Non-self similar blowup solutions to the higher dimensional Yang-Mills heat flows

In this paper, we consider the Yang-Mills heat flow on $\mathbb R^d \times SO(d)$ with $d \ge 11$. Under a certain symmetry preserved by the flow, the Yang-Mills equation can be reduced to: $$\partial_t u =\partial_r^2 u +\frac{d+1}{r} \partial_r u -3(d-2) u^2 - (d-2) r^2 u^3, \text{ and } (r,t) \in \mathbb R_+ \times \mathbb R_+.$$ We are interested in describing the singularity formation of this parabolic equation. We construct non-self-similar blowup solutions for $d \ge 11$ and prove that the asymptotic of the solution is of the form $$u(r,t) \sim \frac{1}{\lambda_\ell(t)} \mathcal{Q} \left( \frac{r}{\sqrt{\lambda_\ell (t)}} \right), \text{ as } t \to T ,$$ where $\mathcal{Q}$ is the ground state with boundary conditions $\mathcal{Q}(0)=-1, \mathcal{Q}'(0)=0$ and the blowup speed $\lambda_\ell$ verifies $$\lambda_\ell (t) = \left( C(u_0) +o_{t\to T}(1) \right) (T-t)^{\frac{2\ell }{\alpha}} \text{ as } t \to T,~~ \ell \in \mathbb{N}^*_+, ~~\alpha>1.$$ In particular, when $\ell = 1$, this asymptotic is stable whereas for $\ell \ge 2$ it becomes stable on a space of codimension $\ell-1$. Our approach here is not based on energy estimates but on a careful construction of time dependent eigenvectors and eigenvalues combined with maximum principle and semigroup pointwise estimates.Comment: 87 page

Sharp equivalent for the blowup profile to the gradient of a solution to the semilinear heat equation

In this paper, we consider the standard semilinear heat equation \begin{eqnarray*} \partial_t u = \Delta u + |u|^{p-1}u, \quad p >1. \end{eqnarray*} The determination of the (believed to be) generic blowup profile is well-established in the literature, with the solution blowing up only at one point. Though the blow-up of the gradient of the solution is a direct consequence of the single-point blow-up property and the mean value theorem, there is no determination of the final blowup profile for the gradient in the literature, up to our knowledge. In this paper, we refine the construction technique of Bricmont-Kupiainen 1994 and Merle-Zaag 1997, and derive the following profile for the gradient: %and derive construct a blowup solution to the above equation with the gradient's asymptotic $$\nabla u(x,T) \sim - \frac{\sqrt{2b}}{p-1} \frac{x}{|x| \sqrt{ |\ln|x||}} \left[\frac{b|x|^2}{2|\ln|x||} \right]^{-\frac{p+1}{2(p-1)}} \text{ as } x \to 0,$$ where $b =\frac{(p-1)^2}{4p}$, which is as expected the gradient of the well-known blowup profile of the solution.Comment: 23 page

The Performance of Faith-based Mutual Funds: A Matched-Pair Approach

Using a matched-pair approach, this study investigates the performance of faith-based mutual funds in the United States from 2007 to 2015. It finds that faith-based funds do not systematically underperform similar secular SRI or conventional funds. Faith-based funds tend to be small and share with similarlysized conventional funds the challenge of attaining sufficient size to fully exploit economies of scale in investing. Given the high growth potential for faith-based investing on a global level, it is possible that this handicap might disappear

Sol–gel synthesis, structural and luminescence properties of MT-doped SiO2/Zn2SiO4 nanocomposites

The sol–gel method is used for the preparation of undoped, Mn and V-doped Zn2SiO4 particles embedded in SiO2 host matrix. The phase purity and morphological features were characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM) investigations. The obtained SiO2/Zn2SiO4 nanocomposite, exhibits a strong photoluminescence (PL) band centered at around 760nm, attributed to energy transfer occurs from Zn2SiO4 particles to NBOHs interfaces defects. In addition, the PL spectrum for the SiO2/Zn2SiO4:Mn nanocomposite showed that a dominant peak at 525nm appeared, which originated from the 4T1–6A1 transitions of Mn2+ ions. In the case of SiO2/Zn2SiO4:V, the PL reveals a band centered at about 540nm attributed to the effect of the V5+ in the host matrix nanocomposite

