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We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension k (i.e. a fixed point of multiplicity $k+1$) under conjugacy. Such generic unfoldings depend real analytically on k real parameters. A preparation of the unfolding allows to identify real analytic canonical parameters, which are preserved by any conjugacy between two prepared generic unfoldings. A modulus of analytic classification is defined, which is an unfolding of the modulus assigned to the antiholomorphic parabolic point. Since the second iterate of such a germ is a real unfolding of a holomorphic parabolic point, the modulus is a special form of an unfolding of the Écalle–Voronin modulus of the second iterate of the antiholomorphic parabolic germ. We also solve the problem of the existence of an antiholomorphic square root to a germ of a generic analytic unfolding of a holomorphic parabolic germ.
Nearly fifty years ago, Roberts (1978) postulated that the Earth’s magnetic field, which is generated by turbulent motions of liquid metal in its outer core, likely results from a subcritical dynamo instability characterised by a dominant balance between Coriolis, pressure and Lorentz forces (requiring a finite-amplitude magnetic field). Here, we numerically explore subcritical convective dynamo action in a spherical shell, using techniques from optimal control and dynamical systems theory to uncover the nonlinear dynamics of magnetic field generation. Through nonlinear optimisation, via direct-adjoint looping, we identify the minimal seed – the smallest magnetic field that attracts to a nonlinear dynamo solution. Additionally, using the Newton-hookstep algorithm, we converge stable and unstable travelling wave solutions to the governing equations. By combining these two techniques, complex nonlinear pathways between attracting states are revealed, providing insight into a potential subcritical origin of the geodynamo. This paper showcases these methods on the widely studied benchmark of Christensen et al. (2001, Phys.EarthPlanet.Inter., vol. 128, pp. 25–34), laying the foundations for future studies in more extreme and realistic parameter regimes. We show that the minimal seed reaches a nonlinear dynamo solution by first approaching an unstable travelling wave solution, which acts as an edge state separating a hydrodynamic solution from a magnetohydrodynamic one. Furthermore, by carefully examining the choice of cost functional, we establish a robust optimisation procedure that can systematically locate dynamo solutions on short time horizons with no prior knowledge of its structure.
Understanding today’s conflicts and compromises requires addressing the entanglement between material processes and the viewpoints of a variety of collective actors: how they understand themselves and the economy within which they act, what objectives they perceive it affords to them, and what constraints it imposes. The structural approach to economic analysis, which builds on the traditions started by Physiocracy and classical political economy, offers a vantage point to understand material processes. The paper proposes three directions to generalise it, thus making it more suitable to address the entanglement between such processes and the emergence and viewpoints of collective actors.
The authors present results of a recent project that challenges the perceived absence of Late Pleistocene human settlements in high-altitude areas of inland Spain. Despite the apparent geographic and bioclimatic constraints, these areas may contain archaeological material from diverse prehistoric periods.
We present a framework for parametric proper orthogonal decomposition (POD)-Galerkin reduced-order modelling (ROM) of fluid flows that accommodates variations in flow parameters and control inputs. As an initial step, to explore how the locally optimal POD modes vary with parameter changes, we demonstrate a sensitivity analysis of POD modes and their spanned subspace, respectively rooted in Stiefel and Grassmann manifolds. The sensitivity analysis, by defining distance between POD modes for different parameters, is applied to the flow around a rotating cylinder with varying Reynolds numbers and rotation rates. The sensitivity of the subspace spanned by POD modes to parameter changes is represented by a tangent vector on the Grassmann manifold. For the cylinder case, the inverse of the subspace sensitivity on the Grassmann manifold is proportional to the Roshko number, highlighting the connection between geometric properties and flow physics. Furthermore, the Reynolds number at which the subspace sensitivity approaches infinity corresponds to the lower bound at which the characteristic frequency of the Kármán vortex street exists (Noack & Eckelmann, J. Fluid Mech., 1994, vol. 270, pp. 297–330). From the Stiefel manifold perspective, sensitivity modes are derived to represent the flow field sensitivity, comprising the sensitivities of the POD modes and expansion coefficients. The temporal evolution of the flow field sensitivity is represented by superposing the sensitivity modes. Lastly, we devise a parametric POD-Galerkin ROM based on subspace interpolation on the Grassmann manifold. The reconstruction error of the ROM is intimately linked to the subspace-estimation error, which is in turn closely related to subspace sensitivity.
