The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP

Fibrils from Designed Non-Amyloid-Related Synthetic Peptides Induce AA-Amyloidosis during Inflammation in an Animal Model

Background: Mouse AA-amyloidosis is a transmissible disease by a prion-like mechanism where amyloid fibrils act by seeding. Synthetic peptides with no amyloid relationship can assemble into amyloid-like fibrils and these may have seeding capacity for amyloid proteins. Principal Findings: Several synthetic peptides, designed for nanotechnology, have been examined for their ability to produce fibrils with Congo red affinity and concomitant green birefringence, affinity for thioflavin S and to accelerate AAamyloidosis in mice. It is shown that some amphiphilic fibril-forming peptides not only produced Congo red birefringence and showed affinity for thioflavin S, but they also shortened the lag phase for systemic AA-amyloidosis in mice when they were given intravenously at the time of inflammatory induction with silver nitride. Peptides, not forming amyloid-like fibrils, did not have such properties. Conclusions: These observations should caution researchers and those who work with synthetic peptides and thei

The Degasperis-Procesi equation with self-consistent sources

The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.Comment: 15 page

On the tau-functions of the Degasperis-Procesi equation

The DP equation is investigated from the point of view of determinant-pfaffian identities. The reciprocal link between the Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and pfaffians, and the $\tau$-functions of the DP equation are obtained from the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system.Comment: 27 pages, 4 figures, Journal of Physics A: Mathematical and Theoretical, to be publishe

Type Ia Supernova Explosion Models

Because calibrated light curves of Type Ia supernovae have become a major tool to determine the local expansion rate of the Universe and also its geometrical structure, considerable attention has been given to models of these events over the past couple of years. There are good reasons to believe that perhaps most Type Ia supernovae are the explosions of white dwarfs that have approached the Chandrasekhar mass, M_ch ~ 1.39 M_sun, and are disrupted by thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent progress in modeling Type Ia supernovae as well as several of the still open questions are addressed in this review. Although the main emphasis will be on studies of the explosion mechanism itself and on the related physical processes, including the physics of turbulent nuclear combustion in degenerate stars, we also discuss observational constraints.Comment: 38 pages, 4 figures, Annual Review of Astronomy and Astrophysics, in pres

Projective dynamics and first integrals

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure

Constrained Simulations of the Real Universe: the Local Supercluster

We present cosmological simulations which closely mimic the real Universe within 100Mpc of the Local Group. The simulations, called Constrained Simulations, reproduce the large-scale density field with major nearby structures, including the Local Group, the Coma and Virgo clusters, the Great Attractor, the Perseus-Pices, and the Local Supercluster, in approximately correct locations. The MARK III survey of peculiar velocities of the observed structures inside 80Mpc/h sphere is used to constrain the initial conditions. Fourier modes on scales larger then 5Mpc/h are dominated by the constraints, while small scale waves are random. The main aim of this paper is the structure of the Local Supercluster (LSC; 30Mpc/h around the Virgo cluster) and the Local Group environment. We find that at the current epoch most of the mass (7.5e14Msun/h) of the LSC is located in a filament roughly centered on the Virgo cluster and extending over 40Mpc/h. The simulated Local Group (LG) is located in an adjacent smaller filament, which is not a part of the main body of the LSC, and has a peculiar velocity of 250kms toward the Virgo cluster. The peculiar velocity field in the LSC region is complicated and is drastically different from the field assumed in the Virgocentric infall models. The peculiar velocity flow in the vicinity of the LG in the simulation is ``cold'': the peculiar line-of-sight velocity dispersion within 7Mpc/h of the LG is less than 60km/s, comparable to the observed velocity dispersion of nearby galaxies.Comment: 22 pages, 9 figures, submitted to ApJ, high resolution version is available at http://astro.nmsu.edu/~aklypin/HOFFMA

Midterm results of the Ross procedure in children: an appraisal of the subannular implantation with interrupted sutures technique

