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# Random Walks - Science topic

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Questions related to Random Walks

I am running a series of state-space density-independent and -dependent population models in PROC MIXED. I have reviewed the literature and found out how to do the gompertz and exponential growth models. I am still struggling to fit a random walk and ricker model. PROC MIXED does not have a restrict statement. How do I restrict parameters in PROC MIXED? Below is the code for the gompertz model:

ODS OUTPUT FITSTATISTICS=FIT_GOMPERTZ2;

ODS OUTPUT CovParms=GOMPERTZ_PARMS2;

PROC MIXED METHOD=REML ALPHA=.05 NOITPRINT NOINFO DATA=FISH_DENSITY;

BY REGION SITE SPECIES;

CLASS TIME;

MODEL LOG_Nt=LOG_Nt_Minus1 / s outp=pred;

RANDOM TIME;

REPEATED / TYPE=AR(1) SUBJECT=INTERCEPT;

ESTIMATE 'INTERCEPT' INTERCEPT 1;

RUN;

Photon diffusion happens when photons travelling through a medium undergo repeated scattering events without the photons being absorbed. It can be interpreted as a random walk of photons through the given medium. The question is:

What is then the speed of photon diffusion in a medium with a given density? In other words, how long it takes for the photons to pass through it?

I need to measure the earnings forecasts accuracy as a dependent variable according to these steps:

1- forecast earning for each year based on the earnings in the prior year

2- calculate the absolute earnings forecasting errors ( the absolute difference between actual and forecasted earnings divided by the actual earnings)

is there any suggestions

Please suggest for computer based system for processing of raw gyroscope data which method is more suitable for bias drift and noise removal from gyroscope? I need angular velocity in my application.

I'm regressing households' spending (PCE) on disposable income (PDI) between 1980 and 2018 for the U.S economy. I noticed that the coefficient of PDI is higher than 1. I first think that coeff. of PDI may be extreme due to possible autocorrelation or non-stationarity.

While conducting the ADF test, I tried the random walk, drift, and a trend.

However, according to the results of the test, PCE and PDI series are stationary with a drift.

I also applied the Gregory-Hansen cointegration test and find out that series are cointegrated in the long run at the breakpoint.

How can I solve this problem?

I am looking for a good couple of reads on game theory, maybe with an historical context. Anything like random walks, or Marvok Process is fine or even, Colonel Blotto, and Prisoners Dilemma. I think my hardship is finding the right literature instead of instructional books. Thank you in advanced.

Hi there,

I am relatively new to ANSYS, with a fairly basic module undertaken in university. For my final year project, I am trying to model aerosol droplets (equivalent to water droplets) in an air flow of 3 litres/min entering the nasal cavity, of which I have approximated as a Y shaped tube.

I am using ANSYS FLUENT version 19.0 (student version).

Have been following tutorials from youtube but they are not exactly what I am looking for.

So far I have the following setup:

(Opened via double precision serial)

General: Pressure based - type solver with gravity enabled (9.81/ms^-22) and

**transiet**Models:
Viscous Laminar model with realizable k-epsilon (2 eqns) and enhanced wall treatment (have also tried scalable wall functions and standard)

**Discrete Phase is on with interaction with continuous flow enabled and Max number of tracking steps is 50000**(have altered this as I kept getting incomplete particles - this did not make a difference so it must be something else). I have enabled unsteady particle tracking and injecting particles at a

**particle time step of 0.001s**. I have enabled the

**pressure gradient force, automated tracking scheme, linearized source terms and accuracy control.**

The injection is a

**surface injection at the inlet**, I chose a roisin rammler distribution with**5 micron diameter mean**sized particles, mass flow rate of**0.05 kg/s and velocity of 0.2 m/s**. Have injected using**face normal direction**. Have also enabled**random walk model under turbulent dispersion and random eddy lifetime**. I said the stop time was**1000s**.I basically need the aerosol to come in via the two inlets (which have been named accordingly). Both the inlet and outlet have been assigned "escape" under DPM boundary conditions and the walls are assigned with "trap".

What I need from this simulation is to assess how many particles deposit within the airways i.e. number of droplets in versus number out. I also would like to see how they break up via the TAB model - have tried this also to no avail. I cannot seem to get any particle tracklines - however the streamlines come out fine.

I would really really appreciate any input or feedback, as this is my first time doing this complexity of simulation - have very little experience and have spent 9 hours on this to no fruition. If someone could just provide me with some guidance on this configuration or a basis configuration for particle deposition along the walls and particle breakup, I would be really grateful.

