Maximum entropy random walk

Namely, the maximum entropy rate is obtained with a Markov random walk in which the probability to step from node i to node j is equal to a ij u j λu i, where λ is the largest eigenvalue of the adjacency matrix A ={a ij}ofthegraphanduistheassociatedeigenvector[16]. The corresponding value of the maximum entropy rate is equal to lnλ. This random walk process has the interestin We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In particular, we consider a lattice with weak dilution This new random walk maximizes Shannon entropy of trajectories and can be thus called maximal entropy random walk (MERW). The difference between GRW and MERW is clearly seen when one considers the stationary probability of finding the particle at a given lattice site after a very long time. In GRW the particle diffuses over the whole lattice while in MERW the diffusion area is constrained to the largest lattice region which is free of defects. It is very similar to the localization. basic Maximal Entropy Random Walk (MERW) choice will be derived and discussed in general form - including asymmetric graphs, multi-edge graphs, periodic graphs and various transition times. Next MERW will be first extended by using potential to assign weights to paths. Withi Stationary properties of maximum-entropy random walks Purushottam D. Dixit* Department of Systems Biology, Columbia University, New York, New York 10032, United States (Received 22 June 2015; published 23 October 2015) Maximum-entropy (ME) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic systems, how state space topology and path-dependent constraint

Entropy of random trajectories St = − P {γ(t) ab} P(γ(t) ab)lnP(γ (t) ab) Entropy production rate (Shannon, McMillan): s ≡ lim t→∞ St t = − X i π∗ i X j P ijlnP s GRW = P P ik lnk ik = hlnkii∗ Maximal entropy: s max = lnNt t = ln(At)ab t ∼ lnλmax Inequality: s GRW ≤ s ma Localization of Maximal Entropy Random Walk Zdzisław Burda Marian Smoluchowski Institute of Physics, Jagellonian University, Krakow, Poland joint work with J. Duda, J.-M. Luck and B. Waclaw PUC, Rio de Janeiro, September the 10th, 201 Maximal Entropy Random Walk - maximizing entropy rate for a graph Notes Edit ^ For example, the class of all continuous distributions X on R with E( X ) = 0 and E( X 2 ) = E( X 3 ) = 1 (see Cover, Ch 12)

In mathematics, a random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.. An elementary example of a random walk is the random walk on the integer number line, , which starts at 0 and at each step moves +1 or −1 with equal probability In this work, we developed a computational model of Maximal Entropy Random Walk on heterogenous network for MiRNA-disease Association prediction (MERWMDA) This new random walk maximizes Shannon entropy of trajectories and can thus be called maximal entropy random walk (MERW). The difference between GRW and MERW is clearly seen when you consider the stationary probability of finding the particle at a given node of a graph after a very long time To address this issue, we use maximal entropy random walk (MERW) for link prediction, which incorporates the centrality of nodes of the network. First, we study certain important properties of MERW on graph $G$ by constructing an eigen-weighted graph G

http://demonstrations.wolfram.com/GenericRandomWalkAndMaximalEntropyRandomWalk/The Wolfram Demonstrations Project contains thousands of free interactive visu.. Maximal entropy random walk on heterogenous network for MIRNA-disease Association prediction Math Biosci. 2018 Dec;306:1-9. doi: 10.1016/j.mbs.2018.10.004. Epub 2018 Oct 16. Authors Ya-Wei Niu 1 , Hua Liu 1 , Guang-Hui Wang 2 , Gui-Ying Yan 3 Affiliations 1 School of Mathematics, Shandong. The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their key part is a (dis)similarity matrix, according to which nodes are grouped. This study en- compasses the use of a stochastic matrix of a random walk, its mean.

In this sense, MERW is the most random of random walks, which maximizes the entropy rate 12, 13 and is in striking contrast with the traditional unbiased random walks (TURW) and other biased random.. Maximal Entropy Random Walk for Region-Based Visual Saliency Abstract: Visual saliency is attracting more and more research attention since it is beneficial to many computer vision applications. In this paper, we propose a novel bottom-up saliency model for detecting salient objects in natural images. First, inspired by the recent advance in the realm of statistical thermodynamics, we adopt a. Maximal entropy random walk (MERW) is a popular type of biased random walk on a graph, in which transition probabilities are chosen accordingly to the principle of maximum entropy, which says that the probability distribution which best represents the current state of knowledge is the one with largest entropy. While standard random walk chooses for every vertex uniform probability distribution.

