Algebraic aspects of the computably enumerable degrees

A set A of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. The class of sets B which contain the same information as A under Turing computability (相似文献   

Constructing Turing complete Euler flows in dimension 3

Can every physical system simulate any Turing machine? This is a classical problem that is intimately connected with the undecidability of certain physical phenomena. Concerning fluid flows, Moore [C. Moore, Nonlinearity 4, 199 (1991)] asked if hydrodynamics is capable of performing computations. More recently, Tao launched a program based on the Turing completeness of the Euler equations to address the blow-up problem in the Navier–Stokes equations. In this direction, the undecidability of some physical systems has been studied in recent years, from the quantum gap problem to quantum-field theories. To the best of our knowledge, the existence of undecidable particle paths of three-dimensional fluid flows has remained an elusive open problem since Moore’s works in the early 1990s. In this article, we construct a Turing complete stationary Euler flow on a Riemannian S3 and speculate on its implications concerning Tao’s approach to the blow-up problem in the Navier–Stokes equations.

The computational power of a physical system is measured in terms of its ability to simulate a universal Turing machine. During the last decades, several physical processes have been shown to exhibit such Turing completeness, from ray-tracing problems in three-dimensional (3D) optical systems (1) to neural networks (2) or nonabelian topological quantum-field theories (3). Additionally, Turing completeness of a physical system is intimately related to the undecidability of its evolution, which can be understood as an emergence of complexity in physics totally different from the chaotic behavior. For instance, the spectral gap problem (checking if the Hamiltonian of a quantum many-body system has a spectral gap) has recently been proved to be undecidable (4). Other undecidable problems in physics are the stability of an n-body system (5), the problem of finding an Einstein metric for a fixed fourfold as observed by Wolfram (6), or the reachability problem in potential well dynamics (7).In contrast, the computational power of fluid dynamics is much less understood. In this direction, Moore asked in ref. 8 if hydrodynamics is capable of performing computations, or, in other words, can a fluid flow simulate a universal Turing machine? This question (universality) has been recently analyzed by Tao related to the problem of the regularity of the Euler and Navier–Stokes equations (9–11). In particular, in ref. 12, Tao suggests a connection between a potential blow-up of the Navier–Stokes equations, Turing completeness, and fluid computation.In this article, we construct a steady incompressible fluid flow on a Riemannian 3D sphere that can simulate any Turing machine (see Theorem 6.1 for a precise formulation). This implies the existence of undecidable fluid particle paths, because the question of determining whether a certain trajectory will enter a certain open set is as difficult as the halting problem for Turing machines. To prove this result, we construct a Turing complete area-preserving diffeomorphism of the disk with additional nice properties, using Moore’s theory of generalized shifts (8); cf. Theorem 5.2. Then, techniques from symplectic/contact geometry allow us to embed this diffeomorphism as the Poincaré map on a certain cross section of a Reeb field defined on the three-sphere (actually, the spatial domain is irrelevant, and we can do the construction on any three-manifold). Finally, using the Reeb-Beltrami correspondence established in ref. 13, we obtain a Riemannian metric for which the constructed field becomes a Beltrami flow and, hence, a stationary solution to the incompressible Euler equations.We end up this article with a discussion on the Turing universality of the Navier–Stokes equations. More precisely, taking the steady Eulerian fluid flow that we construct as initial datum, we obtain a global solution to the Navier–Stokes equations that can simulate just a (fixed) finite number of steps of any Turing machine. Accordingly, we cannot deduce the Turing completeness of Navier–Stokes, thus raising the challenging question of the universality of the 3D Navier–Stokes equations.     

