Porous measures on : Local structure and dimensional properties

We study dimensional properties of porous measures on . As a corollary of a theorem describing the local structure of nearly uniformly porous measures we prove that the packing dimension of any Radon measure on has an upper bound depending on porosity. This upper bound tends to as porosity tends to its maximum value.

     

The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory

We derive sufficient conditions for ∝ λ (dx)6Pⁿ(x, ·) - π6 to be of order o(ψ(n)^-1), where Pⁿ (x, A) are the transition probabilities of an aperiodic Harris recurrent Markov chain, π is the invariant probability measure, λ an initial distribution and ψ belongs to a suitable class of non-decreasing sequences. The basic condition involved is the ergodicity of order ψ, which in a countable state space is equivalent to $\text{Σ ψ(n)}\text{P}{}_{\mathrm{i}}\text{{τ}{}_{\mathrm{i}}\text{?n} <∞}$ for some i, where τ_i is the hitting time of the tate i. We also show that for a general Markov chain to be ergodic of order ψ it suffices that a corresponding condition is satisfied by a small set.We apply these results to non-singular renewal measures on $\text{R}$ providing a probabilisite method to estimate the right tail of the renewal measure when the increment distribution F satisfies ∝ tF(dt) 0; > 0 and ∝ ψ(t)(1- F(t))dt< ∞.     

Kink movements and percolation in the binary additive cellular automaton

We show that under the Bernoulli initial condition two kinks in the cellular automaton (CA) 18/256 will annihilate each other with probability one. It turns out that there is an equivalent statement in terms of percolation in the simple binary additive CA. Namely, under the Bernoulli initial condition, l's do not percolate in the binary additive CA.     

GABA<Subscript>A</Subscript>receptor γ2 subunit knockdown mice have enhanced anxiety-like behavior but unaltered hypnotic response to benzodiazepines

Background  

Gamma-aminobutyric acid type A receptors (GABA_A-Rs) are the major inhibitory receptors in the mammalian brain and are modulated by a number of sedative/hypnotic drugs including benzodiazepines and anesthetics. The significance of specific GABA_A-Rs subunits with respect to behavior and in vivo drug responses is incompletely understood. The γ2 subunit is highly expressed throughout the brain. Global γ2 knockout mice are insensitive to the hypnotic effects of diazepam and die perinatally. Heterozygous γ2 global knockout mice are viable and have increased anxiety-like behaviors. To further investigate the role of the γ2 subunit in behavior and whole animal drug action, we used gene targeting to create a novel mouse line with attenuated γ2 expression, i.e., γ2 knockdown mice.     

(Non)regularity of Projections of Measures Invariant Under Geodesic Flow

We show that, unlike in the 2-dimensional case [LL], the Hausdorff dimension of a measure invariant under the geodesic flow is not necessarily preserved under the projection from the unit tangent bundle onto the base manifold if the base manifold is at least 3-dimensional. In the 2-dimensional case we reprove the preservation theorem due to Ledrappier and Lindenstrauss [LL] using the general projection formalism of Peres and Schlag [PS]. The novelty of our proof is that it illustrates the reason behind the failure of the preservation in the higher dimensional case. Finally, we show that the projected measure has fractional derivatives of order for all <(–2)/2 provided that the invariant measure has finite -energy for some >2 and the base manifold has dimension 2.MJ and ML acknowledge the support of the Academy of Finland, project #48557.Acknowledgement. We thank the referee for valuable comments clarifying the exposition.     

Locked conformations for proline pyrrolidine ring: synthesis and conformational analysis of cis- and trans-4-tert-butylprolines

The motional restrictions of the proline pyrrolidine ring allow this secondary amine amino acid to act as a turn inducer in many peptides and proteins. The pyrrolidine ring is known to exhibit two predominant pucker modes (i.e., C-4 (Cgamma) exo and endo envelope conformers whose ratio can be controlled by proper substituents in the ring). In nature, the exo puckered 4(R)-hydroxy-l-proline plays a crucial role as a building block in collagen and collagen-like structures. It has been previously concluded that the electronegativity of the 4-cis-substituent increases the endo puckering while the electronegativity of the 4-trans-substituent favors the exo puckering. Here, we have introduced a sterically demanding tert-butyl group at C-4 in trans- and cis-configurations. In the case of trans-substitution, the induced puckering effect on the pyrrolidine ring was studied with X-ray crystallography and 1H NMR spectral simulations. Both cis- and trans-4-tert-butyl groups strongly favor pseudoequatorial orientation, thereby causing opposite puckering effects for the pyrrolidine ring, cis-exo and trans-endo for l-prolines, in contrast to the effects observed in the case of electronegative C-4 substituents. The syntheses and structural analysis are presented for the conformationally constrained 4-tert-butylprolines. The prolines were synthesized from 4-hydroxy-l-proline, substitution with t-BuCuSPhLi being the key transformation. This reaction gave N-Boc-trans-4-tert-butyl-l-proline tert-butyl ester in 94% ee and 57% de. Enantioselectivity was increased to 99.2% ee by crystallization of N-Boc-trans-4-tert-butyl-l-proline in the final step of the synthesis.     

