Approximating the ground state of gapped quantum spin systems

We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset, X, of V the ground state projector can be approximated by the product of two projections, one supported on X and one supported on X^c, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue

Lipemic serum in hyperlipidemic pancreatitis

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DNA methylation and differential gene regulation in photoreceptor cell death

Retinitis pigmentosa (RP) defines a group of inherited degenerative retinal diseases causing progressive loss of photoreceptors. To this day, RP is still untreatable and rational treatment development will require a thorough understanding of the underlying cell death mechanisms. Methylation of the DNA base cytosine by DNA methyltransferases (DNMTs) is an important epigenetic factor regulating gene expression, cell differentiation, cell death, and survival. Previous studies suggested an involvement of epigenetic mechanisms in RP, and in this study, increased cytosine methylation was detected in dying photoreceptors in the rd1, rd2, P23H, and S334ter rodent models for RP. Ultrastructural analysis of photoreceptor nuclear morphology in the rd1 mouse model for RP revealed a severely altered chromatin structure during retinal degeneration that coincided with an increased expression of the DNMT isozyme DNMT3a. To identify disease-specific differentially methylated DNA regions (DMRs) on a genomic level, we immunoprecipitated methylated DNA fragments and subsequently analyzed them with a targeted microarray. Genome-wide comparison of DMRs between rd1 and wild-type retina revealed hypermethylation of genes involved in cell death and survival as well as cell morphology and nervous system development. When correlating DMRs with gene expression data, we found that hypermethylation occurred alongside transcriptional repression. Consistently, motif analysis showed that binding sites of several important transcription factors for retinal physiology were hypermethylated in the mutant model, which also correlated with transcriptional silencing of their respective target genes. Finally, inhibition of DNMTs in rd1 organotypic retinal explants using decitabine resulted in a substantial reduction of photoreceptor cell death, suggesting inhibition of DNA methylation as a potential novel treatment in RP

Pathological and ecological host consequences of infection by an introduced fish parasite

The infection consequences of the introduced cestode fish parasite Bothriocephalus acheilognathi were studied in a cohort of wild, young-of-the-year common carp Cyprinus carpio that lacked co-evolution with the parasite. Within the cohort, parasite prevalence was 42% and parasite burdens were up to 12% body weight. Pathological changes within the intestinal tract of parasitized carp included distension of the gut wall, epithelial compression and degeneration, pressure necrosis and varied inflammatory changes. These were most pronounced in regions containing the largest proportion of mature proglottids. Although the body lengths of parasitized and non-parasitized fish were not significantly different, parasitized fish were of lower body condition and reduced weight compared to non-parasitized conspecifics. Stable isotope analysis (δ15N and δ13C) revealed trophic impacts associated with infection, particularly for δ15N where values for parasitized fish were significantly reduced as their parasite burden increased. In a controlled aquarium environment where the fish were fed ad libitum on an identical food source, there was no significant difference in values of δ15N and δ13C between parasitized and non-parasitized fish. The growth consequences remained, however, with parasitized fish growing significantly slower than non-parasitized fish, with their feeding rate (items s−1) also significantly lower. Thus, infection by an introduced parasite had multiple pathological, ecological and trophic impacts on a host with no experience of the parasite

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

Gapped ground states of quantum spin systems have been referred to in the physics literature as being `in the same phase' if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on $s \in [0,1]$, such that for each $s$, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that 'belong to the same phase' are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an $s$-dependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings' 'quasi-adiabatic evolution' technique, of which we give a proof extended to infinite-dimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasi-local structure and prove that the flow, which we call the {\em spectral flow}, connecting the gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a co-cycle of automorphisms of the algebra of quasi-local observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models $H(s), 0\leq s\leq 1$.Comment: Updated acknowledgments and new email address of S