Diversity, Prevalence, and Longitudinal Occurrence of Type II Toxin-Antitoxin Systems of Pseudomonas aeruginosa Infecting Cystic Fibrosis Lungs

Type II toxin-antitoxin (TA) systems are most commonly composed of two genes encoding a stable toxin, which harms the cell, and an unstable antitoxin that can inactivate it. TA systems were initially characterized as selfish elements, but have recently gained attention for regulating general stress responses responsible for pathogen virulence, formation of drug-tolerant persister cells and biofilms—all implicated in causing recalcitrant chronic infections. We use a bioinformatics approach to explore the distribution and evolution of type II TA loci of the opportunistic pathogen, Pseudomonas aeruginosa, across longitudinally sampled isolates from cystic fibrosis lungs. We identify their location in the genome, mutations, and gain/loss during infection to elucidate their function(s) in stabilizing selfish elements and pathogenesis. We found (1) 26 distinct TA systems, where all isolates harbor four in their core genome and a variable number of the remaining 22 on genomic islands; (2) limited mutations in core genome TA loci, suggesting they are not under negative selection; (3) no evidence for horizontal transmission of elements with TA systems between clone types within patients, despite their ability to mobilize; (4) no gain and limited loss of TA-bearing genomic islands, and of those elements partially lost, the remnant regions carry the TA systems supporting their role in genomic stabilization; (5) no significant correlation between frequency of TA systems and strain ability to establish as chronic infection, but those with a particular TA, are more successful in establishing a chronic infection

Long-term evolution of antibiotic tolerance in Pseudomonas aeruginosa lung infections

Pathogenic bacteria respond to antibiotic pressure with the evolution of resistance but survival can also depend on their ability to tolerate antibiotic treatment, known as tolerance. While a variety of resistance mechanisms and underlying genetics are well characterized in vitro and in vivo, an understanding of the evolution of tolerance, and how it interacts with resistance in situ is lacking. We assayed for tolerance and resistance in isolates of Pseudomonas aeruginosa from chronic cystic fibrosis lung infections spanning up to 40 years of evolution, with 3 clinically relevant antibiotics: meropenem, ciprofloxacin, and tobramycin. We present evidence that tolerance is under positive selection in the lung and that it can act as an evolutionary stepping stone to resistance. However, by examining evolutionary patterns across multiple patients in different clone types, a key result is that the potential for an association between the evolution of resistance and tolerance is not inevitable, and difficult to predict

A comparison of airway interventions and gastrostomy tube placement in infants with Robin sequence

The purpose of this study was to evaluate feeding impairment following non-operative or operative management of airway obstruction in a large series of infants with Robin sequence (RS) by rate of G-tube placement. A retrospective study was conducted at Boston Children's Hospital including 225 patients (47.1% female) with RS treated between 1976 and 2018. Subjects were grouped by intervention required for successful management of airway obstruction: non-operative only (n = 120), tongue–lip adhesion (TLA, n = 75), mandibular distraction osteogenesis (MDO, n = 21), or tracheostomy (n = 9). The operative group had a higher rate of G-tube placement (58.1%) than the non-operative group (28.3%, P < 0.0001). Subjects in the TLA and tracheostomy groups had higher odds of G-tube placement than subjects in the MDO group: odds ratio (OR) 5.5 (95% confidence interval (CI) 1.8–17.3, P = 0.004) and OR 27.0 (95% CI 3.2–293.4, P = 0.007), respectively. Syndromic patients and those with gastrointestinal anomalies also had higher odds of G-tube placement: OR 3.5 (95% CI 1.7–7.2, P = 0.001) and OR 5.9 (95% CI 1.6–21.0, P = 0.007), respectively. Infants with RS who require an airway operation and those with a syndromic diagnosis or gastrointestinal anomalies are more likely to require placement of a G-tube. Of the operative groups, MDO was associated with the lowest G-tube rate, compared to TLA and tracheostomy

Live to cheat another day: bacterial dormancy facilitates the social exploitation of beta-lactamases

