Recent advances in next generation sequencing-based single-cell technologies have allowed high-throughput quantitative detection of cell-surface proteins along with the transcriptome in individual cells, extending our understanding of the heterogeneity of cell populations in diverse tissues that are in different diseased states or under different experimental conditions. Count data of surface proteins from the cellular indexing of transcriptomes and epitopes by sequencing (CITE-seq) technology pose new computational challenges, and there is currently a dearth of rigorous mathematical tools for analyzing the data. This work utilizes concepts and ideas from Riemannian geometry to remove batch effects between samples and develops a statistical framework for distinguishing positive signals from background noise. The strengths of these approaches are demonstrated on two independent CITE-seq data sets in mouse and human.

By applying entropic barriers, we present a rod separation mechanism that induces the movement of rods of different sizes in the opposite directions. This mechanism is based on the combination of the saw-tooth channel, a static force, and an oscillating driving force. The asymmetric shape of the channel and the elongated shape of the rod causesa complicated interaction effect between the rods and the channel walls which reduces the accessible configuration space for the rods and leads to entropic free-energy effects.

We investigate the nature of the polyelectrolyte peak in salt-free solutions by molecular dynamics simulations using a minimal model of polyelectrolyte solutions that includes an explicit solvent and counterions and small angle scattering experiments. It is found that the polyelectrolyte peak progressively disappears as the strength of solvation for the charged species is increased and the scattering profiles start to resemble those of neutral polymer solutions. The disappearance of the polyelectrolyte peak coincides with the emergence of attractive interchain interactions over a wide range of length scales. These findings provide insights into the microscopic origin of the polyelectrolyte peak.

Modeling collective motion in nonconservative systems, such as granular materials, is difficult since a general microscopic-to-macroscopic approach is not available: there is no Hamiltonian, no known stationary densities in phase space, and not a known small set of relevant variables. Phenomenological coarse-grained models are a good alternative, provided that one has identified a few slow observables and collected a sufficient amount of data for their dynamics. Here we study the case of a vibrofluidized dense granular material. The experimental study of a tracer, dispersed into the media, showed evidence of many time scales: Fast ballistic, intermediate caged, slow superdiffusive, and very slow diffusive. A numerical investigation has demonstrated that a tracer's superdiffusion is related to slow rotating drifts of the granular medium. Here we offer a deeper insight into the slow scales of the granular medium, and we propose a phenomenological model for such a “secular” dynamics. Based upon the model for the granular medium, we also introduce a model for the tracer (fast and slow) dynamics, which consists in a stochastic system of equations for three coupled variables, and is therefore more refined and successful than previous models.

While cracks in isotropic homogeneous materials propagate straight, perpendicularly to the tensile axis, cracks in natural and synthetic composites deflect from a straight path, often increasing the toughness of the material. Here we combine experiments and simulations to identify materials properties that predict whether cracks propagate straight or kink on a macroscale larger than the composite microstructure. Those properties include the anisotropy of the fracture energy, which we vary several fold by increasing the volume fraction of orientationally ordered alumina (${\text{Al}}_2{\text{O}}_3$) platelets inside a polymer matrix, and a microstructure-dependent process zone size that is found to modulate the additional stabilizing or destabilizing effect of the nonsingular stress acting parallel to the crack. Those properties predict the existence of an anisotropy threshold for crack kinking and explain the surprisingly strong dependence of this threshold on sample geometry and load distribution.