A network-assisted flow mobility architecture for optimized mobile medical multimedia transmission

A large part of mobile Health (mHealth) use-cases such as remote patient monitoring/diagnosis, teleconsultation, and guided surgical intervention requires advanced and reliable mobile communication solutions to provide efficient multimedia transmission with strict medical level Quality of Service (QoS) and Quality of Experience (QoE) provision. The increasing deployment of overlapping wireless access networks enables the possibility to offer the required network resources for ubiquitous and pervasive mHealth services. To address the challenges and support the above use-cases in today’s heterogeneous network (HetNet) environments, we propose a network-assisted flow-based mobility management architecture for optimized real-time mobile medical multimedia communication. The proposed system is empirically evaluated in a Pan-European HetNet testbed with multi-access Android-based mobile devices. We observed that the proposed scheme significantly improves the objective QoE of simultaneous real-time high-resolution electrocardiography and high-definition ultrasound transmissions while also enhances traffic load balancing capabilities of wireless architectures.     

Atomic layer deposition as pore diameter adjustment tool for nanoporous aluminum oxide injection molding masks

The wetting properties of polypropylene (PP) surfaces were modified by adjusting the dimensions of the surface nanostructure. The nanostructures were generated by injection molding with nanoporous anodized aluminum oxide (AAO) as the mold insert. Atomic layer deposition (ALD) of molybdenum nitride film was used to control the pore diameters of the AAO inserts. The original 50-nm pore diameter of AAO was adjusted by depositing films of thickness 5, 10, and 15 nm on AAO. Bis(tert-butylimido)-bis(dimethylamido)molybdenum and ammonia were used as precursors in deposition. The resulting pore diameters in the nitride-coated AAO inserts were 40, 30, and 20 nm, respectively. Injection molding of PP was conducted with the coated inserts, as well as with the non-coated insert. Besides the pore diameter, the injection mold temperature was varied with temperatures of 50, 70, and 90 degrees C tested. Water contact angles of PP casts were measured and compared with theoretical contact angles calculated from Wenzel and Cassie-Baxter theories. The highest contact angle, 140 degrees , was observed for PP molded with the AAO mold insert with 30-nm pore diameter. The Cassie-Baxter theory showed better fit than the Wenzel theory to the experimental values. With the optimal AAO mask, the nanofeatures in the molded PP pieces were 100 nm high. In explanation of this finding, it is suggested that some sticking and stretching of the nanofeatures occurs during the molding. Increase in the mold temperature increased the contact angle.     

A combined NMR, DFT, and X-ray investigation of some cinchona alkaloid O-ethers

Structures and conformational behavior of several cinchona alkaloid O-ethers in the solid state (X-ray), in solution (NMR and DFT), and in the gas phase (DFT) were investigated. In the crystal, O-phenylcinchonidine adopts the Open(3) conformation similar to cinchonidine, whereas the O-methyl ether derivatives of both cinchonidine and cinchonine are packed in the Closed(1) conformation. Dynamic equilibria in solutions of the alkaloids were revealed by combined experimental-theoretical spin simulation/iteration techniques for the first time. In the (1)H NMR spectra in CDCl3 and toluene-d8 at room temperature, Closed(1) conformation was observed for the O-silyl ethers as a separate set of signals. For O-methyl ether derivatives Closed(1) could be separated only at -30 degrees C in CDCl3 or toluene-d8 and for O-phenylcinchonidine at -70 degrees C in CDCl3/CD2Cl2. The ratio between the Closed(2) and Open(3) conformers was estimated by analyzing the vicinal coupling constant (3)J(H9,H8) at ambient and low temperatures. The observed conformational equilibria of O-(tert-butyldimethylsilyl)cinchonidine in CDCl 3 and toluene-d8 are in good agreement with the theoretically estimated equilibrium populations of the conformations according to Boltzmann statistics. The conformational equilibria of four cinchona alkaloid O-ether solutes in CDCl3 and toluene-d8 are discussed in the light of their relevance to the mechanism of 1-phenyl-1,2-propanedione (PPD) hydrogenation over cinchona alkaloid modified heterogeneous platinum catalysts. It was demonstrated that the conformation found to be abundant in the liquid phase has no direct correlation with the enantioselectivity of the PPD hydrogenation reaction.