Improved Hilbert space exploration algorithms for finite temperature calculations

Computing correlation functions in strongly-interacting quantum systems is one of the most important challenges of modern condensed matter theory, due to their importance in the description of many physical observables. Simultaneously, this challenge is one of the most difficult to address, due to the inapplicability of traditional perturbative methods or the few-body limitations of numerical approaches. For special cases, where the model is integrable, methods based on the Bethe Ansatz have succeeded in computing the spectrum and given us analytical expressions for the matrix elements of physically important operators. However, leveraging these results to compute correlation functions generally requires the numerical evaluation of summations over eigenstates. To perform these summations efficiently, Hilbert space exploration algorithms have been developed which has resulted most notably in the ABACUS library. While this performs quite well for correlations on ground states or low-entropy states, the case of high entropy states (most importantly at finite temperatures or after a quantum quench) is more difficult, and leaves room for improvement. In this work, we develop a new Hilbert space exploration algorithm for the Lieb-Liniger model, specially tailored to optimize the computational order on finite-entropy states for correlations of density-related operators.Comment: 32 pages, 9 figure

Statistics of matrix elements of local operators in integrable models

We study the statistics of matrix elements of local operators in the basis of energy eigenstates in a paradigmatic integrable many-particle quantum theory, the Lieb-Liniger model of bosons with repulsive delta-function interaction. Using methods of quantum integrability we determine the scaling of matrix elements with system size. As a consequence of the extensive number of conservation laws the structure of matrix elements is fundamentally different from, and much more intricate than, the predictions of the eigenstate thermalization hypothesis for generic models. We uncover an interesting connection between this structure for local operators in interacting integrable models, and the one for local operators that are not local with respect to the elementary excitations in free theories. We find that typical off-diagonal matrix elements $\langle\boldsymbol{\mu}|O|\boldsymbol{\lambda}\rangle$ in the same macro-state scale as $\exp(-c^{ O}L\ln(L)-LM^{O}_{\boldsymbol{\mu},\boldsymbol{\lambda}})$ where the probability distribution function for $M^{O}_{\boldsymbol{\mu},\boldsymbol{\lambda}}$ are well described by Fr\'echet distributions and $c^{O}$ depends only on macro-state information. In contrast, typical off-diagonal matrix elements between two different macro-states scale as $\exp(-d^{ O}L^2)$, where $d^{O}$ depends only on macro-state information. Diagonal matrix elements depend only on macro-state information up to finite-size corrections.Comment: 30 pages, 40 figure

Some geochemical constraints upon models for the crystallization of the upper critical zone-main zone interval, northwestern Bushveld complex

Ratios between elements Mg, Fe, Co, Cr, Ni, V, and Sc are consistently different in mafic rocks of the upper critical zone, and those above the Bastard unit. Within the 300 m section above the Merensky Reef, 87Sr/86Sr ratios increase from c.0.7063 to c.0.7087, irrespective of rock type. Decoupling of Mg/(Mg + Fe2+) ratios and the Ca contents of plagioclase, and wide variations in the proportions of anorthosite within the Bastard, Merensky, and Merensky Footwall units, are inconsistent with anorthosite formation by simple fractional crystallization of magma batches of limited volume

New approximations for the cone of copositive matrices and its dual

We provide convergent hierarchies for the cone C of copositive matrices and its dual, the cone of completely positive matrices. In both cases the corresponding hierarchy consists of nested spectrahedra and provide outer (resp. inner) approximations for C (resp. for its dual), thus complementing previous inner (resp. outer) approximations for C (for the dual). In particular, both inner and outer approximations have a very simple interpretation. Finally, extension to K-copositivity and K-complete positivity for a closed convex cone K, is straightforward.Comment: 8

Effect of Extending the Original Eligibility Criteria for the CROSS Neoadjuvant Chemoradiotherapy on Toxicity and Survival in Esophageal Cancer

