Developing a numerical inverse-theory-based extraction of orientation-dependent relaxation rates from partially- relaxed spectra

Second-rank tensor interactions, such as quadrupolar interactions between the spin- 1 deuterium nuclei and the electric field gradients created by chemical bonds, are affected by rapid random molecular motions that modulate the orientation of the molecule with respect to the external magnetic field. In biological and model membrane systems, where a distribution of dynamically averaged anisotropies (quadrupolar splittings, chemical shift anisotropies, etc.) is present and where, in addition, various parts of the sample may undergo a partial magnetic alignment, the numerical analysis of the resulting Nuclear Magnetic Resonance (NMR) spectra is a mathematically ill-posed problem. However, numerical methods (de-Pakeing, Tikhonov regularization) exist that allow for a simultaneous determination of both the anisotropy and orientational distributions. An additional complication arises when relaxation is taken into account. This work presents a method of obtaining the orientation dependence of the relaxation rates that can be used for the analysis of the molecular motions on a broad range of time scales. An arbitrary set of exponential decay rates is described by a three-term truncated Legendre polynomial expansion in the orientation dependence, as appropriate for a second-rank tensor interaction, and a linear approximation to the individual decay rates is made. Thus a severe numerical instability caused by the presence of noise in the experimental data is avoided. At the same time, enough flexibility in the inversion algorithm is retained to achieve a meaningful mapping from raw experimental data to a set of intermediate, model-free

Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

Subjective Ambivalence and the Expression of Anti-Gay Bias

Univalent attitudes toward gay people have been widely studied, but no research to date has examined ambivalent (i.e., torn, conflicted) attitudes toward gay people. However, the Justification-Suppression Model (JSM; Crandall & Eshleman, 2003) proposes that ambivalence leads to biased expressions through intrapsychic processes which facilitate biased expression, particularly in contexts presenting strong justifications for expressing prejudice and weak pressures to suppress prejudice. I test these implications in the context of bias toward gay people. In Study 1, the measurement of ambivalence is examined in terms of both subjective ambivalence (i.e., the reported experience of “torn” attitudes) and calculated ambivalence (i.e., mathematical conflict between positive and negative attitude components). I find that higher subjective ambivalence is only associated with more negative attitudes toward gay people (and not positive attitudes toward gay people), and that higher subjective ambivalence predicts less gay rights support even after taking negative and positive attitudes toward gay people into account. Further, higher subjective ambivalence is associated with ideological opposition to gay people and more negative intergroup emotions (e.g., intergroup disgust). These findings suggest it is valuable to examine the unique component of subjective ambivalence separate from univalent negativity. Because calculated ambivalence measures are mathematically dependent upon a univalent negative measure, they cannot be examined separately from negativity. Therefore, subjective ambivalence is the focus of Study 2. The main goals of Study 2 were to determine why and when subjective ambivalence is related to bias. I examined the extent to which the negative relation between subjective ambivalence and opposition to anti-gay bullying can be accounted for by lower intergroup empathy and lower collective guilt, which may facilitate the expression of bias in keeping with the JSM. The relation between subjective ambivalence and anti-gay bullying opposition was examined within four social contexts based on a 2 (high vs. low offensiveness) x 2 (normatively unjustified vs. normatively justified) manipulation. I expected that higher subjective ambivalence would be most strongly related to lower intergroup empathy and collective guilt when there are the strongest justifications for bias expression, and that lower intergroup empathy and collective guilt would lead to less opposition to anti-gay bullying. Higher subjective ambivalence predicted less anti-gay bullying opposition. After accounting for positivity and negativity, the direct effect of subjective ambivalence was no longer significant, yet subjective ambivalence uniquely predicted intergroup empathy, which in turn predicted less anti-gay bullying opposition. These findings provide evidence that subjective ambivalence is largely negative in nature, but also presents evidence for a unique component of subjective ambivalence (separate from univalent attitudes) associated with low intergroup empathy and negativity. In contrast to previous research, I found very little evidence for the context-dependency of subjective ambivalence. Further research on subjective ambivalence, including subjective ambivalence toward other social groups, may expand our understanding of the factors leading to biased expressions.

Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

Socio-demographic factors, smoking, symptoms, morbidities and pulmonary function and quality of life in individuals with a heavy smoking history

Objective: To determine which socio-demographic, exposure, morbidity and symptom variables are associated with health-related quality of life among former and current heavy smokers. Methods: Cross sectional data from 2537 participants were studied. All participants were at ≥2% risk of developing lung cancer within 6 years. Linear and logistic regression models utilizing a multivariable fractional polynomial selection process identified variables associated with health-related quality of life, measured by the EQ-5D. Results: Upstream and downstream associations between smoking cessation and higher health-related quality of life were evident. Significant upstream associations, such as education level and current working status and were explained by the addition of morbidities and symptoms to regression models. Having arthritis, decreased forced expiratory volume in one second, fatigue, poor appetite or dyspnea were most highly and commonly associated with decreased HRQoL. Discussion: Upstream factors such as educational attainment, employment status and smoking cessation should be targeted to prevent decreased health-related quality of life. Practitioners should focus treatment on downstream factors, especially symptoms, to improve health-related quality of life.

Reduced power output in skeletal muscles devoid of skMLCK: RLC phosphorylation contributes to peak performance

Regulatory light chain (RLC) phosphorylation in fast twitch muscle is catalyzed by skeletal myosin light chain kinase (skMLCK), a reaction known to increase muscle force, work, and power. The purpose of this study was to explore the contribution of RLC phosphorylation on the power of mouse fast muscle during high frequency (100 Hz) concentric contractions. To determine peak power shortening ramps (1.05 to 0.90 Lo) were applied to Wildtype (WT) and skMLCK knockout (skMLCK-/-) EDL muscles at a range of shortening velocities between 0.05-0.65 of maximal shortening velocity (Vmax), before and after a conditioning stimulus (CS). As a result, mean power was increased to 1.28 ± 0.05 and 1.11 ± .05 of pre-CS values, when collapsed for shortening velocity in WT and skMLCK-/-, respectively (n = 10). In addition, fitting each data set to a second order polynomial revealed that WT mice had significantly higher peak power output (27.67 ± 1.12 W/ kg-1) than skMLCK-/- (25.97 ± 1.02 W/ kg-1), (p < .05). No significant differences in optimal velocity for peak power were found between conditions and genotypes (p > .05). Analysis with Urea Glycerol PAGE determined that RLC phosphate content had been elevated in WT muscles from 8 to 63 % while minimal changes were observed in skMLCK-/- muscles: 3 and 8 %, respectively. Therefore, the lack of stimulation induced increase in RLC phosphate content resulted in a ~40 % smaller enhancement of mean power in skMLCK-/-. The increase in power output in WT mice suggests that RLC phosphorylation is a major potentiating component required for achieving peak muscle performance during brief high frequency concentric contractions.