It May Be True (Complete)

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All studies were repeated, with the exception of the PET scan, 3 months post-implantation. The procedures for data acquisition and analysis for: The standard deviation of the phase angles is a measure of the extent of LV mechanical dyssynchrony. Positron emission tomography imaging and analysis, and tissue characterization, were performed as previously described. The atrial lead was placed in the right atrial appendage; the right ventricular RV lead was placed at the RV apex; the LV lead was implanted in the lateral or posterolateral vein.

Echo optimization of atrioventricular and ventricular—ventricular timing was performed 2 weeks post-implantation using serial measurements of the aortic flow velocity envelopes. All lead ECGs were digitally read by a single observer who was blinded to the results of all investigations. Note in complete left bundle branch block, the absence of an r wave in V1 or q wave in I, V6 and aVL. The diagnosis of intraventricular conduction delay is made by the presence of a q wave in lead V6; note also the small r wave in V1.

Fisher's exact test was performed for comparison of proportions among groups.

Welch's t -test was used for assessment of difference between means. All statistical analysis was performed using Mathematical 8. This study accords with the Declaration of Helsinki. The protocol received ethics approval from the University of Ottawa Heart Institute Research Ethics Board, and all patients signed informed consent.

All potential conflicts of interest have been reported. Nine patients were excluded from this substudy due to the presence of RBBB, atrial fibrillation, or an in situ pacemaker. Thus, 40 patients were available for analysis and were classified into three groups: This compared with rLBBB, 3.

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Change in variables 3 months post-cardiac resynchronization therapy compared with pre-implant stratified by the electrocardiogram group. Clinical response was measured by change in NYHA class. Patients with cLBBB had the greatest reduction in mechanical dyssynchrony without reaching statistical significance. The principal findings of this study are: A significant proportion of their patients developed RBBB rather than complete heart block. However, r-V1 was the most sensitive ECG marker for this finding.

The major limitation of this study is its small size that has resulted in large standard deviations compared with means. Therefore, small treatment effects may have been unobserved. Further, a small study size necessitated the use of a surrogate marker of CRT response—LV remodelling; we took this approach cognizant that is improvement in LV structure and function and not clinical response that is best correlated with reduced mortality, ventricular arrhythmia, and ICD shocks.

A larger study looking at hard clinical endpoints is required before any clinical recommendations may be made. A previous publication found that baseline LV volume is not a predictor of CRT response and is therefore unlikely to have influenced our results. These results should be confirmed in a larger study. Other authors declare no conflict of interest. This study was funded by a project grant from the J. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide.

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Close mobile search navigation Article navigation. Greater response to cardiac resynchronization therapy in patients with true complete left bundle branch block: Cardiac resynchronization therapy , Electrocardiogram , Electrophysiology , Left bundle branch , Cardiac failure. View large Download slide. Effects of multisite biventricular pacing in patients with heart failure and intraventricular conduction delay.

The effect of cardiac resynchronization on morbidity and mortality in heart failure. Combined cardiac resynchronization and implantable cardioversion defibrillation in advanced chronic heart failure: Second, there are types of computations which do not conform to the Turing machine model on which P and NP are defined, such as quantum computation and randomized algorithms.

A key reason for this belief is that after decades of studying these problems no one has been able to find a polynomial-time algorithm for any of more than important known NP -complete problems see List of NP -complete problems. These algorithms were sought long before the concept of NP -completeness was even defined Karp's 21 NP -complete problems , among the first found, were all well-known existing problems at the time they were shown to be NP -complete.

It is also intuitively argued that the existence of problems that are hard to solve but for which the solutions are easy to verify matches real-world experience.

There would be no special value in "creative leaps," no fundamental gap between solving a problem and recognizing the solution once it's found. For example, in these statements were made: This is, in my opinion, a very weak argument. The space of algorithms is very large and we are only at the beginning of its exploration. Being attached to a speculation is not a good guide to research planning.

One should always try both directions of every problem. Prejudice has caused famous mathematicians to fail to solve famous problems whose solution was opposite to their expectations, even though they had developed all the methods required. One of the reasons the problem attracts so much attention is the consequences of the answer. Either direction of resolution would advance theory enormously, and perhaps have huge practical consequences as well. It is also possible that a proof would not lead directly to efficient methods, perhaps if the proof is non-constructive , or the size of the bounding polynomial is too big to be efficient in practice.

The consequences, both positive and negative, arise since various NP -complete problems are fundamental in many fields. Cryptography, for example, relies on certain problems being difficult. A constructive and efficient solution [Note 2] to an NP -complete problem such as 3-SAT would break most existing cryptosystems including:.

These would need to be modified or replaced by information-theoretically secure solutions not inherently based on P - NP equivalence. On the other hand, there are enormous positive consequences that would follow from rendering tractable many currently mathematically intractable problems.

For instance, many problems in operations research are NP -complete, such as some types of integer programming and the travelling salesman problem. Efficient solutions to these problems would have enormous implications for logistics. Many other important problems, such as some problems in protein structure prediction , are also NP -complete; [30] if these problems were efficiently solvable it could spur considerable advances in life sciences and biotechnology.

