On chaotic extensions of dynamical systems

In this paper, inspired by some results in linear dynamics, we will show that every dynamical system (X,f), where f is a continuous self-map on a separable metric space X, can be extended to a chaotic (in the sense of Devaney) dynamical system in an isometric way.     

Network Dynamics in Elemental Assimilation and Metabolism

Metabolism and physiology frequently follow non-linear rhythmic patterns which are reflected in concepts of homeostasis and circadian rhythms, yet few biomarkers are studied as dynamical systems. For instance, healthy human development depends on the assimilation and metabolism of essential elements, often accompanied by exposures to non-essential elements which may be toxic. In this study, we applied laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) to reconstruct longitudinal exposure profiles of essential and non-essential elements throughout prenatal and early post-natal development. We applied cross-recurrence quantification analysis (CRQA) to characterize dynamics involved in elemental integration, and to construct a graph-theory based analysis of elemental metabolism. Our findings show how exposure to lead, a well-characterized toxicant, perturbs the metabolism of essential elements. In particular, our findings indicate that high levels of lead exposure dysregulate global aspects of metabolic network connectivity. For example, the magnitude of each element’s degree was increased in children exposed to high lead levels. Similarly, high lead exposure yielded discrete effects on specific essential elements, particularly zinc and magnesium, which showed reduced network metrics compared to other elements. In sum, this approach presents a new, systems-based perspective on the dynamics involved in elemental metabolism during critical periods of human development.     

Gender effect on neurodegeneration and myelin markers in an animal model for multiple sclerosis

Background  

Multiple sclerosis (MS) varies considerably in its incidence and progression in females and males. In spite of clinical evidence, relatively few studies have explored molecular mechanisms possibly involved in gender-related differences. The present study describes possible cellular- and molecular-involved markers which are differentially regulated in male and female rats and result in gender-dependent EAE evolution and progression. Attention was focused on markers of myelination (MBP and PDGFαR) and neuronal distress and/or damage (GABA synthesis enzymes, GAD65 and GAD67, NGF, BDNF and related receptors), in two CNS areas, i.e. spinal cord and cerebellum, which are respectively severely and mildly affected by inflammation and demyelination. Tissues were sampled during acute, relapse/remission and chronic phases and results were analysed by two-way ANOVA.     

Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].     

A DC optimization-based clustering technique for edge detection

We introduce a method for edge detection which is based on clustering the pixels representing any given digital image into two sets (the edge pixels and the non-edge ones). The process is based on associating to each pixel an appropriate vector representing the differences in brightness w.r.t. the surrounding pixels. Clustering is driven by the norms of such vectors, thus it takes place in \(\mathbb {R}\), which allows us to use a (simple) DC (Difference of Convex) optimization algorithm to get the clusters. A novel thinning technique, based on calculation of the edge phase angles, refines the classification obtained by the clustering algorithm. The results of some numerical experiments are also provided.     

An Aluminophosphate Molecular Sieve with 36 Crystallographically Distinct Tetrahedral Sites

The structure of the new medium‐pore aluminophosphate molecular sieve PST‐6 is determined by the combined use of rotation electron diffraction tomography, synchrotron X‐ray powder diffraction, and computer modeling. PST‐6 was prepared by calcination of another new aluminophosphate material with an unknown structure synthesized using diethylamine as a structure‐directing agent, which is thought to contain bridging hydroxy groups. PST‐6 has 36 crystallographically distinct tetrahedral sites in the asymmetric unit and is thus crystallographically the most complex zeolitic structure ever solved.     

Cholesterylbutyrate solid lipid nanoparticles as a butyric acid prodrug

Cholesterylbutyrate (Chol-but) was chosen as a prodrug of butyric acid. Butyrate is not often used in vivo because its half-life is very short and therefore too large amounts of the drug would be necessary for its efficacy. In the last few years butyric acid's anti-inflammatory properties and its inhibitory activity towards histone deacetylases have been widely studied, mainly in vitro. Solid Lipid Nanoparticles (SLNs), whose lipid matrix is Chol-but, were prepared to evaluate the delivery system of Chol-but as a prodrug and to test its efficacy in vitro and in vivo. Chol-but SLNs were prepared using the microemulsion method; their average diameter is on the order of 100-150 nm and their shape is spherical. The antineoplastic effects of Chol-but SLNs were assessed in vitro on different cancer cell lines and in vivo on a rat intracerebral glioma model. The anti-inflammatory activity was evaluated on adhesion of polymorphonuclear cells to vascular endothelial cells. In the review we will present data on Chol-but SLNs in vitro and in vivo experiments, discussing the possible utilisation of nanoparticles for the delivery of prodrugs for neoplastic and chronic inflammatory diseases.