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The reviewers contacted by the editors to evaluate this work have been unable to confirm that the main results are correct. Flaws that were identified by the reviewers in earlier versions of the paper have been addressed by the author. Although it is possible that future research will uncover a significant mistake in this paper or show that the conclusions are in error, I believe that publishing it may benefit the readership of the Journal and stimulate further work in mathematical physics on an important topic.

We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming that the interactions of the system satisfy a form of local topological quantum order, we prove explicit lower bounds on the ground state spectral gap and higher gaps for spin and fermion chains. By adapting previous methods using the spectral flow, we analyze the bulk and edge dependence of lower bounds on spectral gaps.

We discuss the role of compact symmetry groups, G, in the classification ofgapped ground state phases of quantum spin systems. We consider tworepresentations of G on infinite subsystems. First, in arbitrary dimensions, weshow that the ground state spaces of models within the same G-symmetric phasecarry equivalent representations of the group for each finite or infinitesublattice on which they can be defined and on which they remain gapped. Thisincludes infinite systems with boundaries or with non-trivial topologies.Second, for two classes of one-dimensional models, by two different methods,for G=SU(2) in one, and G\subset SU(d), in the other we construct explicitly an`excess spin' operator that implements rotations of half of the infinite chainon the GNS Hilbert space of the ground state of the full chain. Since thisoperator is constructed as the limit of a sequence of observables, therepresentation itself is, in principle, experimentally observable. We claimthat the corresponding unitary representation of G is closely related to therepresentation found at the boundary of half-infinite chains. We conclude withdetermining the precise relation between the two representations for the classof frustration-free models with matrix product ground states.

We consider entanglement properties of pure finitely correlated states (FCS). We derive bounds for the entanglement of a spin with an interval of spins in an arbitrary pure FCS. Finitely correlated states are also known as matrix product states or generalized valence-bond states. The bounds become exact in the case where one considers the entanglement of a single spin with a half-infinite chain to the right of it. Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for nonvanishing entanglement in terms of a single spin and the memory of the FCS is also sufficient. We also generalize the study of entanglement in the Affleck-Kennedy-Lieb-Tasaki model by Fan, Korepin, and Roychowdhury. Our result permits a more efficient calculation, numerically and in some cases analytically, of the entanglement of arbitrary finitely correlated quantum spin chains.

It is shown rigorously how to translate the ground state energy problem for some quantum systems into an equilibrium problem for an associated one-dimensional classical system. The case of the spin-boson model for which the connection is established with a previously obtained Ising model over R is explicitly treated. [ABSTRACT FROM AUTHOR]

Objectives: The newest mechanical valves have low thrombogenicity, making them candidates for anticoagulation with a direct oral anticoagulant. While these drugs hold great promise to replace warfarin, clinical trials have been disappointing so far. We aimed to evaluate apixaban in a porcine model of mechanical valve thrombosis with On-X® (CryoLife) aortic valves implanted in pulmonary position., Methods: On-X® valves were implanted in pulmonary valve position in 9 Yucatan pigs. Animals received prophylactic enoxaparin 40 mg for 1 week. Pigs in the low-dose group received 5 mg apixaban twice daily for 10 weeks. The intermediary-dose group received 5 mg twice daily for 6 weeks and then 10 mg twice daily afterwards. The high-dose group received 15 mg twice daily for 10 weeks. After sacrifice, valves were macroscopically evaluated and thrombus weight was documented., Results: The median weight of the 9 animals was 64.3 kg, range 52.5-70.9. In the low-dose group (2 animals), both valves showed manifest, chronic thrombosis with blocked hinges. In the intermediary-dose group, a normal functioning valve without thrombosis was seen in 2/4 animals. In the high-dose group (3 pigs), there was no valve thrombosis. No bleeding events occurred. In all animals, apixaban plasma levels were low compared to clinical target levels., Conclusions: The pulmonary position seems to be an aggressive model for mechanical valve thrombosis in pigs. Apixaban has the potential to prevent valve thrombosis, even in these thrombogenic conditions. Detailed pharmacokinetic studies are needed to determine the ideal apixaban dosage for future experiments and to enable extrapolation to the clinical situation., (© The Author(s) 2022. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery.)

For quantum lattice systems with local interactions, the Lieb-Robinson bound serves as an alternative for the strict causality of relativistic systems and allows the proof of many interesting results, in particular, when the energy spectrum exhibits an energy gap. In this Letter, we show that for translation invariant systems, simultaneous eigenstates of energy and momentum with an eigenvalue that is separated from the rest of the spectrum in that momentum sector can be arbitrarily well approximated by building a momentum superposition of a local operator acting on the ground state. The error satisfies an exponential bound in the size of the support of the local operator, with a rate determined by the gap below and above the targeted eigenvalue. We show this explicitly for the Affleck-Kennedy-Lieb-Tasaki model and discuss generalizations and applications of our result.

Complex networks possess a rich, multiscale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one type of interaction, or to go beyond simple pairwise interactions, but currently there is a lack of theoretical and computational methods to address these problems. Here we introduce a framework for clustering and community detection in such systems using hypergraph representations. Our main result is a generalization of the Perron-Frobenius theorem from which we derive spectral clustering algorithms for directed and undirected hypergraphs. We illustrate our approach with applications for local and global alignment of protein-protein interaction networks between multiple species, for tripartite community detection in folksonomies, and for detecting clusters of overlapping regulatory pathways in directed networks.

Topological network motifs represent functional relationships within and between regulatory and protein-protein interaction networks. Enriched motifs often aggregate into self-contained units forming functional modules. Theoretical models for network evolution by duplication-divergence mechanisms and for network topology by hierarchical scale-free networks have suggested a one-to-one relation between network motif enrichment and aggregation, but this relation has never been tested quantitatively in real biological interaction networks. Here we introduce a novel method for assessing the statistical significance of network motif aggregation and for identifying clusters of overlapping network motifs. Using an integrated network of transcriptional, posttranslational and protein-protein interactions in yeast we show that network motif aggregation reflects a local modularity property which is independent of network motif enrichment. In particular our method identified novel functional network themes for a set of motifs which are not enriched yet aggregate significantly and challenges the conventional view that network motif enrichment is the most basic organizational principle of complex networks.

We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains with spins of arbitrary magnitude, thus extending our previous result for the spin-1/2 chain. Ferromagnetic ordering means that the minimum energies in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin. This result provides a ferromagnetic analogue of the well-known theorem by Lieb and Mattis about ordering of energy levels in antiferromagnetic and ferrimagnetic systems on bipartite graphs.