A Review of Stretching Techniques and Their Effects on Exercise

The role of flexibility in exercise performance is a widely debated topic in the exercise science field. In recent years, there has been a shift in the beliefs regarding traditional benefits and appropriate application of static stretching. Static stretching has previously been proposed to increase exercise performance and reduce the risk of injury, however recent research does not support this belief consistently and may even suggest conflicting viewpoints. Several types of stretching methods have also been promoted including proprioceptive neuromuscular facilitation (PNF) stretching, AIS, and dynamic, and ballistic stretching. The role of flexibility in exercise performance continues to be researched with hopes to discover how these techniques affect exercise both acutely and long term. It is important to understand the effects of the various stretching types and determine when each is most appropriate to maximize human motion and performance. The purpose of this thesis is to focus on reviewing each major form of stretching and to provide the reader with the most current research supporting or negating their implementation in the health and fitness fields

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.Comment: 36 pages, 18 figure

Mixed Linear Layouts of Planar Graphs

A $k$-stack (respectively, $k$-queue) layout of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing (non-nested) edges with respect to the vertex ordering. In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed $1$-stack $1$-queue layout in which every edge is assigned to a stack or to a queue that use a common vertex ordering. We disprove this conjecture by providing a planar graph that does not have such a mixed layout. In addition, we study mixed layouts of graph subdivisions, and show that every planar graph has a mixed subdivision with one division vertex per edge.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, to include some finitely additive measures in a natural way. This extended game has a value and the players have optimal strategies. This theorem extends previous results for the multiplication game on a compact group or on the positive integers with a specific payoff. We also prove that the procedure of extending the set of allowed strategies preserves classical solutions: if a semigroup game has a classical solution, this solution solves also the extended game.Comment: 17 pages. To appear in International Journal of Game Theor

Small-molecule lysophosphatidic acid receptor 5 (LPAR5) antagonists: versatile pharmacological tools to regulate inflammatory signaling in BV-2 microglia cells

Lysophosphatidic acid (LPA) species in the extracellular environment induce downstream signaling via six different G protein-coupled receptors (LPAR1-6). These signaling cascades are essential for normal brain development and function of the nervous system. However, in response to acute or chronic central nervous system (CNS) damage, LPA levels increase and aberrant signaling events can counteract brain function. Under neuro-inflammatory conditions signaling along the LPA/LPAR5 axis induces a potentially neurotoxic microglia phenotype indicating the need for new pharmacological intervention strategies. Therefore, we compared the effects of two novel small-molecule LPAR5 antagonists on LPA-induced polarization parameters of the BV-2 microglia cell line. AS2717638 is a selective piperidine-based LPAR5 antagonist (IC(50) 0.038 μM) while compound 3 is a diphenylpyrazole derivative with an IC(50) concentration of 0.7 μM in BV-2 cells. Both antagonists compromised cell viability, however, at concentrations above their IC(50) concentrations. Both inhibitors blunted LPA-induced phosphorylation of STAT1 and STAT3, p65, and c-Jun and consequently reduced the secretion of pro-inflammatory cyto-/chemokines (IL-6, TNFα, IL-1β, CXCL10, CXCL2, and CCL5) at non-toxic concentrations. Both compounds modulated the expression of intracellular (COX-2 and Arg1) and plasma membrane-located (CD40, CD86, and CD206) polarization markers yet only AS2717638 attenuated the neurotoxic potential of LPA-activated BV-2 cell-conditioned medium towards CATH.a neurons. Our findings from the present in vitro study suggest that the two LPAR5 antagonists represent valuable pharmacological tools to interfere with LPA-induced pro-inflammatory signaling cascades in microglia

Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

Probing the electronic transport on the reconstructed Au/Ge(001) surface

By using scanning tunnelling potentiometry we characterized the lateral variation of the electrochemical potential $\mu _{ec}$ on the gold-induced Ge(001)-c(8 × 2)-Au surface reconstruction while a lateral current flows through the sample. On the reconstruction and across domain boundaries we find that $\mu _{ec}$ shows a constant gradient as a function of the position between the contacts. In addition, nanoscale Au clusters on the surface do not show an electronic coupling to the gold-induced surface reconstruction. In combination with high resolution scanning electron microscopy and transmission electron microscopy, we conclude that an additional transport channel buried about 2 nm underneath the surface represents a major transport channel for electrons

Target prediction and a statistical sampling algorithm for RNA-RNA interaction

It has been proven that the accessibility of the target sites has a critical influence for miRNA and siRNA. In this paper, we present a program, rip2.0, not only the energetically most favorable targets site based on the hybrid-probability, but also a statistical sampling structure to illustrate the statistical characterization and representation of the Boltzmann ensemble of RNA-RNA interaction structures. The outputs are retrieved via backtracing an improved dynamic programming solution for the partition function based on the approach of Huang et al. (Bioinformatics). The $O(N^6)$ time and $O(N^4)$ space algorithm is implemented in C (available from \url{http://www.combinatorics.cn/cbpc/rip2.html})Comment: 7 pages, 10 figure

How to compare arc-annotated sequences: The alignment hierarchy

International audienceWe describe a new unifying framework to express comparison of arc-annotated sequences, which we call alignment of arc-annotated sequences. We first prove that this framework encompasses main existing models, which allows us to deduce complexity results for several cases from the literature. We also show that this framework gives rise to new relevant problems that have not been studied yet. We provide a thorough analysis of these novel cases by proposing two polynomial time algorithms and an NP-completeness proof. This leads to an almost exhaustive study of alignment of arc-annotated sequences