(PDF) Binary versus non-binary information in real time

Localization of the maximal entropy random wal

  1. In this spirit we define the entropy of a random walk (or asymptotic entropy) as h = limsup n!1 H(X n) n: Another property of a random walk one might want to discuss is how fast (if at all) the random walker drifts away from a certain reference point, say the identity 1 of G. To measure that, we define the speed of a random walk as '= limsup n!1 EjX nj n
  2. In a nutshell, while a simple random walker is blind (or drunk) and therefore chooses the next node to visit uniformly at random among nearest neighbors, a maximal-entropy random walker is..
  3. Maximum when = = 1=2: degenerate to independent process Dr. Yao Xie, ECE587, Information Theory, Duke University 16. Random walk on graph An undirected graph with m nodes f1;:::;mg Edge i! j has weight Wij 0 (Wij = Wji) A particle walks randomly from node to node Random walk X1;X2;: a sequence of vertices Given Xn = i, next step chosen from neighboring nodes with probability Pij = Wij ∑ k.

Maximal entropy random walk for region-based visual saliency. Yu JG, Zhao J, Tian J, Tan Y. Visual saliency is attracting more and more research attention since it is beneficial to many computer vision applications. In this paper, we propose a novel bottom-up saliency model for detecting salient objects in natural images. First, inspired by the recent advance in the realm of statistical. Maximum-entropy (ME) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic systems, how state space topology and path-dependent constraints affect ME-inferred state probabilities remains unknown. To that end, we derive the transition probabilities and the stationary distribution of a maximum path entropy Markov process. The concept of maximal entropy random walk (MERW) is based on the idea of equiprob-able trajectories (Phys. Rev. Lett. 102, 160602). The most surprising feature of this type of random walk is that it exhibits localisation on almost regular lattices with a weak disorder coming from diluted irregularities of the lattice. In the talk we shortly recall the de nition of MERW and discuss its various.

Generic Random Walk and Maximal Entropy Random Walk

We use maximal entropy random walk (MERW) to study the trapping problem in dendrimers modeled by Cayley trees with a deep trap fixed at the central node. We derive an explicit expression for the mean first passage time from any node to the trap, as well as an exact formula for the average trapping time (ATT), which is the average of the source-to-trap mean first passage time over all non-trap. Maximum entropy random walk. Contribute to alcatras/merw development by creating an account on GitHub Maximal entropy random walk. Media; Formats; Statistics; Available formats. The following formats are available for viewing. 64 views MPEG-4 Video (360p quality for download) - download. File size: 759.61 MB Width: 480, Height: 360.

The calculated AIC weights of the three cross-sectional

Extended Maximal Entropy Random Wal

Maximal Entropy Random Walk on heterogenous network for MiRNA-disease Association prediction - boonty/MERWMD Internet Archive BookReader Maximal-entropy random walk unifies centrality measure

While introducing random walk on given graph, we usually assume that for each vertex, each outgoing edge has equal probability. This random walk usually emphasize some path. If we work on the space of all possible paths, we would like to have uniform distribution among them to maximize entropy. I.. Reset your password. If you have a user account, you will need to reset your password the next time you . You will only need to do this once Stationary States of Maximal Entropy Random Walk and Generic Random Walk on Cayley Tree The maximum entropy nonnegative random variable with mean m is exponentially distributed with parameter X = l/m. Even the Cauchy distribution is a maximum entropy distribution over all distributions satisfying E In (1 + X2) = (Y. In general, the maximum entropy density f(x) under the constraint P(x)f(x) dx = (Y,. where h is a vector-valued function of x, is of the form f(x) = exp (X, + XI/z(x. Routines for fitting maximum entropy models¶ Contains two classes for fitting maximum entropy models subject to linear constraints on the expectations of arbitrary feature statistics. One class, model, is for small discrete sample spaces, using explicit summation. The other, bigmodel, is for sample spaces that are either continuous.

