Patterns in Repeated Trials

1962 ◽  
Vol 88 (3) ◽  
pp. 360-366 ◽  
Author(s):  
M. T. L. Bizley
Keyword(s):  
General Theory ◽  
Generating Functions ◽  
Recurrent Events ◽  
General Pattern ◽  
Recurrent Event ◽  
Expected Number ◽  
Definition Of ◽  
Regular Patterns

In a series of trials with constant probability p of ‘success’ (S) and q ( = I–p) of ‘failure’ (F), the problems arise of determining the expected number of trials required to obtain a specified pattern of results (e.g. SSFSFFSSSFF), and of calculating the probability that such a pattern will appear in a given number of trials. We are here concerned essentially with ‘general’ patterns which may exhibit no clear regularity; many methods are available, and well known, for dealing with regular patterns (e.g. SSSSSS or SFSFSF), which do not apply to irregular ones. Feller, has shown how to solve the problems for general patterns, using an ingenious definition of the event corresponding to the appearance of the pattern whereby it becomes a recurrent event; his powerful general theory of recurrent events then applies and yields the required information by means of generating functions. A different method is given on page 171 of Bizley for finding the expected number of trials required to obtain a general pattern; this uses only the simplest mathematical tools but involves rather a lot of work for long patterns. Under each of these methods, however, every given pattern has to be treated individually and a separate calculation performed.

Recurrent composite events

1967 ◽  
Vol 4 (01) ◽  
pp. 34-61 ◽  
Author(s):  
R.T. Leslie
Keyword(s):  
Recurrent Events ◽  
Recurrent Event ◽  
Complex Pattern ◽  
Bernoulli Trials ◽  
Success Runs ◽  
Trial Number ◽  
Composite Events ◽  
Success Run ◽  
Definition Of ◽  
Two Alternatives

On a sequence of Bernoulli trials, the definition of a recurrent event ε involves the occurrence of a unique pattern of successes (S) and failures (F), the final element of which is the result of the nth trial. Success runs are the best known of such recurrent events, but Feller (1959, §13.8) mentions more complicated patterns, among which two types may be distinguished. The simpler involves a single more complex pattern such as SSFFSS; the second type involves a set of alternative events defining ε, which is said to occur when any one of the alternatives occurs at trial number n. Thus if ε stands for “either a success run of length r or a failure run of length ρ”, there are two alternatives in the set; the problem is elementary because the component events are “non-overlapping”.

Recurrent composite events

1967 ◽  
Vol 4 (1) ◽  
pp. 34-61 ◽  
Author(s):  
R.T. Leslie
Keyword(s):  
Recurrent Events ◽  
Recurrent Event ◽  
Complex Pattern ◽  
Bernoulli Trials ◽  
Success Runs ◽  
Trial Number ◽  
Composite Events ◽  
Success Run ◽  
Definition Of ◽  
Two Alternatives

On a sequence of Bernoulli trials, the definition of a recurrent event ε involves the occurrence of a unique pattern of successes (S) and failures (F), the final element of which is the result of the nth trial. Success runs are the best known of such recurrent events, but Feller (1959, §13.8) mentions more complicated patterns, among which two types may be distinguished. The simpler involves a single more complex pattern such as SSFFSS; the second type involves a set of alternative events defining ε, which is said to occur when any one of the alternatives occurs at trial number n. Thus if ε stands for “either a success run of length r or a failure run of length ρ”, there are two alternatives in the set; the problem is elementary because the component events are “non-overlapping”.

Recurrent Stroke Risk in Pilots with Atrial Fibrillation

2020 ◽  
Vol 91 (4) ◽  
pp. 352-357
Author(s):  
Jessica Tedford ◽  
Valerie Skaggs ◽  
Ann Norris ◽  
Farhad Sahiar ◽  
Charles Mathers
Keyword(s):  
Atrial Fibrillation ◽  
General Population ◽  
Recurrent Events ◽  
Stroke Risk ◽  
Event Rate ◽  
Recurrent Stroke ◽  
Previous History ◽  
Recurrent Event ◽  
Recurrence Rates ◽  
Medical Certification

