###### example of a recurrence relation

- However, the Ackermann numbers are an example of a recurrence relation that do not map to a difference equation, much less points on the solution to a differential equation. (wikipedia.org)

###### Eternal Recurrence

- Yet her latest album, the entrancing and seismic Eternal Recurrence , is unlike anything she's ever recorded. (anticon.com)
- Right before The Expanding Flower Planet was released in 2015, Deradoorian decamped to Big Sur for a formative ten days and began crafting what would become Eternal Recurrence , out October 6, 2017 on Anticon. (anticon.com)
- Fittingly, Eternal Recurrence, brims with meditative affirmations that mimic cycles, planetary and otherwise. (anticon.com)
- The stirring songs comprising Eternal Recurrence also probe an uninhibited form of expression, particularly within the warbles of "Love Arise" and the watery underworld of emotion on the instrumental piece "Ausar Temple. (anticon.com)
- Honoring and extending gratitude towards friends, and their individual strengths, became crucial to constructing Eternal Recurrence , as well. (anticon.com)
- The transcendent "Love Arise," which opens Eternal Recurrence , was also written as an ode to a friend, Nai Palm of Hiatus Kaiyote. (anticon.com)
- Yet the meditative song-in which Deradoorian sings "love's the only thing keeping me alive-also functions as a kind of underlying thesis for Eternal Recurrence , an album whose wonders unfurl further with every listen. (anticon.com)
- Hypothetically, in the extreme, the concept of historic recurrence assumes the form of the Doctrine of Eternal Recurrence, which has been written about in various forms since antiquity and was described in the 19th century by Heinrich Heine and Friedrich Nietzsche. (wikipedia.org)
- Eternal Recurrence is an EP by Deradoorian, a former member of Dirty Projectors. (wikipedia.org)
- Paul Simpson of AllMusic gave Eternal Recurrence 3.5 stars out of 5, calling it "a fine, thoughtful piece of ambient drone-folk that is as challenging as it is assuring. (wikipedia.org)
- gave Eternal Recurrence a 7 out of 10, stating that "[Eternal Recurrence] pulls back on the rhythmic side of her intercontinental folkloric psychedelia in favour of something more meditative, untethered and texturally focused. (wikipedia.org)

###### quantification

- In contrast to the heuristic approach of the recurrence quantification analysis, which depends on the choice of the embedding parameters, some dynamical invariants as correlation dimension, K2 entropy or mutual information, which are independent on the embedding, can also be derived from recurrence plots. (wikipedia.org)
- Cross-recurrence quantification (CRQ) is a non-linear method that quantifies how similarly two observed data series unfold over time. (wikipedia.org)
- Recurrence quantification analysis (RQA) is a method of nonlinear data analysis (cf. chaos theory) for the investigation of dynamical systems. (wikipedia.org)
- The recurrence quantification analysis was developed in order to quantify differently appearing recurrence plots (RPs) based on the small-scale structures therein. (wikipedia.org)
- Recurrence quantification analysis, another approach to quantify recurrence properties. (wikipedia.org)

###### introduced recurrence plots

- 1987) introduced recurrence plots, which provide a way to visualize the periodic nature of a trajectory through a phase space. (wikipedia.org)

###### defined recurrence relations

- Some simply defined recurrence relations can have very complex ( chaotic ) behaviours, and they are a part of the field of mathematics known as nonlinear analysis . (wikipedia.org)

###### phase space trajectory

- In descriptive statistics and chaos theory, a recurrence plot (RP) is a plot showing, for a given moment in time, the times at which a phase space trajectory visits roughly the same area in the phase space. (wikipedia.org)
- However, making a recurrence plot enables us to investigate certain aspects of the m-dimensional phase space trajectory through a two-dimensional representation. (wikipedia.org)
- Caused by characteristic behaviour of the phase space trajectory, a recurrence plot contains typical small-scale structures, as single dots, diagonal lines and vertical/horizontal lines (or a mixture of the latter, which combines to extended clusters). (wikipedia.org)
- It quantifies the number and duration of recurrences of a dynamical system presented by its phase space trajectory. (wikipedia.org)
- Recurrence plots are tools which visualise the recurrence behaviour of the phase space trajectory of dynamical systems. (wikipedia.org)

###### cross recurrence

- Multivariate extensions of recurrence plots were developed as cross recurrence plots and joint recurrence plots. (wikipedia.org)

