Relation recurrence. Medical search. Frequent questions

In mathematics, a recurrence relation is an equation according to which the n {\displaystyle n} th term of a sequence of numbers is equal to some combination of the previous terms. (wikipedia.org)
A recurrence relation is an equation that expresses each element of a sequence as a function of the preceding ones. (wikipedia.org)
A linear recurrence relation is an equation that relates a term in a sequence or a multidimensional array to previous terms using recursion . (brilliant.org)
A linear recurrence relation is an equation that defines the $n^\text{th}$ term in a sequence in terms of the $k$ previous terms in the sequence. (brilliant.org)
A recurrence relation is an equation which is defined in terms of itself. (slidetodoc.com)
Solved: Suppose a recurrence relation an=4an−1−4an−2 where a1=14 and a2=40 can be represented in explicit formula, either as: Formula 1: an=pxn+qnxn or Formula 2: an=pxn+qyn where x and y are roots of the characteristic equation. (sikademy.com)
The roots of the auxiliary equation of the associated recurrence relation were derived in terms of generating functions for Fuss-Catalan numbers. (hindawi.com)

By this we mean something very similar to solving differential equations: we want to find a function of $n$ (a closed formula) which satisfies the recurrence relation, as well as the initial condition. (openmathbooks.org)
This wiki will introduce you to a method for solving linear recurrences when its characteristic polynomial has repeated roots. (brilliant.org)

The risk of distant recurrence in breast cancer patients is difficult to prognostic indices, such as the Nottingham Prognostic Index (6, 7), assess with current clinical and histopathological parameters, and have proven valuable in identifying patients with poor prognosis. (lu.se)
Distant recurrence-free interval (DRFi) was the primary end-point. (lu.se)
Conclusions: High PDGFRα and PDGF-CC expression were linked to breast cancer with an aggressive biological phenotype, e.g. the TNBC subtype, and high PDGF-CC increased the risk of 5-year distant recurrence. (lu.se)

In linear recurrences, the nth term is equated to a linear function of the k {\displaystyle k} previous terms. (wikipedia.org)
As well, linear recurrences with polynomial coefficients depending on n {\displaystyle n} are also important, because many common elementary and special functions have a Taylor series whose coefficients satisfy such a recurrence relation (see holonomic function). (wikipedia.org)

The recurrence of order two satisfied by the Fibonacci numbers is the canonical example of a homogeneous linear recurrence relation with constant coefficients (see below). (wikipedia.org)

We are going to try to solve these recurrence relations. (openmathbooks.org)
Sometimes we can be clever and solve a recurrence relation by inspection. (openmathbooks.org)
We can use this behavior to solve recurrence relations. (openmathbooks.org)
1. Make up your own recurrences and solve them! (brilliant.org)
In the wiki Linear Recurrence Relations, linear recurrence is defined and a method to solve the recurrence is described in the case when its characteristic polynomial has only roots of multiplicity one. (brilliant.org)
We are going to explain how the method explained in Linear Recurrence Relations can be modified to solve this other linear recurrence relations too. (brilliant.org)
Hello, I have four recurrence equations which I would like to solve simultanously but, Mathematica keeps giving me the input line in the output. (wolfram.com)

A famous example is the recurrence for the Fibonacci numbers, F n = F n − 1 + F n − 2 {\displaystyle F_{n}=F_{n-1}+F_{n-2}} where the order k {\displaystyle k} is two and the linear function merely adds the two previous terms. (wikipedia.org)
The Fibonacci sequence is defined using the recurrence F n = F n − 1 + F n − 2 {\displaystyle F_{n}=F_{n-1}+F_{n-2}} with initial conditions F 0 = 0 {\displaystyle F_{0}=0} F 1 = 1. (wikipedia.org)

We generate the sequence using the recurrence relation and keep track of what we are doing so that we can see how to jump to finding just the $a_n$ term. (openmathbooks.org)
They come down to computing linear recurrence relations of a sequence with the Berlekamp-Massey algorithm. (hal.science)
Likewise, sparse multivariate polynomial interpolation and multidi-mensional cyclic code decoding require guessing linear recurrence relations of a multivariate sequence. (hal.science)
We propose a new algorithm for computing the Gröbner basis of the ideal of relations of a sequence based solely on multivariate polynomial arithmetic. (hal.science)
As explained in Linear Recurrence Relations , the sequence $\alpha_n=2^n$ is one of the solutions. (brilliant.org)
Many may not realise that the sequence of a's is in some sense already there, and the recurrence relation tells them how to calculate one term from others no matter what part of the sequence they are looking at. (stackexchange.com)

Explicitly, the recurrence yields the equations F 2 = F 1 + F 0 {\displaystyle F_{2}=F_{1}+F_{0}} F 3 = F 2 + F 1 {\displaystyle F_{3}=F_{2}+F_{1}} F 4 = F 3 + F 2 {\displaystyle F_{4}=F_{3}+F_{2}} etc. (wikipedia.org)
2 Recurrence relations are sometimes called difference equations since they can describe the difference between terms and this highlights the relation to differential equations further. (openmathbooks.org)

