Correspondence between one- and two-equation models for solute\ud transport in two-region heterogeneous porous media

In this work, we study the transient behavior of upscaled models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the time scale of interest (t) is smaller than the characteristic time (T1) for the relaxation of the effective macroscale parameters (i.e., when t ≤ T1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (T1) (i.e., when t » T1); and (3) a one-equation, time-asymptotic formulation (1eq∞). This model can be adopted when (t) is significantly larger than the time scale (T2) associated with exchange processes between the two regions (i.e., when t » T2). In order to obtain some physical insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in simple cases. The main result of this paper is to show that there is weak long-time convergence of the solution of (2eq) toward the solution of (1eq∞) in terms of standardized moments but, interestingly, not in terms of centered moments. Physically, our interpretation of this result is that the spreading of the solute is dominating higher order non-zero perturbations in the asymptotic regime

Estimating the minimizer and the minimum value of a regression function under passive design

We propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise. Our estimator $\boldsymbol{z}_n$ of the minimizer $\boldsymbol{x}^*$ is based on a version of the projected gradient descent with the gradient estimated by a regularized local polynomial algorithm. Next, we propose a two-stage procedure for estimation of the minimum value $f^*$ of regression function $f$. At the first stage, we construct an accurate enough estimator of $\boldsymbol{x}^*$, which can be, for example, $\boldsymbol{z}_n$. At the second stage, we estimate the function value at the point obtained in the first stage using a rate optimal nonparametric procedure. We derive non-asymptotic upper bounds for the quadratic risk and optimization error of $\boldsymbol{z}_n$, and for the risk of estimating $f^*$. We establish minimax lower bounds showing that, under certain choice of parameters, the proposed algorithms achieve the minimax optimal rates of convergence on the class of smooth and strongly convex functions

Estimating the minimizer and the minimum value of a regression function under passive design

We propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise. Our estimator $\boldsymbol{z}_n$ of the minimizer $\boldsymbol{x}^*$ is based on a version of the projected gradient descent with the gradient estimated by a regularized local polynomial algorithm. Next, we propose a two-stage procedure for estimation of the minimum value $f^*$ of regression function $f$. At the first stage, we construct an accurate enough estimator of $\boldsymbol{x}^*$, which can be, for example, $\boldsymbol{z}_n$. At the second stage, we estimate the function value at the point obtained in the first stage using a rate optimal nonparametric procedure. We derive non-asymptotic upper bounds for the quadratic risk and optimization error of $\boldsymbol{z}_n$, and for the risk of estimating $f^*$. We establish minimax lower bounds showing that, under certain choice of parameters, the proposed algorithms achieve the minimax optimal rates of convergence on the class of smooth and strongly convex functions.Comment: 35 page

Two-stage Recognition and Beyond for Compound Facial Emotion Recognition

Facial emotion recognition is an inherently complex problem due to individual diversity in facial features and racial and cultural differences. Moreover, facial expressions typically reflect the mixture of people’s emotional statuses, which can be expressed using compound emotions. Compound facial emotion recognition makes the problem even more difficult because the discrimination between dominant and complementary emotions is usually weak. We have created a database that includes 31,250 facial images with different emotions of 115 subjects whose gender distribution is almost uniform to address compound emotion recognition. In addition, we have organized a competition based on the proposed dataset, held at FG workshop 2020. This paper analyzes the winner’s approach—a two-stage recognition method (1st stage, coarse recognition; 2nd stage, fine recognition), which enhances the classification of symmetrical emotion labels

Nanodiamond emulsions for enhanced quantum sensing and click-chemistry conjugation

Nanodiamonds containing nitrogen-vacancy (NV) centers can serve as colloidal quantum sensors of local fields in biological and chemical environments. However, nanodiamond surfaces are challenging to modify without degrading their colloidal stability or the NV center's optical and spin properties. Here, we report a simple and general method to coat nanodiamonds with a thin emulsion layer that preserves their quantum features, enhances their colloidal stability, and provides functional groups for subsequent crosslinking and click-chemistry conjugation reactions. To demonstrate this technique, we decorate the nanodiamonds with combinations of carboxyl- and azide-terminated amphiphiles that enable conjugation using two different strategies. We study the effect of the emulsion layer on the NV center's spin lifetime, and we quantify the nanodiamonds' chemical sensitivity to paramagnetic ions using $T_1$ relaxometry. This general approach to nanodiamond surface functionalization will enable advances in quantum nanomedicine and biological sensing.Comment: 52 pages, 42 figures (main text plus supplementary information

