Extensions of Picard 2-Stacks and the cohomology groups Ext^i of length 3 complexes

The aim of this paper is to define and study the 3-category of extensions of Picard 2-stacks over a site S and to furnish a geometrical description of the cohomology groups Ext^i of length 3 complexes of abelian sheaves. More precisely, our main Theorem furnishes (1) a parametrization of the equivalence classes of objects, 1-arrows, 2-arrows, and 3-arrows of the 3-category of extensions of Picard 2-stacks by the cohomology groups Ext^i, and (2) a geometrical description of the cohomology groups Ext^i of length 3 complexes of abelian sheaves via extensions of Picard 2-stacks. To this end, we use the triequivalence between the 3-category of Picard 2-stacks and the tricategory T^[-2,0](S) of length 3 complexes of abelian sheaves over S introduced by the second author in arXiv:0906.2393, and we define the notion of extension in this tricategory T^[-2,0](S), getting a pure algebraic analogue of the 3-category of extensions of Picard 2-stacks. The calculus of fractions that we use to define extensions in the tricategory T^[-2,0](S) plays a central role in the proof of our Main Theorem.Comment: 2 New Appendix: in the first Appendix we compute a long exact sequence involving the homotopy groups of an extension of Picard 2-stacks, and in the second Appendix we sketch the proof that the fibered sum of Picard 2-stacks satisfies the universal propert

Higher-dimensional Algebra and Topological Quantum Field Theory

The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and outline a program in which n-dimensional TQFTs are to be described as n-category representations. First we describe a "suspension" operation on n-categories, and hypothesize that the k-fold suspension of a weak n-category stabilizes for k >= n+2. We give evidence for this hypothesis and describe its relation to stable homotopy theory. We then propose a description of n-dimensional unitary extended TQFTs as weak n-functors from the "free stable weak n-category with duals on one object" to the n-category of "n-Hilbert spaces". We conclude by describing n-categorical generalizations of deformation quantization and the quantum double construction.Comment: 36 pages, LaTeX; this version includes all 36 figure

Principal 2-bundles and their gauge 2-groups

In this paper we introduce principal 2-bundles and show how they are classified by non-abelian Cech cohomology. Moreover, we show that their gauge 2-groups can be described by 2-group-valued functors, much like in classical bundle theory. Using this, we show that, under some mild requirements, these gauge 2-groups possess a natural smooth structure. In the last section we provide some explicit examples.Comment: 40 pages; v3: completely revised and extended, classification corrected, name changed, to appear in Forum Mat

Establishing a baseline for the study of maritime cultural heritage in the Gaza Strip

As a result of its geographic location, cultural diversity and historical trajectory, the Gaza strip is a key zone of scholarly enquiry and has a central role in the historical, social, political, economic, legislative and environmental discourses for the wider region. Existing historical knowledge of Gaza is dominated by combative narrative trends that emphasise the events of the 20th and 21st centuries and invoke archaeology extensively. In this context, cycles of material preservation and damage—often accompanying other forms of violence—have attracted the attention of academics and international media. Among the corollaries of this situation, is the destruction and marginalisation of vulnerable cultural heritage, particularly maritime cultural heritage, which is subjected to additional environmental, climatic, and anthropogenic pressures. As a means of countering the challenges on current field research in the region and to further assess the damage and threats faced by archaeological fabric, this paper combines data from coastal and archaeological research conducted in the Gaza Strip to create a benchmark for the study of its maritime archaeology. Additional information on the alteration of coastal landscape is deduced through the analysis of aerial photographs and satellite imagery. This study falls within the scope of the Maritime Endangered Archaeology in the Middle East and Africa Project (MarEA). MarEA aims to comprehensively document and assess vulnerable maritime archaeology (underwater, nearshore, coastal) and produce baseline information that can enhance existing infrastructure on archaeological monitoring and management.</p

Crossed Module Bundle Gerbes; Classification, String Group and Differential Geometry

We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to any crossed module there is a simplicial group NC, the nerve of the 1-category defined by the crossed module and its geometric realization |NC|. Equivalence classes of principal bundles with structure group |NC| are shown to be one-to-one with stable equivalence classes of what we call crossed module gerbes bundle gerbes. We can also associate to a crossed module a 2-category C'. Then there are two equivalent ways how to view classifying spaces of NC-bundles and hence of |NC|-bundles and crossed module bundle gerbes. We can either apply the W-construction to NC or take the nerve of the 2-category C'. We discuss the string group and string structures from this point of view. Also a simplicial principal bundle can be equipped with a simplicial connection and a B-field. It is shown how in the case of a simplicial principal NC-bundle these simplicial objects give the bundle gerbe connection and the bundle gerbe B-field

