A Dynamic 6,000-Year Genetic History of Eurasia's Eastern Steppe.

The Eastern Eurasian Steppe was home to historic empires of nomadic pastoralists, including the Xiongnu and the Mongols. However, little is known about the region's population history. Here, we reveal its dynamic genetic history by analyzing new genome-wide data for 214 ancient individuals spanning 6,000 years. We identify a pastoralist expansion into Mongolia ca. 3000 BCE, and by the Late Bronze Age, Mongolian populations were biogeographically structured into three distinct groups, all practicing dairy pastoralism regardless of ancestry. The Xiongnu emerged from the mixing of these populations and those from surrounding regions. By comparison, the Mongols exhibit much higher eastern Eurasian ancestry, resembling present-day Mongolic-speaking populations. Our results illuminate the complex interplay between genetic, sociopolitical, and cultural changes on the Eastern Steppe.

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.

Genomic insights into the formation of human populations in East Asia.

The deep population history of East Asia remains poorly understood owing to a lack of ancient DNA data and sparse sampling of present-day people1,2. Here we report genome-wide data from 166 East Asian individuals dating to between 6000 BC and AD 1000 and 46 present-day groups. Hunter-gatherers from Japan, the Amur River Basin, and people of Neolithic and Iron Age Taiwan and the Tibetan Plateau are linked by a deeply splitting lineage that probably reflects a coastal migration during the Late Pleistocene epoch. We also follow expansions during the subsequent Holocene epoch from four regions. First, hunter-gatherers from Mongolia and the Amur River Basin have ancestry shared by individuals who speak Mongolic and Tungusic languages, but do not carry ancestry characteristic of farmers from the West Liao River region (around 3000 BC), which contradicts theories that the expansion of these farmers spread the Mongolic and Tungusic proto-languages. Second, farmers from the Yellow River Basin (around 3000 BC) probably spread Sino-Tibetan languages, as their ancestry dispersed both to Tibet-where it forms approximately 84% of the gene pool in some groups-and to the Central Plain, where it has contributed around 59-84% to modern Han Chinese groups. Third, people from Taiwan from around 1300 BC to AD 800 derived approximately 75% of their ancestry from a lineage that is widespread in modern individuals who speak Austronesian, Tai-Kadai and Austroasiatic languages, and that we hypothesize derives from farmers of the Yangtze River Valley. Ancient people from Taiwan also derived about 25% of their ancestry from a northern lineage that is related to, but different from, farmers of the Yellow River Basin, which suggests an additional north-to-south expansion. Fourth, ancestry from Yamnaya Steppe pastoralists arrived in western Mongolia after around 3000 BC but was displaced by previously established lineages even while it persisted in western China, as would be expected if this ancestry was associated with the spread of proto-Tocharian Indo-European languages. Two later gene flows affected western Mongolia: migrants after around 2000 BC with Yamnaya and European farmer ancestry, and episodic influences of later groups with ancestry from Turan.

Cartilage-Specific Gene Expression and Extracellular Matrix Deposition in the Course of Mesenchymal Stromal Cell Chondrogenic Differentiation in 3D Spheroid Culture.

Articular cartilage damage still remains a major problem in orthopedical surgery. The development of tissue engineering techniques such as autologous chondrocyte implantation is a promising way to improve clinical outcomes. On the other hand, the clinical application of autologous chondrocytes has considerable limitations. Mesenchymal stromal cells (MSCs) from various tissues have been shown to possess chondrogenic differentiation potential, although to different degrees. In the present study, we assessed the alterations in chondrogenesis-related gene transcription rates and extracellular matrix deposition levels before and after the chondrogenic differentiation of MSCs in a 3D spheroid culture. MSCs were obtained from three different tissues: umbilical cord Wharton's jelly (WJMSC-Wharton's jelly mesenchymal stromal cells), adipose tissue (ATMSC-adipose tissue mesenchymal stromal cells), and the dental pulp of deciduous teeth (SHEDs-stem cells from human exfoliated deciduous teeth). Monolayer MSC cultures served as baseline controls. Newly formed 3D spheroids composed of MSCs previously grown in 2D cultures were precultured for 2 days in growth medium, and then, chondrogenic differentiation was induced by maintaining them in the TGF-ß1-containing medium for 21 days. Among the MSC types studied, WJMSCs showed the most similarities with primary chondrocytes in terms of the upregulation of cartilage-specific gene expression. Interestingly, such upregulation occurred to some extent in all 3D spheroids, even prior to the addition of TGF-ß1. These results confirm that the potential of Wharton's jelly is on par with adipose tissue as a valuable cell source for cartilage engineering applications as well as for the treatment of osteoarthritis. The 3D spheroid environment on its own acts as a trigger for the chondrogenic differentiation of MSCs.

