Some neglected evidence on Vulgar Latin 'glide suppression': Consentius, 27.17-20 N

Both i and u played an important role in the phonetic evolution of many Latin words. The complexity of that evolution is related to the ambiguous phonetic nature of those phonemes, which from the time of ancient grammarians are recognised to have the capacity of acting as either a vowel or a consonant.This double capacity is particularly relevant in contexts where either of them is followed by another vowel forming a hiatus, for the possibility arises of either preserving the hiatus (this is the regular solution of standard Latin: ui.ti.um) or grouping the two vowels into the same syllable (this is the most common solution in substandard Latin: ui.tjum)..

Pro-C congruence properties for groups of rooted tree automorphisms

We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-$\mathcal{C}$ completions of the group, where $\mathcal{C}$ is a pseudo-variety of finite groups. A group acting on a rooted, locally finite tree has the $\mathcal{C}$-congruence subgroup property ($\mathcal{C}$-CSP) if its pro-$\mathcal{C}$ completion coincides with the completion with respect to level stabilizers. We give a sufficient condition for a weakly regular branch group to have the $\mathcal{C}$-CSP. In the case where $\mathcal{C}$ is also closed under extensions (for instance the class of all finite $p$-groups for some prime $p$), our sufficient condition is also necessary. We apply the criterion to show that the Basilica group and the GGS-groups with constant defining vector (odd prime relatives of the Basilica group) have the $p$-CSP

Multi-GGS groups have the congruence subgroup property

We generalize the result about the congruence subgroup property for GGS-groups to the family of multi-GGS-groups; that is, all multi-GGS-groups except the one defined by the constant vector have the congruence subgroup property. Even if the result remains, new ideas are needed in order to generalize the proof

Grigorchuk-Gupta-Sidki groups as a source for Beauvile surfaces

If $G$ is a Grigorchuk-Gupta-Sidki group defined over a $p$-adic tree, where p is an odd prime, we study the existence of Beauville surfaces associated to the quotients of $G$ by its level stabilizers $st_G(n)$. We prove that if $G$ is periodic then the quotients $G/st_G(n)$ are Beauville groups for every $n\geq 2$ if $p\geq 5$ and $n\geq 3$ if $p=3$. On the other hand, if $G$ is non-periodic, then none of the quotients $G/st_G(n)$ are Beauville groups

Inflection, Canards and Folded Singularities in Excitable Systems: Application to a 3D FitzHugh–Nagumo Model

Specific kinds of physical and biological systems exhibit complex Mixed-Mode Oscillations mediated by folded-singularity canards in the context of slow-fast models. The present manuscript revisits these systems, specifically by analysing the dynamics near a folded singularity from the viewpoint of inflection sets of the flow. Originally, the inflection set method was developed for planar systems [Brøns and Bar-Eli in Proc R Soc A 445(1924):305–322, 1994; Okuda in Prog Theor Phys 68(6):1827–1840, 1982; Peng et al. in Philos Trans R Soc A 337(1646):275–289, 1991] and then extended to N-dimensional systems [Ginoux et al. in Int J Bifurc Chaos 18(11):3409–3430, 2008], although not tailored to specific dynamics (e.g. folded singularities). In our previous study, we identified components of the inflection sets that classify several canard-type behaviours in 2D systems [Desroches et al. in J Math Biol 67(4):989– 1017, 2013]. Herein, we first survey the planar approach and show how to adapt it for 3D systems with an isolated folded singularity by considering a suitable reduction of such 3D systems to planar non-autonomous slow-fast systems. This leads us to the computation of parametrized families of inflection sets of one component of that planar (non-autonomous) system, in the vicinity of a folded node or of a folded saddle. We then show that a novel component of the inflection set emerges, which approximates and follows the axis of rotation of canards associated to folded-node and folded-saddle singularities. Finally, we show that a similar inflection-set component occurs in the vicinity of a delayed Hopf bifurcation, a scenario that can arise at the transition between folded node and folded saddle. These results are obtained in the context of a canonical model for folded-singularity canards and subsequently we show it is also applicable to complex slow-fast models. Specifically, we focus the application towards the self-coupled 3D FitzHugh–Nagumo model, but the method is generically applicable to higher-dimensional models with isolated folded singularities, for instance in conductance-based models and other physical-chemical systems.Ikerbasque (The Basque Foundation for Science

Invariants for neural automata

Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. One particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. Specifically, neural automata result from the assignment of symbols and symbol strings to numbers, known as Gödel encoding. Under this assignment, symbolic computation becomes represented by trajectories of state vectors in a real phase space, that allows for statistical correlation analyses with real-world measurements and experimental data. However, these assignments are usually completely arbitrary. Hence, it makes sense to address the problem which aspects of the dynamics observed under a Gödel representation is intrinsic to the dynamics and which are not. In this study, we develop a formally rigorous mathematical framework for the investigation of symmetries and invariants of neural automata under different encodings. As a central concept we define patterns of equality for such systems. We consider different macroscopic observables, such as the mean activation level of the neural network, and ask for their invariance properties. Our main result shows that only step functions that are defined over those patterns of equality are invariant under symbolic recodings, while the mean activation, e.g., is not. Our work could be of substantial importance for related regression studies of real-world measurements with neurosymbolic processors for avoiding confounding results that are dependant on a particular encoding and not intrinsic to the dynamics.RTI2018-093860-BC21 funded by (AEI/FEDER, UE) and acronym MathNEURO PID2020-117281GB-I00 PID2019-107444GA-I00 European Regional Development Fund (ERDF) Basque Government, grant IT1483-2