In this work, a detrending-moving-average- (DMA) based bivariate linear regression analysis method is proposed. The method is combination of detrended moving average analysis and standard regression methodology, which allows us to estimate the scale-dependent regression coefficients for nonstationary and power-law correlated time series. By using synthetic simulations with error of estimation for different position parameter $\theta$ of detrending windows, we test our DMA-based bivariate linear regression algorithm and find that the centered detrending technique ($\theta =0.5$) is of best performance, which provides the most accurate estimates. In addition, the estimated regression coefficients are in good agreement with the theoretical values. The center DMA-based bivariate linear regression estimator is applied to analyze the return series of Shanghai stock exchange composite index, the Hong Kong Hangseng index and the NIKKEI 225 index. The dependence among the Asian stock market across timescales is confirmed. Furthermore, two statistics based on the scale-dependent $t$ statistic and the partial detrending-moving-average cross-correlation coefficient are used to demonstrate the significance of the dependence. The scale-dependent evaluation parameters also show that the DMA-based bivariate regression model can provide rich information than standard regression analysis.

Epidemic spreading in heterogeneous networks has attracted great interest in recent years. To capture the significant effect of residence of individuals on epidemic spreading, we consider herein a simple susceptible-infected-susceptible model with random waiting time in heterogeneous networks. We provide the analytical dynamical expressions for the time evolution for infected individuals and find a fractional memory effect of power-law waiting time on anomalous epidemic spreading. This work provides new quantitative insights in describing contagion processes and could help model other spreading phenomena in social and technological networks.

We explore the role that the obstacle position plays in the evacuation time of agents when leaving a room. To this end, we simulate a system of nonsymmetric spherocylinders that have a prescribed desired velocity and angular orientation. In this way, we reproduce the nonmonotonous dependence of the pedestrian flow rate on the obstacle distance to the door. For short distances, the obstacle delays the evacuation because the exit size is effectively reduced; i.e., the distance between the obstacle and the wall is smaller than the door width. By increasing the obstacle distance to the door, clogging is reduced leading to an optimal obstacle position (maximum flow rate) in agreement with results reported in numerical simulations of pedestrian evacuations and granular flows. For further locations, however, a counterintuitive behavior occurs as the flow rate values fall again below the one corresponding to the case without obstacle. Analyzing the head-times distribution, we evidence that this new feature is not linked to the formation of clogs, but is caused by a reduction of the efficiency of the agent's instantaneous flow rate when the exit is not blocked.

An intense radiation field can modify plasma properties and the corresponding refractive index and lead to nonlinear propagation effects such as self-focusing. We estimate the corresponding effects in pair plasmas for circularly polarized waves, in both unmagnetized and strongly magnetically dominated cases. First, in the unmagnetized pair plasma the ponderomotive force does not lead to charge separation but to density depletion. Second, for astrophysically relevant plasmas of pulsar magnetospheres [and possible loci of fast radio bursts (FRBs)], where the cyclotron frequency ${\omega }_B$ dominates over the plasma frequency ${\omega }_p$ and the frequency of the electromagnetic wave ${\omega }_B\gg {\omega }_p,\omega$, we show that (i) there is virtually no nonlinearity due to changing effective mass in the field of the wave; (ii) the ponderomotive force is $F_p^{\left(B\right)}=-m_e{c}^2/4B_0^2\mathbf{\nabla }{E}^2$, which is reduced by a factor ${(\omega /{\omega }_B)}^2$ if compared to the unmagnetized case ($B_0$ is the external magnetic field and $E$ is the electric field of the wave); and (iii) for a radiation beam propagating along a constant magnetic field in the pair plasma with density $n_{\pm }$, the ponderomotive force leads to the appearance of circular currents that lead to a decrease of the field within the beam by a factor $\mathrm{\Delta }B/B_0=2\pi n_{\pm }{m}_e{c}^2{E}^2/B_0^4$. Applications to the physics of FRBs are discussed; we conclude that for the parameters of FRBs, the dominant magnetic field completely suppresses nonlinear self-focusing or filamentation.

A method of generating spin-polarized proton beams from a gas jet by using a multipetawatt laser is put forward. With currently available techniques of producing prepolarized monatomic gases from photodissociated hydrogen halide molecules and petawatt lasers, proton beams with energy $\gtrsim 50$ MeV and $\approx 80\%$ polarization are proved to be obtained. Two-stage acceleration and spin dynamics of protons are investigated theoretically and by means of fully self-consistent three-dimensional particle-in-cell simulations. Our results predict the dependence of the beam polarization on the intensity of the driving laser pulse. Generation of bright energetic polarized proton beams would open a domain of polarization studies with laser driven accelerators and have potential application to enable effective detection in explorations of quantum chromodynamics.