OBJECTIVES: The support of the pulmonary autograft root by the fibromuscular left ventricular outflow tract is emphasized to address the concern related to the dilatation of the pulmonary autograft structures in the paediatric population. METHODS: This retrospective study analyses the outcomes of 75 children who were operated between 1998 and 2012 with the subannular interrupted sutures technique at a median age of 10.2 years (range, 5.3 months–18.0 years). Median follow-up time was 5.2 years (range, 3 days–13.2 years). RESULTS: There were no deaths, but there were 3 reinterventions on the autograft for regurgitation and 2 resections of left ventricular outflow tract obstruction. There was no significant autograft stenosis, and freedom from moderate-to-severe regurgitation was 95% (95% confidence interval: 89–100) and 88% (95% confidence interval: 77–99) at 5 and 10 years, respectively. Median z-scores at the latest follow-up examination were, at the annulus, 0.31 [interquartile range (IQR) = −0.81 to 1.2]; at the sinus of Valsalva, 2.7 (IQR = 1.5–3.5); and at the sinotubular junction, 3.1 (IQR = 1.7–4.2). The correlation between z-scores and time after the operation was negative at the level of the annulus (r = −0.29, P = 0.034) but positive at the level of the sinus (r = +0.37, P = 0.005) and the sinotubular junction (r = +0.26, P = 0.068). The median rate of change in the z-score at the annulus was low, 0.065 z-score/year (IQR = −0.13 to 0.43). CONCLUSIONS: The subannular interrupted sutures implantation technique is associated with acceptable risks and, in the midterm, delivers limited annular dilatation, autograft regurgitation and delayed need for autograft reintervention

Projective dynamics and classical gravitation

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is a 2-plane containing the ray. Throwing the particle with a given initial impulsion defines a projective trajectory. It is a curve in the space of rays S(V), together with an impulsion attached to each ray. In the simplest example where the force is identically zero, the curve is a straight line and the impulsion a constant bivector. A striking feature of projective dynamics appears: the trajectories are not parameterized. Among the projective force fields corresponding to a central force, the one defining the Kepler problem is simpler than those corresponding to other homogeneities. Here the thrown ray describes a quadratic cone whose section by a hyperplane corresponds to a Keplerian conic. An original point of view on the hidden symmetries of the Kepler problem emerges, and clarifies some remarks due to Halphen and Appell. We also get the unexpected conclusion that there exists a notion of divergence-free field of projective forces if and only if dim V=4. No metric is involved in the axioms of projective dynamics.Comment: 20 pages, 4 figure

When Is a Principal Charged With an Agent’s Knowledge?

Question: Detecting species presence in vegetation and making visual assessment of abundances involve a certain amount of skill, and therefore subjectivity. We evaluated the magnitude of the error in data, and its consequences for evaluating temporal trends. Location: Swedish forest vegetation. Methods: Vegetation data were collected independently by two observers in 342 permanent 100-m2 plots in mature boreal forests. Each plot was visited by one observer from a group of 36 and one of two quality assessment observers. The cover class of 29 taxa was recorded, and presence/absence for an additional 50. Results: Overall, one third of each occurrence was missed by one of the two observers, but with large differences among species. There were more missed occurrences at low abundances. Species occurring at low abundance when present tended to be frequently overlooked. Variance component analyses indicated that cover data on 5 of 17 species had a significant observer bias. Observer-explained variance was < 10% in 15 of 17 species. Conclusion: The substantial number of missed occurrences suggests poor power in detecting changes based on presence/absence data. The magnitude of observer bias in cover estimates was relatively small, compared with random error, and therefore potentially analytically tractable. Data in this monitoring system could be improved by a more structured working model during field work.Original publication: Milberg, P., Bergstedt, J., Fridman, J., Odell, G & Westerberg, L., Systematic and random variation in vegetation monitoring data, 2008, Journal of Vegetation Science, (19), 633-644. http://dx.doi.org/10.3170/2008-8-18423. Copyright: Opulus Press, http://www.opuluspress.se/index.ph