​ The Monte Carlo theory, named after the famous Monaco casino, is a versatile and powerful computational technique used in various fields to solve complex problems, estimate probabilities, and make informed decisions. This probabilistic method relies on randomness to approximate numerical results when analytical solutions are impractical or impossible to obtain. In this essay, we will delve into the Monte Carlo theory, its history, principles, applications across diverse domains, and demonstrate its implementation using Python with several illustrative examples.
 
Historical Background
 
The origins of the Monte Carlo method can be traced back to the Manhattan Project during World War II, where scientists faced complex mathematical problems related to nuclear physics. Enrico Fermi and John von Neumann pioneered this method to tackle these intricate calculations, leading to its widespread use in various fields today.
 
Fundamental Principles
 
At its core, Monte Carlo simulation relies on randomness and statistical sampling to approximate solutions to problems. The fundamental principles are as follows:
 
1. Random Sampling: Monte Carlo simulations generate random samples from probability distributions to approximate outcomes. These random samples are generated using pseudorandom number generators.
 
2. Probability Distributions: The choice of probability distributions plays a crucial role in the accuracy of simulations. Common distributions include uniform, normal (Gaussian), exponential, and others, depending on the problem at hand.
 
3. Repetition: Multiple iterations of the simulation are performed to gather a large enough sample size to make statistically significant inferences.
 
Applications of Monte Carlo Simulation
 
Monte Carlo simulations find applications in diverse fields, including finance, engineering, physics, biology, and more. Let's explore a few examples:
 
1. Finance: In financial modeling, Monte Carlo simulations are used to estimate the future value of investments, assess portfolio risk, and price complex derivatives. For instance, they can help investors make informed decisions about asset allocation based on their risk tolerance.
 
2. Engineering: Engineers use Monte Carlo simulations to analyze the reliability and safety of complex systems. For example, in aerospace, simulations can predict the probability of a spacecraft successfully reaching its destination, accounting for various uncertainties.
 
3. Physics: In particle physics, Monte Carlo methods are employed to simulate the behavior of subatomic particles in high-energy collisions. This aids in understanding the fundamental particles and their interactions.
 
4. Biology: Monte Carlo simulations are utilized in modeling biological processes, such as the folding of proteins, the spread of diseases, and genetic evolution. These simulations help researchers understand complex biological systems.
 
Implementing Monte Carlo Simulations in Python
 
Python is a popular language for implementing Monte Carlo simulations due to its simplicity and rich libraries. Below, we'll provide a simple example of estimating the value of π using a Monte Carlo simulation:

​The human brain, often referred to as the most complex and enigmatic organ in the known universe, has been a subject of fascination for centuries. Mapping the intricacies of the brain has been a longstanding goal of scientists and researchers. Technological advancements in recent years have brought us closer than ever to understanding the brain's inner workings. In this blog, we will explore some of the cutting-edge technologies that are revolutionizing our ability to map and comprehend the human brain.
 
1. Magnetic Resonance Imaging (MRI) - Unveiling Brain Structure
 
Magnetic Resonance Imaging, commonly known as MRI, has been one of the most transformative technologies in brain mapping. MRI uses powerful magnets and radio waves to produce detailed images of the brain's structure. It allows researchers to visualize different brain regions, white matter tracts, and abnormalities with remarkable precision, providing valuable insights into brain anatomy and function.
 
Advanced MRI techniques, such as diffusion tensor imaging (DTI), can also map the brain's complex network of neural connections, enabling us to better understand the brain's communication pathways.
 
2. Functional Magnetic Resonance Imaging (fMRI) - Unraveling Brain Activity
 
Functional Magnetic Resonance Imaging, or fMRI, takes brain mapping to the next level by providing a glimpse into brain activity in real-time. By measuring changes in blood flow, fMRI can detect which brain regions are active during specific tasks or in response to stimuli. This has been instrumental in studying cognitive processes like attention, memory, language, and emotion.
 
