QUIVER VARIETIES AND BEILINSON-DRINFELD GRASSMANNIANS OF TYPE A

We construct Nakajima’s quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy’s) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into Beilinson-Drinfeld Grassmannians of type A. Our construction provides a compactification of Nakajima’s quiver varieties and a decomposition of an affine Grassmannian into a disjoint union of quiver varieties. As an application we provide a geometric version of skew and symmetric (GL(m), GL(n)) duality

On quiver varieties and affine Grassmanians of type A

We construct Nakajima\u27s quiver varieties of type A in terms of affine Grassmannians of type A. This gives a compactification of quiver varieties and a decomposition of affine Grassmannians into a disjoint union of quiver varieties. Consequently, singularities of quiver varieties, nilpotent orbits and affine Grassmannians are the same in type A. The construction also provides a geometric framework for skew (GL(m),GL(n)) duality and identifies the natural basis of weight spaces in Nakajima\u27s construction with the natural basis of multiplicity spaces in tensor products which arises from affine Grassmannians. To cite this article: I. Mirkovi , M. Vybornov, C. R. Acad. Sci. Paris, Ser. I 336 (2003)

SEMIINFINITE FLAGS. I. CASE OF GLOBAL CURVE P1.

The Semiinfinite Flag Space appeared in the works of B.Feigin and E.Frenkel, and under different disguises was found by V.Drinfeld and G.Lusztig in the early 80-s. Another recent discovery (Beilinson-Drinfeld Grassmannian) turned out to conceal a new incarnation of Semiinfinite Flags. We write down these and other results scattered in folklore. We define the local semiinfinite flag space attached to a semisimple group $G$ as the quotient $G((z))/HN((z))$ (an ind-scheme), where $H$ and $N$ are a Cartan subgroup and the unipotent radical of a Borel subgroup of $G$. The global semiinfinite flag space attached to a smooth complete curve $C$ is a union of Quasimaps from $C$ to the flag variety of $G$. In the present work we use $C=P^1$ to construct the category $PS$ of certain collections of perverse sheaves on Quasimaps spaces, with factorization isomorphisms. We construct an exact convolution functor from the category of perverse sheaves on affine Grassmannian, constant along Iwahori orbits, to the category $PS$. Conjecturally, this functor should correspond to the restriction functor from modules over quantum group with divided powers to modules over the small quantum group.Comment: References update

Quantitative Analysis of DoS Attacks and Client Puzzles in IoT Systems

Denial of Service (DoS) attacks constitute a major security threat to today's Internet. This challenge is especially pertinent to the Internet of Things (IoT) as devices have less computing power, memory and security mechanisms to mitigate DoS attacks. This paper presents a model that mimics the unique characteristics of a network of IoT devices, including components of the system implementing `Crypto Puzzles' - a DoS mitigation technique. We created an imitation of a DoS attack on the system, and conducted a quantitative analysis to simulate the impact such an attack may potentially exert upon the system, assessing the trade off between security and throughput in the IoT system. We model this through stochastic model checking in PRISM and provide evidence that supports this as a valuable method to compare the efficiency of different implementations of IoT systems, exemplified by a case study

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

Characterizing animal anatomy and internal composition for electromagnetic modelling in radar entomology

The use of radar as an observational tool in entomological studies has a long history, and ongoing advances in operational radar networks and radio‐frequency technology hold promise for advances in applications such as aerial insect detection, identification and quantification. Realizing this potential requires increasingly sophisticated characterizations of radio‐scattering signatures for a broad set of insect taxa, including variability in probing radar wavelength, polarization and aspect angle. Although this task has traditionally been approached through laboratory measurement of radar cross‐sections, the effort required to create a comprehensive specimen‐based library of scattering signatures would be prohibitive. As an alternative, we investigate the performance of electromagnetic modelling for creating such a database, focusing particularly on the influence of geometric and dielectric model properties on the accuracy of synthesized scattering signatures. We use a published database which includes geometric size measurements and laboratory‐measured radar cross‐sections for 194 insect specimens. The insect anatomy and body composition were emulated using six different models, and radar cross‐sections of each model were obtained through electromagnetic modelling and compared with the original laboratory measurements. Of the models tested, the prolate ellipsoid with an internal dielectric of homogenized chitin and hemolymph mixture best replicates the measurements, providing an appropriate technique for further modelling efforts

Can megavoltage computed tomography reduce proton range uncertainties in treatment plans for patients with large metal implants?

