Infinite Transitivity on Affine Varieties

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

The SU(3)-invariant sector of new maximal supergravity

We investigate the SU(3)-invariant sector of the one-parameter family of SO(8) gauged maximal supergravities that has been recently discovered. To this end, we construct the N=2 truncation of this theory and analyse its full vacuum structure. The number of critical point is doubled and includes new N=0 and N=1 branches. We numerically exhibit the parameter dependence of the location and cosmological constant of all extrema. Moreover, we provide their analytic expressions for cases of special interest. Finally, while the mass spectra are found to be parameter independent in most cases, we show that the novel non-supersymmetric branch with SU(3) invariance provides the first counterexample to this.

Defining the role of IL-15 trans-presentation by distinct cell-types during the development and homeostasis of Natural Killer and invariant Natural Killer T cells

The immuno-regulatory functions displayed by NK and iNKT cells have highlighted their importance as key lymphocytes involved in innate and adaptive immunity. Therefore, understanding the dynamics influencing the generation of NK and iNKT cells is extremely important. IL-15 has been shown to provide a critical signal throughout the development and homeostasis of NK and iNKT cells; however, the cellular source of IL-15 has remained unclear. In this investigation, I provide evidence that the cell-type providing IL-15 to NK and iNKT cells via trans-presentation is determined by the tissue site and the maturation status of NK and iNKT cells. For NK cells, I revealed the non-hematopoietic compartment provides IL-15 to NK cells in the early stages of development while hematopoietic cells were crucial for the generation and maintenance of mature NK cells. Regarding iNKT cells in the thymus, IL-15 trans-presentation by non-hematopoietic cells was crucial for the survival of mature iNKT cells. In the liver, both hematopoietic and non-hematopoietic compartments provided IL-15 to both immature and mature iNKT cells. This IL-15 signal helped mediate the survival and proliferation of both NK and iNKT cells as well as induce the functional maturation of mature iNKT cells via enhanced T-bet expression. In conclusion, my work illustrates an important notion that the immunological niche of NK and iNKT cells is tightly regulated and that this regulation is meticulously influenced by the tissue microenvironment.

Transcriptional regulation of the invariant chain associated with MHC class II molecules

The invariant chain associated with the major histocompatibility complex (MHC) class II molecules is a non-polymorphic glycoprotein implicated in antigen processing and class II molecule intracellular transport. Class II molecules and invariant chain (In) are expressed primarily by B lymphocytes and antigen-presenting cells such as macrophages and can be induced by interferon gamma (IFN-$\gamma$) in a variety of cell types such as endothelial cells, fibroblasts, and astrocytes. In this study the cis-acting sequences involved in the constitutive, tissue-specific, and IFN-$\gamma$ induced expression of the human In gene were investigated and nuclear proteins which specifically bound these sequences were identified.^ To define promoter sequences involved in the regulation of the human In gene, 790 bp 5$\sp\prime$ to the initiation of transcription were subcloned upstream of the gene encoding chloramphenicol acetyl transferase (CAT). Transfection of this construct into In expressing and non-expressing cell lines demonstrated that this 790 bp In promoter sequence conferred tissue specificity to the CAT gene. Deletion mutants were created in the promoter to identify sequences important for transcription. Three regulatory regions were identified $-$396 to $-$241, $-$241 to $-$216, and $-$216 to $-$165 bp 5$\sp\prime$ to the cap site. Transfection into a human glioblastoma cell line, U-373 MG, and treatment with IFN-$\gamma$, demonstrated that this 5$\sp\prime$ region is responsive to IFN-$\gamma$. An IFN-$\gamma$ response element was sublocalized to the region $-$120 to $-$61 bp. This region contains homology to the interferon-stimulated response element (ISRE) identified in other IFN responsive genes. IFN-$\gamma$ induces a sequence-specific DNA binding factor which binds to an oligonucleotide corresponding to $-$107 to $-$79 bp of the In promoter. This factor also binds to an oligonucleotide corresponding to $-$91 to $-$62 of the interferon-$\beta$ gene promoter, suggesting this factor may be member of the IRF-1/ISGF2, IRF-2, ICSBP family of ISRE binding proteins. A transcriptional enhancer was identified in the first intron of the In gene. This element, located in a 2.6 kb BamHI/PstI fragment, enhances the IFN-$\gamma$ response of the promoter in U-373 MG. The majority of the In enhancer activity was sublocalized to a 550 bp region $\sim$1.6 kb downstream of the In transcriptional start site. ^

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Search for Quantum Black Hole Production in High-Invariant-Mass Lepton plus Jet Final States Using pp Collisions at root s=8 TeV and the ATLAS Detector

This Letter presents a search for quantum black-hole production using 20.3 fb(-1) of data collected with the ATLAS detector in pp collisions at the LHC at root s = 8 TeV. The quantum black holes are assumed to decay into a final state characterized by a lepton (electron or muon) and a jet. In either channel, no event with a lepton-jet invariant mass of 3.5 TeV or more is observed, consistent with the expected background. Limits are set on the product of cross sections and branching fractions for the lepton + jet final states of quantum black holes produced in a search region for invariant masses above 1 TeV. The combined 95% confidence level upper limit on this product for quantum black holes with threshold mass above 3.5 TeV is 0.18 fb. This limit constrains the threshold quantum black-hole mass to be above 5.3 TeV in the model considered.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Shape-invariant multibeam backscatter data of the eastern slope of the Porcupine Seabight (50 m grid size)

In this study multibeam angular backscatter data acquired in the eastern slope of the Porcupine Seabight are analysed. Processing of the angular backscatter data using the 'NRGCOR' software was made for 29 locations comprising different geological provinces like: carbonate mounds, buried mounds, seafloor channels, and inter-channel areas. A detailed methodology is developed to produce a map of angle-invariant (normalized) backscatter data by correcting the local angular backscatter values. The present paper involves detailed processing steps and related technical aspects of the normalization approach. The presented angle-invariant backscatter map possesses 12 dB dynamic range in terms of grey scale. A clear distinction is seen between the mound dominated northern area (Belgica province) and the Gollum channel seafloor at the southern end of the site. Qualitative analyses of the calculated mean backscatter values i.e., grey scale levels, utilizing angle-invariant backscatter data generally indicate backscatter values are highest (lighter grey scale) in the mound areas followed by buried mounds. The backscatter values are lowest in the inter-channel areas (lowest grey scale level). Moderate backscatter values (medium grey level) are observed from the Gollum and Kings channel data, and significant variability within the channel seafloor provinces. The segmentation of the channel seafloor provinces are made based on the computed grey scale levels for further analyses based on the angular backscatter strength. Three major parameters are utilized to classify four different seafloor provinces of the Porcupine Seabight by employing a semi-empirical method to analyse multibeam angular backscatter data. The predicted backscatter response which has been computed at 20° is the highest for the mound areas. The coefficient of variation (CV) of the mean backscatter response is also the highest for the mound areas. Interestingly, the slope value of the buried mound areas are found to be the highest. However, the channel seafloor of moderate backscatter response presents the lowest slope and CV values. A critical examination of the inter-channel areas indicates less variability within the estimated three parameters.