Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO(nn)

Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.Comment: Minor changes, journal reference adde

Detonation wave diffraction in H₂-O₂-Ar mixtures

In the present study, we have examined the diffraction of detonation in weakly unstable hydrogen–oxygen–argon mixtures. High accuracy and computational efficiency are obtained using a high-order WENO scheme together with adaptive mesh refinement, which enables handling realistic geometries with resolution at the micrometer level. Both detailed chemistry and spectroscopic models of laser induced fluorescence and chemiluminescence were included to enable a direct comparison with experimental data. Agreement was found between the experiments and the simulations in terms of detonation diffraction structure both for sub-critical and super-critical regimes. The predicted wall reflection distance is about 12–14 cell widths, in accordance with previous experimental studies. Computations show that the re-initiation distance is relatively constant, at about 12–15 cell widths, slightly above the experimental value of 11 cell widths. The predicted critical channel height is 10–11 cell widths, which differs from experiments in circular tubes but is consistent with rectangular channel results

On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis

The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem. Although backward reachability is property-directed, it can unnecessarily explore (large) portions of the state space of a system which are not required to verify the safety property under consideration. To avoid this, invariants can be used to dramatically prune the search space. Indeed, the problem is to guess such appropriate invariants. In this paper, we present a fully declarative and symbolic approach to the mechanization of backward reachability of infinite state systems manipulating arrays by Satisfiability Modulo Theories solving. Theories are used to specify the topology and the data manipulated by the system. We identify sufficient conditions on the theories to ensure the termination of backward reachability and we show the completeness of a method for invariant synthesis (obtained as the dual of backward reachability), again, under suitable hypotheses on the theories. We also present a pragmatic approach to interleave invariant synthesis and backward reachability so that a fix-point for the set of backward reachable states is more easily obtained. Finally, we discuss heuristics that allow us to derive an implementation of the techniques in the model checker MCMT, showing remarkable speed-ups on a significant set of safety problems extracted from a variety of sources.Comment: Accepted for publication in Logical Methods in Computer Scienc

Cognitive Impairment, Frailty, and Adverse Outcomes Among Prevalent Hemodialysis Recipients:Results From a Large Prospective Cohort Study in the United Kingdom

RATIONALE &amp; OBJECTIVE: Frailty and cognitive impairment are common in hemodialysis recipients and have been associated with high mortality. There is considerable heterogeneity in frailty reporting, with little comparison between commonly used frailty tools and little exploration of the interplay between cognition and frailty. The aims were to explore the relationship between frailty scores and cognition and their associations with hospitalization and mortality.STUDY DESIGN: Prospective cohort study.SETTING &amp; POPULATION: Prevalent hemodialysis recipients linked to national datasets for hospitalization and mortality.PREDICTORS: Montreal Cognitive Assessment (MoCA), Frailty Phenotype, Frailty Index (FI), Edmonton Frailty Scale, and Clinical Frailty Scale (CFS) were performed at baseline. Cognitive impairment was defined as MoCA scores of &lt;26, or &lt;21 in dexterity impairment, &lt;18 in visual impairment.OUTCOMES: Mortality, hospitalization.ANALYTICAL APPROACH: Cox proportional hazards model for mortality, censored for end of follow-up. Negative binomial regression for admission rates, censored for death/end of follow-up.RESULTS: In total, 448 participants were recruited with valid MoCAs and followed up for a median of 685 days. There were 103 (23%) deaths and 1,120 admissions of at least one night. Cognitive impairment was identified in 346 (77.2%) participants. Increasing frailty by all definitions was associated with poorer cognition. Cognition was not associated with mortality (HR, 0.99; 95% CI, 0.95-1.03; P = 0.41) or hospitalization (IRR, 1.01; 95% CI, 0.99-1.04; P = 0.39) on multivariable analyses. There were interactions between MoCA scores and increasing frailty by FI (P = 0.002) and Clinical Frailty Scale (P = 0.005); admissions were highest when both MoCA and frailty scores were high, and when both scores were low.LIMITATIONS: As frailty is a dynamic state, a single cross-sectional assessment may not accurately reflect its year-to-year variability. In addition, these findings are in maintenance dialysis and may not be transferable to incident hemodialysis. There were small variations in application of frailty tool criteria from other studies, which may have influenced the results.CONCLUSIONS: Cognitive impairment is highly prevalent in this hemodialysis cohort. The interaction between cognition and frailty on rates of admission suggests the MoCA offers value in identifying higher risk hemodialysis populations with both high and low degrees of frailty.</p