Although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic (EE) states in the asymptotic limit, for the finite quantum systems, the relation is not so linear and requires detailed investigation. Toward this, we have considered a resource theoretic framework taking the energy preserving operations (EPOs) as free, to compare the amount of extractable work from two different quantum states. Under the EPO, majorization becomes a necessary criterion for state transformation. It is also shown that the passive-state energy is a concave function, and, for EE states, it becomes proportional to the ergotropy in absolute sense. Invariance of the passive-state energy under unitary action on the given state makes it an entanglement measure for the pure bipartite states. Furthermore, due to the nonadditivity of passive-state energy for the different system Hamiltonians, one can generate ${\mathrm{Vidal}}^{\prime }$s monotones which would give the optimal probability for pure entangled state transformation. This measure also quantifies the ergotropic gap which is employed to distinguish some specific classes of three-qubit pure entangled states.

Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form $D\left(x\right)=D_0{\left|x\right|}^{\alpha }$. Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble- and time-averaged mean-squared displacements couple the scaling exponents $\alpha$ of HDPs and the Hurst exponent $H$ of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable $y\sim {\left|x\right|}^{1/(2/(2-\alpha \left)\right)}/t^H$ coupling particle position $x$ and time $t$ yields a simple, Gaussian probability density function (PDF), $P_{\text{HDP-FBM}}\left(y\right)=e^{-y^2}/\sqrt{\pi }$. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.

Reckoning of pairwise dynamical correlations significantly improves the accuracy of mean-field theories and plays an important role in the investigation of dynamical processes in complex networks. In this work, we perform a nonperturbative numerical analysis of the quenched mean-field theory (QMF) and the inclusion of dynamical correlations by means of the pair quenched mean-field (PQMF) theory for the susceptible-infected-susceptible model on synthetic and real networks. We show that the PQMF considerably outperforms the standard QMF theory on synthetic networks of distinct levels of heterogeneity and degree correlations, providing extremely accurate predictions when the system is not too close to the epidemic threshold, while the QMF theory deviates substantially from simulations for networks with a degree exponent $\gamma >2.5$. The scenario for real networks is more complicated, still with PQMF significantly outperforming the QMF theory. However, despite its high accuracy for most investigated networks, in a few cases PQMF deviations from simulations are not negligible. We found correlations between accuracy and average shortest path, while other basic network metrics seem to be uncorrelated with the theory accuracy. Our results show the viability of the PQMF theory to investigate the high-prevalence regimes of recurrent-state epidemic processes in networks, a regime of high applicability.

A bredge (bridge-edge) in a network is an edge whose deletion would split the network component on which it resides into two separate components. Bredges are vulnerable links that play an important role in network collapse processes, which may result from node or link failures, attacks, or epidemics. Therefore, the abundance and properties of bredges affect the resilience of the network to these collapse scenarios. We present analytical results for the statistical properties of bredges in configuration model networks. Using a generating function approach based on the cavity method, we calculate the probability $\widehat{P}(e\in \mathrm{B})$ that a random edge $e$ in a configuration model network with degree distribution $P\left(k\right)$ is a bredge (B). We also calculate the joint degree distribution $\widehat{P}(k,k^{\prime }|\mathrm{B})$ of the end-nodes $i$ and $i^{\prime }$ of a random bredge. We examine the distinct properties of bredges on the giant component (GC) and on the finite tree components (FC) of the network. On the finite components all the edges are bredges and there are no degree-degree correlations. We calculate the probability $\widehat{P}(e\in \mathrm{B}|\mathrm{GC})$ that a random edge on the giant component is a bredge. We also calculate the joint degree distribution $\widehat{P}(k,k^{\prime }|\mathrm{B},\mathrm{GC})$ of the end-nodes of bredges and the joint degree distribution $\widehat{P}(k,k^{\prime }|\mathrm{NB},\mathrm{GC})$ of the end-nodes of nonbredge edges on the giant component. Surprisingly, it is found that the degrees $k$ and $k^{\prime }$ of the end-nodes of bredges are correlated, while the degrees of the end-nodes of nonbredge edges are uncorrelated. We thus conclude that all the degree-degree correlations on the giant component are concentrated on the bredges. We calculate the covariance $\mathrm{\Gamma }(\mathrm{B},\mathrm{GC})$ of the joint degree distribution of end-nodes of bredges and show it is negative, namely bredges tend to connect high degree nodes to low degree nodes. We apply this analysis to ensembles of configuration model networks with degree distributions that follow a Poisson distribution (Erdős-Rényi networks), an exponential distribution and a power-law distribution (scale-free networks). The implications of these results are discussed in the context of common attack scenarios and network dismantling processes.

