An Invitation to Higher Gauge Theory

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra that governs 11-dimensional supergravity.Comment: 60 pages, based on lectures at the 2nd School and Workshop on Quantum Gravity and Quantum Geometry at the 2009 Corfu Summer Institut

From propositional to first-order monitoring

Abstract. The main purpose of this paper is to introduce a first-order temporal logic, LTL FO, and a corresponding monitor construction based on a new type of automaton, called spawning automaton. Specifically, we show that monitoring a specification in LTL FO boils down to an undecidable decision problem. The proof of this result revolves around specific ideas on what we consider a “proper ” monitor. As these ideas are general, we outline them first in the setting of standard LTL, before lifting them to the setting of first-order logic and LTL FO. Although due to the above result one cannot hope to obtain a complete monitor for LTL FO, we prove the soundness of our automatabased construction and give experimental results from an implementation. These seem to substantiate our hypothesis that the automata-based construction leads to efficient runtime monitors whose size does not grow with increasing trace lengths (as is often observed in similar approaches). However, we also discuss formulae for which growth is unavoidable, irrespective of the chosen monitoring approach.

[¹¹¹In-DTPA-D-Phe¹]-octreotide, a potential radiopharmaceutical for imaging of somatostatin receptor-positive tumors:synthesis, radiolabeling and in vitro validation

Somatostatin receptor-positive human tumors can be detected using radioiodinated analogues of somatostatin, both in vitro and in vivo. [123I-Tyr3]-octreotide has been successfully used in the visualization of somatostatin receptor-positive tumors by gamma camera scintigraphy, but this radiopharmaceutical has some major drawbacks, which can be overcome with other radionuclides such as 111In. As starting material for a potentially convenient radiopharmaceutical, a diethylenetriaminopentaacetic acid (DTPA) conjugated derivative of octreotide (SMS 201-995) was prepared. This peptide, [DTPA-D-Phe1]-octreotide (SDZ 215-811) binds more than 95 % of added 111In in an easy, single-step labeling procedure without necessity of further purification. The specific somatostatin-like biologic effect of these analogues was proven by the inhibition of growth hormone secretion by cultured rat pituitary cells in a dose-dependent fashion by octreotide, [DTPA-D-Phe1]-octreotide and non-radioactive [115In-DTPA-D-Phe1]-octreotide. The binding of [111In-DTPA-D-Phe1]-octreotide to rat brain cortex membranes proved to be displaced similarly by natural somatostatin as well as by octreotide, suggesting specific binding of [111In-DTPA-D-Phe1]-octreotide to somatostatin receptors. The binding of the indium-labeled compound showed a somewhat lower affinity when compared with the iodinated [Tyr3]-octreotide, but indium-labeled [DTPA-D-Phe1]-octreotide still binds with nanomolar affinity. In conjunction with in vivo studies, these results suggest that [111In-DTPA-D-Phe1]-octreotide is a promising radiopharmaceutical for scintigraphic imaging of somatostatin receptor-positive tumors.</p