A cell growth model revisited

In this paper a stochastic model for the simultaneous growth and division of a cell-population cohort structured by size is formulated. This probabilistic approach gives straightforward proof of the existence of the steady-size distribution and a simple derivation of the functional-differential equation for it. The latter one is the celebrated pantograph equation (of advanced type). This firmly establishes the existence of the steady-size distribution and gives a form for it in terms of a sequence of probability distribution functions. Also it shows that the pantograph equation is a key equation for other situations where there is a distinct stochastic framework

Natural Boundaries for Solutions to a Certain Class of Functional Differential Equations

AbstractThis paper is concerned with a generalization of a functional differential equation known as the pantograph equation. The pantograph equation contains a linear functional argument. In this paper we generalize this functional argument to include nonlinear polynomials. In contrast to the entire solutions generated by the pantograph equation for the retarded case, we show that in the nonlinear case natural boundaries occur. These boundaries are linked to the Julia set of the polynomial functional argument

Development of a multimedia tutorial to educate how to assess the critical view of safety in laparoscopic cholecystectomy using expert review and crowd-sourcing

We sought to determine the feasibility of developing a multimedia educational tutorial to teach learners to assess the critical view of safety using input from expert surgeons, non-surgeons and crowd-sourcing. We intended to develop a tutorial that would teach learners how to identify the basic anatomy and physiology of the gallbladder, identify the components of the critical view of safety criteria, and understand its significance for performing a safe gallbladder removal. Using rounds of assessment with experts, laypersons and crowd-workers we developed an educational video with improving comprehension after each round of revision. We demonstrate that the development of a multimedia educational tool to educate learners of various backgrounds is feasible using an iterative review process that incorporates the input of experts and crowd sourcing. When planning the development of an educational tutorial, a step-wise approach as described herein should be considered

Assessment of ICESat-2 Ice Sheet Surface Heights, Based on Comparisons over the Interior of the Antarctic Ice Sheet

We collected kinematic Global Navigation Satellite Systems (GNSS) surface height data, on a 750km groundbased traverse of the flat interior of the Antarctic ice sheet, for comparison with Ice, Cloud, and Land Elevation Satellite2 (ICESat2) surface heights. Vertical errors in the GNSS data are estimated to be 5.6 cm, comparable to results from a previous traverse and with yeartoyear comparisons. Comparisons of the GNSS heights and 6 months of ICESat2 ATL03 photonbased heights and ATL06 segmentbased heights indicate that the accuracy and precision of ICESat2 data are comparable to that of results from the ICESat mission: ATL03 is currently accurate to better than 5 cm with better than 13 cm of surface measurement precision, while ATL06 is currently accurate to better than 3 cm with better than 9 cm of surface measurement precision

Ciliated hepatic foregut cyst: A report of 6 cases and a review of the English literature

BACKGROUND: Ciliated hepatic foregut cyst (CHFC) is a rare cystic lesion most commonly identified in segment 4 of the liver that arises from the embryonic foregut. The classic histologic pattern is comprised of 4 distinct layers (inner ciliated epithelial lining, smooth muscle, loose connective tissue, fibrous capsule). Although rare, cases of metaplastic and malignant epithelial lining have been described in CHFC. METHODS: We report 6 additional cases of CHFC, one of which had gastric metaplasia of the cyst lining, and review all reported cases of CHFC in the English literature. We describe the clinicopathologic analysis of 6 cases, with selective immunohistochemical analysis on 1 case with gastric metaplasia. RESULTS: Cases occurred in 4 women and 2 men (average age 55 years, range 42 to 67 years). Cysts ranged in size from 0.7 to 17 cm (average 7.2 cm) and were grossly tan-pink to white with blood-filled contents. The majority were located in segment 4 of the liver, however 2 were located in the porta hepatis. Tumor serologies (CA19-9 and/or CEA) were performed in 3 cases; 1 case demonstrated elevated CA19-9, and 2 cases had laboratory values within normal limits. All cases showed the classic histologic findings, however one case additionally had extensive gastric metaplasia. CONCLUSIONS: In conclusion, CHFC is a rare diagnostic entity that should be considered in the differential diagnosis for cystic hepatic lesions, particularly those located in segment 4 of the liver. Metaplasia and squamous carcinoma can occur, therefore complete surgical excision is the recommended treatment. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13000-015-0321-1) contains supplementary material, which is available to authorized users

