Sync and Swarm: Solvable Model of Nonidentical Swarmalators.

We study a model of nonidentical swarmalators, generalizations of phase oscillators that both sync in time and swarm in space. The model produces four collective states: asynchrony, sync clusters, vortexlike phase waves, and a mixed state. These states occur in many real-world swarmalator systems such as biological microswimmers, chemical nanomotors, and groups of drones. A generalized Ott-Antonsen ansatz provides the first analytic description of these states and conditions for their existence. We show how this approach may be used in studies of active matter and related disciplines.

Improvement of bone marrow mononuclear cells cryopreservation methods to increase the efficiency of dendritic cell production.

Cryopreservation is now considered an integral part of the biotechnological process, exploiting different types of cells and tissues in clinical practice. Among them, dendritic cells (DCs) deserve special attention, notably the immature tolerogenic cells (tolDCs), which provide natural tolerance in humans and animals. High cryolability of tolDCs has necessitated the search for the methods that would provide cryopreservation of their precursors; those more resistant to negative effects of cryopreservation factors, in particular, bone marrow or peripheral blood mononuclear cells (MNCs). Based on this, the aim of our research was to optimize the cryopreservation conditions for mice bone marrow MNCs with further assessment of their ability to form tolDCs ex vivo. A cryopreservation mode for bone marrow MNCs has been developed which provides structural and functional completeness of tolDCs obtained from them ex vivo. The ability of DCs derived from cryopreserved MNCs by the developed mode to induce T-regulatory (FOXP3+) cells in vitro when co-cultured with CD4+-lymphocytes was shown.Tolerogenic properties of the DCs derived from cryopreserved MNCs are implemented by increasing the content of hsp70 heat shock proteins and the expression rate of glucocorticoid-induced leucine zipper (GILZ). DCs with increased tolerogenic activities, obtained by the developed cryopreservation regimen, can be used in treatment of autoimmune diseases. In this research we not only evaluated the qualitative characteristics and tolerogenic activity of DCs produced in vitro from cryopreserved MNCs, but also outlined the prospects of accumulating their reserves in low-temperature banks for clinical use.

Effect of different cryopreservation regimens on Ehrlich carcinoma growth.

The freezing rate is a decisive factor in determining the purpose of using low temperatures, i.e., for cryoablation or cryobanking of tumor cells. The research aim was to determine effect of different cryopreservation regimens on Ehrlich carcinoma (EC) growth in vivo and subpopulation composition of the formed ascites. The previously cryopreserved with slow and rapid rates EC cells were cultured in peritoneal cavity (PC) of mice for 7 days. Absolute number of cells in the PC, the subpopulation composition of tumor with flow cytometry using CD44 and CD24 markers were determined. Immediately after warming, a significant redistribution of EC subpopulation composition with a decreased content of the most tumorigenic CD44high cells after both freezing regimens was found. Culturing in vivo for 7 days contributed to the restoration of EC subpopulation composition, but with some a decrease in the tumor growth intensity when slow cooling was used. Rapid cooling contributed to significant inhibition of tumor growth with a reduced number of CD44+ and increased CD24+ cells. None of the cryopreservation regimens resulted in a complete elimination of tumorigenic CD44high tumor cells. The freezing rate determines the preservation of the subpopulation composition of the EC and intensity of its growth in vivo.

Mapping the Structure of Directed Networks: Beyond the Bow-Tie Diagram.

We reveal a hierarchical, multilayer organization of finite components-i.e., tendrils and tubes-around the giant connected components in directed networks and propose efficient algorithms allowing one to uncover the entire organization of key real-world directed networks, such as the World Wide Web, the neural network of Caenorhabditis elegans, and others. With increasing damage, the giant components decrease in size while the number and size of tendril layers increase, enhancing the susceptibility of the networks to damage.

Cryopreservation effect on proliferation and differentiation potential of cultured chorion cells.