###### dynamical

- Moreover, the recurrence of states, in the meaning that states are again arbitrarily close after some time of divergence, is a fundamental property of deterministic dynamical systems and is typical for nonlinear or chaotic systems (cf. (wikipedia.org)
- The base for these dynamical invariants are the recurrence rate and the distribution of the lengths of the diagonal lines. (wikipedia.org)
- The RQA quantifies the small-scale structures of recurrence plots, which present the number and duration of the recurrences of a dynamical system. (wikipedia.org)
- This measure is called determinism and is related with the predictability of the dynamical system, because white noise has a recurrence plot with almost only single dots and very few diagonal lines, whereas a deterministic process has a recurrence plot with very few single dots but many long diagonal lines. (wikipedia.org)
- Recurrence period density entropy (RPDE) is a method, in the fields of dynamical systems, stochastic processes, and time series analysis, for determining the periodicity, or repetitiveness of a signal. (wikipedia.org)
- Recurrence plot, a powerful visualisation tool of recurrences in dynamical (and other) systems. (wikipedia.org)

###### tumor

- Failure to completely remove the tumor results in recurrence within 6-12 months. (hindawi.com)
- Many factors can cause a rise in tumor markers other than a recurrence. (medhelp.org)
- We were surprised to find that even with relatively low thyroglobulin levels, and even when there is no sign of a tumor, about 80 percent of patients had a recurrence of their cancer within three to five years," says first author Richard T. Kloos, associate professor of internal medicine and of radiology. (redorbit.com)

###### nonlinear

- The recurrence period density is a sparse representation for nonlinear, non-Gaussian and nondeterministic signals, whereas the Fourier transform is only sparse for purely periodic signals. (wikipedia.org)
- M.A. Little, P.E. McSharry, S.J. Roberts, D.A.E. Costello, I.M. Moroz (2007) Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection, BioMedical Engineering OnLine, 6:23 J. Stark, D. S. Broomhead, M. E. Davies and J. Huke (2003) Delay Embeddings for Forced Systems. (wikipedia.org)

###### displaystyle

- 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 (seed values) F 0 = 0 {\displaystyle F_{0}=0} F 1 = 1. (wikipedia.org)
- 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)
- A simple example of a multidimensional recurrence relation is given by the binomial coefficients ( n k ) {\displaystyle {\tbinom {n}{k}}} , which count the number of ways of selecting k elements out of a set of n elements. (wikipedia.org)
- An order-d homogeneous linear recurrence with constant coefficients is an equation of the form a n = c 1 a n − 1 + c 2 a n − 2 + ⋯ + c d a n − d , {\displaystyle a_{n}=c_{1}a_{n-1}+c_{2}a_{n-2}+\cdots +c_{d}a_{n-d},} where the d coefficients ci (for all i) are constants. (wikipedia.org)
- To make the plot, continuous time and continuous phase space are discretized, taking e.g. x → ( i ) {\displaystyle {\vec {x}}(i)} as the location of the trajectory at time i τ {\displaystyle i\tau } and counting as a recurrence any time the trajectory gets sufficiently close (say, within ε) to a point it has been previously. (wikipedia.org)
- The difference is that the relative time between recurrences is used for the y {\displaystyle y} -axis (instead of absolute time). (wikipedia.org)
- The simplest measure is the recurrence rate, which is the density of recurrence points in a recurrence plot: RR = 1 N 2 ∑ i , j = 1 N R ( i , j ) . {\displaystyle {\text{RR}}={\frac {1}{N^{2}}}\sum _{i,j=1}^{N}\mathbf {R} (i,j). (wikipedia.org)

###### homogeneous

- The recurrence satisfied by the Fibonacci numbers is the archetype of a homogeneous linear recurrence relation with constant coefficients (see below). (wikipedia.org)

###### plots

- Close returns plots are similar to recurrence plots. (wikipedia.org)
- The main advantage of recurrence plots is that they provide useful information even for short and non-stationary data, where other methods fail. (wikipedia.org)

###### relation

- In mathematics , a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms. (wikipedia.org)
- The term difference equation sometimes (and for the purposes of this article) refers to a specific type of recurrence relation. (wikipedia.org)
- However, "difference equation" is frequently used to refer to any recurrence relation. (wikipedia.org)
- This is a recurrence relation (or simply recurrence ) defining a function T(n). (cornell.edu)
- The recurrence relation is an inductive definition of a function. (cornell.edu)
- This particular recurrence relation has a unique closed-form solution that defines T(n) without any recursion. (cornell.edu)
- We somehow need to figure out how often the first versus the second branch of this recurrence relation will be taken. (cornell.edu)