INTRODUCTION: Atrial fibrillation (AF) is one of the most common cardiac arrhythmias in the general population and is considered disqualifying aeromedically. This study is a unique examination of significant outcomes in aviators with previous history of both AF and stroke.METHODS: Pilots examined by the FAA between 2002 and 2012 who had had AF at some point during his or her medical history were reviewed, and those with an initial stroke or transient ischemic attack (TIA) during that time period were included in this study. All records were individually reviewed to determine stroke and AF history, medical certification history, and recurrent events. Variables collected included medical and behavior history, stroke type, gender, BMI, medication use, and any cardiovascular or neurological outcomes of interest. Major recurrent events included stroke, TIA, cerebrovascular accident, death, or other major events. These factors were used to calculate CHA2DS2-VASc scores.RESULTS: Of the 141 pilots selected for the study, 17.7% experienced a recurrent event. At 6 mo, the recurrent event rate was 5.0%; at 1 yr, 5.8%; at 3 yr 6.9%; and at 5 yr the recurrent event rate was 17.3%. No statistical difference between CHA2DS2-VASc scores was found as it pertained to number of recurrent events.DISCUSSION: We found no significant factors predicting risk of recurrent event and lower recurrence rates in pilots than the general population. This suggests CHA2DS2-VASc scores are not appropriate risk stratification tools in an aviation population and more research is necessary to determine risk of recurrent events in aviators with atrial fibrillation.Tedford J, Skaggs V, Norris A, Sahiar F, Mathers C. Recurrent stroke risk in pilots with atrial fibrillation. Aerosp Med Hum Perform. 2020; 91(4):352–357.

Dualism QM and GR

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Noncommutative Geometry ◽  
Quantum Tunneling ◽  
Closed Surface ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Surface Integral ◽  
Definition Of

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.

General Schema Theory for Genetic Programming with Subtree-Swapping Crossover: Part II

2003 ◽  
Vol 11 (2) ◽  
pp. 169-206 ◽  
Author(s):  
Riccardo Poli ◽  
Nicholas Freitag McPhee
Keyword(s):  
Genetic Programming ◽  
Schema Theory ◽  
Exact Formulation ◽  
Expected Number ◽  
Size Evolution ◽  
General Schema ◽  
Definition Of ◽  
Effective Fitness ◽  
Selection Of ◽  
Exact Definition

This paper is the second part of a two-part paper which introduces a general schema theory for genetic programming (GP) with subtree-swapping crossover (Part I (Poli and McPhee, 2003)). Like other recent GP schema theory results, the theory gives an exact formulation (rather than a lower bound) for the expected number of instances of a schema at the next generation. The theory is based on a Cartesian node reference system, introduced in Part I, and on the notion of a variable-arity hyperschema, introduced here, which generalises previous definitions of a schema. The theory includes two main theorems describing the propagation of GP schemata: a microscopic and a macroscopic schema theorem. The microscopic version is applicable to crossover operators which replace a subtree in one parent with a subtree from the other parent to produce the offspring. Therefore, this theorem is applicable to Koza's GP crossover with and without uniform selection of the crossover points, as well as one-point crossover, size-fair crossover, strongly-typed GP crossover, context-preserving crossover and many others. The macroscopic version is applicable to crossover operators in which the probability of selecting any two crossover points in the parents depends only on the parents' size and shape. In the paper we provide examples, we show how the theory can be specialised to specific crossover operators and we illustrate how it can be used to derive other general results. These include an exact definition of effective fitness and a size-evolution equation for GP with subtree-swapping crossover.

Abstract 3632: Secondary Vascular Events and Sleep Adequacy: the SWIFT Study

Stroke ◽  
2012 ◽  
Vol 43 (suppl_1) ◽  
Author(s):  
LAURA EVENSEN ◽  
Nan Liu ◽  
Yijun Wang ◽  
Bernadette Boden-Albala
Keyword(s):  
Risk Factors ◽  
Recurrent Events ◽  
Sleep Problems ◽  
Recurrent Event ◽  
Vascular Events ◽  
Respiratory Impairment ◽  
Vascular Death ◽  
Increased Risk ◽  
Falling Asleep ◽  
The Relationship