BACKGROUND: Fetoplacental tissues including the early chorion contain stem cells with various morphological and functional characteristics. Cultured chorionic cells may be used in perspective therapies of different pathologies. OBJECTIVE: To investigate the effect of cryopreservation on proliferation and differentiation potential of chorion cell culture (ChCC). MATERIALS AND METHODS: Five freezing programs for ChCC were compared: Program 1, cooling from 25 degrees C down to -30 degrees C at 0.5 degrees C/min; Program 2, cooling from 25 degrees C down to -30 degrees C at 1 degrees C/min; Program 3, cooling from 25 degrees C down to -10 degrees C at 1 degrees C/min with further cooling down to - 80 degrees C at 10 degrees C/min; Program 4, cooling from 25 degrees C down to -5 degrees C at 1 degrees C/min with further cooling down to -80 degrees C at 10 degrees C/min; Program 5, cooling from 25 degrees C down to -6 degrees C at 1 degrees C/min with further crystal seeding by adding the surplus nitrogen into the chamber, and cooling down to -80 degrees C at 10 degrees C/min. Viability, adhesion, proliferation and directed differentiation were examined. RESULTS: Freezing program 5 achieved the best result, with the highest viability, adhesion, proliferation and directed differentiation. CONCLUSION: The data may help establishing better cryopreservation protocols for perspective chorionic cell lines and their further application in biotechnology.

Avalanche collapse of interdependent networks.

We reveal the nature of the avalanche collapse of the giant viable component in multiplex networks under perturbations such as random damage. Specifically, we identify latent critical clusters associated with the avalanches of random damage. Divergence of their mean size signals the approach to the hybrid phase transition from one side, while there are no critical precursors on the other side. We find that this discontinuous transition occurs in scale-free multiplex networks whenever the mean degree of at least one of the interdependent networks does not diverge.

Localization and spreading of diseases in complex networks.

Using the susceptible-infected-susceptible model on unweighted and weighted networks, we consider the disease localization phenomenon. In contrast to the well-recognized point of view that diseases infect a finite fraction of vertices right above the epidemic threshold, we show that diseases can be localized on a finite number of vertices, where hubs and edges with large weights are centers of localization. Our results follow from the analysis of standard models of networks and empirical data for real-world networks.

Impact of field heterogeneity on the dynamics of the forced Kuramoto model.

We studied the impact of field heterogeneity on entrainment in a system of uniformly interacting phase oscillators. Field heterogeneity is shown to induce dynamical heterogeneity in the system. In effect, the heterogeneous field partitions the system into interacting groups of oscillators that feel the same local field strength and phase. Based on numerical and analytical analysis of the explicit dynamical equations derived from the periodically forced Kuramoto model, we found that the heterogeneous field can disrupt entrainment at different field frequencies when compared to the homogeneous field. This transition occurs when the phase- and frequency-locked synchronization between groups of oscillators is broken at a critical field frequency, causing each group to enter a new dynamical state (disrupted state). Strikingly, it is shown that disrupted dynamics can differ between groups.

Explosive percolation transition is actually continuous.

Recently a discontinuous percolation transition was reported in a new "explosive percolation" problem for irreversible systems [D. Achlioptas, R. M. D'Souza, and J. Spencer, Science 323, 1453 (2009)] in striking contrast to ordinary percolation. We consider a representative model which shows that the explosive percolation transition is actually a continuous, second order phase transition though with a uniquely small critical exponent of the percolation cluster size. We describe the unusual scaling properties of this transition and find its critical exponents and dimensions.

Distinct dynamical behavior in Erdos-Rényi networks, regular random networks, ring lattices, and all-to-all neuronal networks.

Neuronal network dynamics depends on network structure. In this paper we study how network topology underpins the emergence of different dynamical behaviors in neuronal networks. In particular, we consider neuronal network dynamics on Erdos-Rényi (ER) networks, regular random (RR) networks, ring lattices, and all-to-all networks. We solve analytically a neuronal network model with stochastic binary-state neurons in all the network topologies, except ring lattices. Given that apart from network structure, all four models are equivalent, this allows us to understand the role of network structure in neuronal network dynamics. While ER and RR networks are characterized by similar phase diagrams, we find strikingly different phase diagrams in the all-to-all network. Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations (with a richer repertoire of bifurcations in ER and RR compared to all-to-all networks). This suggests that local heterogeneity in the ratio between excitation and inhibition plays a crucial role on emergent dynamics. Furthermore, we also observe one subtle discrepancy between ER and RR networks, namely, ER networks undergo a neuronal activity jump at lower noise levels compared to RR networks, presumably due to the degree heterogeneity in ER networks that is absent in RR networks. Finally, a comparison between network oscillations in RR networks and ring lattices shows the importance of small-world properties in sustaining stable network oscillations.