1.} This is an example of a linear recurrence with polynomial coefficients of order 1, with the simple polynomial f ( n ) = n {\displaystyle f(n)=n} as its only coefficient. (wikipedia.org)
The use of the word linear refers to the fact that previous terms are arranged as a 1st degree polynomial in the recurrence relation. (brilliant.org)
Moving the terms over, we get \[r^k-c_1r^{k-1}-c_2r^{k-2}-\cdots-c_k=0,\] which is a polynomial in $r$, so the solution satisfies the recurrence only if $r$ is a root of this polynomial. (brilliant.org)
This polynomial is called the characteristic polynomial of the recurrence. (brilliant.org)
A linear recurrence with repeated roots is a linear recurrence of the form \[x_n=c_1x_{n-1}+c_2x_{n-2}+\cdots+c_kx_{n-k},\] where all the $c$'s are constants, and whose characteristic polynomial, $r^k-c_1r^{k-1}-c_2r^{k-2}-\cdots-c_k,$ may have repeated roots, that is, roots with multiplicity higher than 1. (brilliant.org)
The characteristic polynomial of this recurrence relation is \(r^2-4r+4. (brilliant.org)
Since the order of the recurrence, which is also equal to the degree of the characteristic polynomial, is 2, we need to get another independent solution. (brilliant.org)

Methods: Protein expression of tumour and/or stromal cell PDGFRα, PDGFRβ and PDGF-CC was evaluated in primary tumours (N = 489), synchronous lymph node metastases (N = 135) and asynchronous recurrences (N = 39) using immunohistochemistry in a prospectively maintained cohort of primary breast cancer patients included during 1999-2003. (lu.se)
High primary tumour PDGFRα was associated with increased risk of central nervous system (CNS) recurrence. (lu.se)
Tumour cell PDGFRα was significantly up-regulated in lymph node metastases and asynchronous recurrences. (lu.se)
Radiological findings do not support lateral residual tumour as a major cause of local recurrence of rectal cancer. (cancercentrum.se)

Recall that the recurrence relation is a recursive definition without the initial conditions. (openmathbooks.org)

No obvious predictors for maternal events or child outcome were determined, except for a possible relation between severe pulmonary regurgitation and symptomatic heart failure. (bmj.com)
We aimed to describe the management and outcome of patients with CIED and monomicrobial EfsB, in relation to extraction and recurrent EfsB. (lu.se)
Colon cancer management and outcome in relation to individual hospitals in a defined population. (cancercentrum.se)

Sixty percent of patients with triple-negative breast cancer will survive more than five years without disease, but four out of ten women will have a rapid recurrence of the disease. (utah.edu)

Regarding prognosis, high pMVD, Ktrans, kep, and low ADC were associated with reduced biochemical recurrence-free- and metastasis-free survival (p ≤ 0.044) and high blood flow with reduced time to biochemical- and clinical recurrence (p (bvsalud.org)

Plaque progression was significantly associated with clinical stroke recurrence. (eurekaselect.com)
The authors say the next step is a new clinical study expected to begin in early 2020, which utilizes this discovery to enroll patients who are at high risk for recurrence and evaluates new treatment options for them. (iu.edu)

Currently, MammaPrint is the only breast cancer recurrence assay available that accurately yields a binary result, without an intermediate group, addressing the panel's recommendations. (science20.com)

This defines recurrence relation of first order. (wikipedia.org)

Remember, the recurrence relation tells you how to get from previous terms to future terms. (openmathbooks.org)
The recurrence relation tells you how to calculate a$_{n+1}$ from a$_n$, and you can represent this as an arrow. (stackexchange.com)

Background and Purpose: The purpose of this study was to show dynamic changes in carotid and vertebral artery using carotid Doppler ultrasonography (DUS) through a long-term follow- up exam, and determine their associations with stroke recurrence. (eurekaselect.com)
Stroke recurrence during follow-up was also investigated by reviewing medical records. (eurekaselect.com)
The relationship between plaque change and stroke recurrence was investigated. (eurekaselect.com)
After adjustment of age, sex, diabetes, and stroke subtype, multiple logistic regression showed a significant association of plaque progression with stroke recurrence (odds ratio: 3.8, 95% confidence interval: 1.1 to 13.1, p = 0.034). (eurekaselect.com)

Here, we studied microvascular proliferation by Nestin-Ki67 co-expression in prostate cancer, focusing on relations to quantitative imaging parameters from anatomically matched areas obtained by preoperative mpMRI, clinico-pathological features and prognosis. (bvsalud.org)
Host, reproductive, and lifestyle factors in relation to quantitative histologic metrics of the normal breast. (medscape.com)