Orbital angular momentum of paraxial propagation-invariant laser beams.

For propagation-invariant laser beams represented as a finite superposition of the Hermite-Gaussian beams with the same Gouy phase and with arbitrary weight coefficients, we obtain an analytical expression for the normalized orbital angular momentum (OAM). This expression is represented also as a finite sum of weight coefficients. We show that a certain choice of the weight coefficients allows obtaining the maximal OAM, which is equal to the maximal power of the Hermite polynomial in the sum. In this case, the superposition describes a single-ringed Laguerre-Gaussian beam with a topological charge equal to the maximal OAM and to the maximal power of the Hermite polynomial.

Propagation of a multi-vortex beam: far-field diffraction of a Gaussian beam from a multi-fork phase grating.

In this work, the far-field propagation of multi-vortex beams is investigated. We consider diffraction of a Gaussian wave from a spatial light modulator (SLM) in which a multi-fork grating is implemented on it at the waist plane of the Gaussian wave. In the first-order diffraction pattern a multi-vortex beam is produced, and we consider its evolution under propagation when different multi-fork gratings are implemented on the SLM. We consider two different schemes for the phase singularities of the implemented grating. A topological charge (TC) equal to l1 is considered at the center of the grating, and four similar phase singularities all having a TC equal to l2=l14 (or l2=-l14) are located on the corners of a square where the l1 singularity is located on the square center. Some cases with different values of l1, and consequently l2, are investigated. Experimental and simulation results show that if signs of the TCs at the corners and center of the square are the same, the radius of the central singularity on the first-order diffracted beam increases, and it convolves the other singularities. If their signs are opposite, the total TC value equals zero, and at the far-field, the light beam distribution becomes a Gaussian beam. For determining the TCs of the resulting far-field beams, we interfere experimentally and by simulation the resulting far-field beams with a plane wave and count the forked interference fringes. All the results are consistent.

Optical Polarization Sensor Based on a Metalens.

We investigated an optical microsensor of the polarization state of a laser light based on a metalens. In contrast to known polarization sensors based on metasurfaces that deflect different polarization types using various angles to the optical axis, the studied polarization sensor generated different patterns in the metalens focus to realize varied polarization states: left circular polarization generated a light ring in the focus, right circular polarization generated a circular focal spot, and linear polarization generated an elliptic spot with two sidelobes. Moreover, the tilt angle of the linear polarization matched the tilt angle of the elliptic focal spot. The simulation results were consistent with the theoretical predictions. A metalens with a diameter of several tens of microns was designed and fabricated in a thin amorphous silicon film with a thickness of 120 µm and a low aspect ratio, high numerical aperture, and short focal distance equal to a wavelength of 633 nm.

Optical vortex beams with a symmetric and almost symmetric OAM spectrum.

We show both theoretically and numerically that if an optical vortex beam has a symmetric or almost symmetric angular harmonics spectrum [orbital angular momentum (OAM) spectrum], then the order of the central harmonic in the OAM spectrum equals the normalized-to-power OAM of the beam. This means that an optical vortex beam with a symmetric OAM spectrum has the same topological charge and the normalized-to-power OAM has an optical vortex with only one central angular harmonic. For light fields with a symmetric OAM spectrum, we give a general expression in the form of a series. We also study two examples of form-invariant (structurally stable) vortex beams with their topological charges being infinite, while the normalized-to-power OAM is approximately equal to the topological charge of the central angular harmonic, contributing the most to the OAM of the entire beam.

