Closing the gap in the solutions of the strong explosion problem: An expansion of the family of second-type self-similar solutions

Shock waves driven by the release of energy at the center of a cold ideal gas sphere of initial density rho\propto r^{-omega} approach a self-similar (SLS) behavior, with velocity \dot{R}\propto R^delta, as R->\infty. For omega>3 the solutions are of the second-type, i.e., delta is determined by the requirement that the flow should include a sonic point. No solution satisfying this requirement exists, however, in the 3\leq omega\leq omega_{g}(gamma) ``gap'' (\omega_{g}=3.26 for adiabatic index gamma=5/3). We argue that second-type solutions should not be required in general to include a sonic point. Rather, it is sufficient to require the existence of a characteristic line r_c(t), such that the energy in the region r_c(t)\infty, and an asymptotic solution given by the SLS solution at r_c(t)<r<R and deviating from it at r<r_c may be constructed. The two requirements coincide for omega>omega_g and the latter identifies delta=0 solutions as the asymptotic solutions for 3\leq omega\leq omega_{g} (as suggested by Gruzinov03). In these solutions, r_c is a C_0 characteristic. It is difficult to check, using numerical solutions of the hydrodynamic equations, whether the flow indeed approaches a delta=0 SLS behavior as R->\infty, due to the slow convergence to SLS for omega~3. We show that in this case the flow may be described by a modified SLS solution, d\ln\dot{R}/d\ln R=delta with slowly varying delta(R), eta\equiv d delta/d\ln R<<1, and spatial profiles given by a sum of the SLS solution corresponding to the instantaneous value of delta and a SLS correction linear in eta. The modified SLS solutions provide an excellent approximation to numerical solutions obtained for omega~3 at large R, with delta->0 (and eta\neq0) for 3\leq omega\leq omega_{g}. (abridged)Comment: 10 pages, 11 figures, somewhat revised, version accepted to Ap

Outcomes of Congenital Nasolacrimal Duct Obstruction Surgery Converted into Balloon Dilation and Silicone Intubation due to Probing Difficulty

Background. To report the outcomes of balloon catheter dilatation and silicone intubation as a sequential secondary surgery under the same anesthesia, a stepwise approach for congenital nasolacrimal duct obstruction (NLDO) when probing and irrigation as primary procedure fails. Methods. A retrospective study included children with NLDO who underwent probing and irrigation only, and those who underwent in the same surgery under anesthesia, adjunct balloon catheter dilation and silicone intubation due to difficulty of the probe passage or fluid regurgitation from the punctum. The primary outcome was surgical success defined as resolution of preoperative symptoms and signs at 1 month. Results. A total of 105 NLDO cases were included. Eighty-four cases underwent probing and irrigation only, whereas 21 cases required balloon dilation and silicone intubation consecutively after the first procedure. Patient age at surgery was higher for those requiring balloon dilatation and intubation (30.3 +/- 8.0 months) when compared to those with probing and irrigation only (22.4 +/- 10.3 months, p < 0.001). The onset of symptoms, preoperative clinical findings regarding tearing and discharge and gender distribution of patients were comparable between the two groups. During the follow-up, the overall success rate for probing and irrigation only was 76.2% (64 out of 84 cases) and for balloon dilatation and silicone tube intubation was 90.5% (19 out of 21 cases). Conclusions. The surgical team may prepare to proceed with secondary surgery under the same anesthesia after the initial attempt of probing and irrigation. This stepwise two-stage approach in patients with congenital NLDO failing primary surgery resulted in a high success rate with minimal interventions, avoiding repeated general anesthesia.Peer reviewe

Predicting mental imagery based BCI performance from personality, cognitive profile and neurophysiological patterns

