Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians

A key feature of ground states of gapped local 1D Hamiltonians is their relatively low entanglement --- they are well approximated by matrix product states (MPS) with bond dimension scaling polynomially in the length $N$ of the chain, while general states require a bond dimension scaling exponentially. We show that the bond dimension of these MPS approximations can be improved to a constant, independent of the chain length, if we relax our notion of approximation to be more local: for all length-$k$ segments of the chain, the reduced density matrices of our approximations are $\epsilon$-close to those of the exact state. If the state is a ground state of a gapped local Hamiltonian, the bond dimension of the approximation scales like $(k/\epsilon)^{1+o(1)}$, and at the expense of worse but still $\text{poly}(k,1/\epsilon)$ scaling of the bond dimension, we give an alternate construction with the additional features that it can be generated by a constant-depth quantum circuit with nearest-neighbor gates, and that it applies generally for any state with exponentially decaying correlations. For a completely general state, we give an approximation with bond dimension $\exp(O(k/\epsilon))$, which is exponentially worse, but still independent of $N$. Then, we consider the prospect of designing an algorithm to find a local approximation for ground states of gapped local 1D Hamiltonians. When the Hamiltonian is translationally invariant, we show that the ability to find $O(1)$-accurate local approximations to the ground state in $T(N)$ time implies the ability to estimate the ground state energy to $O(1)$ precision in $O(T(N)\log(N))$ time.Comment: 24 pages, 3 figures. v2: Theorem 1 extended to include construction for general states; Lemma 7 & Theorem 2 slightly improved; figures added; lemmas rearranged for clarity; typos fixed. v3: Reformatted & additional references inserte

Genotypic Effects on Condensed Tannins in the Leucaena Genus

One hundred and eighteen accessions of the Leucaena genus were assayed for extractable and bound condensed tannins (CT). Leucaena taxa varied from low or no CT (0-1%) to extremely high levels (\u3e15%). There was considerable intraspecific variation in CT within key taxa. The proportion of bound tannin decreased with increasing total CT content

A Revised Method of Condensed Tannin Analysis in Leucaena spp.

The proanthocyanidin (butanol-HCl) assay was used to measure condensed tannin (CT) in extracts from Leucaena spp. at the University of Queensland. Inconsistent results were found to be caused by the iron catalyst in the butanol/HCl reagent and the presence of ascorbic acid in the sample matrix which enhanced anthocyanidin development. In addition, preparation of sample extracts by back extraction with organic solvents reduced CT recoveries. An accurate and rapid technique was developed that measures CT directly in 70% aqueous acetone 0.1% (w/v) sodium metabisulphite plant extracts

Peripartum cardiomyopathy: diagnosis and management

No abstract available

Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end

We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local constraint satisfaction problems ($k$-CSP). We show that either (a) the algorithm finds the optimal solution in time $O^*(2^{(0.5-c)n})$ for an $n$-independent constant $c$, a $2^{cn}$ advantage over Grover's algorithm; or (b) there are sufficiently many low-cost solutions such that classical random guessing produces a $(1-\eta)$ approximation to the optimal cost value in sub-exponential time for arbitrarily small choice of $\eta$. Additionally, we show that for a large fraction of random instances from the $k$-spin model and for any fully satisfiable or slightly frustrated $k$-CSP formula, statement (a) is the case. The algorithm and its analysis is largely inspired by Hastings' short-path algorithm [$\textit{Quantum}$ $\textbf{2}$ (2018) 78].Comment: 49 pages, 3 figure

Root canal instrumentation efficacy of non-fused and fused primary molar roots:a micro-computed tomography study

Purpose Pulpectomy may be indicated in restorable primary teeth exhibiting irreversible pulpitis or pulpal necrosis. The purpose of this study was to compare the cleaning and shaping efficacy of NiTi systems (Reciproc(R) Blue and MTwo(R)) with manual stainless-steel instrumentation in primary molars using micro-CT analysis. Methods Fifty-seven maxillary second primary molars were scanned using micro-CT. Teeth with three divergent roots were divided randomly (n = 15) according to instrument type (K file, MTwo (R), and Reciproc (R) Blue). Teeth with root fusion were instrumented manually as a separate group (n = 12). Pre- and post-instrumentation micro-CT images were superimposed, and the instrumentation area (IA) and procedural complications were recorded. Results No statistically significant differences in IA between file systems was observed in the non-fused teeth. The mean IA of fused roots was significantly lower than in the non-fused distobuccal (p = 0.003) and palatal (p 60%) occurred in both non-fused and fused primary teeth with fewer procedural complications observed after manual instrumentation

