Morphogenetic action through flux-limited spreading

A central question in biology is how secreted morphogens act to induce different cellular responses within a group of cells in a concentration-dependent manner. Modeling morphogenetic output in multicellular systems has so far employed linear diffusion, which is the normal type of diffusion associated with Brownian processes. However, there is evidence that at least some morphogens, such as Hedgehog (Hh) molecules, may not freely diffuse. Moreover, the mathematical analysis of such models necessarily implies unrealistic instantaneous spreading of morphogen molecules, which are derived from the assumptions of Brownian motion in its continuous formulation. A strict mathematical model considering Fick?s diffusion law predicts morphogen exposure of the whole tissue at the same time. Such a strict model thus does not describe true biological patterns, even if similar and attractive patterns appear as results of applying such simple model. To eliminate non-biological behaviors from diffusion models we introduce flux-limited spreading (FLS), which implies a restricted velocity for morphogen propagation and a nonlinear mechanism of transport. Using FLS and focusing on intercellular Hh-Gli signaling, we model a morphogen gradient and highlight the propagation velocity of morphogen particles as a new key biological parameter. This model is then applied to the formation and action of the Sonic Hh (Shh) gradient in the vertebrate embryonic neural tube using our experimental data on Hh spreading in heterologous systems together with published data. Unlike linear diffusion models, FLS modeling predicts concentration fronts and the evolution of gradient dynamics and responses over time. In addition to spreading restrictions by extracellular binding partners, we suggest that the constraints imposed by direct bridges of information transfer such as nanotubes or cytonemes underlie FLS. Indeed, we detect and measure morphogen particle velocity in such cell extensions in different systems.     

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ∗ and embedding dimension p for phase space reconstruction. The value of τ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p−1)τ∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ∗. In this paper, we suggest a simple method for estimating τ∗ and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ∗ is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes     

Vorticity‐pressure formulations for the Brinkman‐Darcy coupled problem

We introduce a new variational formulation for the Brinkman‐Darcy equations formulated in terms of the scaled Brinkman vorticity and the global pressure. The velocities in each subdomain are fully decoupled through the momentum equations, and can be later recovered from the principal unknowns. A new finite element method is also proposed, consisting in equal‐order Nédélec and piecewise continuous elements, for vorticity and pressure, respectively. The error analysis for the scheme is carried out in the natural norms, with bounds independent of the fluid viscosity. An adequate modification of the formulation and analysis permits us to specify the presentation to the case of axisymmetric configurations. We provide a set of numerical examples illustrating the robustness, accuracy, and efficiency of the proposed discretization.     

Testing heteroskedasticity of unknown form using symbolic dynamics

This paper aims to provide a new step towards statistical inference based on symbolic dynamics. Relevant null hypotheses can be expressed in probabilities associated with a given set of symbols, and therefore new nonparametric tests can be developed. Symbolic analysis of the dynamics of the second moment of a stochastic process has lead us to present a new semi-parametric test of heteroskedasticity. The test is fairly general as minimal assumptions are required to be used. Monte Carlo experiments mainly show the great power of the test and the fact that is very competitive test as compared with other powerful tests currently available in the relevant literature.     

On the Factors behind the Photocatalytic Activity of Graphene Quantum Dots for Organic Dye Degradation

Graphene quantum dots (GQD) are promising visible-light photocatalysts for organic dye degradation. Besides having improved visible-light activity compared with commercial TiO₂, GQD are versatile photocatalysts as their chemical composition and, consequently, optical properties can be tuned synthetically, with a direct impact on photoactivity. However, there is a lack of systematic comparative studies to benchmark GQD photocatalytic performance and relate it to their intrinsic properties. This is undertaken in this work for three types of GQD, which are prepared using well-established synthetic methods representative of top-down and bottom-up approaches using different precursors. Resulting GQD are similar in size but differ in chemical composition, crystallinity, bandgap (ranging from 2.63 to 3.63 eV) and visible-light absorptivity. Photoactivity measurements under comparable experimental conditions (visible-light illumination) reveal enormous activity differences for rhodamine B (RhB) degradation, with up to tenfold higher degradation yields at the same time for certain GQD types. The enormous influence of intrinsic and tunable GQD factors, like visible-light absorptivity and surface charge, on their photoactivity for the degradation of organic dyes is demonstrated, highlighting the importance of tailoring such parameters for enhanced photocatalytic performance. A plausible mechanism for GQD-catalyzed photodegradation of RhB is also proposed.     

Infrared Fingerprint Engineering: A Molecular‐Design Approach to Long‐Wave Infrared Transparency with Polymeric Materials

Optical technologies in the long‐wave infrared (LWIR) spectrum (7–14 μm) offer important advantages for high‐resolution thermal imaging in near or complete darkness. The use of polymeric transmissive materials for IR imaging offers numerous cost and processing advantages but suffers from inferior optical properties in the LWIR spectrum. A major challenge in the design of LWIR‐transparent organic materials is that nearly all organic molecules absorb in this spectral window which lies within the so‐called IR‐fingerprint region. We report on a new molecular‐design approach to prepare high refractive index polymers with enhanced LWIR transparency. Computational methods were used to accelerate the design of novel molecules and polymers. Using this approach, we have prepared chalcogenide hybrid inorganic/organic polymers (CHIPs) with enhanced LWIR transparency and thermomechanical properties via inverse vulcanization of elemental sulfur with new organic co‐monomers.     

Efficient and Magnetically Recoverable “Click” PEGylated γ‐Fe2O3–Pd Nanoparticle Catalysts for Suzuki–Miyaura,Sonogashira, and Heck Reactions with Positive Dendritic Effects

The engineering of novel catalytic nanomaterials that are highly active for crucial carbon–carbon bond formations, easily recoverable many times, and biocompatible is highly desirable in terms of sustainable and green chemistry. To this end, catalysts comprising dendritic “click” ligands that are immobilized on a magnetic nanoparticle (MNP) core, terminated by triethylene glycol (TEG) groups, and incorporate Pd nanoparticles (PdNPs) have been prepared. These nanomaterials are characterized by transmission electron microscopy (TEM), high‐resolution TEM, inductively coupled plasma analysis, Fourier transform infrared spectroscopy, X‐ray photoelectron spectra and energy‐dispersive X‐ray spectroscopy. They are shown to be highly active, dispersible, and magnetically recoverable many times in Suzuki, Sonogashira, and Heck reactions. In addition, a series of pharmacologically relevant or natural products were successfully synthesized using these magnetic PdNPs as catalyst. For comparison, related PdNP catalysts deposited on MNPs bearing linear “click” PEGylated ligands are also prepared. Strong positive dendritic effects concerning ligand loading, catalyst loading, catalytic activity, and recyclability are observed, that is, the dendritic catalysts are much more efficient than non‐dendritic analogues.