The a priori Tan Theta Theorem for spectral subspaces

Let A be a self-adjoint operator on a separable Hilbert space H. Assume that the spectrum of A consists of two disjoint components s_0 and s_1 such that the set s_0 lies in a finite gap of the set s_1. Let V be a bounded self-adjoint operator on H off-diagonal with respect to the partition spec(A)=s_0 \cup s_1. It is known that if ||V||<\sqrt{2}d, where d=\dist(s_0,s_1), then the perturbation V does not close the gaps between s_0 and s_1 and the spectrum of the perturbed operator L=A+V consists of two isolated components s'_0 and s'_1 grown from s_0 and s_1, respectively. Furthermore, it is known that if V satisfies the stronger bound ||V||< d then the following sharp norm estimate holds: ||E_L(s'_0)-E_A(s_0)|| \leq sin(arctan(||V||/d)), where E_A(s_0) and E_L(s'_0) are the spectral projections of A and L associated with the spectral sets s_0 and s'_0, respectively. In the present work we prove that this estimate remains valid and sharp also for d \leq ||V||< \sqrt{2}d, which completely settles the issue.Comment: v3: some typos fixed; Examples adde

The Effects of a Combined Supplementation of Creatine and Sodium Bicarbonate on Repeated Sprint Performance

Abstract The Effects of a Combined Supplementation of Creatine and Sodium Bicarbonate on Repeated Sprint Performance James Jeremy Barber There is well-established research that suggests both creatine and sodium bicarbonate are effective ergogenic aids. However, only one published study has examined the combined effects of creatine and sodium bicarbonate. The primary purpose of this study was to determine if a combined supplementation of creatine monohydrate and sodium bicarbonate would further enhance the well-documented effects of creatine supplementation alone on repeated sprint performance. Thirteen healthy and fit males (Mean age = 21.15 ± 0.65 years and mean VO2 max = 66.72 ± 5.78) participated in this experimental study using a double-blinded crossover study design in which each subject was used as his own control. All subjects completed 3 conditions, followed by a 3-week washout period between each condition: 1) Placebo (Pl; 5 g maltodextrin + 0.5 g/kg maltodextrin), 2) Creatine (Cr; 5 g + 0.5 g/kg maltodextrin), and 3) Creatine plus sodium bicarbonate (Cr+Sb; 5g + 0.5 g/kg sodium bicarbonate). Each condition was a 2-day supplementation. In the morning after each supplementation, peak power, RPP, mean power, RMP, fatigue index, and perceptions of fatigue and GI distress were assessed during six 10-second repeated Wingate tests. Blood bicarbonate, pH, and lactate were measured 5 minutes before testing and immediately after the last Wingate sprint. The main findings were; 1) Cr+Sb produced 7% greater relative peak power and 4.6% greater peak power values than placebo, and 2) Cr+Sb demonstrated the greatest attenuation of decline in relative peak power over six repeated sprints. However, in contrast to our hypotheses, no benefits from either supplementation were observed for relative mean power, fatigue index, and perception of fatigue. Considering that this current study found benefits from combining creatine and sodium bicarbonate, it suggests that combining the supplements may improve repeated sprint performance. Future research on a greater sample size, a specific athletic population, various exercise modes, and comparing results with a sodium bicarbonate alone supplementation would be beneficial in determining if this combined supplementation is worthwhile

Kansas Speaks Fall 2022 Statewide Public Opinion Survey

The 2022 Kansas Speaks fall survey was conducted from September 19 to October 2, 2022. A panel of 520 adult residents of Kansas age 18 and older were surveyed online to assess their attitudes and opinions regarding various issues of interest to Kansas citizens

On the degree of scale invariance of inflationary perturbations

Many, if not most, inflationary models predict the power-law index of the spectrum of density perturbations is close to one, though not precisely equal to one, |n-1| \sim O(0.1), implying that the spectrum of density perturbations is nearly, but not exactly, scale invariant. Some models allow n to be significantly less than one (n \sim 0.7); a spectral index significantly greater than one is more difficult to achieve. We show that n \approx 1 is a consequence of the slow-roll conditions for inflation and ``naturalness,'' and thus is a generic prediction of inflation. We discuss what is required to deviate significantly from scale invariance, and then show, by explicit construction, the existence of smooth potentials that satisfy all the conditions for successful inflation and give $n$ as large as 2.Comment: 7 pages, 2 figures, submitted to Phys. Rev.

