Correlations in excited states of local Hamiltonians

Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix)

Diversity and Composition of the Adult Fecal Microbiome Associated with History of Cesarean Birth or Appendectomy: Analysis of the American Gut Project

AbstractBackgroundCesarean birth is associated with altered composition of the neonate's microbiota and with increased risk for obesity and other diseases later in life. The mechanisms of these associations, and whether cesarean birth is associated with an altered adult microbiota, are unknown.MethodsIn 1097 adult volunteers without diabetes, inflammatory bowel disease, or recent antibiotic use, fecal microbiome metrics were compared by history of cesarean birth (N=92) or appendectomy (N=115). Associations with potential confounders, microbiome alpha diversity, and individual microbial taxa were estimated by logistic regression. Permutation tests assessed differences in microbial composition (beta diversity) based on Jensen–Shannon divergence.FindingsCesarean birth history was associated with younger age; appendectomy with older age and higher body mass index. Neither was associated with fecal microbiome alpha diversity. Microbial composition at all taxonomic levels differed significantly with cesarean birth (P≤0.008) but not with appendectomy (P≥0.29). Relative abundance differed nominally for 17 taxa with cesarean birth and for 22 taxa with appendectomy, none of which was significant with adjustment for multiple comparisons.InterpretationAdults born by cesarean section appear to have a distinctly different composition of their fecal microbial population. Whether this distinction was acquired during birth, and whether it affects risk of disease during adulthood, are unknown.FundingSupported by the Intramural Research Program, National Cancer Institute, National Institutes of Health (Z01-CP-010214)

Different evolutionary fates of recently integrated human and chimpanzee LINE-1 retrotransposons

The long interspersed element-1 (LINE-1 or L1) is a highly successful retrotransposon in mammals. L1 elements have continued to actively propagate subsequent to the human-chimpanzee divergence, ∼ 6 million years ago, resulting in species-specific inserts. Here, we report a detailed characterization of chimpanzee-specific L1 subfamily diversity and a comparison with their human-specific counterparts. Our results indicate that L1 elements have experienced different evolutionary fates in humans and chimpanzees within the past ∼ 6 million years. Although the species-specific L1 copy numbers are on the same order in both species (1200-2000 copies), the number of retrotransposition-competent elements appears to be much higher in the human genome than in the chimpanzee genome. Also, while human L1 subfamilies belong to the same lineage, we identified two lineages of recently integrated L1 subfamilies in the chimpanzee genome. The two lineages seem to have coexisted for several million years, but only one shows evidence of expansion within the past three million years. These differential evolutionary paths may be the result of random variation, or the product of competition between L1 subfamily lineages. Our results suggest that the coexistence of several L1 subfamily lineages within a species may be resolved in a very short evolutionary period of time, perhaps in just a few million years. Therefore, the chimpanzee genome constitutes an excellent model in which to analyze the evolutionary dynamics of L1 retrotransposons. © 2006 Elsevier B.V. All rights reserved

Neuronal LRP1 knockout in adult mice leads to impaired brain lipid metabolism and progressive, age-dependent synapse loss and neurodegeneration

The vast majority of Alzheimer’s disease (AD) cases are late-onset with progressive synapse loss and neurodegeneration. Although the amyloid hypothesis has generated great insights into the disease mechanism, several lines of evidence indicate that other risk factors might precondition the brain to amyloid toxicity. Here, we show that the deletion of a major lipoprotein receptor, LRP1, in forebrain neurons in mice leads to a global defect in brain lipid metabolism characterized by decreased brain levels of cholesterol, sulfatide, galactosylceramide and triglyceride. These lipid deficits correlate with progressive, age-dependent dendritic spine degeneration, synapse loss, neuroinflammation, memory loss, and eventual neurodegeneration. We further show that the levels of glutamate receptor subunits NMDAR1 and GluR1 are selectively reduced in LRP1 forebrain knockout mice and in LRP1 knockdown neurons, which is partially rescued by restoring neuronal cholesterol. Together, these studies support a critical role for LRP1 in maintaining brain lipid homeostasis and associated synaptic and neuronal integrity, and provide important insights into the pathophysiological mechanisms in AD

HiTrust: building cross-organizational trust relationship based on a hybrid negotiation tree

Small-world phenomena have been observed in existing peer-to-peer (P2P) networks which has proved useful in the design of P2P file-sharing systems. Most studies of constructing small world behaviours on P2P are based on the concept of clustering peer nodes into groups, communities, or clusters. However, managing additional multilayer topology increases maintenance overhead, especially in highly dynamic environments. In this paper, we present Social-like P2P systems (Social-P2Ps) for object discovery by self-managing P2P topology with human tactics in social networks. In Social-P2Ps, queries are routed intelligently even with limited cached knowledge and node connections. Unlike community-based P2P file-sharing systems, we do not intend to create and maintain peer groups or communities consciously. In contrast, each node connects to other peer nodes with the same interests spontaneously by the result of daily searches

Evidence for the microwave effect during the annealing of zinc oxide

A microwave/conventional hybrid furnace has been used to anneal virtually fully dense zinc oxide ceramics under pure conventional and a microwave/conventional hybrid heating regime with a view to obtaining evidence for the ‘microwave effect’ during the resulting grain growth. In each case it was ensured that each sample within a series had an identical thermal history in terms of its temperature/time profile. The results showed that grain growth was enhanced during hybrid heating compared to pure conventional heating; the greatest enhancement, a factor of ~3 increase in average grain size, was observed in the range 1100-1150°C. The grain growth exponent decreased from 3 during conventional heating to 1.4 during hybrid heating in this temperature range, suggesting an acceleration of the diffusional processes involved. Temperature gradients within the samples were found to be too small to explain the results. This suggests that clear evidence has been found to support the existence of a genuine ‘microwave effect’