Can material reparations change political participation? To examine whether material reparations can increase political engagement among survivors of state violence, I use content analysis of survivor testimonies, interviews, and plausibly exogenous variation in the timing of reparations approval for surviving victims of the Pinochet dictatorship in Chile. After being approved for reparations, survivors are more likely to register to vote compared to those not yet enrolled in the reparations program. I present evidence that the symbolic value of reparations payments holds particular significance for survivors and suggest that the transitional justice experience provides an opportunity for them to revise their views of the state. These findings indicate that in post-violence contexts, policy experiences can be a consequential determinant of future political behavior, potentially expanding electoral engagement as societies move toward building peace and consolidating democracy.
Religious poems sung with music, the Alevi deyiş are an integral part of Alevi ritual and social life. Due to the dynamics of oral transmission, the same deyiş can be performed with all kinds of music, the words of the deyiş can change from one performance to the next, and pen names can multiply. The unique experiential function of the deyiş lies precisely in this dynamic and fluid plurality. The deyiş serve as the anchor of communal identity, linking the group to a mythico-historical past that also constitutes the hermeneutical background for making sense of the present and near past. Born from an affect that is at once personal and communal, the oral tradition of deyiş is an experience of collective and personal agency, re-created at each moment in the acts of performance and active listening. Grounded in conceptual frameworks on emotion, embodiment, and orality, the article explores the transmission of deyiş through the cases of early Republican singer–poet Âşık Veysel (d. 1973), poems by Kaygusuz Abdal (flourished late fourteenth–early fifteenth century) and Pir Sultan Abdal (flourished sixteenth century) in the compilation of Ottoman palace musician Ali Ufuki (d. 1675), and modern musical interpretations of Kaygusuz Abdal’s poem.
Experimental studies of natural convection in yield stress fluids have revealed transient behaviours that contradict predictions from viscoplastic models. For example, at a sufficiently large yield stress, these models predict complete motionlessness; below a critical value, yielding and motion onset can be delayed in viscoplastic models. In both cases, however, experiments observe immediate motion onset. We present numerical simulations of the transient natural convection of elastoviscoplastic (EVP) fluids in a square cavity with differentially heated side walls, exploring the role of elasticity in reconciling theoretical predictions with experimental observations. We consider motion onset in EVP fluids under two initial temperature distributions: (i) a linear distribution characteristic of steady pure conduction, and (ii) a uniform distribution representative of experimental conditions. The Saramito EVP model exhibits an asymptotic behaviour similar to the Kelvin-Voigt model as $t\to 0^+$, where material behaviour is primarily governed by elasticity and solvent viscosity. The distinction between motion onset and yielding, a hallmark of EVP models, is the key feature that bridges theoretical predictions with experimental observations. While motion onset is consistently immediate (as seen in experiments), yielding occurs with a delay (as predicted by viscoplastic models). Scaling analysis suggests that this delay varies logarithmically with the yield stress and is inversely proportional to the elastic modulus. The intensity of the initial pre-yield motion increases with higher yield stress and lower elastic modulus. The observed dynamics resemble those of under- and partially over-damped systems, with a power-law fit providing an excellent match for the variation of oscillation frequency with the elastic modulus.
The breakup and coalescence of particle aggregates confined at the interface of turbulent liquid layers are investigated experimentally and theoretically. In particular, we consider conductive fluid layers driven by Lorentz forces and laden with millimetre-scale floating particles. These form aggregates held together by capillary attraction and disrupted by the turbulent motion. The process is fully characterised by imaging at high spatio-temporal resolution. The breakup frequency $\varOmega$ is proportional to the mean strain rate and follows a power-law scaling $\varOmega \sim D^{3\text{/}2}$, where $D$ is the size of the aggregate, attributed to the juxtaposition of particle-scale strain cells. The daughter aggregate size distribution exhibits a robust U-shape, which implies erosion of small fragments as opposed to even splitting. The coalescence kernel $\varGamma$ between pairs of aggregates of size $D_{1}$ and $D_{2}$ scales as $\varGamma \sim ( D_{1} + D_{2} )^{2}$, which is consistent with gas-kinetic dynamics. These relations, which apply to regimes dominated both by capillary-driven aggregation and by drag-driven breakup, are implemented into the population balance equation for the evolution of the aggregate number density. Comparison with the experiments shows that the framework captures the observed distribution for aggregates smaller than the forcing length scale.
Synbiotic beverages have become a boon for health-conscious people as these beverages can offer a variety of health benefits. The present study aimed to produce a novel synbiotic beverage from browntop millet (Urochloa ramosa, previously Brachiaria ramosa). Lacticaseibacillus rhamnosus was used for the fermentation of the browntop millet. Multi-response methodology optimization was performed, and maximum ferric-reducing antioxidant power (FRAP) concentration, reducing sugar and protein concentration was observed at 757.42 µ mol Fe (II)/ml, 90.38 mg/ml, and 1.31 mg/ml, respectively. The study also observed an excellent cell hydrophobicity (85.7%) of the probiotic strain. Thus, the final product obtained had a DPPH value of 54.89 ± 2.2 %.
