Exponential number of equilibria and depinning threshold for a directed polymer in a random potential

By extending the Kac-Rice approach to manifolds of finite internal dimension, we show that the mean number $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle$ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension $d=1+1$, grows exponentially $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle\sim\exp{(r\,L)}$ with its length $L$. The growth rate $r$ is found to be directly related to the generalised Lyapunov exponent (GLE) which is a moment-generating function characterising the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schr\"odinger operator of the 1D Anderson localization problem. For strong confinement, the rate $r$ is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate $r$ is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape "topology trivialization" phenomenon, we obtain an upper bound for the depinning threshold $f_c$, in the presence of an applied force, for elastic lines and $d$-dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.Comment: v1: 6 pages main text + 14 pages supplemental material, 10 figures. v2: LaTeX, 79 pages, 18 eps figures, new material (Sections 6, 10, 11 & Appendices C, E, F, G

Biomimicking Extracellular Vesicles with Fully Artificial Ones: A Rational Design of EV-BIOMIMETICS toward Effective Theranostic Tools in Nanomedicine

Extracellular Vesicles (EVs) are the protagonists in cell communication and membrane trafficking, being responsible for the delivery of innumerable biomolecules and signaling moieties. At the moment, they are of paramount interest to researchers, as they naturally show incredibly high efficiency and specificity in delivering their cargo. For these reasons, EVs are employed or inspire the development of nanosized therapeutic delivery systems. In this Perspective, we propose an innovative strategy for the rational design of EV-mimicking vesicles (EV-biomimetics) for theranostic scopes. We first report on the current state-of-the-art use of EVs and their byproducts, such as surface-engineered EVs and EV-hybrids, having an artificial cargo (drug molecule, genetic content, nanoparticles, or dye incorporated in their lumen). Thereafter, we report on the new emerging field of EV-mimicking vesicles for theranostic scopes. We introduce an approach to prepare new, fully artificial EV-biomimetics, with particular attention to maintaining the natural reference lipidic composition. We overview those studies investigating natural EV membranes and the possible strategies to identify key proteins involved in site-selective natural homing, typical of EVs, and their cargo transfer to recipient cells. We propose the use also of molecular simulations, in particular of machine learning models, to approach the problem of lipid organization and self-assembly in natural EVs. We also discuss the beneficial feedback that could emerge combining the experimental tests with atomistic and molecular simulations when designing an EV-biomimetics lipid bilayer. The expectations from both research and industrial fields on fully artificial EV-biomimetics, having the same key functions of natural ones plus new diagnostic or therapeutic functions, could be enormous, as they can greatly expand the nanomedicine applications and guarantee on-demand and scalable production, off-the-shelf storage, high reproducibility of morphological and functional properties, and compliance with regulatory standards

On quantization of r-matrices for Belavin-Drinfeld Triples

We suggest a formula for quantum universal $R$-matrices corresponding to quasitriangular classical $r$-matrices classified by Belavin and Drinfeld for all simple Lie algebras. The $R$-matrices are obtained by twisting the standard universal $R$-matrix.Comment: 12 pages, LaTe

Short time relaxation of a driven elastic string in a random medium

We study numerically the relaxation of a driven elastic string in a two dimensional pinning landscape. The relaxation of the string, initially flat, is governed by a growing length $L(t)$ separating the short steady-state equilibrated lengthscales, from the large lengthscales that keep memory of the initial condition. We find a macroscopic short time regime where relaxation is universal, both above and below the depinning threshold, different from the one expected for standard critical phenomena. Below the threshold, the zero temperature relaxation towards the first pinned configuration provides a novel, experimentally convenient way to access all the critical exponents of the depinning transition independently.Comment: 4.2 pages, 3 figure

Factors affecting the vaccination choices of pregnant women for their children. A systematic review of the literature

In recent years, an increase in vaccine hesitancy has led to a decrease in vaccination coverage in several countries. We conducted a systematic review of studies that assessed knowledge of and attitudes toward pediatric vaccinations, and the vaccination choices and their determinants among pregnant women. A total of 6,277 records were retrieved, and 16 full texts were included in the narrative synthesis. The published literature on the topic shows that, overall, pregnant women believe that vaccines are important for the protection of their children and the community, but various concerns and misunderstandings persist around vaccine safety and efficacy, which reduce the trust of expectant mothers in immunization. Nevertheless, such attitudes and choices vary depending on the vaccine being considered and the corresponding determinants should therefore be studied in the context of each specific vaccination. Further research on this topic is needed, particularly in non-western countries

Free-energy distribution of the directed polymer at high temperature

We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is described, upon scaling 'time' $t \sim T^5/\kappa$ and space $x = T^3/\kappa$ (with $\kappa=T$ for the discrete model) by a continuum model with $\delta$-function disorder correlation. Using the Bethe Ansatz solution for the attractive boson problem, we obtain all positive integer moments of the partition function. The lowest cumulants of the free energy are predicted at small time and found in agreement with numerics. We then obtain the exact expression at any time for the generating function of the free energy distribution, in terms of a Fredholm determinant. At large time we find that it crosses over to the Tracy Widom distribution (TW) which describes the fixed $T$ infinite $t$ limit. The exact free energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.Comment: 6 pages, 3 figures large time limit corrected and convergence to Tracy Widom established, 1 figure changed

Representations of the quantum matrix algebra Mq,p(2)M_{q,p}(2)

It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra $M_{ q,p}(2)$ ( the coordinate ring of $GL_{q,p}(2)$) exist only when both q and p are roots of unity. In this case th e space of states has either the topology of a torus or a cylinder which may be thought of as generalizations of cyclic representations.Comment: 20 page

Vapor pressure measurements over supercooled water in the temperature range from −10 1 °C to +10 −2 °C

An accurate measurement of saturation vapor pressure of supercooled water is a strong challenge in metrology, mainly due to difficulties concerning keeping water at a liquid state at temperatures well below the melting point; thus few experimental data covering limited temperature ranges (down to about 253 K) are reported in literature. For this reason, an investigation of the water vapor – supercooled water equilibrium along the saturation line is carried out at Istituto Nazionale di Ricerca Metrologica (INRIM). Measurements cover the temperature range from 261.26 K to 273.25 K, corresponding to a saturation vapor pressure from about 244 Pa to 611 Pa. The experimental apparatus includes a borosilicate glass sample cell, kept in a liquid bath at a constant temperature with millikelvin stability and connected to a manifold where the pressure is measured using a capacitive diaphragm pressure gauge. In this work, the water sample preparation, the measuring method and measurement corrections are reported; moreover, a comparison between experimental and literature data is conducted along with the most used vapor pressure formulations. Measurement results are discussed and uncertainty sources estimated. The resulting expanded relative uncertainty (k = 2) varies from 0.085% at 261.26 K to 0.039% at 273.25 K