System-level properties of metabolic networks may be the direct product of natural selection or arise as a by-product of selection on other properties. Here we study the effect of direct selective pressure for growth or viability in particular environments on two properties of metabolic networks: latent versatility to function in additional environments and carbon usage efficiency. Using a Markov chain Monte Carlo (MCMC) sampling based on flux balance analysis (FBA), we sample from a known biochemical universe random viable metabolic networks that differ in the number of directly constrained environments. We find that the latent versatility of sampled metabolic networks increases with the number of directly constrained environments and with the size of the networks. We then show that the average carbon wastage of sampled metabolic networks across the constrained environments decreases with the number of directly constrained environments and with the size of the networks. Our work expands the growing body of evidence about nonadaptive origins of key functional properties of biological networks.

Medication is applied to the HIV-infected nodes of high-risk contact networks with the aim of controlling the spread of disease to a predetermined maximum level. This intervention, known as pinning control, is performed both selectively and randomly in the network. These strategies are applied to 300 independent realizations per reference level of incidence on connected undirectional networks without isolated components and varying in size from 100 to 10 000 nodes per network. It is shown that a selective on-off pinning control strategy can control the networks studied with limited steady-state error and, comparing the medians of the doses from both strategies, uses 51.3% less medication than random pinning of all infected nodes. Selective pinning could possibly be used by public health specialists to identify the maximum level of HIV incidence in a population that can be achieved in a constrained funding environment.

We propose two recommendation methods, based on the appropriate normalization of already existing similarity measures, and on the convex combination of the recommendation scores derived from similarity between users and between objects. We validate the proposed measures on three data sets, and we compare the performance of our methods to other recommendation systems recently proposed in the literature. We show that the proposed similarity measures allow us to attain an improvement of performances of up to 20% with respect to existing nonparametric methods, and that the accuracy of a recommendation can vary widely from one specific bipartite network to another, which suggests that a careful choice of the most suitable method is highly relevant for an effective recommendation on a given system. Finally, we study how an increasing presence of random links in the network affects the recommendation scores, finding that one of the two recommendation algorithms introduced here can systematically outperform the others in noisy data sets.

We have studied the exchange corrections to linear electrostatic wave propagation in a plasma using a quantum kinetic formalism. Specifically, we have considered the zero-temperature limit. In order to simplify the calculations we have focused on the long-wavelength limit, i.e., wavelengths much longer than the de Broglie wavelength. For the case of ion-acoustic waves we have calculated the exchange correction both to the damping rate and the real part of the frequency. For Langmuir waves the frequency shift due to exchange effects is found. Our results are compared with the frequency shifts deduced from commonly used exchange potentials which are computed from density-functional theory.

Bento et al. [Phys. Rev. E 91, 022105 (2015)] state that the Tsallis entropy violates the third law of thermodynamics for $q\le 0$ and $0<q<1$. We show that their results are valid only for $q\ge 1$, since there is no distribution maximizing the Tsallis entropy for the intervals $q\le 0$ and $0<q<1$ compatible with the system energy expression.

In Bento et al. [Phys. Rev. E 91, 039901 (2015)] we develop a method to verify if an arbitrary generalized statistics does or does not obey the third law of thermodynamics. As examples, we address two important formulations, Kaniadakis and Tsallis. In their Comment on the paper, Bagci and Oikonomou suggest that our examination of the Tsallis statistics is valid only for $q\ge 1$, using arguments like there is no distribution maximizing the Tsallis entropy for the interval $q<0$ (in which the third law is not verified) compatible with the problem energy expression. In this Reply, we first (and most importantly) show that the Comment misses the point. In our original work we have considered the now already standard construction of the Tsallis statistics. So, if indeed such statistics lacks a maximization principle (a fact irrelevant in our protocol), this is an inherent feature of the statistics itself and not a problem with our analysis. Second, some arguments used by Bagci and Oikonomou (for $0<q<1)$ reflect a misunderstanding of our explicit calculations. These arguments are then clarified under our approach and illustrated through a simple two-level system.

