Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation

We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all times. We prove the uniqueness of such a solution and we deduce the existence from a propagation of chaos result on a system of scalar diffusion processes, the interactions of which only depend on their ranking. We then investigate the long time behaviour of the solution. Using a probabilistic argument and under weak assumptions, we show that the flow of the Wasserstein distance between two solutions is contractive. Under more stringent conditions ensuring the regularity of the probabilistic solutions, we finally derive an explicit formula for the time derivative of the flow and we deduce the convergence of solutions to equilibrium.Comment: Stochastic partial differential equations: analysis and computations (2013) http://dx.doi.org/10.1007/s40072-013-0014-

Logics of Finite Hankel Rank

We discuss the Feferman-Vaught Theorem in the setting of abstract model theory for finite structures. We look at sum-like and product-like binary operations on finite structures and their Hankel matrices. We show the connection between Hankel matrices and the Feferman-Vaught Theorem. The largest logic known to satisfy a Feferman-Vaught Theorem for product-like operations is CFOL, first order logic with modular counting quantifiers. For sum-like operations it is CMSOL, the corresponding monadic second order logic. We discuss whether there are maximal logics satisfying Feferman-Vaught Theorems for finite structures.Comment: Appeared in YuriFest 2015, held in honor of Yuri Gurevich's 75th birthday. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-23534-9_1

The white dwarf in dwarf nova SDSS J080434.20+510349.2: Entering the instability strip?

SDSS J080434.20+510349.2 is the WZ type binary that displayed rare outburst in 2006 (Pavlenko et al., 2007). During the long-lasting tail of the late stage of the outburst binary shown the two-humped or four-humped profile of the orbital light modulation. The amplitude of orbital light curve decreased while the mean brightness decreased, more over that occurred $\sim$ 10 times faster during the fast outburst decline in respect to the late quiet state of slow outburst fading. There were no white dwarf pulsations detected neither 1 - 1.5 months prior to the outburst nor in 1.5 - 2 months after the 2006 outburst in this system. However the strong non-radial pulsations with period 12.6 minutes and mean amplitude of 0.05^m were first detected in V band with 2.6-m Shajn mirror telescope of the Crimean astrophysical observatory in ~ 8 months after the outburst. The evolution of pulsations over two years in 2006 - 2008 is considered. It is supposed that pulsations first appeared when the cooling white dwarf (after the outburst) entered the instability strip although the possibility of temporary lack of pulsations at some occasions also could not be excluded.Comment: Submitted to Proceedings of 16th European White Dwarf Workshop (EUROWD08

Room temperature "optical nanodiamond hyperpolarizer": Physics, design, and operation.

Dynamic Nuclear Polarization (DNP) is a powerful suite of techniques that deliver multifold signal enhancements in nuclear magnetic resonance (NMR) and MRI. The generated athermal spin states can also be exploited for quantum sensing and as probes for many-body physics. Typical DNP methods require the use of cryogens, large magnetic fields, and high power microwave excitation, which are expensive and unwieldy. Nanodiamond particles, rich in Nitrogen-Vacancy (NV) centers, have attracted attention as alternative DNP agents because they can potentially be optically hyperpolarized at room temperature. Here, unraveling new physics underlying an optical DNP mechanism first introduced by Ajoy et al. [Sci. Adv. 4, eaar5492 (2018)], we report the realization of a miniature "optical nanodiamond hyperpolarizer," where 13C nuclei within the diamond particles are hyperpolarized via the NV centers. The device occupies a compact footprint and operates at room temperature. Instrumental requirements are very modest: low polarizing fields, low optical and microwave irradiation powers, and convenient frequency ranges that enable miniaturization. We obtain the best reported optical 13C hyperpolarization in diamond particles exceeding 720 times of the thermal 7 T value (0.86% bulk polarization), corresponding to a ten-million-fold gain in averaging time to detect them by NMR. In addition, the hyperpolarization signal can be background-suppressed by over two-orders of magnitude, retained for multiple-minute long periods at low fields, and deployed efficiently even to 13C enriched particles. Besides applications in quantum sensing and bright-contrast MRI imaging, this work opens possibilities for low-cost room-temperature DNP platforms that relay the 13C polarization to liquids in contact with the high surface-area particles

Regional diversity in the murine cortical vascular network is revealed by synchrotron X-ray tomography and is amplified with age

