Ab initio study of the vapour-liquid critical point of a symmetrical binary fluid mixture

A microscopic approach to the investigation of the behaviour of a symmetrical binary fluid mixture in the vicinity of the vapour-liquid critical point is proposed. It is shown that the problem can be reduced to the calculation of the partition function of a 3D Ising model in an external field. For a square-well symmetrical binary mixture we calculate the parameters of the critical point as functions of the microscopic parameter r measuring the relative strength of interactions between the particles of dissimilar and similar species. The calculations are performed at intermediate ($\lambda=1.5$) and moderately long ($\lambda=2.0$) intermolecular potential ranges. The obtained results agree well with the ones of computer simulations.Comment: 14 pages, Latex2e, 5 eps-figures included, submitted to J.Phys:Cond.Ma

The importance of early arthroscopy in athletes with painful cartilage lesions of the ankle: a prospective study of 61 consecutive cases

BACKGROUND Ankle sprains are common in sports and can sometimes result in a persistent pain condition. PURPOSE Primarily to evaluate clinical symptoms, signs, diagnostics and outcomes of surgery for symptomatic chondral injuries of the talo crural joint in athletes. Secondly, in applicable cases, to evaluate the accuracy of MRI in detecting these injuries. Type of study: Prospective consecutive series. METHODS Over around 4 years we studied 61 consecutive athletes with symptomatic chondral lesions to the talocrural joint causing persistent exertion ankle pain. RESULTS 43% were professional full time athletes and 67% were semi-professional, elite or amateur athletes, main sports being soccer (49%) and rugby (14%). The main subjective complaint was exertion ankle pain (93%). Effusion (75%) and joint line tenderness on palpation (92%) were the most common clinical findings. The duration from injury to arthroscopy for 58/61 cases was 7 months (5.7–7.9). 3/61 cases were referred within 3 weeks from injury. There were in total 75 cartilage lesions. Of these, 52 were located on the Talus dome, 17 on the medial malleolus and 6 on the Tibia plafond. Of the Talus dome injuries 18 were anteromedial, 14 anterolateral, 9 posteromedial, 3 posterolateral and 8 affecting mid talus. 50% were grade 4 lesions, 13.3% grade 3, 16.7% grade 2 and 20% grade 1. MRI had been performed pre operatively in 26/61 (39%) and 59% of these had been interpreted as normal. Detection rate of cartilage lesions was only 19%, but subchondral oedema was present in 55%. At clinical follow up average 24 months after surgery (10–48 months), 73% were playing at pre-injury level. The average return to that level of sports after surgery was 16 weeks (3–32 weeks). However 43% still suffered minor symptoms. CONCLUSION Arthroscopy should be considered early when an athlete presents with exertion ankle pain, effusion and joint line tenderness on palpation after a previous sprain. Conventional MRI is not reliable for detecting isolated cartilage lesions, but the presence of subchondral oedema should raise such suspicion

Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators

Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition. First, we show that a low-rank density matrix can be estimated using fewer copies of the state, i.e., the sample complexity of tomography decreases with the rank. Second, we show that unknown low-rank states can be reconstructed from an incomplete set of measurements, using techniques from compressed sensing and matrix completion. These techniques use simple Pauli measurements, and their output can be certified without making any assumptions about the unknown state. We give a new theoretical analysis of compressed tomography, based on the restricted isometry property (RIP) for low-rank matrices. Using these tools, we obtain near-optimal error bounds, for the realistic situation where the data contains noise due to finite statistics, and the density matrix is full-rank with decaying eigenvalues. We also obtain upper-bounds on the sample complexity of compressed tomography, and almost-matching lower bounds on the sample complexity of any procedure using adaptive sequences of Pauli measurements. Using numerical simulations, we compare the performance of two compressed sensing estimators with standard maximum-likelihood estimation (MLE). We find that, given comparable experimental resources, the compressed sensing estimators consistently produce higher-fidelity state reconstructions than MLE. In addition, the use of an incomplete set of measurements leads to faster classical processing with no loss of accuracy. Finally, we show how to certify the accuracy of a low rank estimate using direct fidelity estimation and we describe a method for compressed quantum process tomography that works for processes with small Kraus rank.Comment: 16 pages, 3 figures. Matlab code included with the source file

The Convex Geometry of Linear Inverse Problems

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems. The class of simple models considered are those formed as the sum of a few atoms from some (possibly infinite) elementary atomic set; examples include well-studied cases such as sparse vectors and low-rank matrices, as well as several others including sums of a few permutations matrices, low-rank tensors, orthogonal matrices, and atomic measures. The convex programming formulation is based on minimizing the norm induced by the convex hull of the atomic set; this norm is referred to as the atomic norm. The facial structure of the atomic norm ball carries a number of favorable properties that are useful for recovering simple models, and an analysis of the underlying convex geometry provides sharp estimates of the number of generic measurements required for exact and robust recovery of models from partial information. These estimates are based on computing the Gaussian widths of tangent cones to the atomic norm ball. When the atomic set has algebraic structure the resulting optimization problems can be solved or approximated via semidefinite programming. The quality of these approximations affects the number of measurements required for recovery. Thus this work extends the catalog of simple models that can be recovered from limited linear information via tractable convex programming

