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Register a new userHandling Handles. Part II. Stratification and Data Analysis
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In a previous work, we proposed an integrability setup for computing non-planar corrections to correlation functions in $mathcal{N}=4$ super Yang-Mills theory at any value of the coupling constant. The procedure consists of drawing all possible tree-level graphs on a Riemann surface of given genus, completing each graph to a triangulation, inserting a hexagon form factor into each face, and summing over a complete set of states on each edge of the triangulation. The summation over graphs can be interpreted as a quantization of the string moduli space integration. The quantization requires a careful treatment of the moduli space boundaries, which is realized by subtracting degenerate Riemann surfaces; this procedure is called stratification. In this work, we precisely formulate our proposal and perform several perturbative checks. These checks require hitherto unknown multi-particle mirror contributions at one loop, which we also compute.
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We study the stratification of the singular locus of four dimensional $mathcal{N}=2$ Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant rank 1 Coulomb branch geometries to two complex dimensions, and beyond. The calculational simplicity of the arguments presented here stems from the fact that the main ingredients needed -- the rank 1 deformation patterns and the pattern of inclusions of rank 2 strata -- are discrete topological data which satisfy strong self-consistency conditions through their relationship to the central charges of the SCFT. This relationship of the stratification data to the central charges is used here, but is derived and explained in a companion paper by one of the authors. We illustrate the use of these conditions by re-analyzing many previously-known examples of rank 2 SCFTs, and also by finding examples of new theories. The power of these conditions stems from the fact that for Coulomb branch stratifications a conjecturally complete list of physically allowed elementary slices is known. By contrast, constraining the possible elementary slices of symplectic singularities relevant for Higgs branch stratifications remains an open problem.
The analysis and proper documentation of the properties of closed-loop control software presents many distinct aspects from the analysis of the same software running open-loop. Issues of physical system representations arise, and it is desired that such representations remain independent from the representations of the control program. For that purpose, a concurrent program representation of the plant and the control processes is proposed, although the closed-loop system is sufficiently serialized to enable a sequential analysis. While dealing with closed-loop system properties, it is also shown by means of examples how special treatment of nonlinearities extends from the analysis of control specifications to code analysis.
We have conducted an observing campaign with FORS at the ESO-VLT to explore the kinematical properties of spiral galaxies in distant galaxy clusters. Our main goal is to analyse transformation- and interaction processes of disk galaxies within the special environment of clusters as compared to the hierarchical evolution of galaxies in the field. Spatially resolved MOS-spectra have been obtained for seven galaxy clusters at 0.3<z<0.6 to measure rotation velocities of cluster members. For three of the clusters, Cl0303+17, Cl0413-65, and MS1008-12, for which we presented results including a TF-diagram in Ziegler et al. 2003, we describe here in detail the observations and data analysis. Each of them was observed with two setups of the standard FORS MOS-unit.With typical exposure times of >2 hours we reach an S/N>5 in the emission lines appropriate for the deduction of the galaxies internal rotation velocities from [OII], Hbeta, or [OIII] profiles. Preselection of targets was done on the basis of available redshifts as well as from photometric and morphological information gathered from own observations, archive data, and from the literature. Emphasis was laid on the definition of suitable setups to avoid the typical restrictions of the standard MOS unit for this kind of observations. In total we assembled spectra of 116 objects of which 50 turned out to be cluster members. Position velocity diagrams, finding charts as well as tables with photometric, spectral, and structural parameters of individual galaxies are presented.
In arXiv:1906.11820 and arXiv:1907.05404 we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d $mathcal{N}= (1,0)$ SCFTs. The graphs, so-called combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi--Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions and demonstrate that the CFD as recovered from the gauge theory approach is consistent with that as determined by geometry. To each quiver description we also associate a graph, and the embedding of this graph into the CFD that is associated to an SCFT provides a systematic way to enumerate all possible consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore, different embeddings of gauge theory graphs into a fixed CFD can give rise to new UV-dualities for which we provide evidence through an analysis of the prepotential, and which, for some examples, we substantiate by constructing the M-theory geometry in which the dual quiver descriptions are manifest.
In Part I cite{Zhao13TSPasync1}, we introduced a fairly general model for asynchronous events over adaptive networks including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. We performed a stability analysis and established the notable fact that the network is still able to converge in the mean-square-error sense to the desired solution. Once stable behavior is guaranteed, it becomes important to evaluate how fast the iterates converge and how close they get to the optimal solution. This is a demanding task due to the various asynchronous events and due to the fact that agents influence each other. In this Part II, we carry out a detailed analysis of the mean-square-error performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We derive analytical expressions for the mean-square convergence rate and the steady-state mean-square-deviation. The expressions reveal how the various parameters of the asynchronous behavior influence network performance. In the process, we establish the interesting conclusion that even under the influence of asynchronous events, all agents in the adaptive network can still reach an $O( u^{1 + gamma_o})$ near-agreement with some $gamma_o > 0$ while approaching the desired solution within $O( u)$ accuracy, where $ u$ is proportional to the small step-size parameter for adaptation.
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