Field-induced magnetic states in holmium tetraboride

A study of the zero field and field induced magnetic states of the frustrated rare earth tetraboride HoB4 has been carried out using single crystal neutron diffraction complemented by magnetization measurements. In zero field, HoB4 shows magnetic phase transitions at TN1 = 7.1 K to an incommensurate state with a propagation vector (delta, delta, delta'), where delta = 0.02 and delta' = 0.43 and at TN2 = 5.7 K to a noncollinear commensurate antiferromagnetic structure. Polarized neutron diffraction measurements in zero field have revealed that the incommensurate reflections, albeit much reduced in intensity, persist down to 1.5 K despite antiferromagnetic ordering at 5.7 K. At lower temperatures, application of a magnetic field along the c axis initially re-establishes the incommensurate phase as the dominant magnetic state in a narrow field range, just prior to HoB4 ordering with an up-up-down ferrimagnetic structure characterized by the (h k 1/3)-type reflections between 18 and 24 kOe. This field range is marked by the previously reported M/M-sat = 1 3 magnetization plateau, which we also see in our magnetization measurements. The region between 21 and 33 kOe is characterized by the increase in the intensity of the antiferromagnetic reflections, such as (100), the maximum of which coincides with the appearance of the narrow magnetization plateau with M/M-sat approximate to 3/5. Further increase of the magnetic field results in the stabilization of a polarized state above 33 kOe, while the incommensurate reflections are clearly present in all fields up to 59 kOe. We propose the H-T phase diagram of HoB4 for the H parallel to c containing both stationary and transitionary magnetic phases which overlap and show significant history dependence

Sequential and Spontaneous Star Formation Around the Mid-Infrared Halo HII Region KR 140

We use 2MASS and MSX infrared observations, along with new molecular line (CO) observations, to examine the distribution of young stellar objects (YSOs) in the molecular cloud surrounding the halo HII region KR 140 in order to determine if the ongoing star-formation activity in this region is dominated by sequential star formation within the photodissociation region (PDR) surrounding the HII region. We find that KR 140 has an extensive population of YSOs that have spontaneously formed due to processes not related to the expansion of the HII region. Much of the YSO population in the molecular cloud is concentrated along a dense filamentary molecular structure, traced by C18O, that has not been erased by the formation of the exciting O star. Some of the previously observed submillimetre clumps surrounding the HII region are shown to be sites of recent intermediate and low-mass star formation while other massive starless clumps clearly associated with the PDR may be the next sites of sequential star formation.Comment: Accepted for publication in MNRAS, 8 pages, 10 figure

Euler-Lagrange equations for composition functionals in calculus of variations on time scales

In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function $H$ with the delta integral of a vector valued field $f$, i.e., of the form $H(\int_{a}^{b}f(t,x^{\sigma}(t),x^{\Delta}(t))\Delta t)$. Euler-Lagrange equations, natural boundary conditions for such problems as well as a necessary optimality condition for isoperimetric problems, on a general time scale, are given. A number of corollaries are obtained, and several examples illustrating the new results are discussed in detail.Comment: Submitted 10-May-2009 to Discrete and Continuous Dynamical Systems (DCDS-B); revised 10-March-2010; accepted 04-July-201

Ice-Shelf Flexure and Tidal Forcing of Bindschadler Ice Stream, West Antarctica

Viscoelastic models of ice-shelf flexure and ice-stream velocity perturbations are combined into a single efficient flowline model to study tidal forcing of grounded ice. The magnitude and timing of icestream response to tidally driven changes in hydrostatic pressure and/or basal drag are found to depend significantly on bed rheology, with only a perfectly plastic bed allowing instantaneous velocity response at the grounding line. The model can reasonably reproduce GPS observations near the grounding zone of Bindschadler Ice Stream (formerly Ice Stream D) on semidiurnal time scales; however, other forcings such as tidally driven ice-shelf slope transverse to the flowline and flexurally driven till deformation must also be considered if diurnal motion is to be matche