Objective: To describe the relationship between sleep problems, measured by the Medical Outcomes Sleep scale (MOS) at baseline, in ischemic stroke and TIA (IS/TIA) patients and the likelihood of having a recurrent event, leading to vascular death. Background: Among IS/TIA patients, there is increased risk for recurrent vascular events, including stroke, MI and vascular death. While history of stroke is a major predictor of recurrent events, there may be unidentified factors in play. Sleep quality may predict recurrent vascular events, but little is known about the relationship between sleep and recurrent events in IS/TIA patients. Methods: The Stroke Warning Information and Faster Treatment (SWIFT) Study is an NINDS SPOTRIAS funded randomized trial to study the effect of culturally appropriate, interactive education on stroke knowledge and time to arrival after IS/TIA. Sleep problems and recurrent event information were collected among consentable IS/TIA patients. Cox proportional hazards models were used to describe relationships between sleep and recurrent vascular events in IS/TIA patients. The MOS, a 12 item sleep assessment, measures 6 dimensions of sleep: initiation, maintenance, quantity, adequacy, somnolence and respiratory impairment. Results: Over 5 years, the SWIFT study cohort of 1198 [77% IS; 23% TIA] patients were prospectively enrolled. This cohort was 50% female; 50% Hispanic, 31% White and 18% Black, with a mean NIHSS of 3.2 [SD ±3.8]. 750 subjects completed the MOS scale at baseline. In a multivariate analysis, after adjusting for demographics and vascular risk factors: gender, age, race ethnicity, NIHSS, stroke history, qualifying event type, hypertension, diabetes, smoking and family stroke history, longer sleep initiation is associated with combined outcome of IS/TIA, MI and vascular death [p=0.1, HR=1.09]. Significant predictors of vascular death included: trouble falling asleep (initiation) [p=0.05, HR=1.15]; not ‘getting enough sleep to feel rested’ and not ‘getting the amount of sleep you need’ (adequacy) [p=0.06, HR=1.18 and p=0.03, HR=1.18, respectively]; shortness of breath or headache upon waking (respiratory impairment) [p=0.003, HR=1.33]; restless sleep [p=0.07, HR=1.15] and waking at night with trouble resuming sleep [p=0.004, HR=1.23] (maintenance); daytime drowsiness [p=0.05, HR=1.18] and trouble staying awake [p=0.01, HR=1.25] (somnolence); and taking naps (quantity) [p=0.03, HR=1.22]. Conclusions: Sleep problems represent diverse, modifiable risk factors for secondary vascular events, particularly vascular death. Exploring sleep dimensions may yield crucial information for reduction of secondary vascular events in IS/TIA patients. Further investigation is needed to fully understand the effects of sleep on secondary vascular event incidence.

scholarly journals Estimating the ratio of multivariate recurrent event rates with application to a blood transfusion study

2015 ◽  
Vol 26 (4) ◽  
pp. 1969-1981 ◽  
Author(s):  
Jing Ning ◽  
Mohammad H Rahbar ◽  
Sangbum Choi ◽  
Jin Piao ◽  
Chuan Hong ◽  
...  
Keyword(s):  
Blood Cells ◽  
Latent Variables ◽  
Recurrent Events ◽  
Blood Product ◽  
Massive Transfusion ◽  
Informative Censoring ◽  
Recurrent Event ◽  
Dependence Structure ◽  
Blood Product Transfusion ◽  
Finite Sample

In comparative effectiveness studies of multicomponent, sequential interventions like blood product transfusion (plasma, platelets, red blood cells) for trauma and critical care patients, the timing and dynamics of treatment relative to the fragility of a patient’s condition is often overlooked and underappreciated. While many hospitals have established massive transfusion protocols to ensure that physiologically optimal combinations of blood products are rapidly available, the period of time required to achieve a specified massive transfusion standard (e.g. a 1:1 or 1:2 ratio of plasma or platelets:red blood cells) has been ignored. To account for the time-varying characteristics of transfusions, we use semiparametric rate models for multivariate recurrent events to estimate blood product ratios. We use latent variables to account for multiple sources of informative censoring (early surgical or endovascular hemorrhage control procedures or death). The major advantage is that the distributions of latent variables and the dependence structure between the multivariate recurrent events and informative censoring need not be specified. Thus, our approach is robust to complex model assumptions. We establish asymptotic properties and evaluate finite sample performance through simulations, and apply the method to data from the PRospective Observational Multicenter Major Trauma Transfusion study.