So far, I have:

number tracked = 4156, escaped = 4077, aborted = 0, trapped = 0, evaporated = 0, incomplete = 79, incomplete_parallel = 0

I cannot get anything to show up when i try to create a particle tracking plot - nothing will come up at all

During test of cycle_gate, we ask people to walk, then they pay attention to it and their way of walking is changed, also darkness can change it too.

but that is question, whether mental illness such as depression change the cycle_gate?that could help us to find therapies for these diseases.

I am modeling the collective behavior of random walkers (using CTRW) on a 2d lattice and I am having trouble finding a "correct" rule that won't eventually violate the uniformly random motion of my agents. Any ideas?

I need random walk code for matrix 20*20 in MATLAB. but without repeatation in each place. I mean we can walk just once in each room.

Adaptive Market Hypothesis (AMH) and Random walk model are the underpinning theories of technical analysis of stock market return? Is there any more theories for technical analysis?

I am doing 2D random walk simulation in a confined circle to simulate Brownian motion. I have two questions.

1. When the particle reaches the boundary, which boundary conditions should I use for Brownian motion? Mirror reflection (opposite direction) OR diffuse reflection (using Knudsen law)?

2. If I would like to simulate multiple particles Brownian motion in a confined circle, how should I describe the particle interactions?

Thank you so much for your consideration.

I want to improve the specification performance of my MEMS Gyro, As we know, the measurement errors of a MEMS gyroscope usually contain deterministic errors and stochastic errors. I just focus on stochastic part and so we have:

y(t) = w(t)+b(t)+n(t)

where:

{w(t) is "True Angular Rate"}

{b(t) is "Bias Drift"}

{n(t) is "Measurement Noise"}

The bias drift and other noises are usually modeled in a filtering system to compensate for the outputs of gyroscope to improve accuracy. In order to achieve a considerable noise reduction, there's another solution that the true angular rate and bias drift are both modeled to set as the system state vector to design a KF.

Now if I want model the true angular rate, How could I do this? I just have a real dynamic test of gyro that includes above terms and I don't know how can I determine parameters required by the different models (such as Random Walk, 1st Gauss Markov or AR) for modeling ture angular rate from an unknown true angular rate signal!

While analyzing the trajectories of 40 nm Au nanoparticles diffusing on a surface ( dark-field optical image), I often land up with trajectories which cross. As a result the trajectory of a single particle is identified as several discreet trajectories by the algorithm. I use the standard centre of mass method for tracking. Is there a better technique which can take care of crossed trajectories by taking into consideration velocity/directionality or other parameters of a moving particle? However this is random walk, so this may be difficult. The particles are quite faint, and the background noise is appreciable even after post -processing, so the method also has to be robust in locating two very close spaced particles.

For example, such a one-dimensional model, in which the particle is a movable ring on the torus, and the spatial coordinate is the irrational winding of the torus, suitable for the role of the pre-quant model? Even not to mention the random walk of the ring as a quantum behavior of the particle, we can talk about the uniform motion of the ring along the helical lines of the torus, which will immediately give an interpretation of the spin of the particle as the direction of rotation of the ring.

It is about such models that I tried to speak in the article about the application of local algebras of vector fields to the modeling of physical phenomena.

Dear Researchers,

I’m working on a panel N= 13 and T = 54.

I ran fixed and random effects models. In addition, I wanted to run GMM model as a kind of robustness check and to control for potential endogetinty issues, knowing that GMM is preferable with small T and large N.

The problem is : the Arellano – Bond test for autocorrelation AR(1) is non-significant.

I know that the test for AR (1) process in first differences usually rejects the null hypothesis since

Δe

_{it}=e_{it}−e_{i,t−1}and Δe_{i,t−1}=e_{i,t−1}−e_{i,t−2}and both have e_{i,t−1}What could be the justification behind the failure to reject H0? Does this give any evidence to a Random Walk process? I will appreciate if you can guide me to any interpretation..

Thank you so much.

From the point of view of mathematics, there seems to be no obstacle for a noncompact manifold to be embedded in a closed manifold (for example, the winding of a torus everywhere densely filling a torus). However, this is not enough, since such an investment must be "revived", that is, populated with material objects and made to move them. It seems that this area is open for research, but I will be happy if you indicate to me the work corresponding to this topic. In turn, I can offer you a drop, which has the form of a 7-dimensional sphere, which is populated by a vector field of velocities of particles of a continuous medium. In this model, the topological singularities of a vector field should serve as material objects (particles), since linear vector fields form the Dirac matrix algebra. However, interesting consequences of this model from the viewpoint of physics also arise in the two-dimensional case. Thus, in the study of a random walk along broken lines of a winding of a classical sphere, one can obtain a generalized one-dimensional Schrödinger equation.

