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Index theory for locally compact noncommutative geometries
(2014-09-01) Carey, A. L.; Gayral, V.; Rennie, A.; Sukochev, F. A.
Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, we prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and we illustrate this point with two examples in the text. In order to understand what is new in our approach in the commutative setting we prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds our index formula appears to be completely new. As we prove our local index formula in the framework of semifinite noncommutative geometry we are also able to prove, for manifolds of bounded geometry, a version of Atiyah's L2-index Theorem for covering spaces. We also explain how to interpret the McKean-Singer formula in the nonunital case. To prove the local index formula, we develop an integration theory compatible with a refinement of the existing pseudodifferential calculus for spectral triples. We also clarify some aspects of index theory for nonunital algebras.
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Practical undoability checking via contingent planning
(2016) Daum, Jeanette; Torralba, Álvaro; Hoffmann, Jörg; Haslum, Patrik; Weber, Ingo
We consider a general concept of undoability, asking whether a given action can always be undone, no matter which state it is applied to. This generalizes previous concepts of invertibility, and is relevant for search as well as applications. Naïve undoability checking requires to enumerate all states an action is applicable to. Extending and operationalizing prior work in this direction, we introduce a compilation into contingent planning, replacing such enumeration by standard techniques handling large belief states. We furthermore introduce compilations for checking whether one can always get back to an at-least-as-good state, as well as for determining partial undoability, i. e., undoability on a subset of states an action is applicable to. Our experiments on IPC benchmarks and in a cloud management application show that contingent planners are often effective at solving this kind of problem, hence providing a practical means for undoability checking.
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Organometallic Complexes in Nonlinear Optics II: Third-Order Nonlinearities and Optical Limiting Studies
(Academic Press Inc., 1999) Whittall, Ian R.; Mcdonagh, Andrew M.; Humphrey, Mark G.; Samoc, Marek
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Imaged-based multiscale network modelling of microporosity in carbonates
(2015-05-24) Prodanović, Maša; Mehmani, Ayaz; Sheppard, Adrian P.
Diagenetic changes such as cementation or dissolution have a strong control on carbonate pore structure, and often disconnect the original intergranular pore space. Spatial distribution of submicron porosity (microporosity) that develops in the process, as well as its influence on flow properties, is difficult to image and characterize. Yet, a petrophysically rigorous pore-scale model that accounts for submicron porosity interconnectivity would help in the understanding and development of carbonate reservoirs dominated by microporosity. We present algorithms to geometrically match pore-throat networks from two separate length scales that can be extracted directly from three-dimensional (3D) rock images, or be constructed to match the relevant measured properties. We evaluate the combined influence of cementation and dissolution using a Bentheimer Sandstone sample, as well as image-identified microporosity on flow transport properties in an Estaillades Limestone sample.
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Multi-Mutual Consistency Induced Transfer Subspace Learning for Human Motion Segmentation
(2020) Zhou, Tao; Fu, Huazhu; Gong, Chen; Shen, Jianbing; Shao, Ling; Porikli, Fatih
Human motion segmentation based on transfer subspace learning is a rising interest in action-related tasks. Although progress has been made, there are still several issues within the existing methods. First, existing methods transfer knowledge from source data to target tasks by learning domain-invariant features, but they ignore to preserve domain-specific knowledge. Second, the transfer subspace learning is employed in either low-level or high-level feature spaces, but few methods consider fusing multi-level features for subspace learning. To this end, we propose a novel multi-mutual consistency induced transfer subspace learning framework for human motion segmentation. Specifically, our model factorizes the source and target data into distinct multi-layer feature spaces and reduces the distribution gap between them through a multi-mutual consistency learning strategy. In this way, the domain-specific knowledge and domain-invariant properties can be explored simultaneously. Our model also conducts the transfer subspace learning on different layers to capture multi-level structural information. Further, to preserve the temporal correlations, we project the learned representations into a block-like space. The proposed model is efficiently optimized by using the Augmented Lagrange Multiplier (ALM) algorithm. Experimental results on four human motion datasets demonstrate the effectiveness of our method over other state-of-the-art approaches.