Ongoing research and development efforts continue to augment Agendia's ability to accurately predict breast cancer recurrence, and help physicians tailor individual treatment plans to their patients. (science20.com)
This predict the likelihood of a later recurrence, i.e., an indicator that unique longitudinal sample material was collected from each pa- allows risk assessment for breast cancer metastasis, would be tient between 0 and 36 mo after the primary operation. (lu.se)

Agendia, a world leader in molecular cancer diagnostics, today announced the inclusion of its breast cancer recurrence test MammaPrint in St. Gallen's 2009 International Expert Consensus on the primary therapy of early breast cancer. (science20.com)
This study aimed to evaluate the expression of PDGFRα, PDGFRβ and ligand PDGF-CC in breast cancer in relation to molecular subtypes and prognosis. (lu.se)
Learn more about CanAssist Breast -- a novel prognostic test for predicting the risk of breast cancer recurrence ten years after diagnosis. (medscape.com)

Also, note that if two geometric series satisfy a recurrence, the sum of them also satisfies the recurrence. (brilliant.org)

To determine in women with surgically corrected tetralogy of Fallot the risk of pregnancy for mother and fetus, whether fertility was compromised, and the recurrence risk of congenital heart disease. (bmj.com)
UTI affects all age to assess its relation with some possible groups, but women are more susceptible risk factors such as age, duration of preg- than men, due to short urethra, absence of nancy and parity. (who.int)
Even more importantly, we veal important information about the risk of recurrence. (lu.se)
Agency is provided by the study of of carcinogenesis associated with the treatment of invasive cervical cancer the role of cutaneous HPV types in important risk factors for two common by decreasing recurrences of cancerous skin carcinogenesis, carried out by the human cancers. (who.int)

identified to interpret the significance in complementarity between laboratory relation to cancer prevention. (who.int)

Symptomatic infections can be characterized by significant morbidity and recurrence. (medscape.com)

Find the order and degree of the following recurrence relation. (ignougroup.com)
We find that the success of cooperation depends on a simple relation between the benefits and costs of the public good, the amount retained by a producer, and the average amount retained by each of the producer's neighbors. (cdc.gov)

No infections involving the CIED were diagnosed during the recurrences. (lu.se)

this number k {\displaystyle k} is called the order of the relation. (wikipedia.org)
Considering the increase time life expectation, the need of a continuous working life in order to maintain a financial independence and social recognition, it is concluded that vocational guidance before retirement is important, mainly, in respect to constructing future choices and life projects, and shaping images about the retired condition, attending the relation between identity and work. (bvsalud.org)

No clear relation between offspring mortality, premature birth or being small for gestational age, and cardiac characteristics of the mother was identified. (bmj.com)
A relation between migraine with aura and cardiac right-to-left shunts has been reported. (nih.gov)

8: Papers on Linear Recurrence Relations. (gale.com)

A solution to a recurrence relation gives the value of $x_n$ in terms of $n$, and does not require the value of any previous terms. (brilliant.org)
Patients with high PDGF-CC had inferior prognosis (P = 0.04) in terms of 5-year DRFi, whereas PDGFRα was up-regulated in lymph node metastasis and recurrences compared to primary tumours. (lu.se)

Recurrences were found in seven of 68 patients (10%) not subjected to extraction and in none of the extracted. (lu.se)

Stirling numbers of the second kind: How to obtain a recurrence relation from a generating function? (stackexchange.com)

given the initial term x 0 {\displaystyle x_{0}} , each subsequent term is determined by this relation. (wikipedia.org)

Both have easy recurrence relations that are found in any educational resource. (stackexchange.com)

The list below includes all high-impact factor Recurrence relation journals as well as new up and comming journals where it might also be more affordable to publish. (oa.mg)

Surgical excision is the treatment of choice, recurrence being rare. (bvsalud.org)

2.4 Recurrence Relations" Discrete Mathematics: An Open Introduction openmathbooks.org University of Northern Colorado. (blogspot.com)

Anatomy12

Diseases82

Chemicals and Drugs18

Analytical, Diagnostic and Therapeutic Techniques and Equipment121

Psychiatry and Psychology2

Phenomena and Processes15

Disciplines and Occupations1

Anthropology, Education, Sociology and Social Phenomena1

Technology, Industry, Agriculture1

Humanities1

Information Science6

Named Groups2

Health Care49

Geographicals5

Equation7

Solving2

Distant recurrence3

Linear recurrences2

Constant coefficients1

Solve7

Fibonacci2

Sequence6

Equations2

Polynomial7

Tumour4

Recursive1

Outcome3

Triple-Negati1

Survival1

Clinical2

Yields1

Defines1

Tells2

Stroke4

Quantitative2

Predict2

Breast cancer3

Satisfy1

Risk4

Prevention1

Symptomatic1

Find2

Infections1

Order2

Cardiac2

Papers1

Terms2

Patients1

Function1

Term1

Found1

High1

Treatment1

University1