The self-diffusion coefficient of a granular gas in the homogeneous cooling state is analyzed near the shearing instability. Using mode-coupling theory, it is shown that the coefficient diverges logarithmically as the instability is approached, due to the coupling of the diffusion process with the shear modes. The divergent behavior, which is peculiar in granular gases and disappears in the elastic limit, does not depend on any other transport coefficient. The theoretical prediction is confirmed by molecular dynamics simulation results for two-dimensional systems.

The quantum analog of Carnot cycles in few-particle systems consists of two quantum adiabatic steps and two isothermal steps. This construction is formally justified by use of a minimum work principle. It is then shown, using minimal assumptions of work or heat in nanoscale systems, that the heat-to-work efficiency of such quantum heat engine cycles can be further optimized via two conditions regarding the expectation value of some generalized force operators evaluated at equilibrium states. In general the optimized efficiency is system specific, lower than the Carnot efficiency, and dependent upon both temperatures of the cold and hot reservoirs. Simple computational examples are used to illustrate our theory. The results should be an important guide towards the design of favorable working conditions of a realistic quantum heat engine.

We study, using general scaling arguments and mean-field type calculations, the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance $L$ from each other, confining some fluctuating fluid medium, say a nonpolar one-component fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials ensuring the so-called $(+,+)$ boundary conditions. The slabs, on the other hand, influence the fluid by long-range competing dispersion potentials, which represent irrelevant interactions in renormalization-group sense. Under such conditions, one usually expects attractive Casimir force governed by universal scaling function, pertinent to the extraordinary surface universality class of Ising type systems, to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given threshold thickness of the system $L_{\mathrm{crit}}$ for a suitable set of slabs-fluid and fluid-fluid coupling parameters the competition between the effects due to the coatings and the slabs can result in sign change of the Casimir force acting between the surfaces confining the fluid when one changes the temperature $T$, the chemical potential of the fluid $\mu$, or $L$. The last implies that by choosing specific materials for the slabs, coatings, and the fluid for $L\lesssim L_{\mathrm{crit}}$ one can realize repulsive Casimir force with nonuniversal behavior which, upon increasing $L$, gradually turns into an attractive one described by a universal scaling function, depending only on the relevant scaling fields related to the temperature and the excess chemical potential, for $L\gg L_{\mathrm{crit}}$. We present arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force. It can be of interest, e.g., for designing nanodevices and for governing behavior of objects, say colloidal particles, at small distances. We formulate the corresponding criterion for determination of $L_{\mathrm{crit}}$. The universality is regained for $L\gg L_{\mathrm{crit}}$. We also show that for systems with $L\lesssim L_{\mathrm{crit}}$, the capillary condensation phase diagram suffers modifications which one does not observe in systems with purely short-ranged interactions.

Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.

We study the structural and thermodynamic properties of patchy particle liquids, with a special focus on the role of “color,” i.e., specific interactions between individual patches. A possible experimental realization of such “chromatic” interactions is by decorating the particle patches with single-stranded DNA linkers. The complementarity of the linkers can promote selective bond formation between predetermined pairs of patches. By using MD simulations, we compare the local connectivity, the bond orientation order, and other structural properties of the aggregates formed by the “colored” and “colorless” systems. The analysis is done for spherical particles with two different patch arrangements (tetrahedral and cubic). It is found that the aggregated (liquid) phase of the “colorless” patchy particles is better connected, denser and typically has stronger local order than the corresponding “colored” one. This, in turn, makes the colored liquid less stable thermodynamically. Specifically, we predict that in a typical case the chromatic interactions should increase the relative stability of the crystalline phase with respect to the disordered liquid, thus expanding its region in the phase diagram.