###### 2002

- Relentless Recurrence is the third studio album by the Taiwanese black metal band Chthonic, released in 2002. (wikipedia.org)

###### breast cancer

- In today's podcast, we're going to discuss HER2-positive breast cancer and its recurrence risk. (breastcancer.org)
- Every person's risk of breast cancer recurrence is unique, we know that. (breastcancer.org)
- So, when we talk to our patients about breast cancer and risk of recurrence, often it's very frightening to go online or to read about the risk of recurrence. (breastcancer.org)

###### sequences

- Single-variable or one-dimensional recurrence relations are about sequences (i.e. functions defined on one-dimensional grids). (wikipedia.org)
- Recurrence sequences. (wikipedia.org)

###### cancers

- A hysterectomy is usually curative because most cancers have a low risk of spreading (metastasising) to other sites which may result in a later recurrence. (cochrane.org)

###### prove

- E: Exercise The Dana Farber Cancer Institute has done several studies which prove recurrence can be avoided at a rate of 55% in Stage III women who exercise regularly. (dailystrength.org)
- More generally, we guess a closed form solution for a recurrence, and then prove by induction that it holds. (cornell.edu)

###### percentage

- CRQ produces measures reflecting coordination, such as how often two data series have similar values or reflect similar system states (called percentage recurrence, or %REC), among other measures. (wikipedia.org)

###### solve

- I missed the lectures that addressed how to solve these kinds of problems, and while studying my recommended text book it only went as far as solving recurrence relations that are equal to 0 as opposed to 2 n . (physicsforums.com)
- I understand how to solve the simple recurrence relations but I have no clue as to what to do with these. (physicsforums.com)

###### density

- Recurrence period density entropy is useful for characterising the extent to which a time series repeats the same sequence, and is therefore similar to linear autocorrelation and time delayed mutual information, except that it measures repetitiveness in the phase space of the system, and is thus a more reliable measure based upon the dynamics of the underlying system that generated the signal. (wikipedia.org)

###### radiation

- For instance, when used as part of a mesothelioma recurrence treatment plan, radiation therapy is primarily intended to shrink tumors to reduce pressure within the chest or abdomen. (moffitt.org)
- At Moffitt Cancer Center, our oncologists can expertly treat your mesothelioma recurrence using the best possible combination of options, from chemotherapy and radiation therapy to surgery and clinical trials. (moffitt.org)
- Biochemical recurrence is a rise in the blood level of prostate-specific antigen (PSA) in prostate cancer patients after treatment with surgery or radiation. (wikipedia.org)

###### probability

- The recurrence rate corresponds with the probability that a specific state will recur. (wikipedia.org)

###### cancer

- In many cases, the small reduction in the cancer recurrence risk may not be worth the side effects of adjuvant treatment. (cochrane.org)
- Learn more about cancer recurrence and living with this possibility here. (cancer.org)
- What Is Cancer Recurrence? (cancer.org)
- If cancer is found after treatment, and after a period of time when the cancer couldn't be detected, it's called a cancer recurrence. (cancer.org)
- Can I Do Anything to Prevent Cancer Recurrence? (cancer.org)
- Many issues and questions come with cancer recurrence. (cancer.org)
- Easy reading information about cancer recurrence. (cancer.org)
- Some mesothelioma survivors will experience a recurrence, or a return of their cancer after a period of it being undetectable. (moffitt.org)
- These cells are resistant to current treatments and play a significant role in both metastasis and recurrence, which are two of the biggest challenges in cancer treatment. (medicalnewstoday.com)
- In addition, about 330,000 living Americans have been treated for thyroid cancer, about 20 percent of whom are likely to have a recurrence. (redorbit.com)
- Biochemical recurrence Defining Biochemical Recurrence of Prostate Cancer After Radical Prostatectomy: A Proposal for a Standardized Definition. (wikipedia.org)
- 2005 Guidelines:Prostate cancer/Management/Locally advanced and metastatic/Biochemical relapse alternative causes, and implications for treatment Defining Biochemical Recurrence of Prostate Cancer After Radical Prostatectomy: A Proposal for a Standardized Definition 10 definitions compared. (wikipedia.org)
- Electronic Saviors Volume 2: Recurrence is the second Electronic Saviors cancer charity compilation compiled by Jim Semonik of Rein[Forced], a cancer survivor. (wikipedia.org)

###### occur

- However, there isn't a way to predict with any certainty which patients will have a recurrence or when it might occur. (moffitt.org)
- Biochemical recurrence may occur in patients who do not have symptoms. (wikipedia.org)