The integration of fMRI with advanced analysis techniques, such as resting-state fMRI, allows researchers to examine brain connectivity and identify functional networks within the brain. These findings have shed light on how different brain regions collaborate and communicate to perform complex tasks.
 
3. Positron Emission Tomography (PET) - Investigating Brain Chemistry
 
Positron Emission Tomography, or PET, provides valuable insights into the brain's chemistry and neurotransmitter activity. By using radioactive tracers, PET can measure metabolic processes and receptor binding in the brain. This technology has been pivotal in studying various neurological and psychiatric disorders, such as Alzheimer's disease and depression.
 
The combination of PET with specific ligands has enabled researchers to visualize the distribution of neurotransmitters, providing valuable information about their role in brain function and dysfunction.
 
4. Electroencephalography (EEG) - Capturing Brain Electrical Activity
 
Electroencephalography, or EEG, is a non-invasive technique that records the brain's electrical activity through electrodes placed on the scalp. EEG is particularly useful for studying brain dynamics in real-time, such as during sleep, cognition, and neurological disorders.
 
Recent advancements in EEG technology, such as high-density EEG and wearable EEG devices, have made it easier to collect data outside the laboratory, allowing for more extensive and diverse studies.
 
5. Optogenetics - Controlling Brain Activity with Light
 
Optogenetics is a groundbreaking technique that allows researchers to control specific neurons in the brain using light. By genetically modifying neurons to express light-sensitive proteins, researchers can selectively activate or inhibit neural activity with remarkable precision.
 
This technology has been instrumental in understanding the causal relationship between specific neural circuits and behavior, providing a deeper understanding of brain function and potential therapeutic targets for neurological disorders.
 
Technological advances have revolutionized our ability to map the human brain, bringing us closer to understanding its complexity and unraveling its mysteries. From imaging techniques like MRI and fMRI, which provide detailed structural and functional information, to technologies like PET and EEG that probe brain chemistry and electrical activity, each tool contributes uniquely to our expanding knowledge of the brain.
 
With continued advancements and integration of these technologies, we are on the cusp of groundbreaking discoveries that will not only deepen our understanding of the brain but also pave the way for novel treatments and interventions for neurological and psychiatric disorders. As we continue to explore the frontiers of brain mapping, the future holds exciting possibilities for unlocking the full potential of the human brain.

 The COVID-19 pandemic, caused by the novel coronavirus, has been an unprecedented global crisis that has affected virtually every aspect of society. Beyond its physical health consequences, COVID-19 has also had a profound psychological impact on individuals, communities, and entire societies worldwide. This post explores the psychological repercussions of the pandemic, focusing on its effects on mental health, social relationships, and overall well-being.
 
Mental Health Challenges
 
The pandemic has brought about a surge in mental health challenges across the globe. The fear of infection, uncertainty about the future, and social isolation have all contributed to increased rates of anxiety, depression, and stress. The prolonged lockdowns, work-from-home arrangements, and limited social interactions have disrupted people's routines and led to feelings of loneliness and helplessness.
 
Healthcare workers have been at the frontline of the pandemic, facing immense pressure, fear, and burnout. The constant exposure to the virus, coupled with the emotional toll of witnessing suffering and loss, has led to higher rates of post-traumatic stress disorder (PTSD) and other mental health disorders among these essential workers.
 
Children and adolescents have also been significantly impacted. The abrupt shift to online learning and the lack of social interactions with peers have affected their emotional and academic development. The uncertainty about their future and the disruptions in their education have added to the burden of stress and anxiety.
 
Social Impact and Isolation
 
Social isolation has been a significant consequence of the pandemic, leading to feelings of loneliness, sadness, and disconnection. With restrictions on gatherings and travel, people were compelled to stay away from their loved ones, which particularly affected the elderly and vulnerable populations. As a result, mental health professionals reported an increase in cases of depression and suicidal thoughts during the pandemic.
 
The loss of social support networks and the inability to engage in communal activities and celebrations have also taken a toll on people's well-being. Humans are social creatures, and the absence of social interactions has affected their emotional and psychological resilience.
 
