Tannakian categories, linear differential algebraic groups, and parameterized linear differential equations

We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the category of representations of a linear algebraic group.Comment: 26 pages; corrected misprints; simplified Definition 2; more references adde

Maximum likelihood estimation of cloud height from multi-angle satellite imagery

We develop a new estimation technique for recovering depth-of-field from multiple stereo images. Depth-of-field is estimated by determining the shift in image location resulting from different camera viewpoints. When this shift is not divisible by pixel width, the multiple stereo images can be combined to form a super-resolution image. By modeling this super-resolution image as a realization of a random field, one can view the recovery of depth as a likelihood estimation problem. We apply these modeling techniques to the recovery of cloud height from multiple viewing angles provided by the MISR instrument on the Terra Satellite. Our efforts are focused on a two layer cloud ensemble where both layers are relatively planar, the bottom layer is optically thick and textured, and the top layer is optically thin. Our results demonstrate that with relative ease, we get comparable estimates to the M2 stereo matcher which is the same algorithm used in the current MISR standard product (details can be found in [IEEE Transactions on Geoscience and Remote Sensing 40 (2002) 1547--1559]). Moreover, our techniques provide the possibility of modeling all of the MISR data in a unified way for cloud height estimation. Research is underway to extend this framework for fast, quality global estimates of cloud height.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS243 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Surface Operators in N=2 Abelian Gauge Theory

We generalise the analysis in [arXiv:0904.1744] to superspace, and explicitly prove that for any embedding of surface operators in a general, twisted N=2 pure abelian theory on an arbitrary four-manifold, the parameters transform naturally under the SL(2,Z) duality of the theory. However, for nontrivially-embedded surface operators, exact S-duality holds if and only if the "quantum" parameter effectively vanishes, while the overall SL(2,Z) duality holds up to a c-number at most, regardless. Nevertheless, this observation sets the stage for a physical proof of a remarkable mathematical result by Kronheimer and Mrowka--that expresses a "ramified" analog of the Donaldson invariants solely in terms of the ordinary Donaldson invariants--which, will appear, among other things, in forthcoming work. As a prelude to that, the effective interaction on the corresponding u-plane will be computed. In addition, the dependence on second Stiefel-Whitney classes and the appearance of a Spin^c structure in the associated low-energy Seiberg-Witten theory with surface operators, will also be demonstrated. In the process, we will stumble upon an interesting phase factor that is otherwise absent in the "unramified" case.Comment: 46 pages. Minor refinemen

Proposal to demonstrate the non-locality of Bohmian mechanics with entangled photons

Bohmian mechanics reproduces all statistical predictions of quantum mechanics, which ensures that entanglement cannot be used for superluminal signaling. However, individual Bohmian particles can experience superluminal influences. We propose to illustrate this point using a double double-slit setup with path-entangled photons. The Bohmian velocity field for one of the photons can be measured using a recently demonstrated weak-measurement technique. The found velocities strongly depend on the value of a phase shift that is applied to the other photon, potentially at spacelike separation.Comment: 6 pages, 4 figure

Characterization of Probability Law by Absolute Moments of Its Partial Sums

If Sn = X1 + . . . + Xn, where Xi are independent and identically distributed (i.i.d.) standard normal, then E|Sn| ≡ √2n/π, n ≧ 0. We show that no other symmetric law has exactly these “moments”; the general case remains (stubbornly) open. If X is standard two-sided exponential, then E|Sn| = 2n2-2n(2n/n). We show the latter moments are obtained exactly for all n also for Xi ~ B(2;0.5), the sum of two standard (± 1-valued) Bernoulli’s as well as for many other laws including unsymmetrical ones: Xi ~ G - 1, where G is geometric with mean 1, is one example. Our interest in this delicate nonlinear inverse problem (which was initiated by Klebanov, cf. [12]) of inverting the moments to recover the law was also drawn by the fact that it gives a way to study positive definite functions through the formula E|Sn| = (2/π) ∫0∞Re(1 - φn(1 / u))du, n ≧ 0, expressing E|Sn| in terms of the moments of φ, where φ is the characteristic function of X, φ(u) = Eexp(iuX). We show that if for some b \u3e 0, ψb (u) = φ (btan (u / b)) is a positive definite function then the distributions corresponding to φ and ψb have the same E|Sn| moments for all n. We show that if X is Bernoulli with zero mean and values ±1 then the moments characterize the distribution uniquely even among nonsymmetric laws. In general however we expect that the moments do not characterize the law, and this may well be the only nontrivial case of uniqueness. We extend some of our results to the case of pth moments, p different from an even integer

Mesoscopic Superconducting Disc with Short-Range Columnar Defects

Short-range columnar defects essentially influence the magnetic properties of a mesoscopic superconducting disc.They help the penetration of vortices into the sample, thereby decrease the sample magnetization and reduce the upper critical field. Even the presence of weak defects split a giant vortex state (usually appearing in a clean disc in the vicinity of the transition to a normal state) into a number of vortices with smaller topological charges. In a disc with a sufficient number of strong enough defects vortices are always placed onto defects. The presence of defects lead to the appearance of additional magnetization jumps related to the redistribution of vortices which are already present on the defects and not to the penetration of new vortices.Comment: 14 pgs. RevTex, typos and figures corrected. Submitted to Phys. Rev.

On the six-dimensional origin of the AGT correspondence

We argue that the six-dimensional (2,0) superconformal theory defined on M \times C, with M being a four-manifold and C a Riemann surface, can be twisted in a way that makes it topological on M and holomorphic on C. Assuming the existence of such a twisted theory, we show that its chiral algebra contains a W-algebra when M = R^4, possibly in the presence of a codimension-two defect operator supported on R^2 \times C \subset M \times C. We expect this structure to survive the \Omega-deformation.Comment: References added. 14 page

Molecular Identification, Phylogenetic Status, and Geographic Distribution of Culicoides oxystoma (Diptera: Ceratopogonidae) in Israel

Culicoides oxystoma (Diptera: Ceratopogonidae) is an important vector species, reported mainly from Asia, with high potential to transmit viral diseases affecting livestock. In Japan, many arboviruses have been isolated from C. oxystoma, suggesting it as a key player in the epidemiology of several Culicoides-borne diseases. Over the years, C. oxystoma has also been reported in the Middle East region, including Israel. In this region, however, C. oxystoma cannot be easily distinguished morphologically from its sibling species included in the Culicoides schultzei complex. We therefore used genomic data for species identification and phylogeny resolution. Phylogenetic analyses based on internal transcribed spacer 1 (ITS-1) of ribosomal DNA and the mitochondrial gene encoding cytochrome oxidase subunit I (COI) showed that C. oxystoma from Israel is closely related to C. oxystoma from Japan. Using differential probing PCR, we showed that C. oxystoma is distributed all over the country, especially in Mediterranean climate regions. Culicoides oxystoma is less common or even absent in arid regions, while the other genetic cluster of C. schultzei complex was found only in the east of the country (mostly arid and semiarid regions). The molecular finding of C. oxystoma in wide geographical regions, together with its high proportion in the general Culicoides population and its vectoring potential, imply that it may be an important vector species in the Middle East