Mathematical notes on the nature of things (in Russian)

Hi all,

I have a model that runs a mass balance profile for a glacier (i.e. the net result between melt and snow accumulation). However, I have a set of 7 variables to calibrate the model. I was wondering if there is some kind of small program I can write to run the model several times with all different values for the parameters within a certain range, in order to find the minimum RMSE. For example, parameter 1 from 0.4 to 0.6, parameter 2 from 0.34 to 0.42, etc. I can then check afterwards which combination gives minimized RMSE I was thinking about a random walk method but it is hard to write these kind of things. It would be very much appreciated. Can anybody help me getting started?

Thanks!

I am currently carrying out an assignment in which we need to compare our GARCH( p, q) forecast against a Naive Benchmark model, such as a Random Walk model.

I have considered an IGARCH (1, 1) model to fall under this defintion, due to the coefficents of alpha and beta adding to 1.

Is this therefore a random walk with a drift model, as I am struggling with its interpretation?

I have attached a sample of the Eviews output for reference.

Thanks in advance!

What is the difference between Spectral moments of surface and spectral moments of surface profile?

At the moment, I'm trying to analyse a difficult set of data that I've been thinking but really don't know how to do it.

So basically, i have two populations of cells and I notice one of them doesn't seem to undergo random migration and are in some kind of patterned movement while the other one looks more like it. There's no external chemotax and the cells are in a homogenous environment, so the non-random migration is potentially intrinsic to one cell type, while the other doesn't have this ability.

So I would like to analyse this but can't think of any way to do so. So I bring the problem on here to ask if anyone knows any kind of way/algorithm/software that will be able to quantify this to confirm my hypothesis?

I can ask to make a simulation, one is random walk, the other is not, but this would take a lot of effort, so I'm looking for a simpler way to do this.

I would really appreciate if anyone can shed some light!

Is the hypothesis on the representation of the Riemann zeta function true by the product of the sums (or the sum of products) of the probability amplitudes of a random walk along broken lines of the winding of a sphere?

Deleted research item The research item mentioned here has been deleted

If we train a data model once on a dataset using a machine learning algorithm, save the model, and then train it again using the same algorithm and the same dataset and data ordering, will the first model be the same as the second?

I would propose a classification of ml algorithms based on their "determinism"

in this respect. On the one extreme we would have:

(i) those which always produce an identical model when trained from the same dataset with the records presented in the same order and on the other end we would have:

(ii) those which produce a different model each time with a very high variability.

Two reasons for why a resulting model varies could be (a) in the machine learning algorithm itself there could be a random walk somewhere, or (b) a sampling of a probability distribution to assign a component of an optimization function. More examples would be welcome !

Also, it would be great to do an inventory of the main ML algorithms based on their "stability" with respect to retraining under the same conditions (i.e. same data in same order). E.g. decision tree induction vs support vector vs neural networks. Any suggestions of an initial list and ranking would be great !

for quite a comprehensive list of methods.

Assuming random walk model with a drift is used.

Several theoretical models have been proposed for the study of the lasing behavior in random media such as "Correlated Random Walk", "diffusion with gain", "disorder induced localization coupled with non-linearity". But it seems that none of them have been able to cover the diverse experimental results. I need a model that predicts both localized and extended modes in two and three dimension.

I want to simulate the flow field in the emitter of drip irrigation and use DPM to get the particle trajectory in the emitter. when the computation is converged(the mass flow rate of inlet and outlet is tending towards stability), the result of particle trajectory is satisfactory, and there are many eddy currents in the flow field. But if I change convergence condition, the iteration continues iterating several steps(maybe about 10-50 steps). The new result of particle trajectory becomes different, the residence time of particles also become different. And the flow field doesn't change when the iteration continues iterating.

First,I use k-e turbulence model, surface injection, interaction with continuous phase, discrete random walk model.

when I discover the problem，I change the surface injection to point injection, don't select the options of interaction with continuous phase and discrete random walk model but the problem still exists.

I've been thinking about it for a long time. I think the particle is sand, and the diameter is 0.01mm-0.1mm, its motion is greatly affected by the flow field, when the iteration continues iterating several steps, the flow field is also changes, although the value changes only little， the influence of particle trajectory is significant.

So what's the problem?

Please please let me know, if you have any idea about the problem mentioned. Any help is highly appreciated.

Thanks a lot!

Since Random walker is used for both segmentation as well as classification. But it works on supervised learning so is it better to comapre it with other segmentation techniques or classification techniques like SVM.

I've seen in many places where these terms were addressed separately. But the more i've read about triangulation, it appears the same as mixed methods. Can I get some help on this?