Infodemic and Fear
 
The rapid spread of information, both accurate and inaccurate, during the pandemic contributed to an "infodemic." The constant bombardment of news, misinformation, and conspiracy theories generated fear and confusion among the population. Fear of the unknown and uncertain information about the virus led to panic-buying, hoarding, and irrational behaviors.
 
This infodemic also fueled anxiety and stress, with individuals feeling overwhelmed by the constant stream of pandemic-related news and updates. The constant exposure to negative information has a psychological impact on society as it heightens feelings of vulnerability and perceived threat.
 
Coping Mechanisms and Resilience
 
Despite the challenges posed by the pandemic, individuals and communities have demonstrated remarkable resilience and adaptation. People sought various coping mechanisms to manage stress and anxiety, such as engaging in physical activities, practicing mindfulness, and connecting with others through virtual platforms.
 
The pandemic also fostered a sense of solidarity and compassion. Communities came together to support vulnerable members, frontline workers, and those facing financial hardships. Acts of kindness and collective efforts to combat the virus have been critical in maintaining a sense of hope and unity during difficult times.
 
Impact on Mental Health Services
 
The surge in mental health challenges during the pandemic has highlighted the need for accessible and adequate mental health services. Many mental health facilities were overwhelmed, leading to increased waiting times and limited resources. Moreover, the stigma surrounding mental health remains an obstacle to seeking help for some individuals.
 
The COVID-19 pandemic has left an indelible mark on society, impacting the psychological well-being of individuals worldwide. From mental health challenges to social isolation and fear, the pandemic has presented a unique set of psychological stressors. Nonetheless, the resilience and collective efforts demonstrated by individuals and communities have also shown that solidarity and compassion can help mitigate the psychological impact of such global crises. As the world continues to navigate the aftermath of the pandemic, it is crucial to address and prioritize mental health support and resources to aid individuals in their recovery and healing process.

As I am quickly drafting this, think of targeting an audience. 

​There are few things in life that cannot be refuted. Race, age, language, sex, height, weight and net worth. These are essentially biological patterns and one social. Stereotypes exist to reiterate that we act individually but we learn and survive collectively. Actions are defined by our surroundings and our existential need for survival. 
 
So, data, is psychological patterns or strategic information?
 
Think about these two sentences again “Stereotypes exist to reiterate that we act individually but we learn and survive collectively. Actions are defined by our surroundings and our existential need for survival” and now remove “for survival” and add and “s” at the end of the sentence. Relatively, everything is surrounded by consumption, shelf life and scarcity. From essential products to luxury ones that have and are expected to be limited for a certain period. This definition almost includes every aspect of life, economics and decisions. So, when it comes to the same question, the answer is psychological patterns. 
 
Consumption, unless the source is a monopoly, is open to the same characteristics a person would choose to drink water over an alco
 
holic beverage. And it is influence by the same surrounding factors the same person uses to choose the same spot to have the drink. 
 
Selling a product should not be a difficult task to do if one: it is a great product. And two: it has the right pricing. 
 
But nowadays people are given the difficult task of deciding among different and different options. Some of them are good, some of them not too good, and others are literally worthless.
 
Therefore, psychology patterns are often taken into consideration to sell the worthless product to shape the opportunity that wasn’t there before. Data isn’t only used to sell a tangible object. Data is helpful in a variety of reasons and areas including branding, politics, changing spending behavior, etc. giving to it the fundaments of being composed of patterns. Psychological Patterns.
 
Why isn’t just strategic? Because data must be shaped to meet the outcome that you are looking for.  

​There is an endless debate on the future of humanity. From climate change to thousands of subjects that you might never heard of. But all comes down to a single unit. A unit that encloses ultimately every issue because we depend upon it to convey an action… In every state, in every city, in every home there is valuable future for generations to come and it is: character. 
 
Character, also known as education, moral values, personality or culture is define by how we deal with current issues and transform them into a perceptible attitude for younger generations. But not only that, there is also a combination of tradition inherited by previous generations and stained by the ongoing. 
 
