Sons, Ltd

Mild versus conventional ovarian stimulation for poor responders undergoing IVF/ICSI

Background/Aim: Mild stimulation protocols have been implemented to be offered to subfertile patients who respond poorly to ovarian stimulation. We aimed to compare the efficacy of mild versus conventional gonadotropin-releasing hormone (GnRH)-Agonist and antagonist protocols in poor responders undergoing in vitro fertilization/intra-cytoplasmic sperm injection (IVF/ICSI) cycles. Patients and Methods: A total of 58 poorlyresponding patients were divided into two groups: mild group (n=33), receiving clomiphene citrate 100 mg and 0.25 mg of cetrorelix with 150 IU of gonadotrophins daily; conventional group (n=25), undergoing the long GnRHagonist or-Antagonist protocols. The primary outcome was the number of cumulus oocyte complexes (COCs) retrieved. Results: A lower number of COCs [median (range)=1 (0-4) vs. 3 (0-8.4), p<0.001] was retrieved in the mild stimulation compared to the conventional group. Secondary outcomes favored the conventional group, whereas live birth (9.1% vs. 12%), clinical pregnancy (12.1% vs. 20%) and miscarriage rate (40% vs. 40%) were similar in the two groups. Conclusion: Mild ovarian stimulation is inferior to conventional regimes when applied to poor responders undergoing IVF/ICSI, in terms of the numbers of retrieved COCs

Gonadotrophin-releasing hormone agonist protocols for pituitary suppression in assisted reproduction

Background: Gonadotrophin-releasing hormone agonists (GnRHa) are commonly used in assisted reproduction technology (ART) cycles to prevent a luteinising hormone surge during controlled ovarian hyperstimulation (COH) prior to planned oocyte retrieval, thus optimising the chances of live birth. Objectives: To evaluate the effectiveness of the different GnRHa protocols as adjuncts to COH in women undergoing ART cycles. Search methods: We searched the following databases from inception to April 2015: the Cochrane Menstrual Disorders and Subfertility Group Specialised Register, the Cochrane Central Register of Controlled Trials (CENTRAL) in the Cochrane Library (2015, Issue 3), MEDLINE, EMBASE, CINAHL, PsycINFO, and registries of ongoing trials. Reference lists of relevant articles were also searched. Selection criteria: We included randomised controlled trials (RCTs) comparing any two protocols of GnRHa used in in vitro fertilisation (IVF) or intracytoplasmic sperm injection (ICSI) cycles in subfertile women. Data collection and analysis: Two review authors independently selected studies, assessed trial eligibility and risk of bias, and extracted the data. The primary outcome measure was number of live births or ongoing pregnancies per woman/couple randomised. Secondary outcome measures were number of clinical pregnancies, number of oocytes retrieved, dose of gonadotrophins used, adverse effects (pregnancy losses, ovarian hyperstimulation, cycle cancellation, and premature luteinising hormone (LH) surges), and cost and acceptability of the regimens. We combined data to calculate odds ratios (OR) for dichotomous variables and mean differences (MD) for continuous variables, with 95% confidence intervals (CIs). We assessed statistical heterogeneity using the I2 statistic. We assessed the overall quality of the evidence for the main comparisons using &apos;Grading of Recommendations Assessment, Development and Evaluation&apos; (GRADE) methods. Main results: We included 37 RCTs (3872 women), one ongoing trial, and one trial awaiting classification. These trials made nine different comparisons between protocols. Twenty of the RCTs compared long protocols and short protocols. Only 19/37 RCTs reported live birth or ongoing pregnancy. There was no conclusive evidence of a difference between a long protocol and a short protocol in live birth and ongoing pregnancy rates (OR 1.30, 95% CI 0.94 to 1.81; 12 RCTs, n = 976 women, I2 = 15%, low quality evidence). Our findings suggest that in a population in which 14% of women achieve live birth or ongoing pregnancy using a short protocol, between 13% and 23% will achieve live birth or ongoing pregnancy using a long protocol. There was evidence of an increase in clinical pregnancy rates (OR 1.50, 95% CI 1.18 to 1.92; 20 RCTs, n = 1643 women, I2 = 27%, moderate quality evidence) associated with the use of a long protocol. There was no evidence of a difference between the groups in terms of live birth and ongoing pregnancy rates when the following GnRHa protocols were compared: long versus ultrashort protocol (OR 1.78, 95% CI 0.72 to 4.36; one RCT, n = 150 women, low quality evidence), long luteal versus long follicular phase protocol (OR 1.89, 95% CI 0.87 to 4.10; one RCT, n = 223 women, low quality evidence), when GnRHa was stopped versus when it was continued (OR 0.75, 95% CI 0.42 to 1.33; three RCTs, n = 290 women, I2 = 0%, low quality evidence), when the dose of GnRHa was reduced versus when the same dose was continued (OR 1.02, 95% CI 0.68 to 1.52; four RCTs, n = 407 women, I2 = 0%, low quality evidence), when GnRHa was discontinued versus continued after human chorionic gonadotrophin (HCG) administration in the long protocol (OR 0.89, 95% CI 0.49 to 1.64; one RCT, n = 181 women, low quality evidence), and when administration of GnRHa lasted for two versus three weeks before stimulation (OR 1.14, 95% CI 0.49 to 2.68; one RCT, n = 85 women, low quality evidence). Our primary outcomes were not reported for any other comparisons. Regarding adverse events, there were insufficient data to enable us to reach any conclusions except about the cycle cancellation rate. There was no conclusive evidence of a difference in cycle cancellation rate (OR 0.95, 95% CI 0.59 to 1.55; 11 RCTs, n = 1026 women, I2 = 42%, low quality evidence) when a long protocol was compared with a short protocol. This suggests that in a population in which 9% of women would have their cycles cancelled using a short protocol, between 5.5% and 14% will have cancelled cycles when using a long protocol. The quality of the evidence ranged from moderate to low. The main limitations in the evidence were failure to report live birth or ongoing pregnancy, poor reporting of methods in the primary studies, and imprecise findings due to lack of data. Only 10 of the 37 included studies were conducted within the last 10 years. Authors&apos; conclusions: When long GnRHa protocols and short GnRHa protocols were compared, we found no conclusive evidence of a difference in live birth and ongoing pregnancy rates, but there was moderate quality evidence of higher clinical pregnancy rates in the long protocol group. None of the other analyses showed any evidence of a difference in birth or pregnancy outcomes between the protocols compared. There was insufficient evidence to make any conclusions regarding adverse effects. © 2015 The Cochrane Collaboration