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Understanding the Origins of Bacterial Resistance to Aminoglycosides through Molecular Dynamics Mutational Study of the Ribosomal A-Site

Paromomycin is an aminoglycosidic antibiotic that targets the RNA of the bacterial small ribosomal subunit. It binds in the A-site, which is one of the three tRNA binding sites, and affects translational fidelity by stabilizing two adenines (A1492 and A1493) in the flipped-out state. Experiments have shown that various mutations in the A-site result in bacterial resistance to aminoglycosides. In this study, we performed multiple molecular dynamics simulations of the mutated A-site RNA fragment in explicit solvent to analyze changes in the physicochemical features of the A-site that were introduced by substitutions of specific bases. The simulations were conducted for free RNA and in complex with paromomycin. We found that the specific mutations affect the shape and dynamics of the binding cleft as well as significantly alter its electrostatic properties. The most pronounced changes were observed in the U1406C∶U1495A mutant, where important hydrogen bonds between the RNA and paromomycin were disrupted. The present study aims to clarify the underlying physicochemical mechanisms of bacterial resistance to aminoglycosides due to target mutations

Recurrence dynamics does not depend on the recurrence site

Introduction: The dynamics of breast cancer recurrence and death, indicating a bimodal hazard rate pattern, has been confirmed in various databases. A few explanations have been suggested to help interpret this finding, assuming that each peak is generated by clustering of similar recurrences and different peaks result from distinct categories of recurrence. Methods: The recurrence dynamics was analysed in a series of 1526 patients undergoing conservative surgery at the National Cancer Institute of Milan, Italy, for whom the site of first recurrence was recorded. The study was focused on the first clinically relevant event occurring during the follow up (ie, local recurrence, distant metastasis, contralateral breast cancer, second primary tumour), the dynamics of which was studied by estimating the specific hazard rate.Results The hazard rate for any recurrence (including both local and distant disease relapses) displayed a bimodal pattern with a first surge peaking at about 24 months and a second peak at almost 60 months. The same pattern was observed when the whole recurrence risk was split into the risk of local recurrence and the risk of distant metastasis. However, the hazard rate curves for both contralateral breast tumours and second primary tumours revealed a uniform course at an almost constant level. When patients with distant metastases were grouped by site of recurrence (soft tissue, bone, lung or liver or central nervous system), the corresponding hazard rate curves displayed the typical bimodal pattern with a first peak at about 24 months and a later peak at about 60 months.Conclusions The bimodal dynamics for early stage breast cancer recurrence is again confirmed, providing support to the proposed tumour-dormancy-based model. The recurrence dynamics does not depend on the site of metastasis indicating that the timing of recurrences is generated by factors influencing the metastatic development regardless of the seeded organ. This finding supports the view that the disease course after surgical removal of the primary tumour follows a common pathway with well-defined steps and that the recurrence risk pattern results from inherent features of the metastasis development process, which are apparently attributable to tumour cells

A Computational Framework for Influenza Antigenic Cartography

Influenza viruses have been responsible for large losses of lives around the world and continue to present a great public health challenge. Antigenic characterization based on hemagglutination inhibition (HI) assay is one of the routine procedures for influenza vaccine strain selection. However, HI assay is only a crude experiment reflecting the antigenic correlations among testing antigens (viruses) and reference antisera (antibodies). Moreover, antigenic characterization is usually based on more than one HI dataset. The combination of multiple datasets results in an incomplete HI matrix with many unobserved entries. This paper proposes a new computational framework for constructing an influenza antigenic cartography from this incomplete matrix, which we refer to as Matrix Completion-Multidimensional Scaling (MC-MDS). In this approach, we first reconstruct the HI matrices with viruses and antibodies using low-rank matrix completion, and then generate the two-dimensional antigenic cartography using multidimensional scaling. Moreover, for influenza HI tables with herd immunity effect (such as those from Human influenza viruses), we propose a temporal model to reduce the inherent temporal bias of HI tables caused by herd immunity. By applying our method in HI datasets containing H3N2 influenza A viruses isolated from 1968 to 2003, we identified eleven clusters of antigenic variants, representing all major antigenic drift events in these 36 years. Our results showed that both the completed HI matrix and the antigenic cartography obtained via MC-MDS are useful in identifying influenza antigenic variants and thus can be used to facilitate influenza vaccine strain selection. The webserver is available at http://sysbio.cvm.msstate.edu/AntigenMap

Assessment of therapeutic responses to gametocytocidal drugs in Plasmodium falciparum malaria.

Indirect clinical measures assessing anti-malarial drug transmission-blocking activity in falciparum malaria include measurement of the duration of gametocytaemia, the rate of gametocyte clearance or the area under the gametocytaemia-time curve (AUC). These may provide useful comparative information, but they underestimate dose-response relationships for transmission-blocking activity. Following 8-aminoquinoline administration P. falciparum gametocytes are sterilized within hours, whereas clearance from blood takes days. Gametocytaemia AUC and clearance times are determined predominantly by the more numerous female gametocytes, which are generally less drug sensitive than the minority male gametocytes, whereas transmission-blocking activity and thus infectivity is determined by the more sensitive male forms. In choosing doses of transmission-blocking drugs there is no substitute yet for mosquito-feeding studies