On finitely ambiguous B\"uchi automata

Unambiguous B\"uchi automata, i.e. B\"uchi automata allowing only one accepting run per word, are a useful restriction of B\"uchi automata that is well-suited for probabilistic model-checking. In this paper we propose a more permissive variant, namely finitely ambiguous B\"uchi automata, a generalisation where each word has at most $k$ accepting runs, for some fixed $k$. We adapt existing notions and results concerning finite and bounded ambiguity of finite automata to the setting of $\omega$-languages and present a translation from arbitrary nondeterministic B\"uchi automata with $n$ states to finitely ambiguous automata with at most $3^n$ states and at most $n$ accepting runs per word

Twisted Superspace for N=D=2 Super BF and Yang-Mills with Dirac-K\"ahler Fermion Mechanism

We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-K\"ahler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.Comment: 36 page

Cavitation inception of a van der Waals fluid at a sack-wall obstacle

Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle and, depending on the pressure drop between inlet and outlet, vapor formation underneath the corner of the sack-wall is observed. The circumstances of cavitation formation are investigated and it is found that the local bulk pressure and mean stress are insufficient to explain the phenomenon. Results obtained in this study strongly suggest that the viscous stress, interfacial contributions to the local pressure, and the Laplace pressure are relevant to the opening of a vapor cavity. This can be described by a generalization of Joseph's criterion that includes these contributions. A macroscopic investigation measuring mass flow rate behavior and discharge coefficient was also performed. As theoretically predicted, mass flow rate increases linearly with the square root of the pressure drop. However, when cavitation occurs, the mass flow growth rate is reduced and eventually it collapses into a choked flow state. In the cavitating regime, as theoretically predicted and experimentally verified, the discharge coefficient grows with the Nurick cavitation number

A holomorphic representation of the Jacobi algebra

A representation of the Jacobi algebra $\mathfrak{h}_1\rtimes \mathfrak{su}(1,1)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}\times \mathcal{D}_1$ is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.Comment: 34 pages, corrected typos in accord with the printed version and the Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI: 10.1142/S0129055X12920018, references update

On local boundary CFT and non-local CFT on the boundary

The holographic relation between local boundary conformal quantum field theories (BCFT) and their non-local boundary restrictions is reviewed, and non-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067 with R. Long

Extensive characterization of a high Reynolds number decelerating boundary layer using advanced optical metrology

An experiment conducted in the framework of the EUHIT project and designed to characterize large scale structures in an adverse pressure gradient boundary layer flow is presented. Up to 16 sCMOS cameras were used in order to perform large scale turbulent boundary layer PIV measurements with a large field of view and appropriate spatial resolution. To access the span-wise / wall-normal signature of the structures as well, stereoscopic PIV measurements in span-wise/wall-normal planes were performed at specific stream-wise locations. To complement these large field of view measurements, long-range micro-PIV, time resolved near wall velocity profiles and film-based measurements were performed in order to determine the wall-shear stress and its fluctuations at some specific locations along the model.Comment: 50 page

Hypercomplex Integrable Systems

In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax equations, exhibiting the integrability properties of such manifolds. A number of different field equations for such hypercomplex manifolds are derived, one of which is in Cauchy-Kovaleskaya form which enables a formal general solution to be given. Various other properties of the field equations and their solutions are studied, such as their symmetry properties and the associated hierarchy of conservation laws.Comment: Latex file, 19 page

A condensed matter interpretation of SM fermions and gauge fields

We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z^3). This space allows a simple physical interpretation as a phase space of a lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z_2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z_2-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.Comment: Minimal modifications in comparison with the published versio

Analysis of BRAF and NRAS Mutation Status in Advanced Melanoma Patients Treated with Anti-CTLA-4 Antibodies: Association with Overall Survival?

Ipilimumab and tremelimumab are human monoclonal antibodies (Abs) against cytotoxic T-lymphocyte antigen-4 (CTLA-4). Ipilimumab was the first agent to show a statistically significant benefit in overall survival in advanced melanoma patients. Currently, there is no proven association between the BRAFV600 mutation and the disease control rate in response to ipilimumab. This analysis was carried out to assess if BRAFV600 and NRAS mutation status affects the clinical outcome of anti-CTLA-4-treated melanoma patients. This is a retrospective multi-center analysis of 101 patients, with confirmed BRAF and NRAS mutation status, treated with anti-CTLA-4 antibodies from December 2006 until August 2012. The median overall survival, defined from the treatment start date with the anti-CTLA-4. Abs-treatment to death or till last follow up, of BRAFV600 or NRAS mutant patients (n = 62) was 10.12 months (95% CI 6.78-13.2) compared to 8.26 months (95% CI 6.02-19.9) in BRAFV600/NRASwt subpopulation (n = 39) (p = 0.67). The median OS of NRAS mutated patients (n = 24) was 12.1 months and although was prolonged compared to the median OS of BRAF mutated patients (n = 38, mOS = 8.03 months) or BRAFV600/NRASwt patients (n = 39, mOS = 8.26 months) the difference didn't reach statistical significance (p = 0.56). 69 patients were able to complete 4 cycles of anti-CTLA-4 treatment. Of the 24 patients treated with selected BRAF- or MEK-inhibitors, 16 patients received anti-CTLA 4 Abs following either a BRAF or MEK inhibitor with only 8 of them being able to finish 4 cycles of treatment. Based on our results, there is no difference in the median OS in patients treated with anti-CTLA-4 Abs implying that the BRAF/NRAS mutation status alone is not sufficient to predict the outcome of patients treated with anti-CTLA-4 Abs

New Results in Sasaki-Einstein Geometry

This article is a summary of some of the author's work on Sasaki-Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki-Einstein geometry, in low dimensions, to superconformal field theory; properties of the latter are therefore reflected in the former, and vice versa. Despite this physical motivation, many recent results are of independent geometrical interest, and are described here in purely mathematical terms: explicit constructions of infinite families of both quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry; an extremal problem that determines the Reeb vector field for, and hence also the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the existence of Sasaki-Einstein metrics. Some of these results also provide new insights into Kahler geometry, and in particular new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the conference "Riemannian Topology: Geometric Structures on Manifolds"; minor typos corrected, reference added; published version; Riemannian Topology and Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov 2008