We present in this paper an approximation that is able to give an analytical expression for the exit probability of the $q$-voter model in one dimension. This expression gives a better fit for the more recent data about simulations in large networks [A. M. Timpanaro and C. P. C. do Prado, Phys. Rev. E 89, 052808 (2014)] and as such departs from the expression $\frac{{\rho }^q}{{\rho }^q+{(1-\rho )}^q}$ found in papers that investigated small networks only [R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008); P. Przybyła et al., Phys. Rev. E 84, 031117 (2011); F. Slanina et al., Europhys. Lett. 82, 18006 (2008)]. The approximation consists in assuming a large separation on the time scales at which active groups of agents convince inactive ones and the time taken in the competition between active groups. Some interesting findings are that for $q=2$ we still have $\frac{{\rho }^2}{{\rho }^2+{(1-\rho )}^2}$ as the exit probability and for $q>2$ we can obtain a lower-order approximation of the form $\frac{{\rho }^s}{{\rho }^s+{(1-\rho )}^s}$ with $s$ varying from $q$ for low values of $q$ to $q-\frac{1}{2}$ for large values of $q$. As such, this work can also be seen as a deduction for why the exit probability $\frac{{\rho }^q}{{\rho }^q+{(1-\rho )}^q}$ gives a good fit, without relying on mean-field arguments or on the assumption that only the first step is nondeterministic, as $q$ and $q-\frac{1}{2}$ will give very similar results when $q\to \infty$.

Imaging of the microstructure of porous media such as biological tissue or porous solids is of high interest in health science and technology, engineering and material science. Magnetic resonance pore imaging (MRPI) is a recent technique based on nuclear magnetic resonance (NMR) which allows us to acquire images of the average pore shape in a given sample. Here we provide details on the experimental design, challenges, and requirements of MRPI, including its calibration procedures. Utilizing a laser-machined phantom sample, we present images of microscopic pores with a hemiequilateral triangular shape even in the presence of NMR relaxation effects at the pore walls. We therefore show that MRPI is applicable to porous samples without a priori knowledge about their pore shape and symmetry. Furthermore, we introduce “MRPI mapping,” which combines MRPI with conventional magnetic resonance imaging (MRI). This enables one to resolve microscopic pore sizes and shapes spatially, thus expanding the application of MRPI to samples with heterogeneous distributions of pores.

The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show that if the effective phase response curve is everywhere positive (negative), then an entrainment of the oscillator to an envelope frequency is possible only when this frequency is higher (lower) than the natural frequency of the oscillator. Also, by using the Pontryagin maximum principle, we have derived an optimal waveform of the perturbation that ensures an entrainment of the oscillator with minimal power. The theoretical results are demonstrated with the Stuart-Landau oscillator and model neurons.

Condensation of water vapor on active cloud condensation nuclei produces micron-size water droplets. To form rain, they must grow rapidly into at least 50- to $100-\mu \mathrm{m}$ droplets. Observations show that this process takes only 15–20 min. The unexplained physical mechanism of such fast growth is crucial for understanding and modeling of rain and known as “condensation-coalescence bottleneck in rain formation.” We show that the recently discovered phenomenon of the tangling clustering instability of small droplets in temperature-stratified turbulence [Phys. Fluids 25, 085104 (2013)] results in the formation of droplet clusters with drastically increased droplet number densities. The mechanism of the tangling clustering instability is much more effective than the previously considered by us the inertial clustering instability caused by the centrifugal effect of turbulent vortices. This is the reason of strong enhancement of the collision-coalescence rate inside the clusters. The mean-field theory of the droplet growth developed in this study can be useful for explanation of the observed fast growth of cloud droplets in warm clouds from the initial $1-\mu \mathrm{m}$-size droplets to 40- to $50-\mu \mathrm{m}$-size droplets within 15–20 min.

The cylindrical Couette flow of a rarefied gas between a rotating inner cylinder and a stationary outer cylinder is investigated under the following two kinds of kinetic boundary conditions. One is the modified Maxwell-type boundary condition proposed by Dadzie and Méolans [J. Math. Phys. 45, 1804 (2004)] and the other is the Cercignani-Lampis condition, both of which have separate accommodation coefficients associated with the molecular velocity component normal to the boundary and with the tangential component. An asymptotic analysis of the Boltzmann equation for small Knudsen numbers and a numerical analysis of the Bhatnagar-Gross-Krook model equation for a wide range of the Knudsen number are performed to clarify the effect of each accommodation coefficient as well as of the boundary condition itself on the behavior of the gas, especially on the flow-velocity profile. As a result, the velocity-slip and temperature-jump conditions corresponding to the above kinetic boundary conditions are derived, which are necessary for the fluid-dynamic description of the problem for small Knudsen numbers. The parameter range for the onset of the velocity inversion phenomenon, which is related mainly to the decrease in the tangential momentum accommodation, is also obtained.