We investigate the electrostatic interactions of zwitterionic membranes immersed in mixed electrolytes composed of mono- and multivalent ions. We show that the presence of monovalent salt is a necessary condition for the existence of a finite electrostatic force on the membrane. As a result, the mean-field membrane pressure originating from the surface dipoles exhibits a nonuniform salt dependence, characterized by an enhancement for dilute salt conditions and a decrease at intermediate salt concentrations. On addition of multivalent cations to the submolar salt solution, the separate interactions of these cations with the opposite charges of the surface dipoles makes the intermembrane pressure more repulsive at low membrane separation distances and strongly attractive at intermediate distances, resulting in a discontinuous like-charge binding transition followed by the membrane binding transition. By extending our formalism to account for correlation corrections associated with large salt concentrations, we show that membranes of high surface dipole density immersed in molar salt solutions may undergo a membrane binding transition even without the multivalent cations. Hence, the tuning of the surface polarization forces by membrane engineering can be an efficient way to adjust the equilibrium configuration of dipolar membranes in concentrated salt solutions.

A Mpemba effect refers to the counterintuitive result that, when quenched to a low temperature, a system at higher temperature may equilibrate faster than one at intermediate temperatures. This effect has recently been demonstrated in driven granular gases, both for smooth as well as rough hard-sphere systems based on a perturbative analysis. In this paper, we consider the inelastic driven Maxwell gas, a simplified model for a granular gas, where the rate of collision is assumed to be independent of the relative velocity. Through an exact analysis, we determine the conditions under which the Mpemba effect is present in this model. For monodispersed gases, we show that the Mpemba effect is present only when the initial states are allowed to be nonstationary, while for bidispersed gases, it is present for some steady-state initial states. We also demonstrate the existence of the strong Mpemba effect for bidispersed Maxwell gas, wherein the system at higher temperature relaxes to a final steady state at an exponentially faster rate leading to smaller equilibration time.

Plasmas, as well as several other many-body systems of technological interest, have been studied mostly as a purely classical subject. However, in dense plasmas, and in some semiconductor devices, metallic nanostructures and thin metal films, when the de Broglie wavelength of the charge carriers is comparable to the interparticle distance, quantum effects come into play. Because the classical kinetic equations are phase-space equations with positions and momenta as variables, which variables are noncommuting in quantum mechanics, kinetic equations are not directly applicable to quantum plasmas. Therefore, most treatments consider a full quantum many-body problem in Hilbert space and then, by reduction, obtain the quantum version of the kinetic equations. However, quantum mechanics may also be directly formulated in phase space by modifying the Poisson algebra into a new deformed algebra, hence the classical kinetic equations may also be deformed into their corresponding quantum versions. This is the approach followed here and applied to derive the quantum corrections to the Vlasov–Poisson, Vlasov–Maxwell, and Boltzmann equations (in the latter case also within the relaxation-time approximation).