Asymptotically constrained and real-valued system based on Ashtekar's variables

We present a set of dynamical equations based on Ashtekar's extension of the Einstein equation. The system forces the space-time to evolve to the manifold that satisfies the constraint equations or the reality conditions or both as the attractor against perturbative errors. This is an application of the idea by Brodbeck, Frittelli, Huebner and Reula who constructed an asymptotically stable (i.e., constrained) system for the Einstein equation, adding dissipative forces in the extended space. The obtained systems may be useful for future numerical studies using Ashtekar's variables.Comment: added comments, 6 pages, RevTeX, to appear in PRD Rapid Com

Constraint Propagation of C2C^2-adjusted Formulation - Another Recipe for Robust ADM Evolution System

With a purpose of constructing a robust evolution system against numerical instability for integrating the Einstein equations, we propose a new formulation by adjusting the ADM evolution equations with constraints. We apply an adjusting method proposed by Fiske (2004) which uses the norm of the constraints, C2. One of the advantages of this method is that the effective signature of adjusted terms (Lagrange multipliers) for constraint-damping evolution is pre-determined. We demonstrate this fact by showing the eigenvalues of constraint propagation equations. We also perform numerical tests of this adjusted evolution system using polarized Gowdy-wave propagation, which show robust evolutions against the violation of the constraints than that of the standard ADM formulation.Comment: 11 pages, 5 figures. To be published in Phys. Rev.

LINX®, a novel treatment for patients with refractory asthma complicated by gastroesophageal reflux disease: a case report.

BackgroundGastroesophageal reflux disease is one of the most common comorbidities in patients with asthma. Gastroesophageal reflux disease can be linked to difficult-to-control asthma. Current management includes gastric acid suppression therapy and surgical antireflux procedures. The LINX® procedure is a novel surgical treatment for patients with gastroesophageal reflux disease refractory to medical therapy. To the best of our knowledge, we report the first case of successful treatment of refractory asthma secondary to gastroesophageal reflux disease using the LINX® procedure.Case presentationOur patient was a 22-year-old white woman who met the American Thoracic Society criteria for refractory asthma that had remained poorly controlled for 5 years despite progressive escalation to step 6 treatment as recommended by National Institutes of Health-National Asthma Education and Prevention Program guidelines, including high-dose oral corticosteroids, high-dose inhaled corticosteroid plus long-acting β2-agonist, leukotriene receptor antagonist, and monthly omalizumab. Separate trials with azithromycin therapy and roflumilast did not improve her asthma control, nor did bronchial thermoplasty help. Additional consultations with two other university health systems left the patient with few treatment options for asthma, which included cyclophosphamide. Instead, the patient underwent a LINX® procedure after failure of maximal medical therapy for gastroesophageal reflux disease with the additional aim of improving asthma control. After she underwent LINX® treatment, her asthma improved dramatically and was no longer refractory. She had normal exhaled nitric oxide levels and loss of peripheral eosinophilia after LINX® treatment. Prednisone was discontinued without loss of asthma control. The only immediate adverse effects due to the LINX® procedure were bloating, nausea, and vomiting.ConclusionsLINX® is a viable alternative to the Nissen fundoplication procedure for the treatment of patients with gastroesophageal reflux disease and poorly controlled concomitant refractory asthma

Synthesis of speed independent circuits based on decomposition

Journal ArticleThis paper presents a decomposition method for speedindependent circuit design that is capable of significantly reducing the cost of synthesis. In particular, this method synthesizes each output individually. It begins by contracting the STG to include only transitions on the output of interest and its trigger signals. Next, the reachable state space for this contracted STG is analyzed to determine a minimal number of additional signals which must be reintroduced into the STG to obtain CSC. The circuit for this output is then synthesized from this STG. Results show that the quality of the circuit implementation is nearly as good as the one found from the full reachable state space, but it can be applied to find circuits for which full state space methods cannot be successfully applied. The proposed method has been implemented as a part of our tool nutas (Nii-Utah Timed Asynchronous circuit Synthesis system), and its very first version is available at http://research.nii.ac.jp/~yoneda. Key Words: Decomposition, synthesis, STGs, abstraction, speed-independent circuits

Automatic derivation of timing constraints by failure analyis

Journal ArticleAbstract. This work proposes a technique to automatically obtain timing constraints for a given timed circuit to operate correctly. A designated set of delay parameters of a circuit are first set to sufficiently large bounds, and verification runs followed by failure analysis are repeated. Each verification run performs timed state space enumeration under the given delay bounds, and produces a failure trace if it exists. The failure trace is analyzed, and sufficient timing constraints to prevent the failure is obtained. Then, the delay bounds are tightened according to the timing constraints by using an ILP (Integer Linear Programming) solver. This process terminates when either some delay bounds under which no failure is detected are found or no new delay bounds to prevent the failures can be obtained. The experimental results using a naive implementation show that the proposed method can efficiently handle asynchronous benchmark circuits and nontrivial GasP circuits

Synthesis of timed circuits based on decomposition

Journal ArticleAbstract-This paper presents a decomposition-based method for timed circuit design that is capable of significantly reducing the cost of synthesis. In particular, this method synthesizes each output individually. It begins by contracting the timed signal transition graph (STG) to include only transitions on the output of interest and its possible trigger signals. Next, the reachable state space for this contracted STG is analyzed to determine a minimal number of additional signals, which must be reintroduced into the STG to obtain complete state coding. The circuit for this output is then synthesized from this STG. Results show that the quality of the circuit implementation is nearly as good as the one found from the full reachable state space, but it can be applied to find circuits for which full-state-space methods cannot be successfully applied. The proposed method has been implemented as a part of our tool Nii-Utah Timed Asynchronous circuit Synthesis system (nutas), and its first version is available at http://research.nii.ac.jp/~yoneda

Constraint propagation in the family of ADM systems

The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on "asymptotically constrained" systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of Fourier-component of the constraint propagation equations) are negative or pure-imaginary. We show such a system can be obtained by choosing multipliers of adjusted terms. Our discussion covers Detweiler's proposal (1987) and Frittelli's analysis (1997), and we also mention the so-called conformal-traceless ADM systems.Comment: 11 pages, RevTeX, 2 eps figure

Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime

In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in the evolution equations, we try to construct an "asymptotically constrained system" which is expected to be robust against violation of the constraints, and to enable a long-term stable and accurate numerical simulation. We first provide useful expressions for analyzing constraint propagation in a general spacetime, then apply it to Schwarzschild spacetime. We search when and where the negative real or non-zero imaginary eigenvalues of the homogenized constraint propagation matrix appear, and how they depend on the choice of coordinate system and adjustments. Our analysis includes the proposal of Detweiler (1987), which is still the best one according to our conjecture but has a growing mode of error near the horizon. Some examples are snapshots of a maximally sliced Schwarzschild black hole. The predictions here may help the community to make further improvements.Comment: 23 pages, RevTeX4, many figures. Revised version. Added subtitle, reduced figures, rephrased introduction, and a native checked. :-