Topographic basis of bimodal ventilation-perfusion distributions during bronchoconstriction in sheep

The distribution of ventilation-perfusion (VA/Q) ratios during bronchoconstriction measured with the multiple inert gases elimination technique is frequently bimodal. However, the topographic basis and the cause of that bimodality remain unknown. In this article, regional VA/Q is quantified by three-dimensional positron emission tomography (PET) imaging of methacholine-induced bronchoconstriction in sheep. Regional VA/Q ratios were calculated from the imaged kinetics of intravenously injected 13NN-saline bolus, assembled into global VA/Q distributions, and used to estimate gas exchange. During bronchoconstriction, large regions with impaired tracer washout were observed adjacent to regions of normal ventilation. PET-derived VA/Q distributions during bronchoconstriction were consistently bimodal, with areas of low VA/Q receiving a large fraction of Q. The standard deviation of the VA/Q distribution was 38% lower if small-scale (subresolution) heterogeneity (< 2.2 cm3) was ignored. Arterial blood gases predicted from PET data correlated well with measured values for Pa(O2) (r2= 0.91, p < 0.01) and Pa(CO2) (r2= 0.90, p < 0.01). We conclude that the bimodality of VA/Q distributions in bronchoconstriction reflects the involvement of large contiguous regions of hypoventilation with substantial subresolution intraregional VA/Q heterogeneity. Assessment of the subresolution VA/Q heterogeneity is therefore essential to accurately quantify global gas exchange impairment during bronchoconstriction.     

Supercompact cardinals, sets of reals, and weakly homogeneous trees

It is shown that if there exists a supercompact cardinal then every set of reals, which is an element of L(R), is the projection of a weakly homogeneous tree. As a consequence of this theorem and recent work of Martin and Steel [Martin, D. A. & Steel, J. R. (1988) Proc. Natl. Acad. Sci. USA 85, 6582-6586], it follows that (if there is a supercompact cardinal) every set of reals in L(R) is determined.     

At what wavelengths should we search for signals from extraterrestrial intelligence?

It has often been concluded that searches for extraterrestrial intelligence (SETI) should concentrate on attempts to receive signals in the microwave region, the argument being given that communication can occur there at minimum broadcasted power. Such a conclusion is shown to result only under a restricted set of assumptions. If generalized types of detection are considered—in particular, photon detection rather than linear detection alone—and if advantage is taken of the directivity of telescopes at short wavelengths, then somewhat less power is required for communication at infrared wavelengths than in the microwave region. Furthermore, a variety of parameters other than power alone may be chosen for optimization by an extraterrestrial civilization. Hence, while partially satisfying arguments may be given about optimal wavelengths for a search for signals from extraterrestrial intelligence, considerable uncertainty must remain.     

A chemical approach to designing Turing patterns in reaction-diffusion systems

A systematic approach is suggested to design chemical systems capable of displaying stationary, symmetry-breaking reaction diffusion patterns (Turing structures). The technique utilizes the fact that reversible complexation of an activator species to form an unreactive, immobile complex reduces the effective diffusion constant of the activator, thereby facilitating the development of Turing patterns. The chlorine dioxide/iodine/malonic acid reaction is examined as an example, and it is suggested that a similar phenomenon may occur in some biological pattern formation processes.     

Significant correlation of recruitable coronary collateral blood flow determined by coronary wedge pressure with ST-segment elevation during coronary occlusion

OBJECTIVES: Quantitative assessment of coronary collateral blood flow can be archived by measuring coronary pressure. We studied the relationships between recruitable coronary collateral blood flow and electrocardiographic changes during percutaneous coronary intervention (PCI). METHODS: We measured coronary pressure during coronary occlusion with PCI in 119 patients with left anterior descending coronary artery stenosis. During balloon inflation, the electrocardiogram was continuously recorded. The ST-segment elevation in the most elevated lead was defined as MaxST and the sum of the maximal ST elevation in leads V2-V4 was defined as sumST. Fractional collateral flow (Qc/Q(N)) was calculated as the coronary wedge pressure divided by the mean aortic pressure. Myocardial ischemia was defined as an ST-segment shift >0.1 mV in any of the V2, V3 or V4 leads. RESULTS: A significant relationship between Qc/Q(N) and MaxST was observed (r=-0.455, P<0.0001). Similarly, Qc/Q(N) was significantly correlated with sumST (r=-0.477, P<0.0001). The receiver operating characteristic curve showed that a cut-off value of 0.27 for Qc/Q(N), with sensitivity of 71.4% and specificity of 76.2%, was an indicator of electrophysiologically sufficient recruitable coronary collateral blood flow for prevention of ischemia during coronary obstruction. Qc/Q(N) values during the first, second, third and fourth inflation were not significantly different. CONCLUSIONS: Qc/Q(N) could be clinically useful for determining whether there is electrophysiologically sufficient recruitable coronary collateral blood flow for prevention of ischemia during coronary obstruction. Repeat transient coronary occlusion during PCI did not lead to increased collateral blood flow.     

