SBV regularity for Hamilton-Jacobi equations in Rn\mathbb R^n

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$\partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.Comment: 15 page

Power calculation for gravitational radiation: oversimplification and the importance of time scale

A simplified formula for gravitational-radiation power is examined. It is shown to give completely erroneous answers in three situations, making it useless even for rough estimates. It is emphasized that short timescales, as well as fast speeds, make classical approximations to relativistic calculations untenable.Comment: Three pages, no figures, accepted for publication in Astronomische Nachrichte

Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I

We discuss different notions of continuous solutions to the balance law 02tu+ 02x(f(u))=gg bounded,f 08C2 extending previous works relative to the flux f(u)=u2. We establish the equivalence among distributional solutions and a suitable notion of Lagrangian solutions for general smooth fluxes. We eventually find that continuous solutions are Kruzkov iso-entropy solutions, which yields uniqueness for the Cauchy problem. We also reduce the ODE on any characteristics under the sharp assumption that the set of inflection points of the flux f is negligible. The correspondence of the source terms in the two settings is a matter of the companion work [2], where we include counterexamples when the negligibility on inflection points fails

On the structure of phase transition maps for three or more coexisting phases

This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.Comment: 23 pages, 6 figure

On Deciding Local Theory Extensions via E-matching

Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently encountered is that verification problems are often not fully expressible in the theories supported natively by the solvers. Many solvers allow the specification of application-specific theories as quantified axioms, but their handling is incomplete outside of narrow special cases. In this work, we show how SMT solvers can be used to obtain complete decision procedures for local theory extensions, an important class of theories that are decidable using finite instantiation of axioms. We present an algorithm that uses E-matching to generate instances incrementally during the search, significantly reducing the number of generated instances compared to eager instantiation strategies. We have used two SMT solvers to implement this algorithm and conducted an extensive experimental evaluation on benchmarks derived from verification conditions for heap-manipulating programs. We believe that our results are of interest to both the users of SMT solvers as well as their developers

Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant

We here present a high sensitivity gravity-gradiometer based on atom interferometry. In our apparatus, two clouds of laser-cooled rubidium atoms are launched in fountain configuration and interrogated by a Raman interferometry sequence to probe the gradient of gravity field. We recently implemented a high-flux atomic source and a newly designed Raman lasers system in the instrument set-up. We discuss the applications towards a precise determination of the Newtonian gravitational constant G. The long-term stability of the instrument and the signal-to-noise ratio demonstrated here open interesting perspectives for pushing the measurement precision below the 100 ppm level

A mathematical model by route of transmission and fibrosis progression to estimate undiagnosed individuals with HCV in different Italian regions

Background: Although an increase in hepatitis C virus (HCV) prevalence from Northern to Southern Italy has been reported, the burden of asymptomatic individuals in different Italian regions is currently unknown. Methods: A probabilistic approach, including a Markov chain for liver disease progression, was applied to estimate current HCV viraemic burden. The model defined prevalence by geographic area using an estimated annual historical HCV incidence by age, treatment rate, and migration rate from the Italian National database. Viraemic infection by age group was estimated for each region by main HCV transmission routes of individuals for stage F0–F3 (i.e. patients without liver cirrhosis and thus potentially asymptomatic) and F4 (patients with liver cirrhosis, thus potentially symptomatic). Results: By January 2020, it was estimated that there were 409,184 Italian individuals with HCV (prevalence of 0.68%; 95% CI: 0.54–0.82%), of which 300,171 (0.50%; 95% CI: 0.4–0.6%) were stage F0–F3. Considering all individuals with HCV in stage F0–F3, the geographical distributions (expressed as the proportion of HCV infected individuals by macroarea within the overall estimated number of F0–F3 individuals and prevalence values, expressed as the percentage of individuals with HCV versus the overall number of individuals for each macroarea) were as follows: North 42.1% (0.45%; 95% CI: 0.36–0.55%), Central 24.1% (0.61%; 95% CI: 0.48–0.74%), South 23.2% (0.50%; 95% CI: 0.4–0.61%), and the Isles 10.6% (0.49%; 95% CI: 0.39–0.59%). The population of people who inject drugs accounted for 50.4% of all individuals infected (F0–F3). Undiagnosed individuals (F0–F3) were ~ 15 years younger (⁓ 50 years) compared with patients with stage F4 (⁓ 65 years), with similar age distributions across macroareas. In contrast to what has been reported on HCV epidemiology in Italy, an increasing trend in the proportion of potentially undiagnosed individuals with HCV (absolute number within the F0–F3) from South (23.2%) to North (42.1%) emerged, independent of similar regional prevalence values. Conclusion: This targeted approach, which addresses the specific profile of undiagnosed individuals, is helpful in planning effective elimination strategies by region in Italy and could be a useful methodology for other countries in implementing their elimination plans