random walks and spanning trees is documented in [Pem]; the main result that will be used from there is that P(e2T) is determined by certain hitting probabilities, but the reader desiring more details may also consult [Al2] or [Bro]. Section 4 uses these lemmas to show that the Green's function is the unique limit of Green's functions on nite subgraphs and that it in fact determines the f. Burda Z, Duda J, Luck JM, Waclaw B. Localization of the Maximal Entropy Random Walk. Physical Review Letters. 2009 Apr 24;102(16). 160602. https://doi.org/10.1103. Interestingly, the phenomenon of neutral interference connects evolutionary dynamics to a Markov process known in network science as the maximal-entropy random walk; its special properties imply that, when many neutral variants interfere in a population, evolution chooses mutational paths—not individual mutations—uniformly at random Maximal-entropy random walk unifies centrality measures. Phys Rev E Stat Nonlin Soft Matter Phys. 2012; 86(6 Pt 2):066109 (ISSN: 1550-2376) Ochab JK. This paper compares a number of centrality measures and several (dis-)similarity matrices with which they can be defined. These matrices, which are used among others in community detection methods, represent quantities connected to enumeration of. An information‐theoretical background is presented here for the functional random‐walk model of a many‐particle system, which was recently proposed to simulate nonequilibrium statistical mechanics in a certain coarse‐graining sense. Next, entropy productivity and the maximum‐entropy state in the model dynamics are studied with the new definition of entropy, which turns out to be a.

[0810.4113] Localization of maximal entropy random wal

  1. Neutral quasispecies evolution and the maximal entropy random walk. Even if they have no impact on phenotype, neutral mutations are not equivalent in the eyes of evolution: A robust neutral variant—one which remains
  2. Random walk on a graph. Let G be a finite connected graph with neither loops nor multiple edges, and let X be a random walk on G as in Exercise (6.4.6). Show that X is reversible in equilibrium. Exercise (6.4.6): Random walk on a graph. A particle..
  3. In this letter, we establish a multiple small targets detection method derived from hierarchical maximal entropy random walk (HMERW). The HMERW revolves the limitation of strong bias to the most salient target of the primal maximal entropy random walk (MERW) based on a proposed graph decomposition theory. To enhance the characteristics of small targets and suppress strong clutters, we design a.
  4. 4 Maximum entropy-biased rapidly-exploring random tree. The ME-RRT algorithm is outlined in Algorithm 1 (see Fig. 3), where sampleState first randomly selects a sample in feasible configuration space. Then the nearest tree node to the sample is selected as the tree growing point. Entropic force is computed with respect to the growing point after path sampling and path integral calculation.
  5. BibTeX @INPROCEEDINGS{Li_prediction:the, author = {Rong-hua Li and Jeffrey Xu Yu and Jianquan Liu}, title = {prediction: the power of maximal entropy random walk}, booktitle = {In: Proceedings of the 20th ACM International Conference on Information and Knowledge Management}, year = {}, pages = {1147--1156}
  6. Maximum entropy of random variable over range \(R\) with set of constraints \(\left\langle f_{n}(x)\right\rangle =\alpha_{n}\) with \(n=1\dots N\) and \(f_{n}\) is of polynomial order; Introduction. In this post, I derive the uniform, gaussian, exponential, and another funky probability distribution from the first principles of information theory. I originally did it for a class, but I enjoyed.
  7. Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel. A cornerstone of information theory is the idea of quantifying how much information there is in a message. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated using probability