Reconciling inflation with openness

It is already understood that the increasing observational evidence for an open Universe can be reconciled with inflation if our horizon is contained inside one single huge bubble nucleated during the inflationary phase transition. In this frame of ideas, we show here that the probability of living in a bubble with the right $\Omega_0$ (now the observations require $\Omega_0 \approx .2$) can be comparable with unity, rather than infinitesimally small. For this purpose we modify both quantitatively and qualitatively an intuitive toy model based upon fourth order gravity. As this scheme can be implemented in canonical General Relativity as well (although then the inflation driving potential must be designed entirely ad hoc), inferring from the observations that $\Omega_0 < 1$ not only does not conflict with the inflationary paradigm, but rather supports therein the occurrence of a primordial phase transition.Comment: 4 pages, one postscript figure, to be published on Physical Review D PACS: 98.80. C

IN THIS ISSUE: What Are Characteristics of Significant Research?

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67303/2/10.1177_108056999505800214.pd

Protein complex compositions predicted by structural similarity

Proteins function through interactions with other molecules. Thus, the network of physical interactions among proteins is of great interest to both experimental and computational biologists. Here we present structure-based predictions of 3387 binary and 1234 higher order protein complexes in Saccharomyces cerevisiae involving 924 and 195 proteins, respectively. To generate candidate complexes, comparative models of individual proteins were built and combined together using complexes of known structure as templates. These candidate complexes were then assessed using a statistical potential, derived from binary domain interfaces in PIBASE (). The statistical potential discriminated a benchmark set of 100 interface structures from a set of sequence-randomized negative examples with a false positive rate of 3% and a true positive rate of 97%. Moreover, the predicted complexes were also filtered using functional annotation and sub-cellular localization data. The ability of the method to select the correct binding mode among alternates is demonstrated for three camelid VHH domain—porcine α–amylase interactions. We also highlight the prediction of co-complexed domain superfamilies that are not present in template complexes. Through integration with MODBASE, the application of the method to proteomes that are less well characterized than that of S.cerevisiae will contribute to expansion of the structural and functional coverage of protein interaction space. The predicted complexes are deposited in MODBASE ()

"Learning to live with what you can't rise above": control beliefs, symptom control, and adjustment to tinnitus.

The relations between 3 types of perceived control, symptom severity, and 2 adaptational outcomes, depressive symptoms and psychological well-being, were examined in a sample of 319 people with tinnitus. Consistent with previous studies of control and adjustment to chronic health conditions, general health and symptom control were associated with better psychological adjustment, and retrospective control was associated with worse psychological adjustment. Only symptom control emerged as a significant moderator in the symptom severity-adjustment relationship, such that stronger beliefs in one's ability to control symptoms were most strongly associated with better adjustment among those with more severe tinnitus symptoms. These findings were consistent with coping perspectives and cognitive adaptation theory and suggest that symptom-related perceptions of control may be an effective coping resource to nurture in chronic health contexts with severe symptoms

The Need for Tobacco Education: Studies of Collegiate Dental Hygiene Patients and Faculty.

The need for inclusion of comprehensive tobacco control education/training for health care providers continues to be stressed in publications addressing cessation services. The dental appointment presents an excellent opportunity to provide tobacco interventions to basically healthy people on regular intervals. The purpose of this study was twofold: 1) to assess the need (stage of change and concomitant need for tobacco cessation intervention) of dental hygiene patients at a Midwest dental hygiene clinic, and 2) to assess and compare the level of tobacco intervention education currently being offered by dental hygiene educators in a Midwestern state. Patients (n=426) of a collegiate dental health clinic completed a survey that assessed the level and type of tobacco cessation intervention patients might require. A statewide sample of dental hygiene faculty (n=97) were surveyed to determine the attitudes, perceived barriers, and current practices in tobacco education offered in their programs. Of patients who currently smoked (34.5 percent), 24.7 percent indicated being in the Action stage of change; 14.2 percent were in Preparation; 22.2 percent were in Contemplation; and 29 percent were in Precontemplation. Although faculty indicated tobacco education was very important (5.03 on 1–6 scale), they felt only moderately confident delivering tobacco education (3.18 on a 1–5 scale). Only 16 percent to 35 percent of faculty reported that their curriculum included brief motivational interviewing, pharmacotherapies, or setting‐up a private practice tobacco control program. The results strongly suggest the need for a comprehensive, competency‐based tobacco curriculum to enhance and expand existing dental hygiene programs

Radioactive-materials shipping-cask anticontamination enclosure

An anticontamination device for use in storing shipping casks for radioactive materials comprises (1) a seal plate assembly; (2) a double-layer plastic bag; and (3) a water management system or means for water management