Water masers accompanying OH and methanol masers in star formation regions

The ATCA has been used to measure positions with arcsecond accuracy for 379 masers at the 22-GHz transition of water. The principal observation targets were 202 OH masers of the variety associated with star formation regions (SFR)s in the Southern Galactic plane. At a second epoch, most of these targets were observed again, and new targets of methanol masers were added. Many of the water masers reported here are new discoveries. Variability in the masers is often acute, with very few features directly corresponding to those discovered two decades ago. Within our current observations, less than a year apart, spectra are often dissimilar, but positions at the later epoch, even when measured for slightly different features, mostly correspond to the detected maser site measured earlier, to within the typical extent of the whole site, of a few arcseconds. The precise water positions show that approximately 79% (160 of 202) of the OH maser sites show coincident water maser emission, the best estimate yet obtained for this statistic; however, there are many instances where additional water sites are present offset from the OH target, and consequently less than half of the water masers coincide with a 1665-MHz ground-state OH maser counterpart. We explore the differences between the velocities of peak emission from the three species (OH, methanol and water), and quantify the typically larger deviations shown by water maser peaks from systemic velocities. Clusters of two or three distinct but nearby sites, each showing one or several of the principal molecular masing transitions, are found to be common. In combination with an investigation of correlations with IR sources from the GLIMPSE catalogue, these comparative studies allow further progress in the use of the maser properties to assign relative evolutionary stages in star formation to individual sites.Comment: 51 pages, 7 figure

Big Data in Maritime Archaeology: Challenges and Prospects from the Middle East and North Africa

The Middle East and North Africa have witnessed a surfeit of geospatial data collection projects, resulting in big databases with powerful deductive capacities. Despite the valuable insights and expansive evidentiary record offered by those databases, emphasis on anthropogenic threats to cultural heritage, combined with a limited integration of local perspectives, have raised important questions on the ethical and epistemological dimensions of big data. This paper contextualizes maritime cultural heritage (MCH) in those debates through the lens of the Maritime Endangered Archaeology in the Middle East and North Africa project (MarEA). MarEA is developing a unique for the region database for MCH designed to amalgamate a baseline record emphasizing spatial location, state of preservation, and vulnerability. This record will form a stepping stone toward finer-grained research on MCH and its interdisciplinary intersections. It is also developed as an information resource to facilitate local collaborators in prioritizing site monitoring and developing documentation, management, and mitigation strategies

Design, analysis and test verification of advanced encapsulation systems, phase 2 program results

Optical, electrical isolation, thermal structural, structural deflection, and thermal tests are reported. The utility of the optical, series capacitance, and structural deflection models was verified

Quantitative Analysis of Survivin Protein Expression and Its Therapeutic Depletion by an Antisense Oligonucleotide in Human Lung Tumors

RNA-directed antisense and interference therapeutics are a promising treatment option for cancer. The demonstration of depletion of target proteins within human tumors in vivo using validated methodology will be a key to the application of this technology. Here, we present a flow cytometric-based approach to quantitatively determine protein levels in solid tumor material derived by fiber optic brushing (FOB) of non-small cell lung cancer (NSCLC) patients. Focusing upon the survivin protein, and its depletion by an antisense oligonucleotide (ASO) (LY2181308), we show that we can robustly identify a subpopulation of survivin positive tumor cells in FOB samples, and, moreover, detect survivin depletion in tumor samples from a patient treated with LY2181308. Survivin depletion appears to be a result of treatment with this ASO, because a tumor treated with conventional cytotoxic chemotherapy did not exhibit a decreased percentage of survivin positive cells. Our approach is likely to be broadly applicable to, and useful for, the quantification of protein levels in tumor samples obtained as part of clinical trials and studies, facilitating the proof-of-principle testing of novel targeted therapies

L∞L_\infty-Algebras, the BV Formalism, and Classical Fields

We summarise some of our recent works on $L_\infty$-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of $L_\infty$-algebras, we discuss their Maurer-Cartan theory and explain that any classical field theory admitting an action can be reformulated in this context with the help of the Batalin-Vilkovisky formalism. As examples, we explore higher Chern-Simons theory and Yang-Mills theory. We also explain how these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of $L_\infty$-quasi-isomorphisms, and we propose a twistor space action.Comment: 19 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 201