Renyi Entropy and Random Walk Hypothesis to Study Suspended Sediment Concentration The derivation maximizes entropy by invoking the principle of maximum entropy, which selects the least-biased probability distribution out of many probability distributions that satisfy a given set of constraints. By considering point source release of sediment particles along with the assumption that the. The maximum entropy solution on the other hand takes the form of a Boltzmann distribution over the ground and excited states of the cost function to correct for noise. Here we use a programmable annealer for the information decoding problem which we simulate as a random Ising model in a field. We show experimentally that finite temperature maximum entropy decoding can give slightly better bit. Stationary properties of maximum-entropy random walks Published in: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, October 2015 DOI: 10.1103/physreve.92.042149: Pubmed ID: 26565210. Authors: Purushottam D. Dixit View on publisher site Alert me about new mentions. Twitter Demographics . The data shown below were collected from the profiles of 2 tweeters who shared this. The CrossEntropy encourages the 'most uniform' random walk over the MDP. Lemma Given some state s, let Pr(s) be the highest probability of being in s over all policies: Pr(s) = max ˇ d ˇ(s): For all states s, we have that: d ˇ CE (s) Pr(s) 4S S. M. Kakade (UW) Curiosity 9/1 A Maximum Entropy Approach to Natural Language Processing Adam L. Berger t Columbia University Vincent J. Della Pietra ~ Renaissance Technologies Stephen A. Della Pietra ~ Renaissance Technologies The concept of maximum entropy can be traced back along multiple threads to Biblical times. Only recently, however, have computers become powerful enough to permit the widescale application of this.

Localization of the Maximal Entropy Random Wal

Maximal-entropy random walks in complex networks with limited information. R. Sinatra, V. Nicosia, V. Latora, J. Gómez-Gardeñes, R. Lambiotte. Research output: Contribution to journal › Article › peer-review. 100 Downloads (Pure) Overview; Fingerprint; Fingerprint Dive into the research topics of 'Maximal-entropy random walks in complex networks with limited information'. Together they. 14 ENTROPY, RELATIVE ENTROPY, AND MUTUAL INFORMATION We denote the probability mass function by p(x) rather than p X(x),for convenience. Thus, p(x)and p(y)refer to two different random variables and are in fact different probability mass functions, p X(x) and p Y (y), respectively. Definition The entropy H(X)of a discrete random variable X is.

Maximum entropy probability distribution - Wikipedi

Entropy of Random Walk Range. 2009. Itai Benjamin The maximum entropy bootstrap is an algorithm that creates an ensemble for time series inference. Stationarity is not required and the ensemble satis es the ergodic theorem and the central limit theorem. The meboot R package implements such algorithm. This document introduces the procedure and illustrates its scope by means of several guided applications. Keywords: time series, dependent data.

Random walk - Wikipedi

Maximal entropy random walk on heterogenous network for

Evolution of entropy. The entropy is an absolute measure which provides a number between 0 and 1, independently of the size of the set. It is not important if your room is small or large when it is messy. Also, if you separate your room in two, by building a wall in the middle, it does not look less messy This paper uses the principle of maximum entropy to construct a probability distribution of future stock price for a hypothetical investor having specified expectations. The result obtained is in good agreement with observations recorded in the literature. Thus, the paper concludes that the hypothetical individual investor is representative of a large class of investors. This new derivation of.

Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic. The blue social bookmark and publication sharing system Entropy and Random Walk Trails Water Confinement and Non-Thermal Equilibrium in Photon-Induced Nanocavities . by Vassilios Gavriil. 1,2, Margarita Chatzichristidi. 3, Dimitrios Christofilos. 2, Gerasimos A. Kourouklis. 2, Zoe Kollia. 1, Evangelos Bakalis. 1,4, Alkiviadis-Constantinos Cefalas. 1 and . Evangelia Sarantopoulou. 1,* 1. National Hellenic Research Foundation, Theoretical and.

relative entropy, maximum entropy, and several other topics in continuous in-formation theory, concluding with an information-theoretic proof of the Central Limit Theorem using the techniques introduced throughout. 1.1 Goals More speci cally, our goals are as follows: 1. Introduce and evaluate a de nition for continuous entropy. 1. Charles Marsh (crmarsh@) Continuous Entropy 2. Discuss some. Maximum Entropy Method. A deconvolution algorithm (sometimes abbreviated MEM) which functions by minimizing a smoothness function (entropy) in an image.Maximum entropy is also called the all-poles model or autoregressive model. For images with more than a million pixels, maximum entropy is faster than the CLEAN algorithm random walks on graphs that can be represented as Markov chains. Techniques to estimate the number of steps in the chain to reach the stationary distribution (the so-called mixing time), are of great importance in obtaining estimates of running times of such sampling algorithms[1](forareviewofexistingtechniques,seee.g.[2]).Ontheotherhand,studiesof the link between the topology of the. The principle of maximum entropy is invoked when we have some piece(s) of information about a probability distribution, but not enough to characterize it completely- likely because we do not have the means or resources to do so. As an example, if all we know about a distribution is its average, we can imagine infinite shapes that yield a particular average. The principle of maximum entropy.

