Mathematical approach to the psychological aspects of human

Emotion Processing ◽

Mathematical Approach ◽

Human Emotion ◽

One Dimensional ◽

Know How ◽

Group I ◽

Fixed Distribution ◽

Two Stages

When I belonged to a group, I was always bullied no matter how I behaved, so I didn't know how to handle my own emotions, so I considered human emotions. I mathematically modeled human emotion processing in two stages: what kind of emotions we receive from events and how we react from the emotions we receive. The part that receives emotions from events and the part that responds from emotions are modeled by a one-dimensional random walk or Wiener process, and the distribution of individual emotions is represented by a fixed probability distribution, and the response of individual is represented by a fixed distribution. Therefore, I also showed that when individuals gather to form a group, the distribution of emotions and reactions as a group is also represented by a fixed distribution. In addition, I showed as application examples of these models, the nature of events, the meaning of emotional distribution, and how to read the air, and so on.

Mathematical approach to human emotion processing

10.31234/osf.io/qtsgf ◽

2020 ◽

Author(s):

Takuya Yabu

Keyword(s):

Random Walk ◽

Emotion Processing ◽

Mathematical Approach ◽

Human Emotion ◽

One Dimensional ◽

Know How ◽

Group I ◽

Fixed Distribution ◽

Two Stages

When I belonged to a group, I was always bullied no matter how I behaved, so I didn't know how to handle my own emotions, so I considered human emotions. I mathematically modeled human emotion processing in two stages: what kind of emotions we receive from events and how we react from the emotions we receive. The part that receives emotions from events and the part that responds from emotions are modeled by a one-dimensional random walk or Wiener process, and the distribution of individual emotions is represented by a fixed probability distribution, and the response of individual is represented by a fixed distribution. Therefore, I also showed that when individuals gather to form a group, the distribution of emotions and reactions as a group is also represented by a fixed distribution. In addition, I showed as application examples of these models, the nature of events, the meaning of emotional distribution, and how to read the air, and so on.

Mathematical approach to human reaction

10.31234/osf.io/36g5w ◽

2020 ◽

Author(s):

Takuya Yabu

Keyword(s):

Random Walk ◽

Probability Density Function ◽

Probability Density ◽

Density Function ◽

The Other ◽

Mathematical Approach ◽

One Dimensional ◽

Human Reaction ◽

Fixed Distribution

I thought about how to get the magnitude from the event and the reaction of the other party. Evaluating the values of events and opponents' reactions using a one-dimensional random walk shows that the probability density function of the values of events and opponents' reactions has a fixed probability distribution. Similarly, I have shown that the functions that determine the magnitude of events and reactions are also represented by a fixed distribution. Therefore, I also showed that when individuals gather to form a group, the functions that determine the magnitude of events and reactions as a group are also represented by a fixed distribution. Also, as an application example of this model, I described how to show my reaction and what to do when the magnitude of the event is large.

Two models of quantum random walk

Open Physics ◽

10.2478/bf02475903 ◽

2003 ◽

Vol 1 (4) ◽

Cited By ~ 3

Author(s):

Jozef Košík

Keyword(s):

Random Walk ◽

Upper Bound ◽

Explicit Solution ◽

New Method ◽

Speed Of Convergence ◽

Quantum Random Walk ◽

Dimensional Lattice ◽

Special Model ◽

One Dimensional

AbstractWe present an overview of two models of quantum random walk. In the first model, the discrete quantum random walk, we present the explicit solution for the recurring amplitude of the quantum random walk on a one-dimensional lattice. We also introduce a new method of solving the problem of random walk in the most general case and use it to derive the hitting amplitude for quantum random walk on the hypercube. The second is a special model based on a local interaction between neighboring spin-1/2 particles on a one-dimensional lattice. We present explicit results for the relevant quantities and obtain an upper bound on the speed of convergence to limiting probability distribution.

