Tilting exercises

This is an application of the theory of tilting objects to the geometric setting of perverse sheaves. We show that this theory is a natural framework for Beilinson's gluing of perverse sheaves construction. In the special case of Schubert stratification of a flag variety we get a short proof of Soergel's "Struktursatz", and describe (following a conjecture of Kapranov) Serre functor for category O. Some of our results were obtained independently by Rouquier.Comment: This final version to appear in Moscow Math Journal differs very slightly from the previous on

Some results about geometric Whittaker model

Let G be an algebraic reductive group over a field of positive characteristic. Choose a parabolic subgroup P in G and denote by U its unipotent radical. Let X be a G-variety. The purpose of this paper is to give two examples of a situation in which the functor of averaging of ℓ-adic sheaves on X with respect to a generic character commutes with Verdier duality. Namely, in the first example we take X to be an arbitrary G-variety and we prove the above property for all -equivariant sheaves on X where is the unipotent radical of an opposite parabolic subgroup; in the second example we take X=G and we prove the corresponding result for sheaves which are equivariant under the adjoint action (the latter result was conjectured by B. C. Ngo who proved it for G=GL(n)). As an application of the proof of the first statement we reprove a theorem of N. Katz and G. Laumon about local acyclicity of the kernel of the Fourier–Deligne transform

Resampling technique applied to statistics of microsegregation characterization

Characterization of chemical heterogeneities at the dendrite scale is of practical importance for understanding phase transformation either during solidification or during subsequent solid-state treatment. Spot analysis with electron probe is definitely well-suited to investigate such heterogeneities at the micron scale that is relevant for most solidified products. However, very few has been done about the statistics of experimental solute distributions gained from such analyses when they are now more and more used for validating simulation data. There are two main sources generating discrepancies between estimated and actual solute distributions in an alloy: i) data sampling with a limited number of measurements to keep analysis within a reasonable time length; and ii) uncertainty linked to the measurement process, namely the physical noise that accompanies X-ray emission. Focusing on the first of these sources, a few 2-D composition images have been generated by phase field modelling of a Mg-Al alloy. These images were then used to obtain "true" solute distributions to which to compare coarse grid analyses as generally performed with a microanalyser. Resampling, i.e. generating several distributions by grid analyses with limited number of picked-up values, was then used to get statistics of estimates of solute distribution. The discussion of the present results deals first with estimating the average solute content and then focuses on the distribution in the primary phase

Intersection cohomology of Drinfeld‚s compactifications

Let X be a smooth complete curve, G be a reductive group and a parabolic. Following Drinfeld, one defines a (relative) compactification of the moduli stack of P-bundles on X. The present paper is concerned with the explicit description of the Intersection Cohomology sheaf of . The description is given in terms of the combinatorics of the Langlands dual Lie algebra

Solidification of Al-Sn-Cu based immiscible alloys under intense shearing

The official published version of the Article can be accessed from the link below - Copyright @ 2009 The Minerals, Metals & Materials Society and ASM InternationalThe growing importance of Al-Sn based alloys as materials for engineering applications necessitates the development of uniform microstructures with improved performance. Guided by the recently thermodynamically assessed Al-Sn-Cu system, two model immiscible alloys, Al-45Sn-10Cu and Al-20Sn-10Cu, were selected to investigate the effects of intensive melt shearing provided by the novel melt conditioning by advanced shear technology (MCAST) unit on the uniform dispersion of the soft Sn phase in a hard Al matrix. Our experimental results have confirmed that intensive melt shearing is an effective way to achieve fine and uniform dispersion of the soft phase without macro-demixing, and that such dispersed microstructure can be further refined in alloys with precipitation of the primary Al phase prior to the demixing reaction. In addition, it was found that melt shearing at 200 rpm and 60 seconds will be adequate to produce fine and uniform dispersion of the Sn phase, and that higher shearing speed and prolonged shearing time can only achieve minor further refinement.This work is funded by the EPSRC and DT

Chaotic spin-dependent electron dynamics in a field-driven double dot potential

We study the nonlinear classical dynamics of an electron confined in a double dot potential and subjected to a spin-orbit coupling and a constant external magnetic field. It is shown that due to the spin orbit coupling, the energy can be transferred from the spin to the orbital motion. This naturally heats up the orbital motion which, due to the presence of the separatrix line in the phase space of the system, results in a motion of the electron between the dots. It is shown that depending on the strength of the spin orbit coupling and the energy of the system, the electronic orbital motion undergoes a transition from the regular to the chaotic regime.Comment: 15 pages, 5 figure

Absence of the spindle assembly checkpoint restores mitotic fidelity upon loss of sister chromatid cohesion