Mental-Imagery based Brain-Computer Interfaces (MI-BCIs) allow their users to send commands to a computer using their brain-activity alone (typically measured by ElectroEncephaloGraphy— EEG), which is processed while they perform specific mental tasks. While very promising, MI-BCIs remain barely used outside laboratories because of the difficulty encountered by users to control them. Indeed, although some users obtain good control performances after training, a substantial proportion remains unable to reliably control an MI-BCI. This huge variability in user-performance led the community to look for predictors of MI-BCI control ability. However, these predictors were only explored for motor-imagery based BCIs, and mostly for a single training session per subject. In this study, 18 participants were instructed to learn to control an EEG-based MI-BCI by performing 3 MI-tasks, 2 of which were non-motor tasks, across 6 training sessions, on 6 different days. Relationships between the participants’ BCI control performances and their personality, cognitive profile and neurophysiological markers were explored. While no relevant relationships with neurophysiological markers were found, strong correlations between MI-BCI performances and mental-rotation scores (reflecting spatial abilities) were revealed. Also, a predictive model of MI-BCI performance based on psychometric questionnaire scores was proposed. A leave-one-subject-out cross validation process revealed the stability and reliability of this model: it enabled to predict participants’ performance with a mean error of less than 3 points. This study determined how users’ profiles impact their MI-BCI control ability and thus clears the way for designing novel MI-BCI training protocols, adapted to the profile of each user

Random Matrix Theories in Quantum Physics: Common Concepts

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.Comment: 178 pages, Revtex, 45 figures, submitted to Physics Report

The early mathematical education of Ada Lovelace

Ada, Countess of Lovelace, is remembered for a paper published in 1843, which translated and considerably extended an article about the unbuilt Analytical Engine, a general-purpose computer designed by the mathematician and inventor Charles Babbage. Her substantial appendices, nearly twice the length of the original work, contain an account of the principles of the machine, along with a table often described as ‘the first computer program’. In this paper we look at Lovelace's education before 1840, which encompassed older traditions of practical geometry; newer textbooks influenced by continental approaches; wide reading; and a fascination with machinery. We also challenge judgements by Dorothy Stein and by Doron Swade of Lovelace's mathematical knowledge and skills before 1840, which have impacted later scholarly and popular discourse

Effect of Irradiation on Cell Transcriptome and Proteome of Rat Submandibular Salivary Glands

<div><p>Salivary glands (SGs) are irreversibly damaged by irradiation (IR) treatment in head and neck cancer patients. Here, we used an animal irradiation model to investigate and define the molecular mechanisms affecting SGs following IR, focusing on saliva proteome and global transcription profile of submandibular salivary gland (SSG) tissue.</p> <p>We show that saliva secretion was gradually reduced to 50% of its initial level 12 weeks post-IR. Saliva protein composition was further examined by proteomic analysis following mass spectrometry (MS) analysis that revealed proteins with reduced expression originating from SSGs and proteins with increased expression derived from the serum, both indicating salivary tissue damage. To examine alterations in mRNA expression levels microarray analysis was performed. We found significant alterations in 95 genes, including cell-cycle arrest genes, SG functional genes and a DNA repair gene.</p> <p>Tissue damage was seen by confocal immunofluorescence of α-amylase and c-Kit that showed an increase and decrease, respectively, in protein expression. This was coherent with real-time PCR results.</p> <p>This data indicates that IR damages the SSG cells' ability to produce and secrete saliva and proteins, and maintain the physiological barrier between serum and saliva. The damage does not heal due to cell-cycle arrest, which prevents tissue regeneration. Taken together, our results reveal a new insight into IR pathobiology.</p> </div

Fold change in gene expression following irradiation.

<p>Relative quantification (RQ) values of Muc19, Cdh22, Psp, Prb1, CysS, Mgmt, cyclin d1, p21, p57 and Ywhaq gene expression during the 12 weeks post-irradiation. Validation of microarray values for salivary gland functional gene expression following irradiation by TaqMan real-time PCR. The data are expressed as means of n = 3. *<i>P</i><0.05, **<i>P</i><0.005, ***<i>P</i><0.001 compared to control levels, unless otherwise stated.</p