Converting an array of edge dislocations into a multi-vortex beam.

We theoretically show how, using a cylindrical lens, a Gaussian beam with a finite number of parallel zero-intensity lines (edge dislocations) is transformed into a vortex beam that carries orbital angular momentum (OAM) and topological charge (TC). Remarkably, while the original beam is assumed to carry a non-zero OAM and have no TC, the latter is shown to appear during free-space propagation. Considering two parallel center-symmetric zero-intensity lines located as an example, we look into the dynamics of generating two intensity nulls at the double focal length: with increasing distance between the vertical zero-intensity lines, two optical vortices are first generated on the horizontal axis before converging at the origin and then diverging along the vertical axis. Irrespective of the between-line distance, such an optical vortex has ${\rm TC} = - {2}$ at any distance from the optical axis, except for the original plane. With changing distance between the zero-intensity lines, the OAM that the beam carries is changing, taking positive and negative values, or a zero value at a certain between-line distance. We also show that if the number of zero-intensity lines is infinite, a vortex beam with finite OAM and infinite TC is generated.

Topological charge of asymmetric optical vortices.

We obtain theoretical relationships to define topological charge (TC) of vortex laser beams devoid of radial symmetry, namely asymmetric Laguerre-Gaussian (LG), asymmetric Bessel-Gaussian (BG), and asymmetric Kummer beams, as well as Hermite-Gaussian (HG) vortex beams. Although they are obtained as superposition of respective conventional LG, BG, and HG beams, these beams have the same TC equal to that of a single mode, n. At the same time, the normalized orbital angular momentum (OAM) that the beams carry is different, differently responding to the variation of the beam's asymmetry degree. However, whatever the asymmetry degree, TC of the beams remains unchanged and equals n. Although separate HG beam does not have OAM and TC, superposition of only two HG modes with adjacent numbers (n, n + 1) and a π/2-phase shift produces a modal beam whose TC is -(2n + 1). Theoretical findings are validated via numerical simulation.

Topological charge of a linear combination of optical vortices: topological competition.

We theoretically show that optical vortices conserve the integer topological charge (TC) when passing through an arbitrary aperture or shifted from the optical axis of an arbitrary axisymmetric carrier beam. If the beam contains a finite number of off-axis optical vortices with same-sign different TC, the resulting TC of the beam is shown to equal the sum of all constituent TCs. If the beam is composed of an on-axis superposition of Laguerre-Gauss modes (n, 0), the resulting TC equals that of the mode with the highest TC. If the highest positive and negative TCs of the constituent modes are equal in magnitude, the "winning" TC is the one with the larger absolute value of the weight coefficient. If the constituent modes have the same weight coefficients, the resulting TC equals zero. If the beam is composed of two on-axis different-amplitude Gaussian vortices with different TC, the resulting TC equals that of the constituent vortex with the larger absolute value of the weight coefficient amplitude, irrespective of the correlation between the individual TCs. In the case of equal weight coefficients of both optical vortices, TC of the entire beam equals the greatest TC by absolute value. We have given this effect the name "topological competition of optical vortices".

Magnon Landau Levels and Spin Responses in Antiferromagnets.

We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose a model of an AFM topological insulator of magnons. In the long wavelength limit, the Landau levels induced by the inhomogeneous Dzyaloshinskii-Moriya interaction exhibit relativistic physics described by the Klein-Gordon equation. The spin Nernst response due to the formation of magnonic Landau levels is compared to similar topological responses in skyrmion and vortex-antivortex crystal phases of AFM insulators. Our studies show that AFM insulators exhibit rich physics associated with topological magnon excitations.

Orbital angular momentum and topological charge of a multi-vortex Gaussian beam.

