Automated microstructural analysis of titanium alloys using digital image processing

Titanium is a material that exhibits many desirable properties including a very high strength to weight ratio and corrosive resistance. However, the specific properties of any components depend upon the microstructure of the material, which varies by the manufacturing process. This means it is often necessary to analyse the microstructure when designing new processes or performing quality assurance on manufactured parts. For Ti6Al4V, grain size analysis is typically performed manually by expert material scientists as the complicated microstructure of the material means that, to the authors knowledge, no existing software reliably identifies the grain boundaries. This manual process is time consuming and offers low repeatability due to human error and subjectivity. In this paper, we propose a new, automated method to segment microstructural images of a Ti6Al4V alloy into its constituent grains and produce measurements. The results of applying this technique are evaluated by comparing the measurements obtained by different analysis methods. By using measurements from a complete manual segmentation as a benchmark we explore the reliability of the current manual estimations of grain size and contrast this with improvements offered by our approach

Interplay between Symmetric Exchange Anisotropy, Uniform Dzyaloshinskii-Moriya Interaction and Magnetic Fields in the Phase Diagram of Quantum Magnets and Superconductors

We theoretically study the joint influence of uniform Dzyaloshinskii-Moriya (DM) interactions, symmetric exchange anisotropy (with its axis parallel to the DM vector) and arbitrarily oriented magnetic fields on one-dimensional spin 1/2 antiferromagnets. We show that the zero-temperature phase diagram contains three competing phases: (i) an antiferromagnet with Neel vector in the plane spanned by the DM vector and the magnetic field, (ii) a {\em dimerized} antiferromagnet with Neel vector perpendicular to both the DM vector and the magnetic field, and (iii) a gapless Luttinger liquid. Phase (i) is destroyed by a small magnetic field component along the DM vector and is furthermore unstable beyond a critical value of easy-plane anisotropy, which we estimate using Abelian and non-Abelian bosonization along with perturbative renormalization group. We propose a mathematical equivalent of the spin model in a one-dimensional Josephson junction (JJ) array located in proximity to a bulk superconductor. We discuss the analogues of the magnetic phases in the superconducting context and comment on their experimental viability.Comment: 20 pages, 16 figures; submitted to Phys. Rev.

Bicrossed products for finite groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor

Multiple verification in computational modeling of bone pathologies

We introduce a model checking approach to diagnose the emerging of bone pathologies. The implementation of a new model of bone remodeling in PRISM has led to an interesting characterization of osteoporosis as a defective bone remodeling dynamics with respect to other bone pathologies. Our approach allows to derive three types of model checking-based diagnostic estimators. The first diagnostic measure focuses on the level of bone mineral density, which is currently used in medical practice. In addition, we have introduced a novel diagnostic estimator which uses the full patient clinical record, here simulated using the modeling framework. This estimator detects rapid (months) negative changes in bone mineral density. Independently of the actual bone mineral density, when the decrease occurs rapidly it is important to alarm the patient and monitor him/her more closely to detect insurgence of other bone co-morbidities. A third estimator takes into account the variance of the bone density, which could address the investigation of metabolic syndromes, diabetes and cancer. Our implementation could make use of different logical combinations of these statistical estimators and could incorporate other biomarkers for other systemic co-morbidities (for example diabetes and thalassemia). We are delighted to report that the combination of stochastic modeling with formal methods motivate new diagnostic framework for complex pathologies. In particular our approach takes into consideration important properties of biosystems such as multiscale and self-adaptiveness. The multi-diagnosis could be further expanded, inching towards the complexity of human diseases. Finally, we briefly introduce self-adaptiveness in formal methods which is a key property in the regulative mechanisms of biological systems and well known in other mathematical and engineering areas.Comment: In Proceedings CompMod 2011, arXiv:1109.104

Random matrix techniques in quantum information theory

The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review, combined with more detailed examples -- coming from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels

The Hopf modules category and the Hopf equation

We study the Hopf equation which is equivalent to the pentagonal equation, from operator algebras. A FRT type theorem is given and new types of quantum groups are constructed. The key role is played now by the classical Hopf modules category. As an application, a five dimensional noncommutative noncocommutative bialgebra is given.Comment: 30 pages, Letax2e, Comm. Algebra in pres

Debatable results of surgery for lung cancer in a patient with long existing pulmonary metastases from differentiated thyroid carcinoma

Introduction: The appropriate following treatment in a patient with a new presented non-small cell lung cancer (NSCLC) and history of chronic lung metastases of thyroid origin has never been reported. In such cases, the presence of long­standing thyroid metastatic disease with proven “limited malignant potential” could be considered as a minor treatment problem justifying one’s the decision to focus on the primary lung carcinoma as the only serious threat for the patient’s life.Case report: We report the surgical treatment of a new presented NSCLC in a patient with chronic lung metastases of thyroid origin and we present all the diagnostic, staging and treatment problems.Conclusion: The therapeutic results of our surgical approach were not encouraging. This could be owed to our staging prob­lems of NSCLC and the well documented limited immunological response of such patients with multiple neoplasms

Evolutionary Events in a Mathematical Sciences Research Collaboration Network

This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this study traces the evolution of the "here and now" using fixed-duration sliding windows. The analysis uses a suite of common network diagnostics, including the distributions of degrees, distances, and clustering, to track network structure. Several random models that call these diagnostics as parameters help tease them apart as factors from the values of others. Some behaviors are consistent over the entire interval, but most diagnostics indicate that the network's structural evolution is dominated by occasional dramatic shifts in otherwise steady trends. These behaviors are not distributed evenly across the network; stark differences in evolution can be observed between two major subnetworks, loosely thought of as "pure" and "applied", which approximately partition the aggregate. The paper characterizes two major events along the mathematics network trajectory and discusses possible explanatory factors.Comment: 30 pages, 14 figures, 1 table; supporting information: 5 pages, 5 figures; published in Scientometric