Treatment planning calculations for proton therapy require an accurate knowledge of radiological path length, or range, to the distal edge of the target volume. In most cases, the range may be calculated with sufficient accuracy using kilovoltage (kV) computed tomography (CT) images. However, metal implants such as hip prostheses can cause severe streak artifacts that lead to large uncertainties in proton range. The purposes of this study were to quantify streak-related range errors and to determine if they could be avoided by using artifact-free megavoltage (MV) CT images in treatment planning. Proton treatment plans were prepared for a rigid, heterogeneous phantom and for a prostate cancer patient with a metal hip prosthesis using corrected and uncorrected kVCT images alone, uncorrected MVCT images and a combination of registered MVCT and kVCT images (the hybrid approach). Streak-induced range errors of 5-12 mm were present in the uncorrected kVCT-based patient plan. Correcting the streaks by manually assigning estimated true Hounsfield units improved the range accuracy. In a rigid heterogeneous phantom, the implant-related range uncertainty was estimated at approach, the kVCT images provided good delineation of soft tissues due to high-contrast resolution, and the streak-free MVCT images provided smaller range uncertainties because they did not require artifact correction. © 2008 Institute of Physics and Engineering in Medicine

Alkali activation of dif ferent type of ash as a production of combustion process

Presented study deals with the final struc ture and radiological properties of different fly-ash based geopolymers. Lig nite fly-ash (lignite Kolubara – Ser bia) and wood fly ash were obtained in combustion process together with commercial fly-ash. Synthesis of the geopolymers was con ducted by mixing fly-ash, sodium silicate solution, NaOH and water. The sam ples were strength ened 60 °C for 48 hours af ter stay ing at room temperature in covering mold for 24 hours. The X-ray dif frac tion, Fou rier trans form in fra red and SAM mea sure ments were conducted on the sam ples af ter 28 days of geopolymerization pro cess. The X-ray dif frac tion measurements of lignite fly-ash sam ples show anhydrite as the main constituent, while wood fly-ash samples consist of cal cite, albite and gypsum minerals. Besides determination of physicochemical properties, the aim of this study was radiological characterization of lignite fly-ash, wood fly-ash and the obtained geopolymer products. Ac tiv ity con cen tra tion of 40 K and radionuclides from the 238 U and 232 Th decay series, in ash sam ples and fly-ash based geopolymers, were determined by means of gamma-ray spectrometry, and the absorbed dose rate, D, and the annual effective dose rate, E, were calcu lated in accordance with the UNSCEAR 2000 report

Equivariant homology and K-theory of affine Grassmannians and Toda lattices

For an almost simple complex algebraic group G with affine Grassmannian $\text{Gr}_G=G(\mathbb{C}(({\rm t})))/G(\mathbb{C}[[{\rm t}]])$, we consider the equivariant homology $H^{G(\mathbb{C}[[{\rm t}]])}(\text{Gr}_G)$ and K-theory $K^{G(\mathbb{C}[[{\rm t}]])}(\text{Gr}_G)$. They both have a commutative ring structure with respect to convolution. We identify the spectrum of homology ring with the universal group-algebra centralizer of the Langlands dual group $\check G$, and we relate the spectrum of K-homology ring to the universal group-group centralizer of G and of $\check G$. If we add the loop-rotation equivariance, we obtain a noncommutative deformation of the (K-)homology ring, and thus a Poisson structure on its spectrum. We relate this structure to the standard one on the universal centralizer. The commutative subring of $G(\mathbb{C}[[{\rm t}]])$-equivariant homology of the point gives rise to a polarization which is related to Kostant\u27s Toda lattice integrable system. We also compute the equivariant K-ring of the affine Grassmannian Steinberg variety. The equivariant K-homology of GrG is equipped with a canonical basis formed by the classes of simple equivariant perverse coherent sheaves. Their convolution is again perverse and is related to the Feigin–Loktev fusion product of $G(\mathbb{C}[[{\rm t}]])$-modules

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