The Maximum of a Symmetric Next Neighbor Walk on the Nonnegative Integers

10.1017/s0021900200010159 ◽

2014 ◽

Vol 51 (01) ◽

pp. 162-173

Author(s):

Ora E. Percus ◽

Jerome K. Percus

Keyword(s):

Random Walk ◽

Generating Functions ◽

Two Dimensional ◽

Symmetric Random Walk ◽

One Dimensional ◽

Dimensional Distribution

We consider a one-dimensional discrete symmetric random walk with a reflecting boundary at the origin. Generating functions are found for the two-dimensional probability distribution P{S n = x, max1≤j≤n S n = a} of being at position x after n steps, while the maximal location that the walker has achieved during these n steps is a. We also obtain the familiar (marginal) one-dimensional distribution for S n = x, but more importantly that for max1≤j≤n S j = a asymptotically at fixed a 2 / n. We are able to compute and compare the expectations and variances of the two one-dimensional distributions, finding that they have qualitatively similar forms, but differ quantitatively in the anticipated fashion.

Searching for a one-dimensional random walker

10.1017/s0021900200036421 ◽

1974 ◽

Vol 11 (01) ◽

pp. 86-93 ◽

Cited By ~ 4

Author(s):

Bernard J. McCabe

Keyword(s):

Random Walk ◽

Wiener Process ◽

One Dimensional ◽

Random Walker ◽

Search Plan ◽

Crossing Time ◽

Definition Of ◽

First Crossing Time ◽

Finite Moments ◽

Bernoulli Random Walk

Let {xk } k ≧ − r be a simple Bernoulli random walk with x –r = 0. An integer valued threshold ϕ = {ϕ k } k≧1 is called a search plan if |ϕ k+1−ϕ k |≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ 1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

Searching for a one-dimensional random walker

10.2307/3212585 ◽

1974 ◽

Vol 11 (1) ◽

pp. 86-93 ◽

Cited By ~ 11

Author(s):

Bernard J. McCabe

Keyword(s):

Random Walk ◽

Wiener Process ◽

One Dimensional ◽

Random Walker ◽

Search Plan ◽

Crossing Time ◽

Definition Of ◽

First Crossing Time ◽

Finite Moments ◽

Bernoulli Random Walk

Let {xk}k ≧ − r be a simple Bernoulli random walk with x–r = 0. An integer valued threshold ϕ = {ϕk}k≧1 is called a search plan if |ϕk+1−ϕk|≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

The Maximum of a Symmetric Next Neighbor Walk on the Nonnegative Integers

10.1239/jap/1395771421 ◽

2014 ◽

Vol 51 (1) ◽

pp. 162-173

Author(s):

Ora E. Percus ◽

Jerome K. Percus

Keyword(s):

Random Walk ◽

Generating Functions ◽

Two Dimensional ◽

Symmetric Random Walk ◽

One Dimensional ◽

Dimensional Distribution

We consider a one-dimensional discrete symmetric random walk with a reflecting boundary at the origin. Generating functions are found for the two-dimensional probability distribution P{Sn = x, max1≤j≤nSn = a} of being at position x after n steps, while the maximal location that the walker has achieved during these n steps is a. We also obtain the familiar (marginal) one-dimensional distribution for Sn = x, but more importantly that for max1≤j≤nSj = a asymptotically at fixed a2 / n. We are able to compute and compare the expectations and variances of the two one-dimensional distributions, finding that they have qualitatively similar forms, but differ quantitatively in the anticipated fashion.

Limit diffusion process for a non-homogeneous random walk on a one-dimensional lattice

Russian Mathematical Surveys ◽

10.1070/rm1997v052n02abeh001778 ◽

1997 ◽

Vol 52 (2) ◽

pp. 327-340 ◽

Cited By ~ 2

Author(s):

R A Minlos ◽

E A Zhizhina

Keyword(s):

Random Walk ◽

Diffusion Process ◽

Dimensional Lattice ◽

One Dimensional ◽

Limit Diffusion

On coupling of random walks and renewal processes

10.2307/3215269 ◽

1996 ◽

Vol 33 (1) ◽

pp. 122-126

Author(s):

Torgny Lindvall ◽

L. C. G. Rogers

Keyword(s):

Random Walk ◽

Random Walks ◽

Simple Random Walk ◽

Renewal Processes ◽

Renewal Theorem ◽

One Dimensional ◽

Continuous State Space ◽

Continuous State ◽

Efficient Coupling ◽

Blackwell's Renewal Theorem

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.