Split injectivity of A-theoretic assembly maps

We construct an equivariant coarse homology theory arising from the algebraic $K$-theory of spherical group rings and use this theory to derive split injectivity results for associated assembly maps. On the way, we prove that the fundamental structural theorems for Waldhausen's algebraic $K$-theory functor carry over to its nonconnective counterpart defined by Blumberg--Gepner--Tabuada

The differential analytic index in Simons-Sullivan differential K-theory

We define the Simons-Sullivan differential analytic index by translating the Freed-Lott differential analytic index via explicit ring isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We prove the differential Grothendieck-Riemann-Roch theorem in Simons-Sullivan differential K-theory using a theorem of Bismut.Comment: 14 pages. Comments are welcome. Final version. To appear in Annals of Global Analysis and Geometr

Equivariant coarse homotopy theory and coarse algebraic K\boldsymbol{K}-homology

We study equivariant coarse homology theories through an axiomatic framework. To this end we introduce the category of equivariant bornological coarse spaces and construct the universal equivariant coarse homology theory with values in the category of equivariant coarse motivic spectra. As examples of equivariant coarse homology theories we discuss equivariant coarse ordinary homology and equivariant coarse algebraic $K$-homology. Moreover, we discuss the cone functor, its relation with equivariant homology theories in equivariant topology, and assembly and forget-control maps. This is a preparation for applications in subsequent papers aiming at split-injectivity results for the Farrell-Jones assembly map

A generic framework for median graph computation based on a recursive embedding approach

The median graph has been shown to be a good choice to obtain a representative of a set of graphs. However, its computation is a complex problem. Recently, graph embedding into vector spaces has been proposed to obtain approximations of the median graph. The problem with such an approach is how to go from a point in the vector space back to a graph in the graph space. The main contribution of this paper is the generalization of this previous method, proposing a generic recursive procedure that permits to recover the graph corresponding to a point in the vector space, introducing only the amount of approximation inherent to the use of graph matching algorithms. In order to evaluate the proposed method, we compare it with the set median and with the other state-of-the-art embedding-based methods for the median graph computation. The experiments are carried out using four different databases (one semi-artificial and three containing real-world data). Results show that with the proposed approach we can obtain better medians, in terms of the sum of distances to the training graphs, than with the previous existing methods. © 2011 Elsevier Inc. All rights reserved.This work has been supported by the Spanish research programmes Consolider Ingenio 2010 CSD2007-00018, TIN2006-15694-C02-02 and TIN2008-04998 and the fellowship RYC-2009-05031.Peer Reviewe

Graph Edit Distance Reward: Learning to Edit Scene Graph

Scene Graph, as a vital tool to bridge the gap between language domain and image domain, has been widely adopted in the cross-modality task like VQA. In this paper, we propose a new method to edit the scene graph according to the user instructions, which has never been explored. To be specific, in order to learn editing scene graphs as the semantics given by texts, we propose a Graph Edit Distance Reward, which is based on the Policy Gradient and Graph Matching algorithm, to optimize neural symbolic model. In the context of text-editing image retrieval, we validate the effectiveness of our method in CSS and CRIR dataset. Besides, CRIR is a new synthetic dataset generated by us, which we will publish it soon for future use.Comment: 14 pages, 6 figures, ECCV camera ready versio

T-duality and Differential K-Theory

We give a precise formulation of T-duality for Ramond-Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differential K-theory of certain principal torus bundles. Our result combines topological T-duality with the Buscher rules found in physics.Comment: 23 pages, typos corrected, submitted to Comm.Math.Phy

Influence of the Time Scale on the Construction of Financial Networks

BACKGROUND: In this paper we investigate the definition and formation of financial networks. Specifically, we study the influence of the time scale on their construction. METHODOLOGY/PRINCIPAL FINDINGS: For our analysis we use correlation-based networks obtained from the daily closing prices of stock market data. More precisely, we use the stocks that currently comprise the Dow Jones Industrial Average (DJIA) and estimate financial networks where nodes correspond to stocks and edges correspond to none vanishing correlation coefficients. That means only if a correlation coefficient is statistically significant different from zero, we include an edge in the network. This construction procedure results in unweighted, undirected networks. By separating the time series of stock prices in non-overlapping intervals, we obtain one network per interval. The length of these intervals corresponds to the time scale of the data, whose influence on the construction of the networks will be studied in this paper. CONCLUSIONS/SIGNIFICANCE: Numerical analysis of four different measures in dependence on the time scale for the construction of networks allows us to gain insights about the intrinsic time scale of the stock market with respect to a meaningful graph-theoretical analysis

Graph edit distance or graph edit pseudo-distance?

Graph Edit Distance has been intensively used since its appearance in 1983. This distance is very appropriate if we want to compare a pair of attributed graphs from any domain and obtain not only a distance, but also the best correspondence between nodes of the involved graphs. In this paper, we want to analyse if the Graph Edit Distance can be really considered a distance or a pseudo-distance, since some restrictions of the distance function are not fulfilled. Distinguishing between both cases is important because the use of a distance is a restriction in some methods to return exact instead of approximate results. This occurs, for instance, in some graph retrieval techniques. Experimental validation shows that in most of the cases, it is not appropriate to denominate the Graph Edit Distance as a distance, but a pseudo-distance instead, since the triangle inequality is not fulfilled. Therefore, in these cases, the graph retrieval techniques not always return the optimal graph

Higher Structures in M-Theory

The key open problem of string theory remains its non-perturbative completion to M-theory. A decisive hint to its inner workings comes from numerous appearances of higher structures in the limits of M-theory that are already understood, such as higher degree flux fields and their dualities, or the higher algebraic structures governing closed string field theory. These are all controlled by the higher homotopy theory of derived categories, generalised cohomology theories, and $L_\infty$-algebras. This is the introductory chapter to the proceedings of the LMS/EPSRC Durham Symposium on Higher Structures in M-Theory. We first review higher structures as well as their motivation in string theory and beyond. Then we list the contributions in this volume, putting them into context.Comment: 22 pages, Introductory Article to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018, references update

Stability of Mine Car Motion in Curves of Invariable and Variable Radii

We discuss our experiences adapting three recent algorithms for maximum common (connected) subgraph problems to exploit multi-core parallelism. These algorithms do not easily lend themselves to parallel search, as the search trees are extremely irregular, making balanced work distribution hard, and runtimes are very sensitive to value-ordering heuristic behaviour. Nonetheless, our results show that each algorithm can be parallelised successfully, with the threaded algorithms we create being clearly better than the sequential ones. We then look in more detail at the results, and discuss how speedups should be measured for this kind of algorithm. Because of the difficulty in quantifying an average speedup when so-called anomalous speedups (superlinear and sublinear) are common, we propose a new measure called aggregate speedup