We report on a theoretical and numerical study of a Gaussian beam modulated by several optical vortices (OV) that carry same-sign unity topological charge (TC) and are unevenly arranged on a circle. The TC of such a multi-vortex beam equals the sum of the TCs of all OVs. If the OVs are located evenly along an arbitrary-radius circle, a simple relationship for the normalized orbital angular momentum (OAM) is derived for such a beam. It is shown that in a multi-vortex beam, OAM normalized to power cannot exceed the number of constituent vortices and decreases with increasing distance from the optical axis to the vortex centers. We show that for the OVs to appear at the infinity of such a combined beam, an infinite-energy Gaussian beam is needed. On the contrary, the total TC is independent of said distance, remaining equal to the number of constituent vortices. We show that if TC is evaluated not along the whole circle encompassing the singularity centers, but along any part of this circle, such a quantity is also invariant and conserves on propagation. Besides, a multi-spiral phase plate is studied for the first time to our knowledge, and we obtained the TC and OAM of multi-vortices generated by this plate. When propagated through a random phase screen (diffuser) the TC is unchanged, while the OAM changes by less than 10% if the random phase delay on the diffuser does not exceed half wavelength. Such multi-vortices can be used for data transmission in the turbulent atmosphere.

Genetic kinship and admixture in Iron Age Scytho-Siberians.

Scythians are known from written sources as horse-riding nomadic peoples who dominated the Eurasian steppe throughout the Iron Age. However, their origins and the exact nature of their social organization remain debated. Three hypotheses prevail regarding their origins that can be summarized as a "western origin", an "eastern origin" and a "multi-regional origin". In this work, we first aimed to address the question of the familial and social organization of some Scythian groups (Scytho-Siberians) by testing genetic kinship and, second, to add new elements on their origins through phylogeographical analyses. Twenty-eight Scythian individuals from 5 archeological sites in the Tuva Republic (Russia) were analyzed using autosomal Short Tandem Repeats (STR), Y-STR and Y-SNP typing as well as whole mitochondrial (mtDNA) genome sequencing. Familial relationships were assessed using the Likelihood Ratio (LR) method. Thirteen of the 28 individuals tested were linked by first-degree relationships. When related, the individuals were buried together, except for one adult woman, buried separately from her mother and young sister. Y-chromosome analysis revealed a burial pattern linked to paternal lineages, with men bearing closely related Y-haplotypes buried on the same sites. Inversely, various mtDNA lineages can be found on each site. Y-chromosomal and mtDNA haplogroups were almost equally distributed between Western and Eastern Eurasian haplogroups. These results suggest that Siberian Scythians were organized in patrilocal and patrilineal societies with burial practices linked to both kinship and paternal lineages. It also appears that the group analyzed shared a greater genetic link with Asian populations than Western Scythians did.

Calculation of fractional orbital angular momentum of superpositions of optical vortices by intensity moments.

Two simple and high-efficiency techniques for measuring the orbital angular momentum (OAM) of paraxial laser beams are proposed and studied numerically and experimentally. One technique relies on measuring the intensity in the Fresnel zone, followed by calculating the intensity that is numerically averaged over angle at discrete radii and deriving squared modules of the light field expansion coefficients via solving a linear set of equations. With the other technique, two intensity distributions are measured in the Fourier plane of a pair of cylindrical lenses positioned perpendicularly, before calculating the first-order moments of the measured intensities. The experimental error grows almost linearly from ~1% for small fractional OAM (up to 4) to ~10% for large fractional OAM (up to 34).

Reverse and toroidal flux of light fields with both phase and polarization higher-order singularities in the sharp focus area.