The non Q wave myocardial infarction in conventional valvular surgery. Diagnosis with cardiac troponin I

INTRODUCTION: Morbidity and mortality in elective valve surgery is still significant. The main cause of death in these patients is cardiogenic shock, of which the most frequent etiology is acute myocardial infarction (AMI) with Q wave in the ECG. However, there are patients with cardiogenic shock without Q wave in the ECG and with rises in CK-MB enzyme that makes us suspect non-Q wave AMI. OBJECTIVE: To analyze the use of the determination of cardiac troponin-I, a more specific marker of AMI than CK-MB after cardiac surgery, to detect perioperative non-Q wave AMI, and to establish its clinical significance. METHODS: A total of 147 patients without coronary artery disease scheduled for elective valve surgery were included. We used, based in anterior publications, ECG (presence or not of new Q wave) and cardiac troponin I to define perioperative AMI. Levels of cardiac troponin-I were analysed before surgery and 14 hours after. Non-Q wave AMI was diagnosed when troponin I was superior to 38.85 ng/ml and there was not a phatologic Q wave in ECG. RESULTS: One hundred twenty-three (83.67%) of patients did not have AMI, 9 (6.12%) suffered perioperative AMI with Q wave, and 15 (10.27%) carried out criteria of non-Q wave perioperative AMI. Morbidity and mortality in this last group was similar to that in the group with Q wave AMI. Morbidity and mortality were minimum in patients without AMI. CONCLUSIONS: This study suggest the possibility of in vivo identification of non-Q wave perioperative AMI, an entity with important morbidity and mortality in our series, with a simple determination of cardiac troponin I 14 hours after surgery.     

Deforming semistable Galois representations

Let V be a p-adic representation of Gal(Q/Q). One of the ideas of Wiles's proof of FLT is that, if V is the representation associated to a suitable autromorphic form (a modular form in his case) and if V' is another p-adic representation of Gal(Q/Q) "closed enough" to V, then V' is also associated to an automorphic form. In this paper we discuss which kind of local condition at p one should require on V and V' in order to be able to extend this part of Wiles's methods.     

Central fatigue of the diaphragm and quadriceps during incremental loading

Anecdotal observations suggest that low frequency fatigue, as judged by a fall in twitch tension, is more difficult to achieve in the diaphragm than nonrespiratory muscle but this hypothesis has not previously been directly tested. We studied 7 subjects by performing incremental repetitive contraction loading protocols of the diaphragm and quadriceps. We measured twitch transdiaphragmatic pressure (Tw Pdi) and twitch quadriceps tension (Tw Q) during both muscle contraction and relaxation phases during the run. Unpotentiated and potentiated Tw Pdi and Tw Q were measured before and at 20, 40, and 60 minutes after the run. During the run, greater activation of the quadriceps was achieved; for example, at 70% of maximal voluntary effort the interpolated Tw Q was 12.5% of the relaxation phase Tw Q (implying activation of 87.5%) compared with 29.4% (i.e., 70.6% activation) for the diaphragm (p = 0.05). A significantly greater fall in Tw Q than Tw Pdi was observed (unpotentiated Tw Pdi at 20 minutes 94% baseline versus Tw Q 59% baseline, p = 0.007). Low frequency fatigue in humans is more difficult to generate in the diaphragm than in the quadriceps muscle due in part to reduced central activation.     