scholarly journals UKRAINIAN REALIA OF THE XIX CENTURY AND ITS TRANSLATION (BASED ON THE POEM “KATERINA” BY TARAS SHEVCHENKO)

2019 ◽  
Vol 1 (16) ◽  
pp. 124-130
Author(s):  
E.I. Panchenko
Keyword(s):  
General Theory ◽  
Cultural Differences ◽  
Real World ◽  
Species Replacement ◽  
Different Types ◽  
General Meaning ◽  
Definition Of ◽  
Xix Century ◽  
Entire Array

The article is written in line with current research, since the problem of studying Ukrainian realities is of unquestionable interest for several reasons. First, understanding the realities will promote bettermutual understanding of different peoples; and secondly, the definition of optimal means of translating the realities is a definite contribution to the general theory of translation. Different types of real-world classifications are proposed, the difficulties associated with the adequate transfer into the translated text of an entire array of cultural information encoded in the realities contained in the origina text are investigated. Basing on the analysis of numerous translations of literary works, Ukrainian researchers (R. Zorivchak, V. Koptilov, O. Kundzich, O. Cherednichenko, etc.) show ways to overcome linguistic obstacles caused by cultural differences. But, as far as we know, the problem of the translation of Ukrainian realities in the works of T. Shevchenko is not yet exhaustively highlighted. The purpose of this article is to analyze the peculiarities of the use of realities in the work of Taras Shevchenko "Katerina" and their translation into English. We have given an ideographic classification of lexical units - Ukrainian realities in fiction and analyzed such means of their translation as calque, renomination, transcription with explanation, the introduction of neologism, the principle of generic-species replacement, which allows  conveying (approximately) the content of the realities by a broader, general meaning, that is, the reception of generalization. The results of our analysis allow us to make an ideographic classification of Ukrainian realities that are used in fiction, as well as to summarize the prevalence of their means of translation. Prospects for further research are seen in the analysis of certain translation failures in the translation of realities and to offer the best options for their translation.

scholarly journals A General Theory of Wilf-Equivalence for Catalan Structures

10.37236/5629 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Michael Albert ◽  
Mathilde Bouvel
Keyword(s):  
General Theory ◽  
Equivalence Relation ◽  
Generating Functions ◽  
Asymptotic Estimate ◽  
Equivalence Classes ◽  
Catalan Number ◽  
Combinatorial Structures ◽  
Dyck Paths ◽  
Significant Interest ◽  
Wilf Equivalence

The existence of apparently coincidental equalities (also called Wilf-equivalences) between the enumeration sequences or generating functions of various hereditary classes of combinatorial structures has attracted significant interest. We investigate such coincidences among non-crossing matchings and a variety of other Catalan structures including Dyck paths, 231-avoiding permutations and plane forests. In particular we consider principal subclasses defined by not containing an occurrence of a single given structure. An easily computed equivalence relation among structures is described such that if two structures are equivalent then the associated principal subclasses have the same enumeration sequence. We give an asymptotic estimate of the number of equivalence classes of this relation among structures of size $n$ and show that it is exponentially smaller than the $n^{th}$ Catalan number. In other words these "coincidental" equalities are in fact very common among principal subclasses. Our results also allow us to prove in a unified and bijective manner several known Wilf-equivalences from the literature.

scholarly journals Deliberate Practice and Expertise in Martial Arts: The Role of Context in Motor Recall

1998 ◽  
Vol 20 (3) ◽  
pp. 260-279 ◽  
Author(s):  
Thana Hodge ◽  
Janice M. Deakin
Keyword(s):  
General Theory ◽  
Martial Arts ◽  
Recall Performance ◽  
Deliberate Practice ◽  
Expert Performance ◽  
Novice Group ◽  
Definition Of ◽  
The Relationship

This study used participants from the martial arts (karate) to examine the influence of context in the acquisition of novel motor sequences and the applicability of Ericsson, Krampe, and Tesch-Romer's (1993) theory of deliberate practice in this athletic domain. The presence of context did not benefit recall performance for the experts. The performance of the novice group was hindered by the presence of context. Evaluation of the role of deliberate practice in expert performance was assessed through retrospective questionnaires. The findings related to the relationship between relevance and effort, and relevance and enjoyment diverged from Ericsson et al.'s (1993) definition of deliberate practice, suggesting that adaptations should be made if it is to be considered general theory of expertise.

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