A new model for molecule exchange in the brain microvascular system: consequences of capillary occlusions in Alzheimer's disease

The brain microvascular system is a key actor in Alzheimer’s disease (AD) development. Indeed, a significant decrease of cerebral blood flow is the earliest biomarker of AD. In vivo TPLSM of cortical vasculature in APP/PS1 mice suggests the mechanism underlying the blood flow reduction is capillary occlusions. Leucocytes adhere to inflamed vessel walls and limit the flow. The impact of capillary occlusions on blood flow has been quantified numerically in large (>10000 vessels) anatomical networks in humans and mice. The regional blood flow has been found to depend linearly with no threshold effect on the fraction of capillary occlusions, so that a small fraction of stalls (2-4%) yields a significant decrease in blood flow (5-12%). Such flow decrease has a strong impact on nutrient delivery and waste clearance. That is why we devised a new model to study the effect of capillary stalling on molecule transport. The geometry of anatomical networks is too complex to use classic numerical approaches like finite elements. Instead, our model, inspired by pore-network approaches, reduces computational costs while capturing most of the underlying physics. To derive this model, we apply upscaling methods to the 3D transport equations within each vessel to obtain 1D average equations along the axis. Contrary to previous models, this new formulation describes accurately radial concentration gradients, capturing effects like longitudinal dispersion. We further use a Green’s function formulation to calculate the concentration fields inside the tissue where diffusion and reaction occur. The coupling between vessels and tissues is modelled using a membrane condition representing the blood brain barrier. This new molecule transport model is coupled with our previously validated blood flow model to examine the effects of capillary stalling on molecular exchange in transient and stationary regimes in anatomical networks. In particular, in stationnary regimes, we demonstrate an increase of the extraction coefficient with the proportion of stalled capillaries, which does not compensate for the associated blood flow reduction

In vitro evaluation of cutaneous penetration of acyclovir from semisolid commercial formulations and relation with its effective antiviral concentration

ABSTRACT The evaluation of drug permeation/penetration of semisolid formulations into animal skin can be useful to supplement the pharmaceutical equivalence. This paper describes the in vitro assessment of acyclovir (ACV) into porcine skin from commercial formulations with etermination of drug concentration in different layers of cutaneous tissue to correlate with effective antiviral concentration in order to improve the equivalence decision. Studies were conducted using Franz cells and porcine skin. Selected pharmaceutical creams containing ACV had identical (reference and generic) and different (similar) excipients. A software program was employed for the simulation of antiviral effectiveness in the skin. Regarding ACV skin penetration, the first batch of the generic product showed a significant difference from reference and similar products, while in the second batch all products demonstrated equivalent drug penetration in the skin. Simulation studies suggest that formulations analysed exhibit a pharmacological effect even when in contact with Herpes simplex strains of high IC50 (inhibitory concentration required to reduce viral replication by 50%). According to results, it can be assumed that the in vitro cutaneous permeation/penetration study does not supply sensitivity information regarding small alterations of ACV semisolid formulations due to the variability inherent to the method, although it can be relevant to pharmaceutical equivalence studies in the development of semisolid products

Brain capillary networks across species : a few simple organizational requirements are sufficient to reproduce both structure and function

Despite the key role of the capillaries in neurovascular function, a thorough characterization of cerebral capillary network properties is currently lacking. Here, we define a range of metrics (geometrical, topological, flow, mass transfer, and robustness) for quantification of structural differences between brain areas, organs, species, or patient populations and, in parallel, digitally generate synthetic networks that replicate the key organizational features of anatomical networks (isotropy, connectedness, space-filling nature, convexity of tissue domains, characteristic size). To reach these objectives, we first construct a database of the defined metrics for healthy capillary networks obtained from imaging of mouse and human brains. Results show that anatomical networks are topologically equivalent between the two species and that geometrical metrics only differ in scaling. Based on these results, we then devise a method which employs constrained Voronoi diagrams to generate 3D model synthetic cerebral capillary networks that are locally randomized but homogeneous at the network-scale. With appropriate choice of scaling, these networks have equivalent properties to the anatomical data, demonstrated by comparison of the defined metrics. The ability to synthetically replicate cerebral capillary networks opens a broad range of applications, ranging from systematic computational studies of structure-function relationships in healthy capillary networks to detailed analysis of pathological structural degeneration, or even to the development of templates for fabrication of 3D biomimetic vascular networks embedded in tissue-engineered constructs