Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh--Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.     

Insights into UV-induced apoptosis: ultrastructure, trichrome stain and spectral imaging

Nuclear substructures associated with apoptosis in HeLa cells have been examined using light-microscopic morphometry, trichrome staining, spectral imaging and transmission electron microscopy. This detailed analysis reveals several sites where alterations in the normal cellular ultrastructure occur during apoptotic progression. To correlate these ultrastructural changes with the underlying molecular processes, we have characterized and quantified apoptotic cell morphology with and without inhibition of two caspases, which are key effectors of the apoptotic program. Using this analysis, early apoptotic events included: (a) the segregation of nucleolar components, a diminished granular component, and a reduction in number but increase in size of fibrillar centers, (b) an increase in the number of cytoplasmic ribosomes and (c) a very minimal increase in the amount of peripherally condensed DNA. Apoptosis progressed with: (a) an increase in the number of perichromatin granules and perichromatin fibrils, (b) a reduction in number of interchromatin granule centers concomitant with an increase in their size, (c) partial digestion and circumferential condensation of the DNA at the nuclear membrane and (d) rounding of the cytoplasm with an increase in organellar density and shrinkage in cell size. Endstage apoptotic cells showed: (a) one (or two) very large pools of incompletely digested DNA, (b) one (or two) very large interchromatin granule centers, (c) an increased number of perichromatin granules which were distanced from DNA and often closely apposed to the nucleolus, (d) formation of unusually condensed, highly coiled perinucleolar bodies and (e) blebbing of highly dense cytoplasm.In HeLa cells treated with UV and inhibitors of caspase 1 and 3, the length of time from early apoptosis to the formation of apoptotic bodies was greatly extended. Inhibiting caspase activity: (a) prevented the pooling of DNA, (b) retarded the formation of large interchromatin granule centers, (c) increased the number of perichromatin granules, (d) produced disassembly of the nucleolus, (e) prevented the formation of highly coiled perinucleolar bodies, and (f) caused vacuolization in the cell center and a unipolar blebbing of the cytoplasm.Spectral imaging in conjunction with serial section electron microscopy confirmed the staining specificities of the condensed DNA, of the large condensed interchromatin granule centers, and of the nucleoli. The results indicate that the interface between the components of the chromatin domain and the interchromatin space is a critical site of caspase activity in apoptosis, and precedes other events such as internucleosomal DNA degradation.     

A Brief Account on Lagrange’s Algebraic Identity

In Indiscrete Thoughts [18], G.-C. Rota remarked, ??The mystery, as well as the glory of mathematics, lies not so much in the fact that abstract theories do turn out to be useful in solving problems, but, wonder of wonders, in the fact that a theory meant for one type of problem is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended. These coincidences occur so frequently, that they must belong to the essence of mathematics.?? Indeed, it happens often that abstract mathematics leads to concrete applications, and real-life problems constitute a source of inspiration for sophisticated theories. The strong synergy between pure mathematics and its applications advocates for teaching methods that intertwine physical intuition with mathematical abstraction, and recognize the universality of mathematical laws throughout the sciences.     

Conditional weak compactness in vector-valued function spaces

Let be an ideal of over a -finite measure space and let be the Köthe dual of with . Let be a real Banach space, and the topological dual of . Let be a subspace of the space of equivalence classes of strongly measurable functions and consisting of all those for which the scalar function belongs to . For a subset of for which the set is -bounded the following statement is equivalent to conditional -compactness: the set is conditionally -compact and is a conditionally weakly compact subset of for each , with . Applications to Orlicz-Bochner spaces are given.

     

A Variational Characterization of the Effective Yield Set for Ionic Polycrystals

The effective yield set of ionic polycrystals is characterized by means of variational principles in $L^\infty $ associated to supremal functionals acting on matrix-valued divergence-free fields.     

Membrane-bound dehydrogenases from Gluconobacter sp.: Interfacial electrochemistry and direct bioelectrocatalysis

Although membrane-bound dehydrogenases isolated from Gluconobacter sp. (mainly PQQ-dependent alcohol and fructose dehydrogenase) have been used for preparing diverse forms of bioelectronic interfaces for almost 2 decades, it is not an easy task to interpret an electrochemical behaviour correctly. Recent discoveries regarding redox properties of membrane-bound dehydrogenases along with extensive investigations of direct electron transfer (DET) or direct bioelectrocatalysis with these enzymes are summarized in this review. The main aim of this review is to draw general conclusions about possible electronic coupling paths of these enzymes on various interfaces via direct electron transfer or direct bioelectrocatalysis. A short overview of the metabolism and respiration chain in Gluconobacter relevant to interfacial electrochemistry is given. Biosensor devices based on DET or direct bioelectrocatalysis using membrane-bound dehydrogenases from Gluconobacter sp. are described briefly with the emphasis given on practical applications of preparing enzymatic biofuel cells. Moreover, interfacial electrochemistry of Gluconobacter oxydans related to the construction of microbial biofuel cells is also discussed.     

Physical,Thermal and Biological Properties of Yellow Dyes with Two Azodiphenylether Groups of Anthracene

Two yellow bis-azo dyes containing anthracene and two azodiphenylether groups (BPA and BTA) were prepared, and an extensive investigation of their physical, thermal and biological properties was carried out. The chemical structure was confirmed by the FTIR spectra, while from the UV–Vis spectra, the quantum efficiency of the laser fluorescence at the 476.5 nm was determined to be 0.33 (BPA) and 0.50 (BTA). The possible transitions between the energy levels of the electrons of the chemical elements were established, identifying the energies and the electronic configurations of the levels of transition. Both crystals are anisotropic, the optical phenomenon of double refraction of polarized light (birefringence) taking place. Images of maximum illumination and extinction were recorded when the crystals of the bis-azo compounds rotated by 90° each, which confirms their birefringence. A morphologic study of the thin films deposited onto glass surfaces was performed, proving the good adhesion of both dyes. By thermal analysis and calorimetry, the melting temperatures were determined (~224–225 °C for both of them), as well as their decomposition pathways and thermal effects (enthalpy variations during undergoing processes); thus, good thermal stability was exhibited. The interaction of the two compounds with collagen in the suede was studied, as well as their antioxidant activity, advocating for good chemical stability and potential to be safely used as coloring agents in the food industry.