Symmetry protection of measurement-based quantum computation in ground states

The two-dimensional cluster state, a universal resource for measurement-based quantum computation, is also the gapped ground state of a short-ranged Hamiltonian. Here, we examine the effect of perturbations to this Hamiltonian. We prove that, provided the perturbation is sufficiently small and respects a certain symmetry, the perturbed ground state remains a universal resource. We do this by characterising the operation of an adaptive measurement protocol throughout a suitable symmetry-protected quantum phase, relying on generic properties of the phase rather than any analytic control over the ground state.Comment: 20 pages plus appendices, 11 figures, comments very welcome; v2 minor corrections and additional references; v3 published version with minor correction

Mouse brain proteomics establishes MDGA1 and CACHD1 as in vivo substrates of the Alzheimer protease BACE1

The protease beta-site APP cleaving enzyme 1 (BACE1) has fundamental functions in the nervous system. Its inhibition is a major therapeutic approach in Alzheimer's disease, because BACE1 cleaves the amyloid precursor protein (APP), thereby catalyzing the first step in the generation of the pathogenic amyloid beta (A beta) peptide. Yet, BACE1 cleaves numerous additional membrane proteins besides APP. Most of these substrates have been identified in vitro, but only few were further validated or characterized in vivo. To identify BACE1 substrates with in vivo relevance, we used isotope label-based quantitative proteomics of wild type and BACE1-deficient (BACE1 KO) mouse brains. This approach identified known BACE1 substrates, including Close homolog of L1 and contactin-2, which were found to be enriched in the membrane fraction of BACE1 KO brains. VWFA and cache domain-containing protein 1 (CACHD)1 and MAM domain-containing glycosylphosphatidylinositol anchor protein 1 (MDGA1), which have functions in synaptic transmission, were identified and validated as new BACE1 substrates in vivo by immunoblots using primary neurons and mouse brains. Inhibition or deletion of BACE1 from primary neurons resulted in a pronounced inhibition of substrate cleavage and a concomitant increase in full-length protein levels of CACHD1 and MDGA1. The BACE1 cleavage site in both proteins was determined to be located within the juxtamembrane domain. In summary, this study identifies and validates CACHD1 and MDGA1 as novel in vivo substrates for BACE1, suggesting that cleavage of both proteins may contribute to the numerous functions of BACE1 in the nervous system

Fitness Ranking of Individual Mutants Drives Patterns of Epistatic Interactions in HIV-1

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Distributions of epistasis in microbes fit predictions from a fitness landscape model.

How do the fitness effects of several mutations combine? Despite its simplicity, this question is central to the understanding of multilocus evolution. Epistasis (the interaction between alleles at different loci), especially epistasis for fitness traits such as reproduction and survival, influences evolutionary predictions "almost whenever multilocus genetics matters". Yet very few models have sought to predict epistasis, and none has been empirically tested. Here we show that the distribution of epistasis can be predicted from the distribution of single mutation effects, based on a simple fitness landscape model. We show that this prediction closely matches the empirical measures of epistasis that have been obtained for Escherichia coli and the RNA virus vesicular stomatitis virus. Our results suggest that a simple fitness landscape model may be sufficient to quantitatively capture the complex nature of gene interactions. This model may offer a simple and widely applicable alternative to complex metabolic network models, in particular for making evolutionary predictions

An experimental investigation into the dimensional error of powder-binder three-dimensional printing

This paper is an experimental investigation into the dimensional error of the rapid prototyping additive process of powder-binder three-dimensional printing. Ten replicates of a purpose-designed part were produced using a three-dimensional printer, and measurements of the internal and external features of all surfaces were made using a general purpose coordinate measuring machine. The results reveal that the bases of all replicates (nominally flat) have a concave curvature, producing a flatness error of the primary datum. This is in contrast to findings regarding other three-dimensional printing processes, widely reported in the literature, where a convex curvature was observed. All external surfaces investigated in this study showed positive deviation from nominal values, especially in the z-axis. The z-axis error consisted of a consistent positive cumulative error and a different constant error in different replicates. By compensating for datum surface error, the average total height error of the test parts can be reduced by 25.52 %. All the dimensional errors are hypothesised to be explained by expansion and the subsequent distortion caused by layer interaction during and after the printing process