Glassy dynamics of partially pinned fluids: an alternative mode-coupling approach

We use a simple mode-coupling approach to investigate glassy dynamics of partially pinned fluid systems. Our approach is different from the mode-coupling theory developed by Krakoviack [Phys. Rev. Lett. 94, 065703 (2005), Phys. Rev. E 84, 050501(R) (2011)]. In contrast to Krakoviack's theory, our approach predicts a random pinning glass transition scenario that is qualitatively the same as the scenario obtained using a mean-field analysis of the spherical p-spin model and a mean-field version of the random first-order transition theory. We use our approach to calculate quantities which are often considered to be indicators of growing dynamic correlations and static point-to-set correlations. We find that the so-called static overlap is dominated by the simple, low pinning fraction contribution. Thus, at least for randomly pinned fluid systems, only a careful quantitative analysis of simulation results can reveal genuine, many-body point-to-set correlations

Hitting spheres on hyperbolic spaces

For a hyperbolic Brownian motion on the Poincar\'e half-plane $\mathbb{H}^2$, starting from a point of hyperbolic coordinates $z=(\eta, \alpha)$ inside a hyperbolic disc $U$ of radius $\bar{\eta}$, we obtain the probability of hitting the boundary $\partial U$ at the point $(\bar \eta,\bar \alpha)$. For $\bar{\eta} \to \infty$ we derive the asymptotic Cauchy hitting distribution on $\partial \mathbb{H}^2$ and for small values of $\eta$ and $\bar \eta$ we obtain the classical Euclidean Poisson kernel. The exit probabilities $\mathbb{P}_z\{T_{\eta_1}<T_{\eta_2}\}$ from a hyperbolic annulus in $\mathbb{H}^2$ of radii $\eta_1$ and $\eta_2$ are derived and the transient behaviour of hyperbolic Brownian motion is considered. Similar probabilities are calculated also for a Brownian motion on the surface of the three dimensional sphere. For the hyperbolic half-space $\mathbb{H}^n$ we obtain the Poisson kernel of a ball in terms of a series involving Gegenbauer polynomials and hypergeometric functions. For small domains in $\mathbb{H}^n$ we obtain the $n$-dimensional Euclidean Poisson kernel. The exit probabilities from an annulus are derived also in the $n$-dimensional case

Marvels and Pitfalls of the Langevin Algorithm in Noisy High-Dimensional Inference

Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference. In this work, we carry out an analytic study of the performance of the algorithm most commonly considered in physics, the Langevin algorithm, in the context of noisy high-dimensional inference. We employ the Langevin algorithm to sample the posterior probability measure for the spiked mixed matrix-tensor model. The typical behavior of this algorithm is described by a system of integrodifferential equations that we call the Langevin state evolution, whose solution is compared with the one of the state evolution of approximate message passing (AMP). Our results show that, remarkably, the algorithmic threshold of the Langevin algorithm is suboptimal with respect to the one given by AMP. This phenomenon is due to the residual glassiness present in that region of parameters. We also present a simple heuristic expression of the transition line, which appears to be in agreement with the numerical results

Assessment of Methods to Pretreat Microalgal Biomass for Enhanced Biogas Production

In anaerobic digestion of microalgae, the intracellular material may remain intact due to the non-ruptured membrane and/or cell wall, reducing the methane yield. Therefore, different pretreatment methods were evaluated for the solubilization of microalgae Scenedesmus sp. The anaerobic digestion of biomass hydrolyzed at 150 °C for 60 min with sulfuric acid 0.1% v/v showed higher methane yield (204-316 mL methane/g volatile solids applied) compared to raw biomass (104-163 mL methane/g volatile solids applied). The replacement of sulfuric acid with carbonic acid (by bubbling carbon dioxide up to pH 2.0) provided results similar to those obtained with sulfuric acid, reaching solubilization of 41.6% of the biomass. This result shows that part of the flue gas (containing carbon dioxide and other acid gases as well as high temperatures) may be used for the hydrolysis of the residual biomass from microalgae, thus lowering operational costs (e.g., energy consumption and chemical input)

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincar\'e half-plane and Poincar\'e disk) is examined. Each particle can split into two particles only once at Poisson paced times and deviates orthogonally when splitted. At time $t$, after $N(t)$ Poisson events, there are $N(t)+1$ particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as $t$ increases and for different values of the parameters $c$ (hyperbolic velocity of motion) and $\lambda$ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented

Order in glassy systems

A directly measurable correlation length may be defined for systems having a two-step relaxation, based on the geometric properties of density profile that remains after averaging out the fast motion. We argue that the length diverges if and when the slow timescale diverges, whatever the microscopic mechanism at the origin of the slowing down. Measuring the length amounts to determining explicitly the complexity from the observed particle configurations. One may compute in the same way the Renyi complexities K_q, their relative behavior for different q characterizes the mechanism underlying the transition. In particular, the 'Random First Order' scenario predicts that in the glass phase K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis of a nonequilibrium effective temperature may also be directly tested directly from configurations.Comment: Typos corrected, clarifications adde

Criticality of plasma membrane lipids reflects activation state of macrophage cells.

Signalling is of particular importance in immune cells, and upstream in the signalling pathway many membrane receptors are functional only as complexes, co-locating with particular lipid species. Work over the last 15 years has shown that plasma membrane lipid composition is close to a critical point of phase separation, with evidence that cells adapt their composition in ways that alter the proximity to this thermodynamic point. Macrophage cells are a key component of the innate immune system, are responsive to infections and regulate the local state of inflammation. We investigate changes in the plasma membrane's proximity to the critical point as a response to stimulation by various pro- and anti-inflammatory agents. Pro-inflammatory (interferon γ, Kdo 2-Lipid A, lipopolysaccharide) perturbations induce an increase in the transition temperature of giant plasma membrane vesicles; anti-inflammatory interleukin 4 has the opposite effect. These changes recapitulate complex plasma membrane composition changes, and are consistent with lipid criticality playing a master regulatory role: being closer to critical conditions increases membrane protein activity.Research was funded by EUMarie Curie action ITN TransPol (EC), NIH-R01GM110052 and NSF10 MCB1552439 (SLV), Cambridge University Commonwealth, European and International Trust 11 (JS) ITN BioPol (PC), and Wellcome Trust Investigator grant 08045/Z/15/Z (CEB)

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

Comparing dynamics: deep neural networks versus glassy systems

We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (1) the complexity of the loss landscape and of the dynamics within it, and (2) to what extent DNNs share similarities with glassy systems. Our findings, obtained for different architectures and datasets, suggest that during the training process the dynamics slows down because of an increasingly large number of flat directions. At large limes, when the loss is approaching zero, the system diffuses at the bottom of the landscape. Despite some similarities with the dynamics of mean-field glassy systems, in particular, the absence of barrier crossing, we find distinctive dynamical behaviors in the two cases, showing that the statistical properties of the corresponding loss and energy landscapes arc different. In contrast, when the network is under-parametrized we observe a typical glassy behavior, thus suggesting the existence of different phases depending on whether the network is under-parametrized or over-parametrized