This study aimed to develop a predictive model to investigate the effect of temperature, pH, NaCl concentration, initial inoculum concentration and time on enterotoxin A (SEA) production by Staphylococcus aureus. Combinations of three levels of temperature (10, 15 and 25°C ), five levels of pH (5.3, 5.5, 6.0, 6.5 and 6.7), five levels of NaCl (0.8, 1.0, 1.5, 2.0 and 2.2%), three levels of inoculum concentration (0, 3 and 5 log CFU/mL) in brain heart infusion (BHI) broth were studied. Colonies were counted and SEA production was assessed at 24 h intervals for up to 240 h. A probabilistic logistic regression model was used to describe the production of SEA by Staphylococcus aureus. SEA production was influenced by all factors, except NaCl concentration. S. aureus produced SEA in all samples at 25°C, while the temperature of 10°C delayed the growth and SEA production of S. aureus at initial contamination levels of 3 log CFU/mL and 5 log CFU/mL and prevented it at 0 log CFU/mL. The model was statistically and experimentally validated, demonstrating a good fit, with a high percentage agreement, Nagelkerke's R2 and the Hosmer and Lemeshow test for the SEA production model. The experimental validation confirmed the effectiveness of the models for predicting the probability of SEA production by S. aureus in Minas Frescal cheese.
Coarctation of the aorta accounts for approximately 6–8% of CHDs, typically manifesting as narrowing of the proximal thoracic aorta. Clinical and haemodynamic effects vary depending on the severity and associated anomalies. We aimed to compare the outcomes of surgical versus percutaneous interventions in patients with coarctation of the aorta and to identify factors influencing the choice of treatment strategy.
Methods:
We retrospectively analysed the medical records of 120 patients diagnosed and treated for coarctation of the aorta at Ankara University Faculty of Medicine, Department of Pediatric Cardiology over a 12-year period. Patients were grouped by age (0–4 months and >4 months). Clinical and echocardiographic data were reviewed. Treatment selection was based on American Heart Association 2011 guidelines, considering age, weight, and anatomy. Surgical repair was preferred in infants <4 months; balloon angioplasty or stent implantation was used in older patients. Procedural success and complications were assessed.
Results:
A total of 62% were male, the median age at diagnosis was 1.1 months, and 67% were diagnosed before 4 months of age. The most common symptom was a cardiac murmur (62.5%). Initially, balloon angioplasty was performed in 50%, surgical repair in 45%, and stent implantation in 5%. The acute success rate was 98.3%. Complications occurred in 13.3%, including thrombosis (7.5%) and aneurysm (2.5%). Recoarctation developed in 43% and was significantly higher after balloon angioplasty compared to surgery (55% vs. 29.6%, p = 0.004), and in patients <4 months (52.2% vs. 25.5%, p = 0.014). Management strategies typically included surgical repair in infants <4 months, balloon angioplasty in older children, and stenting in those ≥25 kg, while treatment was ultimately individualised.
Conclusion:
Recoarctation was the most frequent complication, especially among infants under four months and after balloon angioplasty. Surgical repair was associated with a lower risk of recoarctation in early infancy. Percutaneous stent implantation for coarctation is an effective and safe procedure, but it is limited by the patient’s weight. Individualised treatment based on age, anatomy, and clinical status is essential to optimise outcomes.
This study examines foraminifers from limestone horizons of the mainly Brigantian Lower Limestone Formation across the Midland Valley of Scotland (MVS), to determine more precisely the correlation of the limestone beds throughout the region and with the marine bands. Three quantitative biostratigraphical methods were applied to the foraminiferal dataset. The Ranking and Scaling method produced unusual mixed associations and a ranked optimum sequence, making it the least reliable. In contrast, the Unitary Associations (UA) and Constrained Optimization (CONOP) methods yielded more consistent sequences and correlations, especially the latter. The main conclusions drawn were: (i) The West Kirkton, First Abden and St Monans Brecciated limestones of the eastern MVS are considered the base of the Lower Limestone Formation; (ii) The Petershill Limestone is considered as the likely lateral equivalent of the Blackhall Limestone; (iii) the Seafield Tower, Charlestown Main and Middle Skateraw limestones can be correlated in the eastern MVS; (iv) the Abden Fauna (marine band) in central Fife, is confirmed just below the base of the Lower Limestone Formation in most sections; and (v) correlation of limestones below the Neilson Shell Band (marine band) in the eastern region is confirmed with the CONOP method, and in the western region with the Unitary Associations.