Patients with curable esophageal cancer (EC) who proceed beyond the original Chemoradiotherapy for Oesophageal Cancer Followed by Surgery Study (CROSS) eligibility criteria are also treated with neoadjuvant chemoradiotherapy (nCRT). This study assessed the effect that extending the CROSS eligibility criteria for nCRT has on treatment-related toxicity and overall survival (OS) in EC. The study enrolled 161 patients with locally advanced EC (T1N1-3/T2-4aN0-3/M0) treated with the CROSS schedule followed by esophagectomy. Group 1 consisted of 89 patients who met the CROSS criteria, and group 2 consisted of 72 patients who met the extended eligibility criteria, i.e. a tumor length greater than 8 cm (n = 24), more than 10% weight loss (n = 35), more than 2-4 cm extension in the stomach (n = 21), celiac lymph node metastasis (n = 13), and/or age over 75 years (n = 2). The study assessed the differences in nCRT-associated toxicity [National Cancer Institute's Common Terminology Criteria for Adverse Events (CTCAE) grade3] and 90-day postoperative mortality. Moreover, the prognostic value for OS was assessed with multivariate Cox regression analysis. No difference was found in nCRT-associated toxicity (P = 0.117), postoperative complications (P = 0.783), and 90-day mortality (P = 0.492). The OS differed significantly (P = 0.004), with a median of 37.3 months [95% confidence interval (CI), 10.4-64.2 months] for group 1 and 17.2 months (95% CI 13.8-20.7 months) for group 2. Pathologic N stage (P = 0.023), pathologic T stage (P = 0.043), and group 2 (P = 0.008) were independent prognostic factors for OS. Extension of the CROSS study eligibility criteria for nCRT did not affect nCRT-associated toxicity, postoperative complications, and postoperative mortality, but was prognostic for OS

Integer Polynomial Optimization in Fixed Dimension

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials that are non-negative over the polytope, these sequences of bounds lead to a fully polynomial-time approximation scheme for the optimization problem.Comment: In this revised version we include a stronger complexity bound on our algorithm. Our algorithm is in fact an FPTAS (fully polynomial-time approximation scheme) to maximize a non-negative integer polynomial over the lattice points of a polytop

Biliary tract visualization using near-infrared imaging with indocyanine green during laparoscopic cholecystectomy: results of a systematic review

Contains fulltext : 174508.pdf (publisher's version ) (Open Access)BACKGROUND: Near-infrared imaging with indocyanine green (ICG) has been extensively investigated during laparoscopic cholecystectomy (LC). However, methods vary between studies, especially regarding patient selection, dosage and timing. The aim of this systematic review was to evaluate the potential of the near-infrared imaging technique with ICG to identify biliary structures during LC. METHODS: A comprehensive systematic literature search was performed. Prospective trials examining the use of ICG during LC were included. Primary outcome was biliary tract visualization. Risk of bias was assessed using ROBINS-I. Secondly, a meta-analysis was performed comparing ICG to intraoperative cholangiography (IOC) for identification of biliary structures. GRADE was used to assess the quality of the evidence. RESULTS: Nineteen studies were included. Based upon the pooled data from 13 studies, cystic duct (Lusch et al. in J Endourol 28:261-266, 2014) visualization was 86.5% (95% CI 71.2-96.6%) prior to dissection of Calot's triangle with a 2.5-mg dosage of ICG and 96.5% (95% CI 93.9-98.4%) after dissection. The results were not appreciably different when the dosage was based upon bodyweight. There is moderate quality evidence that the CD is more frequently visualized using ICG than IOC (RR 1.16; 95% CI 1.00-1.35); however, this difference was not statistically significant. CONCLUSION: This systematic review provides equal results for biliary tract visualization with near-infrared imaging with ICG during LC compared to IOC. Near-infrared imaging with ICG has the potential to replace IOC for biliary mapping. However, methods of near-infrared imaging with ICG vary. Future research is necessary for optimization and standardization of the near-infrared ICG technique

p53 autoantibodies in patients with malignant mesothelioma: stability through disease progression

Malignant mesothelioma (MM) generally occurs as a pleural tumour, related to the inhalation of asbestos fibres. It is highly aggressive and largely unresponsive to treatment. The incidence of MM is particularly high in Western Australia because of the extensive blue asbestos mining operations that occurred in the north of the state until 1966. MM is unusual in that mutations in the tumour suppressor gene p53 are rarely observed, whilst over-expression of p53 protein is common. As the level of antibodies directed against p53 is thought to be of prognostic value in some cancers and as MM is known to be immunogenic, we studied a cohort of Western Australian patients to determine the prevalence of anti-p53 antibodies and their value as diagnostic markers or prognostic indicators. 6/88 (7%) of patients had high titres (>2 SD above the mean of controls) of anti-p53 antibodies. There was no correlation between antibody titre and survival. Although 3/38 (8%) of sera obtained from patients exposed to asbestos but prior to a diagnosis of MM contained antibodies, the same proportion of sera obtained from patients exposed to asbestos but who remained disease free also contained antibodies (2/40; 8%). Sera collected sequentially demonstrated a profound temporal stability in the titre of anti-p53 antibodies in patients with MM throughout the course of their illness. These results show that anti-p53 antibodies are observed only at a low frequency in the sera of MM patients and where they do occur, their elicitation is an early event that may be unrelated to antigen load. The occurrence of anti-p53 antibodies does not serve as either a useful prognostic or diagnostic indicator in MM. © 2001 Cancer Research Campaign http://www.bjcancer.co