Functions and Therapeutic Potential of Extracellular Hsp60, Hsp70, and Hsp90 in Neuroinflammatory Disorders

Neuroinflammation is implicated in central nervous system (CNS) diseases, but the molecular mechanisms involved are poorly understood. Progress may be accelerated by developing a comprehensive view of the pathogenesis of CNS disorders, including the immune and the chaperone systems (IS and CS). The latter consists of the molecular chaperones; cochaperones; and chaperone cofactors, interactors, and receptors of an organism and its main collaborators in maintaining protein homeostasis (canonical function) are the ubiquitin-proteasome system and chaperone-mediated autophagy. The CS has also noncanonical functions, for instance, modulation of the IS with induction of proinflammatory cytokines. This deserves investigation because it may be at the core of neuroinflammation, and elucidation of its mechanism will open roads toward developing efficacious treatments centered on molecular chaperones (i.e., chaperonotherapy). Here, we discuss information available on the role of three members of the CS-heat shock protein (Hsp)60, Hsp70, and Hsp90-in IS modulation and neuroinflammation. These three chaperones occur intra- and extracellularly, with the latter being the most likely involved in neuroinflammation because they can interact with the IS. We discuss some of the interactions, their consequences, and the molecules involved but many aspects are still incompletely elucidated, and we hope that this review will encourage research based on the data presented to pave the way for the development of chaperonotherapy. This may consist of blocking a chaperone that promotes destructive neuroinflammation or replacing or boosting a defective chaperone with cytoprotective activity against neurodegeneration

Protocol for a national audit on self-reported confidence levels, training requirements and current practice among trainee doctors in the UK: The Trainees Own Perception of Delivery of Care in Diabetes (TOPDOC) Study

Background: As the incidence and prevalence of diabetes increases across the world, resource pressures require doctors without specialist training to provide care for people with diabetes. In the UK, national standards have been set to ensure quality diabetes care from diagnosis to the management of complications. In a multi-centre pilot study, we have demonstrated a lack of confidence among UK trainee doctors in managing diabetes. Suboptimal confidence was identified in a number of areas, including the management of diabetes emergencies. A national survey would clarify whether the results of our pilot study are representative and reproducible. Methods/Design: Target cohort: All postgraduate trainee doctors in the UK. Domains Studied: The self reported online survey questionnaire has 5 domains: (1) confidence levels in the diagnosis and management of diabetes, (2) working with diabetes specialists, (3) perceived adequacy of training in diabetes (4) current practice in optimising glycaemic control and (5) perceived barriers to seeking euglycaemia. Assessment tools: Self-reported confidence is assessed using the 'Confidence Rating' (CR) scale for trainee doctors developed by the Royal College of Physicians. This scale has four points - ('not confident' (CR1), 'satisfactory but lacking confidence' (CR2), 'confident in some cases (CR3) and 'fully confident in most cases' (CR4). Frequency of aspects of day-to-day practice is assessed using a six-point scale. Respondents have a choice of 'always' (100%), 'almost always' (80-99%), 'often' (50-79%), 'not very often' (20-49%) and 'rarely' (5-19%) or never (less than 5%). Discussion: It is anticipated that the results of this national study will clarify confidence levels and current practice among trainee doctors in the provision of care for people with diabetes. The responses will inform efforts to enhance postgraduate training in diabetes, potentially improving the quality of care for people with diabetes.</p