Cross Sectional Associations between Socio-Demographic Factors and Cognitive Performance in an Older British Population: The European Investigation of Cancer in Norfolk (EPIC-Norfolk) Study

$\textbf{BACKGROUND}$: Cognition covers a range of abilities, such as memory, response time and language, with tests assessing either specific or generic aspects. However differences between measures may be observed within the same individuals. $\textbf{OBJECTIVE}$: To investigate the cross-sectional association of cognitive performance and socio-demographic factors using different assessment tools across a range of abilities in a British cohort study. $\textbf{METHODS}$: Participants of the European Prospective Investigation of Cancer (EPIC) in Norfolk Study, aged 48-92 years, underwent a cognitive assessment between 2006 and 2011 (piloted between 2004 and 2006) and were investigated over a different domains using a range of cognitive tests. $\textbf{RESULTS}$: Cognitive measures were available on 8584 men and women. Though age, sex, education and social class were all independently associated with cognitive performance in multivariable analysis, different associations were observed for different cognitive tests. Increasing age was associated with increased risk of a poor performance score in all of the tests, except for the National Adult Reading Test (NART), an assessment of crystallized intelligence. Compared to women, men were more likely to have had poor performance for verbal episodic memory, Odds Ratio, OR = 1.99 (95% Confidence Interval, 95% CI 1.72, 2.31), attention OR = 1.62, (95% CI 1.39, 1.88) and prospective memory OR = 1.46, (95% CI 1.29, 1.64); however, no sex difference was observed for global cognition, OR = 1.07 (95%CI 0.93, 1.24). The association with education was strongest for NART, and weakest for processing speed. $\textbf{CONCLUSION}$: Age, sex, education and social class were all independently associated with performance on cognitive tests assessing a range of different domains. However, the magnitude of associations of these factors with different cognitive tests differed. The varying relationships seen across different tests may help explain discrepancies in results reported in the current literature, and provides insights into influences on cognitive performance in later life.The infrastructure for this study was supported by the Medical Research Council, UK http://www.mrc.ac.uk/ (Ref: G0401527) and Cancer Research UK http://www.cancerresearchuk.org/ (CRUK, Ref: C864/A8257). The clinic for EPIC-Norfolk 3 was funded by Research into Ageing, now known as Age UK http://www.ageuk.org.uk/ (Grant Ref: 262). The pilot phase was supported by MRC (Ref: G9502233) and CRUK (Ref: C864/A2883). KK received the above funding. FEM Is supported by MRC (Ref: U105292687)

The Efficacy of \u3cem\u3ein vitro Synergistes jonesii\u3c/em\u3e Inoculum in Preventing DHP Toxicity in Steers Fed Leucaena-Grass Diets

Leucaena leucocephala (leucaena) is a valuable forage tree legume for tropical animal production that contains the toxin mimosine. The breakdown products of mimosine in ruminants (3,4-DHP and 2,3-DHP) can adversely affect their health and limit weight gains (Jones and Hegarty 1984). The rumen bacterium Synergistes jonesii, introduced into Australia in 1983 was shown to completely and rapidly degrade these toxins to safe levels (Jones and Megarrity 1986). Since 1996, an in vitro produced inoculum has been made commercially available to Australian graziers (Klieve et al. 2002). Accordingly, the issue of leucaena toxicity in Australia was thought to be resolved. However, extensive testing in 2004 found that up to 50% of Queensland cattle herds consuming leucaena were excreting high levels of urinary DHP suggesting sub-clinical toxicity remained an issue for graziers (Dalzell et al. 2012). Some of these herds had previously been inoculated with in vitro S. jonesii suggesting the inoculum may not be able to either persist within a herd, or remain effective in degrading DHP. The aim of this study was to assess the capability of the in vitro S. jonesii inoculum to efficiently break down DHP in a controlled feeding trial environment