On the Size Complexity of Non-Returning Context-Free PC Grammar Systems

Improving the previously known best bound, we show that any recursively enumerable language can be generated with a non-returning parallel communicating (PC) grammar system having six context-free components. We also present a non-returning universal PC grammar system generating unary languages, that is, a system where not only the number of components, but also the number of productions and the number of nonterminals are limited by certain constants, and these size parameters do not depend on the generated language

Gravitomagnetic Moments and Dynamics of Dirac's (spin 1/2) fermions in flat space-time Maxwellian Gravity

The gravitational effects in the relativistic quantum mechanics are investigated in a relativistically derived version of Heaviside's speculative Gravity (in flat space-time) named here as Maxwellian Gravity. The standard Dirac's approach to the intrinsic spin in the fields of Maxwellian Gravity yields the gravitomagnetic moment of a Dirac (spin 1/2) particle exactly equals to its intrinsic spin. Violation of The Equivalence Principle (both at classical and quantum mechanical level) in the relativistic domain has also been reported in this work.Comment: 27 page

Expansion in perfect groups

Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an integer q, denote by Ga_q the subgroup of Ga consisting of the elements that project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q with respect to the generating set S form a family of expanders when q ranges over square-free integers with large prime divisors if and only if the connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas are explained in more details in the introduction, typos corrected, results and proofs unchange

Spin, gravity, and inertia

The gravitational effects in the relativistic quantum mechanics are investigated. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. As a direct application, we analyze the non-relativistic limit of the theory. The new term describing the specific spin (gravitational moment) interaction effect is recovered in the Hamiltonian. The comparison of the true gravitational coupling with the purely inertial case demonstrates that the spin relativistic effects do not violate the equivalence principle for the Dirac fermions.Comment: Revtex, 12 pages, no figures, accepted in Phys. Rev. Let

The phase of a quantum mechanical particle in curved spacetime

We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is $S/\hbar = \int p_{\mu} dx^{\mu} / \hbar$, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple managable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has \textit{exactly} the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in $\hbar$. We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in $\hbar$. For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations.Comment: 30 pages, no figures. Submitted to Gen.Rel.Grav 17 Oct 0

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

Risk Related to Pre-Diabetes Mellitus and Diabetes Mellitus in Heart Failure With Reduced Ejection Fraction: Insights From Prospective Comparison of ARNI With ACEI to Determine Impact on Global Mortality and Morbidity in Heart Failure Trial

BACKGROUND: The prevalence of pre-diabetes mellitus and its consequences in patients with heart failure and reduced ejection fraction are not known. We investigated these in the Prospective Comparison of ARNI With ACEI to Determine Impact on Global Mortality and Morbidity in Heart Failure (PARADIGM-HF) trial. METHODS AND RESULTS: We examined clinical outcomes in 8399 patients with heart failure and reduced ejection fraction according to history of diabetes mellitus and glycemic status (baseline hemoglobin A1c [HbA1c]: /=6.5% [>/=48 mmol/mol; diabetes mellitus]), in Cox regression models adjusted for known predictors of poor outcome. Patients with a history of diabetes mellitus (n=2907 [35%]) had a higher risk of the primary composite outcome of heart failure hospitalization or cardiovascular mortality compared with those without a history of diabetes mellitus: adjusted hazard ratio, 1.38; 95% confidence interval, 1.25 to 1.52; P6.5%) and known diabetes mellitus compared with those with HbA1c<6.0% was 1.39 (1.17-1.64); P<0.001 and 1.64 (1.43-1.87); P<0.001, respectively. Patients with pre-diabetes mellitus were also at higher risk (hazard ratio, 1.27 [1.10-1.47]; P<0.001) compared with those with HbA1c<6.0%. The benefit of LCZ696 (sacubitril/valsartan) compared with enalapril was consistent across the range of HbA1c in the trial. CONCLUSIONS: In patients with heart failure and reduced ejection fraction, dysglycemia is common and pre-diabetes mellitus is associated with a higher risk of adverse cardiovascular outcomes (compared with patients with no diabetes mellitus and HbA1c <6.0%). LCZ696 was beneficial compared with enalapril, irrespective of glycemic status. CLINICAL TRIAL REGISTRATION: URL: http://www.clinicaltrials.gov. Unique identifier: NCT01035255

Angiotensin Receptor Neprilysin Inhibition Compared With Enalapril on the Risk of Clinical Progression in Surviving Patients With Heart Failure

BACKGROUND: -Clinical trials in heart failure have focused on the improvement in symptoms or decreases in the risk of death and other cardiovascular events. Little is known about the effect of drugs on the risk of clinical deterioration in surviving patients. METHODS AND RESULTS: -We compared the angiotensin-neprilysin inhibitor LCZ696 (400 mg daily) with the angiotensinconverting enzyme inhibitor enalapril (20 mg daily) in 8399 patients with heart failure and reduced ejection fraction in a double-blind trial. The analyses focused on prespecified measures of nonfatal clinical deterioration. In comparison with the enalapril group, fewer LCZ696-treated patients required intensification of medical treatment for heart failure (520 versus 604; hazard ratio, 0.84; 95% confidence interval, 0.74-0.94; P=0.003) or an emergency department visit for worsening heart failure (hazard ratio, 0.66; 95% confidence interval, 0.52-0.85; P=0.001). The patients in the LCZ696 group had 23% fewer hospitalizations for worsening heart failure (851 versus 1079; P<0.001) and were less likely to require intensive care (768 versus 879; 18% rate reduction, P=0.005), to receive intravenous positive inotropic agents (31% risk reduction, P<0.001), and to have implantation of a heart failure device or cardiac transplantation (22% risk reduction, P=0.07). The reduction in heart failure hospitalization with LCZ696 was evident within the first 30 days after randomization. Worsening of symptom scores in surviving patients was consistently more common in the enalapril group. LCZ696 led to an early and sustained reduction in biomarkers of myocardial wall stress and injury (N-terminal pro-Btype natriuretic peptide and troponin) versus enalapril. CONCLUSIONS: -Angiotensin-neprilysin inhibition prevents the clinical progression of surviving patients with heart failure more effectively than angiotensin-converting enzyme inhibition. Clinical Trial Registration-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01035255