###### historic

- Historic recurrence is the repetition of similar events in history. (wikipedia.org)
- The concept of historic recurrence has variously been applied to the overall history of the world (e.g., to the rises and falls of empires), to repetitive patterns in the history of a given polity, and to any two specific events which bear a striking similarity. (wikipedia.org)
- Historic recurrences can sometimes induce a sense of "convergence", "resonance" or déjà vu. (wikipedia.org)
- Prior to the theory of historic recurrence that was offered by Polybius, a Greek Hellenistic historian (ca 200 - ca 118 BCE), ancient western thinkers who had thought about recurrence had largely been concerned with cosmological rather than historic recurrence. (wikipedia.org)
- Western philosophers and historians who have discussed various concepts of historic recurrence include Polybius, the Greek historian and rhetorician Dionysius of Halicarnassus (c. 60 BCE - after 7 BCE), Luke the Evangelist, Niccolò Machiavelli (1469-1527), Giambattista Vico (1668-1744), Arnold J. Toynbee (1889-1975). (wikipedia.org)
- An eastern concept that bears a kinship to western concepts of historic recurrence is the Chinese concept of the Mandate of Heaven, by which an unjust ruler will lose the support of Heaven and be overthrown. (wikipedia.org)
- G.W. Trompf notes that most western concepts of historic recurrence imply that "the past teaches lessons for. (wikipedia.org)

###### form

- To learn more about treatment for a mesothelioma recurrence, or to schedule a diagnostic consultation if you are experiencing new or recurrent symptoms, schedule an appointment by calling 1-888-MOFFITT or submitting a new patient registration form online. (moffitt.org)
- In order to determine the running time of recursive functions we will write recurrences that describe the running time, find closed form solutions to them, and express those solutions in terms of Big-O notation. (cornell.edu)
- Since difference equations are a very common form of recurrence, some authors use the two terms interchangeably. (wikipedia.org)
- A constant-recursive sequence is a sequence satisfying a recurrence of this form. (wikipedia.org)

###### probe

- In 2006, Farhan Saif used quantum recurrence phenomena of wave packet as a probe to study nano-structures on a surface, naming it Recurrence Tracking Microscope (RTM). (wikipedia.org)

###### relations

- Ahlbrandt C.D., Peterson A.C. (1996) Symmetric Three Term Recurrence Relations. (springer.com)
- Multi-variable or n-dimensional recurrence relations are about n-dimensional grids. (wikipedia.org)

###### Surgery

- Treatment, however, tends to be different for a mesothelioma recurrence - especially if a patient already had a more extensive surgery, such as an extrapleural pneumonectomy, during their first round of treatment. (moffitt.org)

###### symptoms

- Therefore, it is beneficial for patients to carefully adhere to their physician-recommended schedules for follow-up visits, while also staying alert for any symptoms that could indicate a mesothelioma recurrence. (moffitt.org)

###### patients

- The study also found that even when Tg levels are very low or undetectable, about 2 to 5 percent of patients still have a recurrence after three to five years. (redorbit.com)

###### disease

- While some of the reported events are less common than others, they all took a toll on the women and, scientists believe, may have contributed to the recurrence of disease. (medicalnewstoday.com)
- The findings suggest that people treated for the disease should be examined regularly for early signs of recurrence. (redorbit.com)

###### specific

- Other minor cases of recurrence thinking," he writes, "include the isolation of any two specific events which bear a very striking similarity [his emphasis], and the preoccupation with parallelism [his emphasis], that is, with resemblances, both general and precise, between separate sets of historical phenomena. (wikipedia.org)

###### five years

- The small, retrospective study showed that women who faced physical or sexual abuse or life-threatening situations see metastatic tumors return after about 2.5 years, compared with women who have more peaceful lives, who see recurrence at about five years. (medicalnewstoday.com)

###### take

- Recurrences take place due to ascertainable circumstances and chains of causality. (wikipedia.org)

###### consider

- What factors do you consider when you're estimating someone's risk of recurrence? (breastcancer.org)

###### idea

- G.W. Trompf, in his book The Idea of Historical Recurrence in Western Thought, traces historically recurring patterns of political thought and behavior in the west since antiquity. (wikipedia.org)

###### known

- known as Birkhoff Multiple Recurrence theorem. (planetmath.org)
- The recurrence of states in nature has been known for a long time and has also been discussed in early work (e.g. (wikipedia.org)