Percolation on correlated networks.

We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for degree-degree correlations to be irrelevant for critical singularities. We present examples of networks in which assortative and disassortative mixing leads to unusual percolation properties and new critical exponents.

Structural stability of interaction networks against negative external fields.

We explore structural stability of weighted and unweighted networks of positively interacting agents against a negative external field. We study how the agents support the activity of each other to confront the negative field, which suppresses the activity of agents and can lead to collapse of the whole network. The competition between the interactions and the field shape the structure of stable states of the system. In unweighted networks (uniform interactions) the stable states have the structure of k-cores of the interaction network. The interplay between the topology and the distribution of weights (heterogeneous interactions) impacts strongly the structural stability against a negative field, especially in the case of fat-tailed distributions of weights. We show that apart from critical slowing down there is also a critical change in the system structure that precedes the network collapse. The change can serve as an early warning of the critical transition. To characterize changes of network structure we develop a method based on statistical analysis of the k-core organization and so-called "corona" clusters belonging to the k-cores.

Sensitivity of directed networks to the addition and pruning of edges and vertices.

Directed networks have various topologically different extensive components, in contrast to a single giant component in undirected networks. We study the sensitivity (response) of the sizes of these extensive components in directed complex networks to the addition and pruning of edges and vertices. We introduce the susceptibility, which quantifies this sensitivity. We show that topologically different parts of a directed network have different sensitivity to the addition and pruning of edges and vertices and, therefore, they are characterized by different susceptibilities. These susceptibilities diverge at the critical point of the directed percolation transition, signaling the appearance (or disappearance) of the giant strongly connected component in the infinite size limit. We demonstrate this behavior in randomly damaged real and synthetic directed complex networks, such as the World Wide Web, Twitter, the Caenorhabditis elegans neural network, directed Erdos-Rényi graphs, and others. We reveal a nonmonotonic dependence of the sensitivity to random pruning of edges or vertices in the case of C. elegans and Twitter that manifests specific structural peculiarities of these networks. We propose the measurements of the susceptibilities during the addition or pruning of edges and vertices as a new method for studying structural peculiarities of directed networks.

Neuronal network model of interictal and recurrent ictal activity.

We propose a neuronal network model which undergoes a saddle node on an invariant circle bifurcation as the mechanism of the transition from the interictal to the ictal (seizure) state. In the vicinity of this transition, the model captures important dynamical features of both interictal and ictal states. We study the nature of interictal spikes and early warnings of the transition predicted by this model. We further demonstrate that recurrent seizures emerge due to the interaction between two networks.

k-core (bootstrap) percolation on complex networks: critical phenomena and nonlocal effects.

We develop the theory of the -core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the -core percolation is an unusual, hybrid phase transition with a jump emergence of the k-core as at a first order phase transition but also with a critical singularity as at a continuous transition. We describe the properties of the -core, explain the meaning of the order parameter for the k-core percolation, and reveal the origin of the specific critical phenomena. We demonstrate that a so-called "corona" of the k-core plays a crucial role (corona is a subset of vertices in the k-core which have exactly neighbors in the -core). It turns out that the k-core percolation threshold is at the same time the percolation threshold of finite corona clusters. The mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point. We show that a random removal of even one vertex from the k-core may result in the collapse of a vast region of the k-core around the removed vertex. The mean size of this region diverges at the critical point. We find an exact mapping of the k-core percolation to a model of cooperative relaxation. This model undergoes critical relaxation with a divergent rate at some critical moment.

Synchronization in the random-field Kuramoto model on complex networks.

