Graph homology: Koszul and Verdier duality

We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology of both the commutative and Lie types in computations of the cohomology of the outer automorphism group of a free group. Another consequence is an explicit computation of dualizing sheaves on spaces of metric graphs, thus characterizing to which extent these spaces are different from oriented orbifolds. We also provide a relation between the cohomology of the space of metric ribbon graphs, known to be homotopy equivalent to the moduli space of Riemann surfaces, and the cohomology of a certain sheaf on the space of usual metric graphs.Comment: 13 page

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

Analysis of 273 ancient horse genomes reveals that modern domestic horses originated in the Western Eurasian steppes, especially the lower Volga-Don region.Domestication of horses fundamentally transformed long-range mobility and warfare(1). However, modern domesticated breeds do not descend from the earliest domestic horse lineage associated with archaeological evidence of bridling, milking and corralling(2-4) at Botai, Central Asia around 3500 bc(3). Other longstanding candidate regions for horse domestication, such as Iberia(5) and Anatolia(6), 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(7) between horseback riding and the massive expansion of Yamnaya steppe pastoralists into Europe around 3000 bc(8,9) driving the spread of Indo-European languages(10). This contrasts with the scenario in Asia where Indo-Iranian languages, chariots and horses spread together, following the early second millennium bc Sintashta culture(11,12).Descriptive and Comparative Linguistic

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

Estimation of the parameters of traveling ionospheric disturbances using a chirp-ionosondes network

In this article, the results of our observations of traveling ionospheric disturbances are discussed using the data from a network of chirp stations for oblique ionospheric sounding in December 2019. All observations were made with the same type of chirp stations located in the village of Vasilsursk, as well as in the cities of Yoshkar-Ola, Kazan, and Nizhny Novgorod. The stations formed six synchronous sounding paths with a length from 120 to 320 km. The amplitude-frequency and distance-frequency characteristics were registered per minute by the stations of oblique chirp sounding. Based on the data obtained, a method for determining the parameters of traveling ionospheric disturbances using the network of three chirp ionosondes was proposed. Since the ionosonde had both a receiver and a transmitter, it was possible to get data on six radio paths while using three ionosondes and, thus, to estimate the disturbance parameters only from the experimental data, without resorting to any model concepts. From a practical perspective, our research is highly relevant: the international reference ionosphere (IRI) prognostic model is widely used to calculate the ionospheric propagation of radio waves, but variations in the ionosphere can nullify the effectiveness of such forecasting under real conditions