One of my favorite eras after the Renaissance is the late-early 1800-1900. A century that revolutionizes thinking and competition among communities and created awe with every revealed invention. History has never been pleased or prove to be better than during this epoch. 
 
But today, we face different issues that arise and influence heavily in the construction of character. And it just seems that this ‘character’ rather than projecting prosperity is going into the opposite direction. 
 
For many of these issues science has fall behind. But nevertheless, there are ways to approach issues like depression, stress or anxiety. Brain scanning is an approach. An approach the relatively pinpoints brain activity or rather, issues.  
 
Take for example the following image. An individual with Obsessive-Compulsive Disorder would likely have a greater brain activity. A considerable issue that can now be confirmed thanks to this technology. 

Yet, having the access to this technology is very expensive. To a point that most people do not have access to this technology. Which brings us to the next important point: how is science and technology evolving in a way that this type of technology is accessible to any household?
 
The title of this blog post, In the Darkest Dream of a Sleep There Is Light When the Eyes Are Open, is a metaphor that can be interpreted in many ways. And one of them is “if we know what is in the minds of the needed, we can improve their lives.”
   
I leave you with a video that explains more about how helpful is imaging for psychiatry, and this short data analysis. A metric that stands out is suicidal records for Male in their 30-49 age. Note that ages 0-29 and 70-0 is less than or equal to 29 and more than or equal to 70 subsequently.  
 
Sources: 
https://data.world/cityofaustin/cxhd-bvc3
 
 

​ 
Something I often wonder is if educated people are less or more likely to develop Alzheimer’s Disease. I wonder if there is a correlation between knowledge and this disease. Between thinking and this disease. And that is because it requires an amount of pressure to obtain a satisfactory deduction after having overthought.
 
Overthinking is something that naturally happens to any person. “Should I wear these shoes?”, “should I wear this hat?” and drives decision upon a rational evaluation of a situation. But this overthinking grows as the gravity of the premise does. “Why did I buy these shoes?”, “why didn’t I buy shoes to my children instead?”.
 
Naturally, as you noticed on the progression of the questions, the thinking evolves as the personal priorities do. Concluding that a person with bigger responsibilities will be more likely to overthink. 
 
Therefore, my question is whether educated people are more likely to develop Alzheimer’s Disease. 
 
What Is Alzheimer's Disease?
 
Alzheimer's Disease is an irreversible brain disorder that affects cerebral regions in their ability to rationalize. 
 
CDR and Education 
 
Note in the first image on your left top corner, the scatterplot shows a significant peak on CDR among individuals with 12 years of education. Giving a sense that indeed education is related to development of Alzheimer’s Disease.

When analyzing data, we can drive conclusions based on historical references. Historical data that describes which groups developed  Alzheimer’s Disease and whether there is a trend that can be predictable. 

About the data:

The Open Access Series of Imaging Studies (OASIS) is a project aimed at making MRI data sets of the brain freely available to the scientific community. By compiling and freely distributing MRI data sets, we hope to facilitate future discoveries in basic and clinical neuroscience. OASIS is made available by the Washington University Alzheimer’s Disease Research Center, Dr. Randy Buckner at the Howard Hughes Medical Institute (HHMI)( at Harvard University, the Neuroinformatics Research Group (NRG) at Washington University School of Medicine, and the Biomedical Informatics Research Network (BIRN).
 
Content:
 
Cross-sectional MRI Data in Young, Middle Aged, Nondemented and Demented Older Adults: This set consists of a cross-sectional collection of 416 subjects aged 18 to 96. For each subject, 3 or 4 individual T1-weighted MRI scans obtained in single scan sessions are included. The subjects are all right-handed and include both men and women. 100 of the included subjects over the age of 60 have been clinically diagnosed with very mild to moderate Alzheimer’s disease (AD). Additionally, a reliability data set is included containing 20 nondemented subjects imaged on a subsequent visit within 90 days of their initial session.
Longitudinal MRI Data in Nondemented and Demented Older Adults: This set consists of a longitudinal collection of 150 subjects aged 60 to 96. Each subject was scanned on two or more visits, separated by at least one year for a total of 373 imaging sessions. For each subject, 3 or 4 individual T1-weighted MRI scans obtained in single scan sessions are included. The subjects are all right-handed and include both men and women. 72 of the subjects were characterized as nondemented throughout the study. 64 of the included subjects were characterized as demented at the time of their initial visits and remained so for subsequent scans, including 51 individuals with mild to moderate Alzheimer’s disease. Another 14 subjects were characterized as nondemented at the time of their initial visit and were subsequently characterized as demented at a later visit.