We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous and heterogeneous (Gaussian) field magnitude distribution. In our analysis, we apply the Ott-Antonsen method and the annealed-network approximation to find the critical behavior of the order parameter. In the case of homogeneous fields, we find a tricritical point above which a second-order phase transition gives place to a first-order phase transition when the network is either fully connected or scale-free with the degree exponent γ>5. Interestingly, for scale-free networks with 2<γ≤5, the phase transition is of second-order at any field magnitude, except for degree distributions with γ=3 when the transition is of infinite order at K_{c}=0 independent of the random fields. Contrary to the Ising model, even strong Gaussian random fields do not suppress the second-order phase transition in both complete graphs and scale-free networks, although the fields increase the critical coupling for γ>3. Our simulations support these analytical results.

Experimental therapy of graft-versus-host disease by mesenchymal stromal cells grown on oxide nanocoatings.

Immune aggression to transplanted allogeneic bone marrow, i.e. the graft-versus-host disease (GVHD), could be decreased by the suppression of effector and/or activation of T- regulatory cells (Treg). This task could be solved by co-transplantaiton of allogeneic bone marrow and mesenchymal stromal cells (MSCs). This study demonstrated the elevated immune modulating activity of MSCs by their culturing in vitro on Al203 oxide nanocoatings. Introduction of the cells to the animals with GVHD resulted in an increased content of Treg in the spleen of bone marrow recipients, reduced severity of the pathology, and higher survival of animals. Thefindings could be the basis for developing the new approaches to optimize the GVHD treatment methods involving the oxide nanocoating cultured MSCs.

Correlations in interacting systems with a network topology.

We study pair correlations in interacting systems placed on complex networks. We show that usually in these systems, pair correlations between interacting objects (e.g., spins), separated by a distance l, decay, on average, faster than 1/(lzl). Here zl is the mean number of the lth nearest neighbors of a vertex in a network. This behavior, in particular, leads to a dramatic weakening of correlations between second and more distant neighbors on networks with fat-tailed degree distributions, which have a divergent number z2 in the infinite network limit. In large networks of this kind, only pair correlations between the nearest neighbors are actually observable. We find the pair correlation function of the Ising model on a complex network. This exact result is confirmed by a phenomenological approach.

Solution of the explosive percolation quest. II. Infinite-order transition produced by the initial distributions of clusters.

We describe the effect of power-law initial distributions of clusters on ordinary percolation and its generalizations, specifically, models of explosive percolation processes based on local optimization. These aggregation processes were shown to exhibit continuous phase transitions if the evolution starts from a set of disconnected nodes. Since the critical exponents of the order parameter in explosive percolation transitions turned out to be very small, these transitions were first believed to be discontinuous. In this article we analyze the evolution starting from clusters of nodes whose sizes are distributed according to a power law. We show that these initial distributions change dramatically the position and order of the phase transitions in these problems. We find a particular initial power-law distribution producing a peculiar effect on explosive percolation, namely, before the emergence of the percolation cluster, the system is in a "critical phase" with an infinite generalized susceptibility. This critical phase is absent in ordinary percolation models with any power-law initial conditions. The transition from the critical phase is an infinite-order phase transition, which resembles the scenario of the Berezinskii-Kosterlitz-Thouless phase transition. We obtain the critical singularity of susceptibility at this peculiar infinite-order transition in explosive percolation. It turns out that susceptibility in this situation does not obey the Curie-Weiss law.

Critical behavior of the relaxation rate, the susceptibility, and a pair correlation function in the Kuramoto model on scale-free networks.

We study the impact of network heterogeneity on relaxation dynamics of the Kuramoto model on uncorrelated complex networks with scale-free degree distributions. Using the Ott-Antonsen method and the annealed-network approach, we find that the critical behavior of the relaxation rate near the synchronization phase transition does not depend on network heterogeneity and critical slowing down takes place at the critical point when the second moment of the degree distribution is finite. In the case of a complete graph we obtain an explicit result for the relaxation rate when the distribution of natural frequencies is Lorentzian. We also find a response of the Kuramoto model to an external field and show that the susceptibility of the model is inversely proportional to the relaxation rate. We reveal that network heterogeneity strongly impacts a field dependence of the relaxation rate and the susceptibility when the network has a divergent fourth moment of degree distribution. We introduce a pair correlation function of phase oscillators and show that it has a sharp peak at the critical point, signaling emergence of long-range correlations. Our numerical simulations of the Kuramoto model support our analytical results.