Cortical bone is permeated by a system of pores, occupied by the blood supply and osteocytes. With ageing, bone mass reduction and disruption of the microstructure are associated with reduced vascular supply. Insight into the regulation of the blood supply to the bone could enhance the understanding of bone strength determinants and fracture healing. Using synchrotron radiation-based computed tomography, the distribution of vascular canals and osteocyte lacunae was assessed in murine cortical bone and the influence of age on these parameters was investigated. The tibiofibular junction from 15-week- and 10-month-old female C57BL/6J mice were imaged post-mortem. Vascular canals and three-dimensional spatial relationships between osteocyte lacunae and bone surfaces were computed for both age groups. At 15 weeks, the posterior region of the tibiofibular junction had a higher vascular canal volume density than the anterior, lateral and medial regions. Intracortical vascular networks in anterior and posterior regions were also different, with connectedness in the posterior higher than the anterior at 15 weeks. By 10 months, cortices were thinner, with cortical area fraction and vascular density reduced, but only in the posterior cortex. This provided the first evidence of age-related effects on murine bone porosity due to the location of the intracortical vasculature. Targeting the vasculature to modulate bone porosity could provide an effective way to treat degenerative bone diseases, such as osteoporosis

Tyrosine kinase inhibitors for the therapy of anaplastic thyroid cancer

Anaplastic thyroid cancer (ATC) is often incurable so new therapeutic approaches are needed. Tyrosine kinases inhibitors (such as imanitib, sunitinib or sorafenib) are under evaluation for the treatment of ATC. Other vascular disrupting agents, such as combretastatin A4 phosphate, and antiangiogenic agents, such as aplidin, PTK787/ZK222584 and human VEGF monoclonal antibodies (bevacizumab, cetuximab), have been evaluated. Small-molecule adenosine triphosphate competitive inhibitors directed intracellularly at EGFRs tyrosine kinase, such as erlotinib or gefitinib, are also studied. Furthermore, new molecules have been shown to be active against ATC, such as CLM94 and CLM3. However, more research is needed to finally identify therapies able to control and to cure this disease

Effect of antiandrogen flutamide on measures of hepatic regeneration in rats

Male rat liver undergoes a process of demasculinization during hepatic regeneration following partial hepatectomy. The possibility that antiandrogens might potentiate this demasculinization process and in so doing augment the hepatic regenerative response was investigated. Adult male Wistar rats were treated with the antiandrogen flutamide (2 mg/rat/day or 5 mg/rat/day subcutaneously) or vehicle for three days prior to and daily after a 70% partial hepatectomy. At various times after hepatectomy, the liver remnants were removed and weighed. Rates of DNA and polyamine synthesis were assessed by measuring thymidine kinase and ornithine decarboxylase activities, respectively. Hepatic estrogen receptor status and the activity of alcohol dehydrogenase, an androgen-sensitive protein, were measured. Prior to surgery, the administration of 5 mg/day flutamide reduced the hepatic cytosolic androgen receptor activity by 98% and hepatic cytosolic estrogen receptor content by 92% compared to that present in vehicle-treated controls. After hepatectomy, however, all differences in sex hormone receptor activity between the treatment groups were abolished. The rate of liver growth after partial hepatectomy in the three groups was identical. Moreover, hepatectomy-induced increases in ornithine decarboxylase activity and thymidine kinase activity were comparable. These data demonstrate that, although flutamide administration initially alters the sex hormone receptor status of the liver, these affects have no effect on the hepatic regenerative response following a partial hepatectomy. © 1989 Plenum Publishing Corporation

Pauli problem for a spin of arbitrary length: A simple method to determine its wave function

The problem of determining a pure state vector from measurements is investigated for a quantum spin of arbitrary length. Generically, only a finite number of wave functions is compatible with the intensities of the spin components in two different spatial directions, measured by a Stern-Gerlach apparatus. The remaining ambiguity can be resolved by one additional well-defined measurement. This method combines efficiency with simplicity: only a small number of quantities have to be measured and the experimental setup is elementary. Other approaches to determine state vectors from measurements, also known as the ‘‘Pauli problem,’’ are reviewed for both spin and particle systems

Common trends in the critical behavior of the Ising and directed walk models

We consider layered two-dimensional Ising and directed walk models and show that the two problems are inherently related. The information about the zero-field thermodynamical properties of the Ising model is contained into the transfer matrix of the directed walk. For several hierarchical and aperiodic distributions of the couplings, critical exponents for the two problems are obtained exactly through renormalization.Comment: 4 pages, RevTeX file + 1 figure, epsf needed. To be published in PR

Simple model of big-crunch/big-bang transition

We present classical and quantum dynamics of a test particle in the compactified Milne space. Background spacetime includes one compact space dimension undergoing contraction to a point followed by expansion. Quantization consists in finding a self-adjoint representation of the algebra of particle observables. Our model offers some insight into the nature of the cosmic singularity.Comment: 17 pages, no figures, RevTeX4, accepted for publication in Class. Quantum Gra