The D2-triangulation for simplicial homotopy algorithms for computing solutions of nonlinear equations

Nonlinear Equations

The D2-triangulation for continuous deformation algorithms to compute solutions of nonlinear equations

Topology

The D1-triangulation in simplicial variable dimension algorithms for computing solutions of nonlinear equations

Nonlinear Equations

A homotopy approach to the computation of economic equilibria on the unit simplex

Equilibrium Theory

Optimising Matrix Product State Simulations of Shor's Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.Comment: 8 pages, 2 figures, 2 tables. v2 using PDFLaTeX compiler. v3 to include extra references. v4 for publication in Quantu

Effects of aluminum on hydrogen solubility and diffusion in deformed Fe-Mn alloys

We discuss hydrogen diffusion and solubility in aluminum alloyed Fe-Mn alloys. The systems of interest are subjected to tetragonal and isotropic deformations. Based on ab initio modelling, we calculate solution energies, then employ Oriani's theory which reflects the influence of Al alloying via trap site diffusion. This local equilibrium model is complemented by qualitative considerations of Einstein diffusion. Therefore, we apply the climbing image nudged elastic band method to compute the minimum energy paths and energy barriers for hydrogen diffusion. Both for diffusivity and solubility of hydrogen, we find that the influence of the substitutional Al atom has both local chemical and nonlocal volumetric contributions.Comment: 9 page

Brown muscle disease and Manila clam Ruditapes Philippinarum dynamics in Arcachon Bay, France

Brown Muscle Disease (BMD) affects Manila clam Ruditapes philippinarum. It was described for the first time in 2005 in Arcachon Bay, France. The pathology consists in a progressive necrosis of the posterior adductor muscle, valve gaping, clam migration to the sediment surface, and death. This study aims to quantify the prevalence of BMD in the bay and to evaluate the effect of BMD on Manila clam dynamics. The prevalence was assessed on 50 stations spread within Arcachon Bay. About 62% of Manila clam habitat surface was infected by BMD. A survey of buried and surface clams was conducted from November 2006 to March 2008 in Lanton, a site infected by BMD. Modal progression analysis separated confidently cohorts from 2003 to 2005 recruitments. This pathology only affected adult clams (>25 mm, >2 years). For both buried and surface individuals, shell length was significantly correlated with BMD infection. Surface clams had prevalence (67%) higher than buried clams (23%) and showed greater mortality rate after 15 d in running water: 82% against 12% for buried individuals. The final disease index (FDI) and the condition index (CI) were monthly evaluated on 50 clams located at each position in the sediment. CI displayed a significant decrease after BMD's infection from light to severe disease stages. Length data analysis through Bhattacharya's method (FISAT II software) allowed identifying four cohorts. The 2003s cohort enabled to calculate mortality rate that was 39% for 5 months and to estimate that BMD was responsible of 95% of that mortality. The temperature was certainly an important factor in BMD transmission, because cohort dynamics results argued that BMD developed during spring and summer