We use two heat reservoirs. Leave the dividing insulating wall in place, put the left in contact with an infinitesimally cooler reservoir and the right in contact with an infinitesimally hotter reservoir, repeat as needed until state one is reached. Because the dividing wall was non-conducting, each state traversed is a state of equilibrium. Therfore we can calculate the change in entropy of. ONE-DIMENSIONAL RANDOM WALKS 1. SIMPLE RANDOM WALK Definition 1. A random walk on the integers Z with step distribution F and initial state x 2Z is a sequenceSn of random variables whose increments are independent, identically distributed random variables ˘i with common distribution F, that is, (1) Sn =x + Xn i=1 ˘i. The definition extends in an obvious way to random walks on the d. The expected value of a χk -distributed random variable is √2Γ(k + 1 2) Γ(k 2). Hence R = √ d ∑ i = 1Z2i = l√N d√ d ∑ i = 1dZ2i l2N = l√2N d Γ(d + 1 2) Γ(d 2). The derivation above assumes that the walk is on a hypercubic lattice. I am not aware any theoretical derivation of the estimated end-to-end distance for freely.

Exponential families and maximum entropy In this set of notes, we give a very brief introduction to exponential family models, which are a broad class of distributions that have been extensively studied in the statistics literature [4, 1, 2, 7]. There are deep connections between exponential families, convex analysis [7], and information geometry and the geometry of probability measures [1. Middle wall removed allowing gas to expand freely. Molecules will corresponds to absolute maximum of total entropy, i.e. S= (S Σ)max Disorder grows! If you reach thermal equilibrium with untidy roommate, that would correspond to maximum possible disorder. Heat engine takes some substance (e.g. gas) through cyclic process during which: Heat QH absorbed from hot reservoir Work W+ done. Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling SONG CHUN ZHU Department of Computer Science, Stanford University, Stanford, CA 94305 YINGNIAN WU Department of Statistics, University of Michigan, Ann Arbor, MI 48109 DAVID MUMFORD Division of Applied Math, Brown University, Providence, RI 02912 Received February 6, 1996; Revised January 27.

GitHub - sayantann11/all-classification-templetes-for-ML

Stationary States of Maximal Entropy Random Walk and

  1. Entropy is not a property of the string you got, but of the strings you could have obtained instead. In other words, it qualifies the process by which the string was generated.. In the simple case, you get one string among a set of N possible strings, where each string has the same probability of being chosen than every other, i.e. 1/N.In the situation, the string is said to have an entropy of N
  2. The random walk model . 2. The geometric random walk model . 3. More reasons for using the random walk model . 1. THE RANDOM WALK MODEL. 1. One of the simplest and yet most important models in time series forecasting is the random walk model. This model assumes that in each period the variable takes a random step away from its previous value, and the steps are independently and identically.
  3. THE MAXIMUM OF A RANDOM WALK AND ITS APPLICATION TO RECTANGLE PACKING E. G COFFMAN. JR.. Bell Labs, Lucent Technologies 700 Mountain Avenue Murray Hill. New Jersey 07974 PHILIPPE FLAJOLET* INRIA-Rocquencourt F-78153 La Chesney, France LEOPOLD FLATTO Bell Labs, Lucent Technologies 700 Mountain Avenue Murray Hill. New Jersey 07974 MlCHA HOFRI Department of Computer Science Rice University.
  4. Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchang
  5. ed by Markov stopping times and prove that the asymptotic entropy (respectively, rate.
  6. istrative Data. 1. INTRODUCTION Non-random selection of units is.
  7. istic in nature. The measure of disorder from either viewpoint is known as dynamical entropy. Entropy is an essential notion in physics and information theory. Motivated by the study of disorder for the positions and velocities of.

