scholarly journals Mathematical approach to human emotion processing

2020 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
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.

scholarly journals Mathematical approach to human emotion processing

2020 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
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.

scholarly journals Mathematical approach to the psychological aspects of human

2020 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
Wiener Process ◽  
Mathematical Approach ◽  
Large Magnitude ◽  
Human Emotion ◽  
One Dimensional ◽  
Know How ◽  
Fixed Distribution ◽  
Two Stages

Belonging to a group, there are people who are always bullied no matter how they behave. They don't know how to treat their 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. Therefore, I also showed that when individuals gather to form a group, the distribution of emotions 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 how to deal with one's character, and how to show one’s reaction and what to do for events which have a large magnitude. *This paper is a revised version of these papers, https://psyarxiv.com/k3j4z/, https://psyarxiv.com/yrd9v/, https://psyarxiv.com/36g5w/.

scholarly journals Mathematical approach to human reaction

2020 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Random Walk ◽  
Probability Density Function ◽  
Probability Distribution ◽  
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 ◽  
2003 ◽  
Vol 1 (4) ◽  
Author(s):  
Jozef Košík
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
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.

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

2014 ◽  
Vol 51 (01) ◽  
pp. 162-173
Author(s):  
Ora E. Percus ◽  
Jerome K. Percus
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
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.

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

2014 ◽  
Vol 51 (1) ◽  
pp. 162-173
Author(s):  
Ora E. Percus ◽  
Jerome K. Percus
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
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.

On coupling of random walks and renewal processes

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.

scholarly journals Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators

2018 ◽  
Vol 29 (10) ◽  
pp. 1850098 ◽  
Author(s):  
R. F. S. Andrade ◽  
A. M. C. Souza
Keyword(s):  
Wave Function ◽  
Probability Distribution ◽  
Discrete Time ◽  
Numerical Study ◽  
Entanglement Entropy ◽  
Quantum Effects ◽  
Quantum Walks ◽  
Cantor Set ◽  
One Dimensional ◽  
Time Quantum

Properties of one-dimensional discrete-time quantum walks (DTQWs) are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position-dependent coin operators. Deterministic aperiodic sequences of two or more symbols provide ideal environments where these properties can be explored in a controlled way. Based on an exhaustive numerical study, this work discusses a two-coin model resulting from the construction rules that lead to the usual fractal Cantor set. Although the fraction of the less frequent coin [Formula: see text] as the size of the chain is increased, it leaves peculiar properties in the walker dynamics. They are characterized by the wave function, from which results for the probability distribution and its variance, as well as the entanglement entropy, were obtained. A number of results for different choices of the two coins are presented. The entanglement entropy has shown to be very sensitive to uncovering subtle quantum effects present in the model.

scholarly journals Optimal Strategies for Prudent Investors

1998 ◽  
Vol 01 (04) ◽  
pp. 473-486 ◽  
Author(s):  
Roberto Baviera ◽  
Michele Pasquini ◽  
Maurizio Serva ◽  
Angelo Vulpiani
Keyword(s):  
Growth Rate ◽  
Random Walk ◽  
Exponential Growth ◽  
Optimal Strategies ◽  
Maximum Amount ◽  
Exponential Growth Rate ◽  
One Dimensional ◽  
Economic Level ◽  
Random Walk With Drift ◽  
Analytical Expressions

We consider a stochastic model of investment on an asset in a stock market for a prudent investor. she decides to buy permanent goods with a fraction α of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed α. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.

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