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

Seminari d’Estudis i Recerques Prehistòriques (SERP). Núcleo de cohesión en formación e investigación en Prehistoria de la Universitat de Barcelona desde 1987

info:eu-repo/semantics/publishedVersio

The origins and spread of domestic horses from the Western Eurasian steppes

This is the final version. Available on open access from Nature Research via the DOI in this recordData availability: All collapsed and paired-end sequence data for samples sequenced in this study are available in compressed fastq format through the European Nucleotide Archive under accession number PRJEB44430, together with rescaled and trimmed bam sequence alignments against both the nuclear and mitochondrial horse reference genomes. Previously published ancient data used in this study are available under accession numbers PRJEB7537, PRJEB10098, PRJEB10854, PRJEB22390 and PRJEB31613, and detailed in Supplementary Table 1. The genomes of ten modern horses, publicly available, were also accessed as indicated in their corresponding original publications57,61,85-87.NOTE: see the published version available via the DOI in this record for the full list of authorsDomestication of horses fundamentally transformed long-range mobility and warfare. However, modern domesticated breeds do not descend from the earliest domestic horse lineage associated with archaeological evidence of bridling, milking and corralling at Botai, Central Asia around 3500 BC. Other longstanding candidate regions for horse domestication, such as Iberia and Anatolia, have also recently been challenged. Thus, the genetic, geographic and temporal origins of modern domestic horses have remained unknown. Here we pinpoint the Western Eurasian steppes, especially the lower Volga-Don region, as the homeland of modern domestic horses. Furthermore, we map the population changes accompanying domestication from 273 ancient horse genomes. This reveals that modern domestic horses ultimately replaced almost all other local populations as they expanded rapidly across Eurasia from about 2000 BC, synchronously with equestrian material culture, including Sintashta spoke-wheeled chariots. We find that equestrianism involved strong selection for critical locomotor and behavioural adaptations at the GSDMC and ZFPM1 genes. Our results reject the commonly held association between horseback riding and the massive expansion of Yamnaya steppe pastoralists into Europe around 3000 BC driving the spread of Indo-European languages. This contrasts with the scenario in Asia where Indo-Iranian languages, chariots and horses spread together, following the early second millennium BC Sintashta culture

The Origins and Spread of Domestic Horses from the Western Eurasian Steppes

Domestication of horses fundamentally transformed long-range mobility and warfare1. However, modern domesticated breeds do not descend from the earliest domestic horse lineage associated with archaeological evidence of bridling, milking and corralling2–4 at Botai, Central Asia around 3500 bc3. Other longstanding candidate regions for horse domestication, such as Iberia5 and Anatolia6, have also recently been challenged. Thus, the genetic, geographic and temporal origins of modern domestic horses have remained unknown. Here we pinpoint the Western Eurasian steppes, especially the lower Volga-Don region, as the homeland of modern domestic horses. Furthermore, we map the population changes accompanying domestication from 273 ancient horse genomes. This reveals that modern domestic horses ultimately replaced almost all other local populations as they expanded rapidly across Eurasia from about 2000 bc, synchronously with equestrian material culture, including Sintashta spoke-wheeled chariots. We find that equestrianism involved strong selection for critical locomotor and behavioural adaptations at the GSDMC and ZFPM1 genes. Our results reject the commonly held association7 between horseback riding and the massive expansion of Yamnaya steppe pastoralists into Europe around 3000 bc8,9 driving the spread of Indo-European languages10. This contrasts with the scenario in Asia where Indo-Iranian languages, chariots and horses spread together, following the early second millennium bc Sintashta culture11,12. © 2021, The Author(s).We thank all members of the AGES group at CAGT. We are grateful for the Museum of the Institute of Plant and Animal Ecology (UB RAS, Ekaterinburg) for providing specimens. The work by G. Boeskorov is done on state assignment of DPMGI SB RAS. This project was supported by the University Paul Sabatier IDEX Chaire d’Excellence (OURASI); Villum Funden miGENEPI research programme; the CNRS ‘Programme de Recherche Conjoint’ (PRC); the CNRS International Research Project (IRP AMADEUS); the France Génomique Appel à Grand Projet (ANR-10-INBS-09-08, BUCEPHALE project); IB10131 and IB18060, both funded by Junta de Extremadura (Spain) and European Regional Development Fund; Czech Academy of Sciences (RVO:67985912); the Zoological Institute ZIN RAS (АААА-А19-119032590102-7); and King Saud University Researchers Supporting Project (NSRSP–2020/2). The research was carried out with the financial support of the Russian Foundation for Basic Research (19-59-15001 and 20-04-00213), the Russian Science Foundation (16-18-10265, 20-78-10151, and 21-18-00457), the Government of the Russian Federation (FENU-2020-0021), the Estonian Research Council (PRG29), the Estonian Ministry of Education and Research (PRG1209), the Hungarian Scientific Research Fund (Project NF 104792), the Hungarian Academy of Sciences (Momentum Mobility Research Project of the Institute of Archaeology, Research Centre for the Humanities); and the Polish National Science Centre (2013/11/B/HS3/03822). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie (grant agreement 797449). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements 681605, 716732 and 834616)

The origins and spread of domestic horses from the Western Eurasian steppes

Domestication of horses fundamentally transformed long-range mobility and warfare. However, modern domesticated breeds do not descend from the earliest domestic horse lineage associated with archaeological evidence of bridling, milking and corralling at Botai, Central Asia around 3500 bc. Other longstanding candidate regions for horse domestication, such as Iberia and Anatolia, have also recently been challenged. Thus, the genetic, geographic and temporal origins of modern domestic horses have remained unknown. Here we pinpoint the Western Eurasian steppes, especially the lower Volga-Don region, as the homeland of modern domestic horses. Furthermore, we map the population changes accompanying domestication from 273 ancient horse genomes. This reveals that modern domestic horses ultimately replaced almost all other local populations as they expanded rapidly across Eurasia from about 2000 bc, synchronously with equestrian material culture, including Sintashta spoke-wheeled chariots. We find that equestrianism involved strong selection for critical locomotor and behavioural adaptations at the GSDMC and ZFPM1 genes. Our results reject the commonly held association between horseback riding and the massive expansion of Yamnaya steppe pastoralists into Europe around 3000 bc driving the spread of Indo-European languages. This contrasts with the scenario in Asia where Indo-Iranian languages, chariots and horses spread together, following the early second millennium bc Sintashta culture

The self-dual serial cost-sharing rule

Cost sharing, Serial cost-sharing rule, Self-duality,

Equid use and provision during the Early Iron Age in Can Roqueta (NE Iberian Peninsula). Zooarchaeological study and first strontium isotope result (87Sr/86Sr)

International audienceThis article reports the results of a zooarchaeological study (including, mortality profiles, and anatomical and pathological descriptions) of the Early Iron Age (8th-6th c. BCE) equid remains at the Can Roqueta site (Sabadell, Barcelona), together with the first strontium isotope results to determine their geographical origin. The zooarchaeological study reveals a remarkable number of equid remains at the site, the bone pathologies of which suggest their use for riding, drafting and load carrying. The mortality and sex profiles point to the presence of adult animals, while the absence of neonatal and juvenile remains raises the question as to whether these individuals may have originated from other sites specialised in equid breeding. The strontium values obtained from six individuals suggest that some equids were reared in a geological area with a similar strontium signature to that of the Vallès area, where the site is located. However, three equids present a different strontium signature, pointing to a possibly different geographical origin