Link prediction: the power of maximal entropy random wal

  1. Random Eccentricity (2010) Random Walk Centrality (2004) Random Walk Decay Centrality (2019) Random-Walk Betweenness Centrality (2006) Random-Walk Closeness Centrality (2004) Range-limited Centrality (2012) Rank Centrality (2017) Ranking-Betweenness Centrality (2014) RDSH - Relative Degree Structural Hole Centrality (2019) Re-defined Entropy.
  2. Fact 3. H(X) = 0 if and only if X is a constant random variable. Fact 4. Suppose X is a random variable with range fa 1;a 2;:::;a ng; i.e., it can take on n di erent values. Then the maximum possible value of H(X) is log 2 n. Notice that the maximum entropy log 2 n occurs when we have the uniform distribution: i.e., p X(a i) = 1=n for all i
  3. In the maximum entropy approach, the unknown properties are modeled as random properties. As the material's components are generally known, it is straightforward to find the probability function of material properties, but difficult to derive from those the probability distributions of local stresses and strains, even though the mean stresses and strains are known

Generic Random Walk and Maximal Entropy Random Walk - YouTub

  1. The paper is devoted to a study of the exit boundary of random walks on discrete groups and related topics. We give an entropic criterion for triviality of the boundary and prove an analogue of Shannon's theorem for entropy, obtain a boundary triviality criterion in terms of the limit behavior of convolutions and prove a conjecture of Furstenberg about existence of a nondegenerate measure with.
  2. The entropy of the world tends towards a maximum. Thus the entropy of the isolated system tends to go on increasing and reaches maximum value at the state of equilibrium. When the system reaches equilibrium the increase in entropy becomes zero. Entropy and Second Law of Thermodynamics. As per second law of thermodynamics, all the spontaneous processes occur in the nature from higher to lower.
  3. -entropy of a random variable is a lower bound on its entropy. The precise formulation for
  4. Space-filling parameter grids. Source: R/space_filling.R. grid_max_entropy.Rd. Experimental designs for computer experiments are used to construct parameter grids that try to cover the parameter space such that any portion of the space has an observed combination that is not too far from it
  5. Ray Propagation in a Random Lattice: a Maximum Entropy, Anomalous Diffusion Process; Italiano. Italiano; English; The typical model for diffusion in disordered systems is that of a random walk that proceeds in discrete steps over a random lattice, where not all the nearest sites can be reached at each step. We study the related problem of ray propagation in percolating lattices, and observe.

A random walk is a time series model x t such that x t = x t − 1 + w t, where w t is a discrete white noise series. Recall above that we defined the backward shift operator B. We can apply the BSO to the random walk: x t = B x t + w t = x t − 1 + w t. And stepping back further: x t − 1 = B x t − 1 + w t − 1 = x t − 2 + w t − 1 The value of entropy is maximal for a random variable with the uniform distribution and the minimum value of entropy is attained by a constant random variable. This kind of entropy will be further explored in this paper in order to reveal its weaknesses. As an alternative to Shannon entropy, we advocate the use of Kolmogorov complexity. We postpone the discussion of Kolmogorov complexity to. The Shannon entropy in this context is the spectral entropy of the signal. This property can be useful for feature extraction in fault detection and diagnosis [2] , [1] . SE is also widely used as a feature in speech recognition [3] and biomedical signal processing [4] Description: The focus of this test is the maximal excursion (from zero) of the random walk defined by the cumulative sum of adjusted (-1, +1) digits in the sequence. The purpose of the test is to determine whether the cumulative sum of the partial sequences occurring in the tested sequence is too large or too small relative to the expected behavior of that cumulative sum for random sequences. Routines for fitting maximum entropy models ¶. Contains two classes for fitting maximum entropy models (also known as exponential family models) subject to linear constraints on the expectations of arbitrary feature statistics. One class, model, is for small discrete sample spaces, using explicit summation

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