Diagnostic tests and strategies in venous thromboembolism

Venous thromboembolism (VTE) is a term including deep vein thrombosis (DVT) and pulmonary embolism (PE). Timely and accurate diagnosis of both is essential as delayed or missed diagnoses can result in death or longer term complications. Patients with suspected DVT should initially undergo a pretest probability Wells score. Depending on pretest probability Wells score they should then either proceed to two-point ultrasound scanning or D-dimer testing. Likewise, patients suspected of PE should undergo a two-level PE Wells score, and, if scored likely, a computed tomography pulmonary angiogram (CTPA), or, if there is a low pretest probability score, D-dimer testing. If positive, patients should undergo CTPA. Ventilation perfusion scanning (V/Q scan) or V/Q SPECT should be considered in place of CTPA if there is allergy to contrast media or renal impairment.     

Echophonocardiographic estimates of pulmonary artery wedge pressure in mitral stenosis

The efficacy of noninvasive indexes for predicting pulmonary artery wedge (PAW) pressure was reviewed in 77 patients with mitral stenosis. M-mode echocardiography and phonocardiography were used to measure the aortic valve closure-mitral valve E-point interval (A2-E) and the electrocardiographic Q wave-mitral valve closure interval (Q-C) close to the time of diagnostic cardiac catheterization. During catheterization, in 65 patients PAW pressure was measured and in 12 left atrial (LA) pressure was measured. The A2-E and Q-C intervals taken alone had only modest correlation with PAW pressure (r = -0.54 and r = 0.46, respectively). The correlation was weakest in patients with atrial fibrillation and best in sinus rhythm when heart rate variation between invasive and noninvasive studies was within +/- 5 beats. Substitution of V-wave pressure for mean PAW pressure and correction for variation in blood pressure improved the A2-E correlation (r = -0.64), as did combining the A2-E and Q-C intervals into a ratio [(Q-C)/(A2-E)] (r = 0.62). However, the best results were obtained in patients where LA pressure was measured directly (r = -0.91 for A2-E), suggesting the PAW pressure is not always an accurate reflection of LA pressure. In conclusion, many factors in addition to LA pressure affect the Q-C and A2-E intervals which, in many situations, decrease their predictive value. However, if used appropriately, these intervals may allow an estimation of PAW pressure.     

Clark's Theorem on linear programs holds for convex programs

Given a linear minimization program, then there is an associated linear maximization program termed the dual. F. E. Clark proved the following theorem. “If the set of feasible points of one program is bounded, then the set of feasible points of the other program is unbounded.” A convex program is the minimization of a convex function subject to the constraint that a number of other convex functions be nonpositive. As is well known, a dual maximization problem can be defined in terms of the Lagrange function. The dual objection function is the infimum of the Lagrange function. The feasible Lagrange multipliers are those satisfying: (i) the multipliers are nonnegative and (ii) the dual objective function is not negative infinity. It is found that Clark's Theorem applies unchanged to dual convex programs. Moreover, the programs have equal values.     

Identification of the proton pathway in bacterial reaction centers: both protons associated with reduction of QB to QBH2 share a common entry point

The reaction center from Rhodobacter sphaeroides uses light energy for the reduction and protonation of a quinone molecule, Q(B). This process involves the transfer of two protons from the aqueous solution to the protein-bound Q(B) molecule. The second proton, H(+)(2), is supplied to Q(B) by Glu-L212, an internal residue protonated in response to formation of Q(A)(-) and Q(B)(-). In this work, the pathway for H(+)(2) to Glu-L212 was studied by measuring the effects of divalent metal ion binding on the protonation of Glu-L212, which was assayed by two types of processes. One was proton uptake from solution after the one-electron reduction of Q(A) (DQ(A)-->D(+)Q(A)(-)) and Q(B) (DQ(B)-->D(+)Q(B)(-)), studied by using pH-sensitive dyes. The other was the electron transfer k(AB)((1)) (Q(A)(-)Q(B)-->Q(A)Q(B)(-)). At pH 8.5, binding of Zn(2+), Cd(2+), or Ni(2+) reduced the rates of proton uptake upon Q(A)(-) and Q(B)(-) formation as well as k(AB)((1)) by approximately an order of magnitude, resulting in similar final values, indicating that there is a common rate-limiting step. Because D(+)Q(A)(-) is formed 10(5)-fold faster than the induced proton uptake, the observed rate decrease must be caused by an inhibition of the proton transfer. The Glu-L212-->Gln mutant reaction centers displayed greatly reduced amplitudes of proton uptake and exhibited no changes in rates of proton uptake or electron transfer upon Zn(2+) binding. Therefore, metal binding specifically decreased the rate of proton transfer to Glu-L212, because the observed rates were decreased only when proton uptake by Glu-L212 was required. The entry point for the second proton H(+)(2) was thus identified to be the same as for the first proton H(+)(1), close to the metal binding region Asp-H124, His-H126, and His-H128.     

