On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

Properties of dense partially random graphs

We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small World Graphs (SWGs). But we consider the case where the average degree of each node is of order of the size of the graph (unlike SWGs, which are sparse). This allows us to calculate the mean distance and clustering, that are qualitatively similar (although not in such a dramatic scale range) to the case of SWGs. We also obtain analytically the distribution of eigenvalues of the corresponding adjacency matrices. This distribution is discrete for large eigenvalues and continuous for small eigenvalues. The continuous part of the distribution follows a semicircle law, whose width is proportional to the "disorder" of the graph, whereas the discrete part is simply a rescaling of the spectrum of the substrate. We apply our results to the calculation of the mixing rate and the synchronizability threshold.Comment: 14 pages. To be published in Physical Review

Development of a Framework Structuring Themes in the Course of Adverse Drug Reactions from a Patient's Perspective

INTRODUCTION: There is a need for more extensive information about adverse drug reactions (ADRs) for patients than currently available, including information on the course of ADRs. Aspects characterising the course of ADRs from the patient perspective have not been identified before.OBJECTIVE: We aimed to develop a framework based on common themes in the course of ADRs identified from patient descriptions in patient-reported ADRs.METHODS: In this qualitative study, patient descriptions of the course of patient-reported ADRs were analysed by a thematic analysis with an inductive approach using three different existing datasets containing patient-reported ADRs. Two datasets included patient-reported ADRs from cohort event monitoring of biologics and direct oral anticoagulants and one dataset included spontaneous reports from patients concerning medication for lower urinary tract symptoms. A conceptual framework was developed from the identified main themes and subthemes.RESULTS: Patient-reported data concerning 3888 ADRs were analysed. Six main themes with multiple subthemes were identified from patient descriptions of the course of ADRs. Four themes were descriptive: frequency of an ADR episode, duration of an ADR episode, moment or period of ADR occurrence, and development in the intensity of the ADR. Two themes concerned factors influencing the course of ADRs: triggering factors and improving factors.CONCLUSIONS: The presented framework illustrates that patients describe extensive details on the course and timeframe of ADRs. The identified themes provide a basis for improving the systematic data collection of more extensive details about ADRs from patients as a first step towards the provision of more comprehensive ADR information to patients.</p

Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case

Let $p$ be a prime number, $q=p^f$ for some positive integer $f$, $N$ be a positive integer such that $\gcd(N,p)=1$, and let \k be a primitive multiplicative character of order $N$ over finite field \fq. This paper studies the problem of explicit evaluation of Gauss sums in "\textsl{index 2 case}" (i.e. f=\f{\p(N)}{2}=[\zn:\pp], where \p(\cd) is Euler function). Firstly, the classification of the Gauss sums in index 2 case is presented. Then, the explicit evaluation of Gauss sums G(\k^\la) (1\laN-1) in index 2 case with order $N$ being general even integer (i.e. N=2^{r}\cd N_0 where $r,N_0$ are positive integers and $N_03$ is odd.) is obtained. Thus, the problem of explicit evaluation of Gauss sums in index 2 case is completely solved

On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date

Signal and noise of Diamond Pixel Detectors at High Radiation Fluences

CVD diamond is an attractive material option for LHC vertex detectors because of its strong radiation-hardness causal to its large band gap and strong lattice. In particular, pixel detectors operating close to the interaction point profit from tiny leakage currents and small pixel capacitances of diamond resulting in low noise figures when compared to silicon. On the other hand, the charge signal from traversing high energy particles is smaller in diamond than in silicon by a factor of about 2.2. Therefore, a quantitative determination of the signal-to-noise ratio (S/N) of diamond in comparison with silicon at fluences in excess of 10$^{15}$ n$_{eq}$ cm$^{-2}$, which are expected for the LHC upgrade, is important. Based on measurements of irradiated diamond sensors and the FE-I4 pixel readout chip design, we determine the signal and the noise of diamond pixel detectors irradiated with high particle fluences. To characterize the effect of the radiation damage on the materials and the signal decrease, the change of the mean free path $\lambda_{e/h}$ of the charge carriers is determined as a function of irradiation fluence. We make use of the FE-I4 pixel chip developed for ATLAS upgrades to realistically estimate the expected noise figures: the expected leakage current at a given fluence is taken from calibrated calculations and the pixel capacitance is measured using a purposely developed chip (PixCap). We compare the resulting S/N figures with those for planar silicon pixel detectors using published charge loss measurements and the same extrapolation methods as for diamond. It is shown that the expected S/N of a diamond pixel detector with pixel pitches typical for LHC, exceeds that of planar silicon pixels at fluences beyond 10$^{15}$ particles cm$^{-2}$, the exact value only depending on the maximum operation voltage assumed for irradiated silicon pixel detectors

A revised day +7 predictive score for transplant-related mortality: serum cholinesterase, total protein, blood urea nitrogen, γ glutamyl transferase, donor type and cell dose

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