The fidelity of mitosis depends on cohesive forces that keep sister chromatids together. This is mediated by cohesin that embraces sister chromatid fibers from the time of their replication until the subsequent mitosis [1-3]. Cleavage of cohesin marks anaphase onset, where single chromatids are dragged to the poles by the mitotic spindle [4-6]. Cohesin cleavage should only occur when all chromosomes are properly bio-oriented to ensure equal genome distribution and prevent random chromosome segregation. Unscheduled loss of sister chromatid cohesion is prevented by a safeguard mechanism known as the spindle assembly checkpoint (SAC) [7, 8]. To identify specific conditions capable of restoring defects associated with cohesion loss, we screened for genes whose depletion modulates Drosophila wing development when sister chromatid cohesion is impaired. Cohesion deficiency was induced by knockdown of the acetyltransferase separation anxiety (San)/Naa50, a cohesin complex stabilizer [9-12]. Several genes whose function impacts wing development upon cohesion loss were identified. Surprisingly, knockdown of key SAC proteins, Mad2 and Mpsl, suppressed developmental defects associated with San depletion. SAC impairment upon cohesin removal, triggered by San depletion or artificial removal of the cohesin complex, prevented extensive genome shuffling, reduced segregation defects, and restored cell survival. This counterintuitive phenotypic suppression was caused by an intrinsic bias for efficient chromosome biorientation at mitotic entry, coupled with slow engagement of error-correction reactions. Thus, in contrast to SAC's role as a safeguard mechanism for mitotic fidelity, removal of this checkpoint alleviates mitotic errors when sister chromatid cohesion is compromised.Lisboa Regional Operational Programme (Lisboa 2020) through the European Regional Development Fund (FEDER); Fundacao para a Ciencia e a Tecnologia (FCT; Portugal); FCT [SFRH/BPD/87482/2012, SFRH /BD/52438/2013, PD/BD/52428/2013, PD/00117/2012, CRM: 0027030, PTDC/BEX-BID/0395/2014, UID/BIM/04773/2013 CBMR 1334, IF/00851/2012/CP0185/CT0004]; Association for International Cancer Research [AICR 10-0553]; EMBO Installation Grant [IG2778]; European Research Council Starting Grant [ERC-2014-STG-638917]; [PPBI-POCI-01-0145-FEDER-022122]; [LISBOA-01-0145-FEDER-022170

Risk-optimized proton therapy to minimize radiogenic second cancers

Proton therapy confers substantially lower predicted risk of second cancer compared with photon therapy. However, no previous studies have used an algorithmic approach to optimize beam angle or fluence-modulation for proton therapy to minimize those risks. The objectives of this study were to demonstrate the feasibility of risk-optimized proton therapy and to determine the combination of beam angles and fluence weights that minimizes the risk of second cancer in the bladder and rectum for a prostate cancer patient. We used 6 risk models to predict excess relative risk of second cancer. Treatment planning utilized a combination of a commercial treatment planning system and an in-house risk-optimization algorithm. When normal-tissue dose constraints were incorporated in treatment planning, the risk model that incorporated the effects of fractionation, initiation, inactivation, repopulation and promotion selected a combination of anterior and lateral beams, which lowered the relative risk by 21% for the bladder and 30% for the rectum compared to the lateral-opposed beam arrangement. Other results were found for other risk models

How can health systems be strengthened to control and prevent an Ebola outbreak? a narrative review

The emergence and re-emergence of infectious diseases are now more than ever considered threats to public health systems. There have been over 20 outbreaks of Ebola in the past 40 years. Only recently, the World Health Organization has declared a public health emergency of international concern (PHEIC) in West Africa, with a projected estimate of 1.2 million deaths expected in the next 6 months. Ebola virus is a highly virulent pathogen, often fatal in humans and non-human primates. Ebola is now a great priority for global health security and often becomes fatal if left untreated. This study employed a narrative review. Three major databases MEDLINE, EMBASE, and Global Health were searched using both ‘text-words’ and ‘thesaurus terms’. Evidence shows that low- and middle-income countries (LMICs) are not coping well with the current challenges of Ebola, not only because they have poor and fragile systems but also because there are poor infectious disease surveillance and response systems in place. The identification of potential cases is problematic, particularly in the aspects of contact tracing, infection control, and prevention, prior to the diagnosis of the case. This review therefore aims to examine whether LMICs’ health systems would be able to control and manage Ebola in future and identifies two key elements of health systems strengthening that are needed to ensure the robustness of the health system to respond effectively

Adjustment of the lateral and longitudinal size of scanned proton beam spots using a pre-absorber to optimize penumbrae and delivery efficiency

In scanned-beam proton therapy, the beam spot properties, such as the lateral and longitudinal size and the minimum achievable range, are influenced by beam optics, scattering media and drift spaces in the treatment unit. Currently available spot scanning systems offer fewoptions for adjusting these properties. We investigated a method for adjusting the lateral and longitudinal spot size that utilizes downstream plastic pre-absorbers located near a water phantom. The spot size adjustment was characterized usingMonte Carlo simulations of a modified commercial scanned-beam treatment head. Our results revealed that the pre-absorbers can be used to reduce the lateral full width at half maximum (FWHM) of dose spots inwater by up to 14 mm, and to increase the longitudinal extent from about 1 mm to 5 mm at residual ranges of 4 cm and less. A large factor in manipulating the lateral spot sizes is the drift space between the preabsorber and the water phantom. Increasing the drift space from 0 cm to 15 cm leads to an increase in the lateral FWHM from 2.15 cm to 2.87 cm, at a waterequivalent depth of 1 cm. These findings suggest that this spot adjustment method may improve the quality of spot-scanned proton treatments. © 2010 Institute of Physics and Engineering in Medicine