Optimal treatment planning governed by kinetic equations

In this paper we study a problem in radiotherapy treatment planning, where the evolution of the radiation field is governed by a deterministic Boltzmann transport equation. We show existence, uniqueness and regularity of solutions to an optimal dose distribution problem constrained by the Boltzmann Continuous Slowing-Down equation in an appropriate function space. The main new difficulty is the treatment of the stopping power term. Furthermore, we characterize optimal controls for problems governed by this transport equation.Comment: 15 pages, 1 figur

Peak Last Glacial weathering intensity on the North American continent recorded by the authigenic Hf isotope composition of North Atlantic deep-sea sediments

We have retrieved radiogenic hafnium (Hf) isotope compositions (ɛHf) from authigenic Fe–Mn oxyhydroxides of deep northwest Atlantic sediments deposited over the past 26 ka to investigate the oceanic evidence of changes in dissolved weathering inputs from NE America during the last deglaciation. The extraction of seawater-derived Hf isotopic compositions from Fe–Mn oxyhydroxides is not a standard procedure. Comparisons between the Al/Hf ratios and Hf isotopic compositions of the chemically extracted authigenic phase on the one hand, and those of the corresponding detrital fractions on the other, provide evidence that the composition of past seawater has been reliably obtained for most sampled depths with our leaching procedures. This is endorsed most strongly by data for a sediment core from 4250 m water depth at the deeper Blake Ridge, for which consistent replicates were produced throughout. The Hf isotopic composition of the most recent sample in this core also closely matches that of nearby present day central North Atlantic seawater. Comparison with previously published seawater Nd and Pb isotope compositions obtained on the same cores shows that both Hf and Pb were released incongruently during incipient chemical weathering, but responded differently to the deglacial retreat of the Laurentide Ice Sheet. Hafnium was released more congruently during peak glacial conditions of the Last Glacial Maximum (LGM) and changed to typical incongruent interglacial ɛHf signatures either during or shortly after the LGM. This indicates that some zircon-derived Hf was released to seawater during the LGM. Conversely, there is no clear evidence for an increase in the influence of weathering of Lu-rich mineral phases during deglaciation, possibly since relatively unradiogenic Hf contributions from feldspar weathering were superimposed. While the authigenic Pb isotope signal in the same marine sediment samples traced peak chemical weathering rates on continental North America during the transition to the Holocene a similar incongruent excursion is notably absent in the Hf isotope record. The early change towards more radiogenic ɛHf in relation to the LGM may provide direct evidence for the transition from a cold-based to a warm-based Laurentide Ice Sheet on the Atlantic sector of North America

One-dimensional infinite component vector spin glass with long-range interactions

We investigate zero and finite temperature properties of the one-dimensional spin-glass model for vector spins in the limit of an infinite number m of spin components where the interactions decay with a power, \sigma, of the distance. A diluted version of this model is also studied, but found to deviate significantly from the fully connected model. At zero temperature, defect energies are determined from the difference in ground-state energies between systems with periodic and antiperiodic boundary conditions to determine the dependence of the defect-energy exponent \theta on \sigma. A good fit to this dependence is \theta =3/4-\sigma. This implies that the upper critical value of \sigma is 3/4, corresponding to the lower critical dimension in the d-dimensional short-range version of the model. For finite temperatures the large m saddle-point equations are solved self-consistently which gives access to the correlation function, the order parameter and the spin-glass susceptibility. Special attention is paid to the different forms of finite-size scaling effects below and above the lower critical value, \sigma =5/8, which corresponds to the upper critical dimension 8 of the hypercubic short-range model.Comment: 27 pages, 27 figures, 4 table

A study of rotating globular clusters - the case of the old, metal-poor globular cluster NGC 4372

Aims: We present the first in-depth study of the kinematic properties and derive the structural parameters of NGC 4372 based on the fit of a Plummer profile and a rotating, physical model. We explore the link between internal rotation to different cluster properties and together with similar studies of more GCs, we put these in the context of globular cluster formation and evolution. Methods: We present radial velocities for 131 cluster member stars measured from high-resolution FLAMES/GIRAFFE observations. Their membership to the GC is additionally confirmed from precise metallicity estimates. Using this kinematic data set we build a velocity dispersion profile and a systemic rotation curve. Additionally, we obtain an elliptical number density profile of NGC 4372 based on optical images using a MCMC fitting algorithm. From this we derive the cluster's half-light radius and ellipticity as r_h=3.4'+/-0.04' and e=0.08+/-0.01. Finally, we give a physical interpretation of the observed morphological and kinematic properties of this GC by fitting an axisymmetric, differentially rotating, dynamical model. Results: Our results show that NGC 4372 has an unusually high ratio of rotation amplitude to velocity dispersion (1.2 vs. 4.5 km/s) for its metallicity. This, however, puts it in line with two other exceptional, very metal-poor GCs - M 15 and NGC 4590. We also find a mild flattening of NGC 4372 in the direction of its rotation. Given its old age, this suggests that the flattening is indeed caused by the systemic rotation rather than tidal interactions with the Galaxy. Additionally, we estimate the dynamical mass of the GC M_dyn=2.0+/-0.5 x 10^5 M_Sun based on the dynamical model, which constrains the mass-to-light ratio of NGC 4372 between 1.4 and 2.3 M_Sun/L_Sun, representative of an old, purely stellar population.Comment: Accepted for publication in A&A, 12 pages, 14 figures, 2 table

