Painlev\'e I and exact WKB: Stokes phenomenon for two-parameter transseries

For more than a century, the Painlev\'e I equation has played an important role in both physics and mathematics. Its two-parameter family of solutions was studied in many different ways, yet still leads to new surprises and discoveries. Two popular tools in these studies are the theory of isomonodromic deformation that uses the exact WKB method, and the asymptotic description of transcendents in terms of two-parameter transseries. Combining methods from both schools of thought, and following work by Takei and collaborators, we find complete, two-parameter connection formulae for solutions when they cross arbitrary Stokes lines in the complex plane. These formulae allow us to study Stokes phenomenon for the full two-parameter family of transseries solutions. In particular, we recover the exact expressions for the Stokes data that were recently found by Baldino, Schwick, Schiappa and Vega and compare our connection formulae to theirs. We also explain several ambiguities in relating transseries parameter choices to actual Painlev\'e transcendents, study the monodromy of formal solutions, and provide high-precision numerical tests of our results.Comment: 71 pages, 16 figures, 5 tables and 4 appendices. v2: Minor changes (rewrites, typos, added references

Verification of the busy-forbidden protocol (using an extension of the cones and foci framework)

The busy-forbidden protocol is a new readers-writer lock with no resource contention between readers, which allows it to outperform other locks. For its verification, specifications of its implementation and its less complex external behavior are provided by the original authors but are only proven equivalent for up to 7 threads. We provide a general proof using the cones and foci proof framework, which rephrases whether two specifications are branching bisimilar in terms of proof obligations on relations between the data objects occurring in the implementation and specification. We provide an extension of this framework consisting of three additional properties on data objects, When these three additional properties also hold, the two systems are divergence-preserving branching bisimilar, a stronger version of the aforementioned relation that also distinguishes livelock. We prove this extension to be sound and use it to give a general equivalence proof for the busy-forbidden protocol

The Best of Both Worlds: Model-Driven Engineering Meets Model-Based Testing

We study the connection between stable-failures refinement and the ioco conformance relation. Both behavioural relations underlie methodologies that have gained traction in industry: stable-failures refinement is used in several commercial Model-Driven Engineering tool suites, whereas the ioco conformance relation is used in Model-Based Testing tools. Refinement-based Model-Driven Engineering approaches promise to generate executable code from high-level models, thus guaranteeing that the code upholds specified behavioural contracts. Manual testing, however, is still required to gain confidence that the model-to-code transformation and the execution platform do not lead to unexpected contract violations. We identify conditions under which also this last step in the design methodology can be automated using the ioco conformance relation and the associated tools

PMP22 related neuropathies: Charcot-Marie-Tooth disease type 1A and Hereditary Neuropathy with liability to Pressure Palsies

PMP22 related neuropathies comprise (1) PMP22 duplications leading to Charcot-Marie-Tooth disease type 1A (CMT1A), (2) PMP22 deletions, leading to Hereditary Neuropathy with liability to Pressure Palsies (HNPP), and (3) PMP22 point mutations, causing both phenotypes. Overall prevalence of CMT is usually reported as 1:2,500, epidemiological studies show that 20-64% of CMT patients carry the PMP22 duplication. The prevalence of HNPP is not well known. CMT1A usually presents in the first two decades with difficulty walking or running. Distal symmetrical muscle weakness and wasting and sensory loss is present, legs more frequently and more severely affected than arms. HNPP typically leads to episodic, painless, recurrent, focal motor and sensory peripheral neuropathy, preceded by minor compression on the affected nerve. Electrophysiological evaluation is needed to determine whether the polyneuropathy is demyelinating. Sonography of the nerves can be useful. Diagnosis is confirmed by finding respectively a PMP22 duplication, deletion or point mutation. Differential diagnosis includes other inherited neuropathies, and acquired polyneuropathies. The mode of inheritance is autosomal dominant and de novo mutations occur. Offspring of patients have a chance of 50% to inherit the mutation from their affected parent. Prenatal testing is possible; requests for prenatal testing are not common. Treatment is currently symptomatic and may include management by a rehabilitation physician, physiotherapist, occupational therapist and orthopaedic surgeon. Adult CMT1A patients show slow clinical progression of disease, which seems to reflect a process of normal ageing. Life expectancy is norma

Peripartum Cardiomyopathy as a Part of Familial Dilated Cardiomyopathy

BACKGROUND-: Anecdotal cases of familial clustering of peripartum cardiomyopathy (PPCM) and familial occurrences of PPCM and idiopathic dilated cardiomyopathy (DCM) together have been observed, suggesting that genetic factors play a role in the pathogenesis of PPCM. We hypothesized that some cases of PPCM are part of the spectrum of familial DCM, presenting in the peripartum period. METHODS AND RESULTS-: We reviewed our database of 90 DCM families, focusing specifically on the presence of PPCM patients. Then, in a reverse approach, we reviewed 10 PPCM patients seen in our clinic since the early 1990s and performed cardiological screening of the first-degree relatives of 3 PPCM patients who did not show a full recovery. Finally, we analyzed the genes known to be most commonly involved in DCM in the PPCM patients. We identified a substantial number (5 of 90, 6%) of DCM families with PPCM patients. Second, cardiological screening of first-degree relatives of 3 PPCM patients who did not show full recovery revealed undiagnosed DCM in all 3 families. Finally, genetic analyses revealed a mutation (c.149A>G, p.Gln50Arg) in the gene encoding cardiac troponin C (TNNC1) segregating with disease in a DCM family with a member with PPCM, supporting the genetic nature of disease in this case. CONCLUSIONS-: Our findings strongly suggest that a subset of PPCM is an initial manifestation of familial DCM. This may have important implications for cardiological screening in such families

Diphtheria antitoxin levels in the Netherlands: a population-based study.

In a population-based study in the Netherlands, diphtheria antitoxin antibodies were measured with a toxin-binding inhibition assay in 9, 134 sera from the general population and religious communities refusing vaccination. The Dutch immunization program appears to induce long-term protection against diphtheria. However, a substantial number of adults born before the program was introduced had no protective diphtheria antibody levels. Although herd immunity seems adequate, long-term population protection cannot be assured. As more than 60% of orthodox reformed persons have antibody levels lower than 0.01 IU/ml, introduction of diphtheria into religious communities refusing vaccination may constitute a danger of spread of the bacterium