Coenzyme Q10 in patients with end-stage heart failure awaiting cardiac transplantation: a randomized, placebo-controlled study

BACKGROUND: The number of patients awaiting heart transplantation is increasing in proportion to the waiting period for a donor. Studies have shown that coenzyme Q10 (CoQ10) has a beneficial effect on patients with heart failure. HYPOTHESIS: The purpose of the present double-blind, placebo-controlled, randomized study was to assess the effect of CoQ10 on patients with end-stage heart failure and to determine if CoQ10 can improve the pharmacological bridge to heart transplantation. METHODS: A prospective double-blind design was used. Thirty-two patients with end-stage heart failure awaiting heart transplantation were randomly allocated to receive either 60 mg U/day of Ultrasome--CoQ10 (special preparation to increase intestinal absorption) or placebo for 3 months. All patients continued their regular medication regimen. Assessments included anamnesis with an extended questionnaire based partially on the Minnesota Living with Heart Failure Questionnaire, 6-min walk test, blood tests for atrial natriuretic factor (ANF) and tumor necrosis factor (TNF), and echocardiography. RESULTS: Twenty-seven patients completed the study. The study group showed significant improvement in the 6-min walk test and a decrease in dyspnea, New York Heart Association (NYHA) classification, nocturia, and fatigue. No significant changes were noted after 3 months of treatment in echocardiography parameters (dimensions and contractility of cardiac chambers) or ANF and TNF blood levels. CONCLUSIONS: The administration of CoQ10 to heart transplant candidates led to a significant improvement in functional status, clinical symptoms, and quality of life. However, there were no objective changes in echo measurements or ANF and TNF blood levels. Coenzyme Q10 may serve as an optional addition to the pharmacologic armamentarium of patients with end-stage heart failure. The apparent discrepancy between significant clinical improvement and unchanged cardiac status requires further investigation.     

HMG-CoA reductase inhibitors and coenzyme Q10

The most concerning adverse reaction with HMG-CoA reductase inhibitors (statins) is myotoxicity. Statins inhibit the production of mevalonate, a precursor of both cholesterol and coenzyme Q10, a compound believed to be crucial for mitochondrial function and the provision of energy for cellular processes. There is speculation that a reduction in coenzyme Q10 concentrations may promote the myopathies that have been associated with statin treatment as a result of mitochondrial damage. Although studies have repeatedly demonstrated a reduction in circulating coenzyme Q10 concentrations with statin therapy, it is unclear as to whether tissue levels of coenzyme Q10 are significantly affected. Coenzyme Q10 supplementation has been shown to reverse statin-induced decreases in circulating coenzyme Q10 concentrations, although the effect of supplementation on tissue coenzyme Q10 concentrations and any resulting clinical benefit has not been adequately assessed. Although there is not much of a safety concern with coenzyme Q10 supplementation, there is also not enough evidence to support its routine use for preventing the adverse effects of statin therapy, and it is therefore not recommended for this purpose at this time.     