But such changes may pale in significance compared to the revolution an efficient method for solving NP -complete problems would cause in mathematics itself. Namely, it would obviously mean that in spite of the undecidability of the Entscheidungsproblem , the mental work of a mathematician concerning Yes-or-No questions could be completely replaced by a machine. After all, one would simply have to choose the natural number n so large that when the machine does not deliver a result, it makes no sense to think more about the problem. Similarly, Stephen Cook says [33]. Example problems may well include all of the CMI prize problems.

Research mathematicians spend their careers trying to prove theorems, and some proofs have taken decades or even centuries to find after problems have been stated—for instance, Fermat's Last Theorem took over three centuries to prove. A method that is guaranteed to find proofs to theorems, should one exist of a "reasonable" size, would essentially end this struggle. It would allow one to show in a formal way that many common problems cannot be solved efficiently, so that the attention of researchers can be focused on partial solutions or solutions to other problems.

For example, it is possible that SAT requires exponential time in the worst case, but that almost all randomly selected instances of it are efficiently solvable. Russell Impagliazzo has described five hypothetical "worlds" that could result from different possible resolutions to the average-case complexity question. A Princeton University workshop in studied the status of the five worlds. These barriers are another reason why NP -complete problems are useful: These barriers have also led some computer scientists to suggest that the P versus NP problem may be independent of standard axiom systems like ZFC cannot be proved or disproved within them.

The interpretation of an independence result could be that either no polynomial-time algorithm exists for any NP -complete problem, and such a proof cannot be constructed in e. ZFC, or that polynomial-time algorithms for NP -complete problems may exist, but it is impossible to prove in ZFC that such algorithms are correct. Additionally, this result implies that proving independence from PA or ZFC using currently known techniques is no easier than proving the existence of efficient algorithms for all problems in NP.

While the P versus NP problem is generally considered unsolved, [43] many amateur and some professional researchers have claimed solutions. Consider all languages of finite structures with a fixed signature including a linear order relation. Then, all such languages in P can be expressed in first-order logic with the addition of a suitable least fixed-point combinator. Effectively, this, in combination with the order, allows the definition of recursive functions. As long as the signature contains at least one predicate or function in addition to the distinguished order relation, so that the amount of space taken to store such finite structures is actually polynomial in the number of elements in the structure, this precisely characterizes P.

Similarly, NP is the set of languages expressible in existential second-order logic —that is, second-order logic restricted to exclude universal quantification over relations, functions, and subsets. The languages in the polynomial hierarchy , PH , correspond to all of second-order logic.

Introduction

Thus, the question "is P a proper subset of NP " can be reformulated as "is existential second-order logic able to describe languages of finite linearly ordered structures with nontrivial signature that first-order logic with least fixed point cannot? No algorithm for any NP -complete problem is known to run in polynomial time. However, these algorithms do not qualify as polynomial time because their running time on rejecting instances are not polynomial. The following algorithm, due to Levin without any citation , is such an example below.

If there is an algorithm say a Turing machine , or a computer program with unbounded memory that can produce the correct answer for any input string of length n in at most cn k steps, where k and c are constants independent of the input string, then we say that the problem can be solved in polynomial time and we place it in the class P.

Formally, P is defined as the set of all languages that can be decided by a deterministic polynomial-time Turing machine. NP can be defined similarly using nondeterministic Turing machines the traditional way. However, a modern approach to define NP is to use the concept of certificate and verifier.

P versus NP problem

Formally, NP is defined as the set of languages over a finite alphabet that have a verifier that runs in polynomial time, where the notion of "verifier" is defined as follows. In general, a verifier does not have to be polynomial-time. However, for L to be in NP , there must be a verifier that runs in polynomial time. This is a common way of proving some new problem is NP -complete. In the second episode of season 2 of Elementary , "Solve for X" revolves around Sherlock and Watson investigating the murders of mathematicians who were attempting to solve P versus NP.

From Wikipedia, the free encyclopedia. Unsolved problem in computer science: If the solution to a problem is easy to check for correctness, must the problem be easy to solve? Vardi , Rice University. Such a machine could solve an NP problem in polynomial time by falling into the correct answer state by luck , then conventionally verifying it. Such machines are not practical for solving realistic problems but can be used as theoretical models.

Communications of the ACM. P, NP, and the Search for the Impossible. Thomson Course Technology, Retrieved 26 September P , NP , and Friends". Retrieved 27 August Journal of Combinatorial Theory, Series A. Graph isomorphism is in the low hierarchy. Lecture Notes in Computer Science. Journal of Computer and System Sciences.

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Complexity Class of the Week: Advances in linear and integer programming. Oxford Lecture Series in Mathematics and its Applications. Hard instance generation for SAT. Journal of Automated Reasoning. A 3DES problem instance would be about 3 times this size. From pages — of Optimization Stories, M. Retrieved 18 October Retrieved 20 July Journal of the Operational Research Society.

Impagliazzo, "A personal view of average-case complexity," sct, pp. Status of Impagliazzo's Worlds " ". Archived from the original on The New York Times.

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