source: https://www.kaggle.com/
​

Other ​Sources: 
https://www.alz.org/alzheimer-demencia/hechos-y-cifras
https://www.hopkinsmedicine.org/
https://www.alz.org/

There is a well-known and well stablished concept of evolution. And while this gem of Scientific proof reveals the nature of life, it does not explain, neither it aims to show the changes beneath the layers of a thought. 
 
The brain has evolved throughout millions of years. Certain parts of the brain, of course, either have grown or have been created to adapt to the needs of life. And if you followed well these lines of discernment you may have already questioned: What are the needs of today’s life? 
 
Watching the joker may make you wonder that all that exclusive drama played on the big screen is a fantasy of the movie producer. And all that play is nothing but an opposite description of life. However, it is not the actions in that movie that play the important role in this analysis, but specific lines and the process of Joker’s thoughts that are correlated to ordinary lives.  
 
Going back into how a thought is form
 
Science is unprecise when it comes to thinking. Yes, you can point out which regions of the brain are utilized for this process, but when it comes to negative or positive thinking the odds of creating a bad or good thought are certainly connected to data, psychology, and the unknown evolution of thought. 
 
So, what are the needs of today’s life? 
 
Well, we can start by observing the following charts. 

Social issues begin with inequality of wealth. If we measure the probability of seeing a low-income individual committing a crime, the changes will start by creating a group that has 705,507,716 individuals or 9.29% in part of the worldwide population. Now, measuring the intentions versus the actions is quite full of complexities. And while the purpose of this analysis is not to label wealth inequality as the evil of all problems it is indeed an influencer in thought creation. 
 
You know, thinking moves fast from a perceptional thought to a convoluted action. The reason perhaps why philosophers and scientist are never clear or easy to be understood. But the thing is, that most actions mirror societies behavior, and not personal merits. Therefore, while the specific thought is created by the impulse of mobility the road in which the thoughts travel was already built. If building a thought requires of an input, then, are we shaping in the right direction the future generations?    
 
I don’t leave this question to determine how the world is doing, but to conclude that owned actions might be shaping the thoughts of others. 

Data Source: https://data.worldbank.org/indicator/sp.pop.totl
​

Since when thoughts have revolutionized from being a tragedy to become a comedy? ​

​Unlike other sciences, the study of the brain brings magnificence to that natural connections of the physiology and our thinking. To chemistry and our thinking. To anatomy and our thinking. To physics and our thinking. And so on. 
 
Neuroscience, a science that studies the functional mechanisms of the brain is so magnifique that stirs my thinking every time I learn something new. While there are countless wonders about the brain, the existent information overwhelms anyone. And I must say than rather than intimidating, neuroscience is so cool. 
 
As we learn a science or subject in life, our need to apply the skills-learned drive us to conquer the environment in which we live. That means that if we learn how to read or write, we might end up becoming writers or literature judges. As it might always be the case, it is true that a specific learning makes feel awesome. 
 
Now imagine learning about frontal lobes, the occipital lobes, the amygdala or any other region of the brain that we use regularly in life. Wouldn’t feel nerdy to stop and recognize the senses your utilizing this moment, but at the same time would be so cool? 
 
A subject like neuroscience gives us more than just information. It provokes our mind to explore new things relevant to the subject and gives more reasons to learn than to quit. Science in general is amazing, but neuroscience is so cool! Don’t feel intimidated learning more about the old brain!