Relationship Between Cerebral Oxygenation and Metabolism During Rewarming in Newborn Infants After Therapeutic Hypothermia Following Hypoxic-Ischemic Brain Injury

Therapeutic hypothermia (TH) has become a standard of care following hypoxic ischemic encephalopathy (HIE). After TH, body temperature is brought back to 37 °C over 14 h. Lactate/N-acetylasperatate (Lac/NAA) peak area ratio on proton magnetic resonance spectroscopy ((1)H MRS) is the best available outcome biomarker following HIE. We hypothesized that broadband near infrared spectroscopy (NIRS) measured changes in the oxidation state of cytochrome-c-oxidase concentration (Δ[oxCCO]) and cerebral hemodynamics during rewarming would relate to Lac/NAA. Broadband NIRS and systemic data were collected during rewarming from 14 infants following HIE over a mean period of 12.5 h. (1)H MRS was performed on day 5-9. Heart rate increased by 20/min during rewarming while blood pressure and peripheral oxygen saturation (SpO2) remained stable. The relationship between mitochondrial metabolism and oxygenation (measured as Δ[oxCCO] and Δ[HbD], respectively) was calculated by linear regression analysis. This was reviewed in three groups: Lac/NAA values 1. Mean regression coefficient (r (2)) values in these groups were 0.41 (±0.27), 0.22 (±0.21) and 0.01, respectively. The relationship between mitochondrial metabolism and oxygenation became impaired with rising Lac/NAA. Cardiovascular parameters remained stable during rewarming

Changes in Cerebral Oxidative Metabolism during Neonatal Seizures Following Hypoxic-Ischemic Brain Injury.

Seizures are common following hypoxic-ischemic brain injury in newborn infants. Prolonged or recurrent seizures have been shown to exacerbate neuronal damage in the developing brain; however, the precise mechanism is not fully understood. Cytochrome-c-oxidase is responsible for more than 90% of ATP production inside mitochondria. Using a novel broadband near-infrared spectroscopy system, we measured the concentration changes in the oxidation state of cerebral cytochrome-c-oxidase (Δ[oxCCO]) and hemodynamics during recurrent neonatal seizures following hypoxic-ischemic encephalopathy in a newborn infant. A rapid increase in Δ[oxCCO] was noted at the onset of seizures along with a rise in the baseline of amplitude-integrated electroencephalogram. Cerebral oxygenation and cerebral blood volume fell just prior to the seizure onset but recovered rapidly during seizures. Δ[oxCCO] during seizures correlated with changes in mean electroencephalogram voltage indicating an increase in neuronal activation and energy demand. The progressive decline in the Δ[oxCCO] baseline during seizures suggests a progressive decrease of mitochondrial oxidative metabolism

Methodological approaches to the study of cancer risk in the vicinity of pollution sources: the experience of a population-based case–control study of childhood cancer

Background: Environmental exposures are related to the risk of some types of cancer, and children are the most vulnerable group of people. This study seeks to present the methodological approaches used in the papers of our group about risk of childhood cancers in the vicinity of pollution sources (industrial and urban sites). A populationbased case–control study of incident childhood cancers in Spain and their relationship with residential proximity to industrial and urban areas was designed. Two methodological approaches using mixed multiple unconditional logistic regression models to estimate odds ratios (ORs) and 95% confdence intervals (95% CIs) were developed: (a) “near vs. far” analysis, where possible excess risks of cancers in children living near (“near”) versus those living far (“far”) from industrial and urban areas were assessed; and (b) “risk gradient” analysis, where the risk gradient in the vicinity of industries was assessed. For each one of the two approaches, three strategies of analysis were implemented: “joint”, “stratifed”, and “individualized” analysis. Incident cases were obtained from the Spanish Registry of Childhood Cancer (between 1996 and 2011). Results: Applying this methodology, associations between proximity (≤2 km) to specifc industrial and urban zones and risk (OR; 95% CI) of leukemias (1.31; 1.04–1.65 for industrial areas, and 1.28; 1.00–1.53 for urban areas), neuroblastoma (2.12; 1.18–3.83 for both industrial and urban areas), and renal (2.02; 1.16–3.52 for industrial areas) and bone (4.02; 1.73–9.34 for urban areas) tumors have been suggested. Conclusions: The two methodological approaches were used as a very useful and fexible tool to analyze the excess risk of childhood cancers in the vicinity of industrial and urban areas, which can be extrapolated and generalized to other cancers and chronic diseases, and adapted to other types of pollution sources