Constraints on ocean circulation at the Paleocene–Eocene Thermal Maximum from neodymium isotopes

Global warming during the Paleocene-Eocene Thermal Maximum (PETM) ĝ1/4 ĝ€55 million years ago (Ma) coincided with a massive release of carbon to the ocean-atmosphere system, as indicated by carbon isotopic data. Previous studies have argued for a role of changing ocean circulation, possibly as a trigger or response to climatic changes. We use neodymium (Nd) isotopic data to reconstruct short high-resolution records of deep-water circulation across the PETM. These records are derived by reductively leaching sediments from seven globally distributed sites to reconstruct past deep-ocean circulation across the PETM. The Nd data for the leachates are interpreted to be consistent with previous studies that have used fish teeth Nd isotopes and benthic foraminiferal δ13C to constrain regions of convection. There is some evidence from combining Nd isotope and δ13C records that the three major ocean basins may not have had substantial exchanges of deep waters. If the isotopic data are interpreted within this framework, then the observed pattern may be explained if the strength of overturning in each basin varied distinctly over the PETM, resulting in differences in deep-water aging gradients between basins. Results are consistent with published interpretations from proxy data and model simulations that suggest modulation of overturning circulation had an important role for initiation and recovery of the ocean-atmosphere system associated with the PETM

A Formal, Resource Consumption-Preserving Translation of Actors to Haskell

We present a formal translation of an actor-based language with cooperative scheduling to the functional language Haskell. The translation is proven correct with respect to a formal semantics of the source language and a high-level operational semantics of the target, i.e. a subset of Haskell. The main correctness theorem is expressed in terms of a simulation relation between the operational semantics of actor programs and their translation. This allows us to then prove that the resource consumption is preserved over this translation, as we establish an equivalence of the cost of the original and Haskell-translated execution traces

An update on the mosquito species composition and diversity in western and North Western Uganda

Although the west and north western parts of Uganda are historically known homes to a number of mosquito species and arboviruses associated with morbidity and mortality, early studies were highly focal and limited to specific collection methods. We aimed to update mosquito species composition in areas where a febrile illness study had shown evidence of arboviruses circulating. Adult mosquito sampling was done outside and inside houses using light traps baited with solid carbon dioxide and pyrethrum spray respectively. All collected mosquitoes were identified using appropriate morphological identification keys. A total of 22,455 mosquitoes from 89 species, 22 sub species and 11 genera were collected from Arua and Kasese districts. Overall abundance was found to be higher in Kasese (n=13446, 59.9%) than Arua district (n = 9009, 40.1%), though no significant differences were observed across villages in Arua and Kasese districts (Kruskal Wallis, X2 = 2, df = 3, p>0.05). Collection numbers were highest for genus Coquillettidia (n = 7942, 35.4%), followed by Culex (n = 7642, 34.03%), Mansonia (n = 3414, 15.2%), Anopheles (n = 1970, 8.8%) and Aedes (n = 1349, 6.01%). Other species were across 6 genera Eretmopodites (n = 59, 0.26%), Uranoteania (n = 36, 0.16%), Lutzia (n = 26, 0.12%), Mimomyia (n = 13, 0.06%), Aediomyia (n = 3, 0.01%) and Toxorhynchites (n = 1, 0.004%) appeared low in both districts. Species richness was comparatively higher in Kasese than Arua district, however across villages, it was evenly distributed with no significant differences observed, and species diversity was significantly higher in Arua than Kasese (Mann Whitney U test, p<0.05). A number of species identified here have been implied in arbovirus transmission. Moreover, we show the first description of Culex (Culex) litwakae Harbach mosquito in Uganda, a species previously described in the coastal regions of Kenya. The existence of a mosquito species previously not documented in Uganda suggests a likelihood of many invasive species whose potential to transmit viruses to humans and animals remains largely unknown

Seawater osmium isotope evidence for a middle Miocene flood basalt event in ferromanganese crust records

Three ferromanganese crusts from the northeast, northwest and central Atlantic were re-dated using osmium (Os) isotope stratigraphy and yield ages from middle Miocene to the present. The three Os isotope records do not show evidence for growth hiatuses. The reconstructed Os isotope-based growth rates for the sections older than 10 Ma are higher than those determined previously by the combined beryllium isotope (10Be/9Be) and cobalt (Co) constant-flux methods, which results in a decrease in the maximum age of each crust. This re-dating does not lead to significant changes to the interpretation of previously determined radiogenic isotope neodymium, lead (Nd, Pb) time series because the variability of these isotopes was very small in the records of the three crusts prior to 10 Ma. The Os isotope record of the central Atlantic crust shows a pronounced minimum during the middle Miocene between 15 and 12 Ma, similar to a minimum previously observed in two ferromanganese crusts from the central Pacific. For the other two Atlantic crusts, the Os isotope records and their calibration to the global seawater curve for the middle Miocene are either more uncertain or too short and thus do not allow for a reliable identification of an isotopic minimum. Similar to pronounced minima reported previously for the Cretaceous/Tertiary and Eocene/Oligocene boundaries, possible interpretations for the newly identified middle Miocene Os isotope minimum include changes in weathering intensity and/or a meteorite impact coinciding with the formation of the Nördlinger Ries Crater. It is suggested that the eruption and weathering of the Columbia River flood basalts provided a significant amount of the unradiogenic Os required to produce the middle Miocene minimum