Based on the Richards-Wolf formalism, we obtain for the first time a set of explicit analytical expressions that completely describe a light field with a double higher-order singularity (phase and polarization), as well as distributions of its intensity and energy flux near the focus. A light field with the double singularity is an optical vortex with a topological charge m and with nth-order cylindrical polarization (azimuthal or radial). From the theory developed, rather general predictions follow. 1) For any singularity orders m and n, the intensity distribution near the focus has a symmetry of order 2(n - 1), while the longitudinal component of the Poynting vector has always an axially symmetric distribution. 2) If n = m + 2, there is a reverse energy flux on the optical axis near the focus, which is comparable in magnitude with the forward flux. 3) If m ≠0, forward and reverse energy fluxes rotate along a spiral around the optical axis, whereas at m = 0 the energy flux is irrotational. 4) For any values of m and n, there is a toroidal energy flux in the focal area near the dark rings in the distribution of the longitudinal component of the Poynting vector.

Orbital angular momentum of a laser beam behind an off-axis spiral phase plate.

Here we obtain a simple formula for the relative total orbital angular momentum (OAM) of a paraxial light beam with arbitrary rotationally symmetric complex amplitude, passed through an off-axis spiral phase plate (SPP). The formula shows that the OAM is zero if the incident light is bounded by a diaphragm, and the SPP center is outside it. Another consequence of the obtained formula is that if the incident light is limited by an annular diaphragm then the full angular momentum is the same, regardless of the position of the SPP center inside the shaded circle of the annular diaphragm. This means that it is more appropriate to illuminate the SPP by beams with an annular intensity distribution because, in this case, the inaccurate alignment of the SPP center and the center of the annular intensity distribution do not affect the total OAM of the beam. In addition, we obtain a formula for the OAM density of such a light beam in the initial plane. The experimentally measured OAM is in good agreement with that calculated by the obtained formula.

Orbital angular momentum of an elliptic beam after an elliptic spiral phase plate.

We obtain a simple closed expression for the normalized orbital angular momentum (OAM) (OAM per unit power) of an arbitrary paraxial light beam with an elliptic shape, diffracted by an elliptic spiral phase plate (SPP), rotated by an arbitrary angle around the optical axis. Moreover, ellipticities of the beam and of the SPP can be different. It is shown that when an elliptic beam illuminates an elliptic SPP, the normalized OAM of the output beam is maximal (minimal) when both the beam and the SPP are oriented in the same (orthogonal) directions. The results can be used in optical trapping, e.g., for continuous change of the OAM transferred to a particle by rotating the SPP around the optical axis.

Astigmatic laser beams with a large orbital angular momentum.

We show that an elliptic Gaussian beam, focused by a cylindrical lens, can be represented as a linear combination of a countable number of only even angular harmonics with both positive and negative topological charge. For the orbital angular momentum (OAM) of the astigmatic Gaussian beam, an exact expression is obtained in a form of a converging series of the Legendre functions of the second kind. It is shown that at some conditions only the terms with the positive or negative topological charge are remained in this series. Using a hybrid numeric-experimental approach, we obtained the normalized OAM of the astigmatic beam, equal to 109, which is just 6% different from the exact OAM of 116, calculated by the equation. To generate such laser beams, there is no need in special optical elements such as spiral phase plates. The OAM of such beams can be adjusted by varying the waist radius of the Gaussian beam and the focal length of the cylindrical lens. The OAM of such beams can reach large values.

Tailoring polarization singularities in a Gaussian beam with locally linear polarization.

Here we theoretically study Gaussian beams with arbitrarily located polarization singularities (PSs). Under PSs, we mean here an isolated intensity null with radial, azimuthal, or radial-azimuthal polarization around it. An expression is obtained for the complex amplitude of such beams. We study in detail cases in which there is one off-axis PS, two opposite PSs, or more than two PSs located in the vertices of a regular polygon. If such a beam has one or two opposite PSs, these PSs are the centers of radial polarization. If there are three PSs, then one of them has radial polarization, and the other two have mixed radial-azimuthal polarization. If the beam has four PSs, then there are two PSs with radial polarization and two PSs with azimuthal polarization. When propagating in space, PSs are shown to appear in a discrete set of planes, in contrast to the phase singularities existing in any plane. If the beam has two PSs, their polarization is shown to transform from the radial in the initial plane to the azimuthal in the far field. The results can find application in optical communications by using non-uniform polarization.