Cardiac valve orifice equation independent of valvular flow intervals: application to mitral valve area computation in mitral stenosis and comparison with the Gorlin formula and direct anatomical measurements

An orifice equation is developed which relates the effective mitral valve area (A), the average mitral valve pressure gradient (dP), the cardiac output (Q) and the heart frequency (f) through considerations of momentum conservation across the mitral valve. The form of the new equation is A = (4.75 X 10(-5)Qf/dP, where A, Q, and dP are expressed in cm2, ml X min-1 and mmHg respectively. Mitral valve areas computed with the new orifice formula are found to correlate with those computed by the Gorlin formula in conditions of equilibrium associated with the resting state at a level of r = 0.95, SE = 0.15 cm2, with autopsy measurements at a level of r = 0.85, SE = 0.18 cm2 and with direct anatomical measurements of excised valves at a level of r = 0.78, SE = 0.41 cm2. The results suggest that the new formula may be considered as an independent orifice equation enjoying a similar domain of validity as the Gorlin formula. The new equation offers the possibility of deriving additional useful haemodynamic relationships when used in combination with established cardiological formulas.     

Use of the electrocardiogram as an aid in screening for left ventricular aneurysm.

Attempting to cull from a population of patients with coronary artery disease or cardiomyopathy, a subgroup in whom left ventriculography might most reasonably be performed in search of a surgically resectable ventricular aneurysm, the electrocardiograms (ECGs) and ventriculograms of 96 patients were analyzed. This study was conceived to test the value of the ECG as an initial screening technique. Patients with normal ventricular contractile motion in the presence of coronary artery disease rarely showed ST segment elevation exceeding 2 mm in any lead, and even more rarely showed Q waves in corresponding leads. All patients with well defined left ventricular aneurysms had at least 1 mm ST segment elevation, and the majority (73%) had ST elevation of 2 mm or greater; in 80% of these, there were associated Q waves in the same lead. In patients with only local areas of hypocontractility, the frequency of ST segment elevation with concomitant Q waves was significantly less (approximately 50%) than that seen in patients with aneurysms. It is concluded that patients with suspected or proven coronary disease who fail to demonstrate ST segment elevation are unlikely to have ventricular aneurysms and, thus, would receive little diagnostic benefit from left ventriculography. The presence of ST segment elevation, with or without associated Q waves in the same leads, is a helpful screening sign, raising the possibility of a surgically remediable lesion such as a ventricular aneurysm, but similar electrocardiographic patterns are also seen in patients with non-operable localized or generalized disorders of contraction. Having discovered ST elevation, then, left ventriculography becomes a reasonable next step - when otherwise indicated - in delineating the type of contractile disorder as well as the amount of adequately functioning muscle.     

Rapid enzyme release from acutely infarcted myocardium after early thrombolytic therapy: washout or reperfusion damage?

In a randomized study on early intracoronary thrombolytic therapy in patients with acute myocardial infarction (AMI), serial plasma enzyme activities were measured to analyze the rate of enzyme appearance in plasma with reference to treatment allocation, area at risk, and infarct size. Cumulative activities of alpha-hydroxybutyrate dehydrogenase (HBDH) appearing in plasma in the first 24 hours (Q24), 48 hours (Q48), and 72 hours (Q72) were calculated to obtain infarct size (= Q72) and rate of HBDH appearance in plasma (= Q24/Q72). Analyzed on the basis of "intention to treat" in 448 patients with AMI, the mean Q24/Q72 value (+/- SEM) was 0.653 +/- 0.011 in 230 patients receiving thrombolytic therapy; this value was significantly (p less than 0.001) higher than that observed in 218 patients receiving conventional therapy (0.504 +/- 0.012). In the thrombolysis group Q24/Q72 was independent of infarct size, whereas in the control group Q24/Q72 was negatively correlated with infarct size (r = -0.26; p less than 0.001). Plotted against the sum of ST segment elevations at admission (sigma ST) mean Q24 values were similar in both treatment groups, but mean Q48 and especially Q72 values were larger in the control group than in the thrombolysis group. We conclude that: (1) in reperfused infarctions the time course for development of infarct is accelerated in comparison to unreperfused infarcts; (2) this accelerated process of necrosis lasts about 40 to 50 hours, a duration that is hardly influenced by infarct size; and (3) the reperfusion-induced acceleration of enzyme release resembles the reoxygenation-induced enzyme release from anoxic hearts.(ABSTRACT TRUNCATED AT 250 WORDS)