Understanding the relaxation of a system towards equilibrium is a long-standing problem in statistical mechanics. Here we address the role of long-range interactions in this process by considering a class of two-dimensional flows where the interaction between fluid particles varies with the distance as $\sim r^{\alpha -2}$ for $\alpha >0$. We find that changing $\alpha$ with a prescribed initial state leads to different flow patterns: for small $\alpha$, a coarsening process leads to the formation of a sharp interface between two regions of homogenized $\alpha$-vorticity; for large $\alpha$, the flow is attracted to a stable dipolar structure through a filamentation process. Assuming that the energy $E$ and the enstrophy $Z$ are injected at a typical scale smaller than the domain scale $L$, we argue that convergence towards the equilibrium state is expected when the parameter ${\left(\frac{2\pi }{L}\right)}^{\alpha }\frac{E}{Z}$ tends to one, while convergence towards a dipolar state occurs systematically when this parameter tends to zero. This suggests that weak long-range interacting systems are more prone to relax towards an equilibrium state than strong long-range interacting systems.

The dynamics of quasistationary states of long-range interacting systems with $N$ particles can be described by kinetic equations such as the Balescu-Lenard and Landau equations. In the case of one-dimensional homogeneous systems, two-body contributions vanish as two-body collisions in one dimension only exchange momentum and thus cannot change the one-particle distribution. Using a Kac factor in the interparticle potential implies a scaling of the dynamics proportional to $N^{\delta }$ with $\delta =1$ except for one-dimensional homogeneous systems. For the latter different values for $\delta$ were reported for a few models. Recently it was shown by Rocha Filho and collaborators [Phys. Rev. E 90, 032133 (2014)] for the Hamiltonian mean-field model that $\delta =2$ provided that $N$ is sufficiently large, while small $N$ effects lead to $\delta \approx 1.7$. More recently, Gupta and Mukamel [J. Stat. Mech. (2011) P03015] introduced a classical spin model with an anisotropic interaction with a scaling in the dynamics proportional to $N^{1.7}$ for a homogeneous state. We show here that this model reduces to a one-dimensional Hamiltonian system and that the scaling of the dynamics approaches $N^2$ with increasing $N$. We also explain from theoretical consideration why usual kinetic theory fails for small $N$ values, which ultimately is the origin of noninteger exponents in the scaling.

We study the behavior of a nanoparticle under electromigration on a nanopatterned surface. We show that electromigration allows one to control the wetting transitions of the nanoparticle. Suitable surface electromigration conditions to observe these transitions can be achieved with electric currents larger than $1 \mu \text{A}$. Using kinetic Monte Carlo simulations and analytical modeling, we determine the phase diagram of the wetting states, showing how wetting multistability is affected by electromigration. In addition, we show that the dynamics of the transitions is controlled by surface diffusion in our simulations, and we provide a quantitative expression for the transition time.

By using a two-dimensional phase-field-crystal (PFC) model, the liquid crystalline growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from an isotropic phase is compared with that grown from a columnar or smectic-$A$ (CSA) phase. While the shape of a PTC nucleus in the isotropic phase is almost identical to that of the classical PFC model, the shape of a PTC nucleus in CSA is affected by the orientation of stripes in the CSA phase, and irregular hexagonal, elliptical, octagonal, and rectangular shapes are obtained. Concerning the dynamics of the growth process, we analyze the topological structure of the nematic order, which starts from nucleation of $+\frac{1}{2}$ and $-\frac{1}{2}$ disclination pairs at the PTC growth front and evolves into hexagonal cells consisting of $+1$ vortices surrounded by six satellite $-\frac{1}{2}$ disclinations. It is found that the orientational and the positional order do not evolve simultaneously; the orientational order evolves behind the positional order, leading to a large transition zone, which can span over several lattice spacings.