Hello all,

I would like to ask about the following benchmark functions:

Ackley

Bohachevsky 1

Camel 3 hump

Drop wave

Exponential

Paviani

Are these benchmark functions unimodal or multimodal ?

Thanks to all who contribute to the answer.

A random walker starts at the origin, and experiences unbiased diffusion along a continuous line in 1d. What is the probability for this walker to return to the origin for the first time as a function of time? In other words, I am looking for the probability of first return to the starting point. I would greatly appreciate to learn the functional form of this probability, or to learn of references where it is discussed or stated.

I am looking for an analytical expression describing the time evolution of the spatially averaged density (in practice, the average concentration in particles/m

^{3}) of a system of particles hopping with a given frequency on a d=3 lattice where some traps are randomly placed. The idea is that when a particle meets a trap it disappears from the system, so that the average density decreases to zero with some decay law. I expect to find something like a stretched exponential decay and I would like to relate the parameters of this decay curve with the input data of my system (e.g. intial particle density, traps concentration etc.) The lattice can be ordered (say, cubic) or disordered (like in glassy media or polymers) and the traps can have a finite size. As a further complication, the effect of traps saturation can be also taken into account.Thanks!

Also kindly illustrate the key terms in the context of its implementation seeds,masks,labels and beta? what are these terms and what does they represent?

I'm currently doing some research about oil spill models, focusing on particle tracking and random walk diffusion, but can't find a recent survey discussing the topic. Can anyone suggest one? Thanks in advance.

From my understanding Markov clustering (MCL) algorithm is a graph clustering algorithm that takes weighted graph as input and uses Random walk approach for probability assignment of each node on the graph. What is not clear to me is how MCL uses Frobenius norm to perform the final clustering. Also, is there a tool or java codes that I can easily simulate with or adapt? Thanks.

I have 8 years time sires data on maternal and child mortality rate.

I am very interested in predictive walks. I am looking for this term where a person would more likely choose to walk in a path with the shortest distance. What do you call that concept?

I am now working on mobility prediction. I need MATLAB code for simulation of Random Walk Model.

What is the difference between the lexicographic max.min optimization and the max.min optimization? I read the difference in two

1-the lexicographic the iteration of max.min .

2-lexicographic is fairly and efficiently.

this is right ?

and what the best algorithm for solving the discrete numbers ?

tab search, random walk?

Start with a reflexion domain being a polygon A1 A2 ...An, with n summits

A simple computation using formula line 7 page 57 shows that if d(An, An-1)-->0 then P (B5(0)=An)-P(B5(0)=An-1)-->0 as n-->infinity

and P((B5(t+s)€E/B5(0)=An))-P((B5(t+s)€E/B5(0) =An-1))-->0 as n--> infinity

Which allow to derive the distribution of the relected process in a bounded domain with smooth boundaries.

Thanks

Bernard Bellot

l

I want to run Brownian Dynamics simulation and wonder which software package is more popular?

Hello,

Let us consider the classic random walk:

x

_{0}= 0, x_{n+1}= x_{n}+ r_{n},where r

_{n}are equally distributed zero-mean Gaussian random variables. It is well-known that the probability distribution of x_{n}is a zero-mean Gaussian with standard deviation proportional to sqrt(n).Now, I will say that the instant k is a zero-crossing for a particular realization of the random walk iff x

_{k}has opposite sign than x_{k+1}, and I will consider the random variable T defined as the temporal distance between two consecutive zero-crossing.What can we say about the probability distribution of T?

My intuition would suggest such probability distribution is time dependent and its expected value would also grow as sqrt(n). Am I correct or wrong?

I thank you all, Giuseppe Papari

Well, I'm a novice for both matlab and research on machine learning. Can anyone tell me how to represent affinity matrix in random walk graph matching case (i.e. what will be its structure?). e.g. W

_{ia,jb}will it be two dimensional or four dimensional array (matrix)? As you see from the example the affinity matrix W has four indexes (ia, jb). Does it mean the matrix should be four dimensional? Thanks in advance for any kind of explanation.I am confused with Random walk and Red noise. Some people said that random walk is red noise. Both of them can be generated by integrating white noise. However, Random walk is a nonstationary process, which doesn't have PSD. But red noise has its own PSD, which is 1/f^2. How should I understand the difference between them? Is there anybody has some comments on this?

I am aware of one method - for assessing whether a time-series variable follows a random walk (using differences and comparing the standard deviations). However, I am interested in possible explanations for other more rigorous methods.

Pagerank works on a graph which only has direct edges between vertices and there is no weight on edges of the graph but random walk's graph edges are not directed and they have weight. Then, how we should change pagerank which could be applied to these kinds of graphs.