The breakdown of antibiotics by β-lactamases may be cooperative, since resistant cells can detoxify their environment and facilitate the growth of susceptible neighbours. However, previous studies of this phenomenon have used artificial bacterial vectors or engineered bacteria to increase the secretion of β-lactamases from cells. Here, we investigated whether a broad-spectrum β-lactamase gene carried by a naturally occurring plasmid (pCT) is cooperative under a range of conditions. In ordinary batch culture on solid media, there was little or no evidence that resistant bacteria could protect susceptible cells from ampicillin, although resistant colonies could locally detoxify this growth medium. However, when susceptible cells were inoculated at high densities, late-appearing phenotypically susceptible bacteria grew in the vicinity of resistant colonies. We infer that persisters, cells that have survived antibiotics by undergoing a period of dormancy, founded these satellite colonies. The number of persister colonies was positively correlated with the density of resistant colonies and increased as antibiotic concentrations decreased. We argue that detoxification can be cooperative under a limited range of conditions: if the toxins are bacteriostatic rather than bacteridical; or if susceptible cells invade communities after resistant bacteria; or if dormancy allows susceptible cells to avoid bactericides. Resistance and tolerance were previously thought to be independent solutions for surviving antibiotics. Here, we show that these are interacting strategies: the presence of bacteria adopting one solution can have substantial effects on the fitness of their neighbours

Hyoid bone morphology in patients with isolated robin sequence – A case-control study utilizing 3D morphable models

Background: Abnormalities of the hyoid bone are associated with impairment of oropharyngeal functions including feeding, swallowing, and breathing. Few studies have characterized anatomic abnormalities of the hyoid in patients with Robin sequence (RS), e.g. a less mineralized and voluminous hyoid. The purpose of this study was to compare normal hyoid bone morphology and hyoid bone morphology in children with isolated RS. Methods: Three-dimensional (3D) reconstructions of the hyoid bone were obtained from CT-imaging of children with RS and unaffected controls. A 3D morphable model was constructed using Principal Component Analysis (PCA). Partial least squares – Discriminant Analysis (PLS-DA) and multivariate analysis of variance (MANOVA) were used to characterize and compare hyoid shape differences between patients with RS and an age-matched control group. Results: The study included 23 subjects with RS (mean age 9.8 ± 10.3 months) and 46 age-matched control samples. A less voluminous hyoid was observed for the RS group with a larger lateral divergence of the greater horns compared to controls (MANOVA, p-value&lt;0.001). The first shape variable from the PLS-DA model showed a significant correlation for the observed variance between the two groups (Spearman R = −0.56, p-value&lt;0.001). The control samples and 151 CT-scans of subjects up to age 4 years were used to create a 3D morphable model of normal hyoid shape variation (n = 197, mean age 22.1 ± 13.1 months). For the normal 3D morphable model, a high degree of allometric shape variation was observed along the first principal component. Conclusions: The 3D morphable models provide a comprehensive and quantitative description of variation in normal hyoid bone morphology, and allow detection of distinct differences between patients with isolated RS and controls.</p

Hyoid bone morphology in patients with isolated robin sequence – A case-control study utilizing 3D morphable models

Background: Abnormalities of the hyoid bone are associated with impairment of oropharyngeal functions including feeding, swallowing, and breathing. Few studies have characterized anatomic abnormalities of the hyoid in patients with Robin sequence (RS), e.g. a less mineralized and voluminous hyoid. The purpose of this study was to compare normal hyoid bone morphology and hyoid bone morphology in children with isolated RS. Methods: Three-dimensional (3D) reconstructions of the hyoid bone were obtained from CT-imaging of children with RS and unaffected controls. A 3D morphable model was constructed using Principal Component Analysis (PCA). Partial least squares – Discriminant Analysis (PLS-DA) and multivariate analysis of variance (MANOVA) were used to characterize and compare hyoid shape differences between patients with RS and an age-matched control group. Results: The study included 23 subjects with RS (mean age 9.8 ± 10.3 months) and 46 age-matched control samples. A less voluminous hyoid was observed for the RS group with a larger lateral divergence of the greater horns compared to controls (MANOVA, p-value&lt;0.001). The first shape variable from the PLS-DA model showed a significant correlation for the observed variance between the two groups (Spearman R = −0.56, p-value&lt;0.001). The control samples and 151 CT-scans of subjects up to age 4 years were used to create a 3D morphable model of normal hyoid shape variation (n = 197, mean age 22.1 ± 13.1 months). For the normal 3D morphable model, a high degree of allometric shape variation was observed along the first principal component. Conclusions: The 3D morphable models provide a comprehensive and quantitative description of variation in normal hyoid bone morphology, and allow detection of distinct differences between patients with isolated RS and controls.</p