Christos Tsanikidis - Machine Learning, Mathematics, Computer Science, Finance
http://ctsan.github.io/
Recent content on Christos Tsanikidis - Machine Learning, Mathematics, Computer Science, FinanceHugo -- gohugo.ioenChristos TsanikidisFri, 07 Apr 2023 14:47:48 +0800Research
http://ctsan.github.io/research/
Sun, 20 Aug 2017 21:38:52 +0800http://ctsan.github.io/research/Christos Tsanikidis, Javad Ghaderi, Online Scheduling and Routing with End-to-End Deadline Constraints in Multihop Wireless Networks, Proc. ACM MobiHoc 2022, Oct 2022.
Christos Tsanikidis, Javad Ghaderi, Randomized Scheduling of Real-Time Traffic in Wireless Networks Over Fading Channels, IEEE INFOCOM 2021, May 2021. Full version accepted in IEEE/ACM Transactions on Networking, Nov 2022. [Technical Report: arXiv:2101.04815].
Christos Tsanikidis, Javad Ghaderi, On the Power of Randomization for Scheduling Real-Time Traffic in Wireless Networks, IEEE INFOCOM 2020, July 2020.About
http://ctsan.github.io/about/
Sun, 20 Aug 2017 21:38:52 +0800http://ctsan.github.io/about/Christos Tsanikidis is a PhD candidate at Columbia University in the city of New York. He completed his Master’s at Columbia University. Before that he completed his Bachelor’s in Electrical and Computer Engineering at NTUA, majoring in Computer Science.
Christos is currently researching scheduling problems in Networks, focusing on deriving novel online algorithms with performance guarantees. During his PhD he completed an internship at Microsoft, working on the optimization of Large Language Models (LLMs), in the Turing team, under Bing.To Draw with Markov Chain Monte Carlo.
http://ctsan.github.io/post/mcmc/
Fri, 07 Apr 2023 14:47:48 +0800http://ctsan.github.io/post/mcmc/In this post we will explore Markov Chain Monte Carlo Methods (MCMC), and specifically Metropolis-Hastings. MCMC Methods allow us to sample from a distribution, if all we know is $\phi(x)=c\times f(x)$, where $f(x)$ is the density at point $x$ of the distribution we wish to sample from, and $c$ is any fixed constant. This allows us to sample from the distribution without knowing the normalization term of the distribution. Recall that all density functions technically need to integrate to $1$, i.CheatsheetGPT
http://ctsan.github.io/other/the-wall/
Tue, 04 Apr 2023 15:43:48 +0800http://ctsan.github.io/other/the-wall/I prompted GPT4 to help me create a cheatsheet for areas spanning AI, Computer Science, Finance, Operations Research, and Mathematics. Then, asked to grade the importance of each relationship for different people, and in some cases, to explain its answers. π Click me to see how it works. π Click to see the purpose. π Limitations & Disclaimers, Future Work. Loading might take some time. Alpha Version. Last Update: 06/24/2023.A Fresh Random Walk Down Wall Street - Part A
http://ctsan.github.io/post/wolf-of-wall-street/
Fri, 03 Mar 2023 14:47:48 +0800http://ctsan.github.io/post/wolf-of-wall-street/A common model for the evolution of the price of a financial security, such as a stock, is that it follows a brownian motion. There are two common styles of brownian motions: the arithmetic Brownian motion (ABM), and the geometric brownian motion (GBM). Letβs talk about ABM First.
Arithmetic Brownian Motion The most basic brownian motion is the Wiener process $Z(t)$ with $Z(0)=0$ and $Z(t)\sim \mathcal N(0,1)$. This is the analogue of the discrete unbiased random walk in continuous time and values.The diffusion of discovery
http://ctsan.github.io/post/scientific-process/
Fri, 03 Mar 2023 14:47:48 +0800http://ctsan.github.io/post/scientific-process/How do humans make discoveries? How do they venture into the unknown and push the frontiers of knowledge? In this article, we offer a new perspective on human discoveries, based on a simple but powerful analogy: humans are like particles diffusing out of a labyrinth. Imagine that each human is an explorer who tries to find an exit from a maze-like environment, where every turn is a gamble and every step is a risk.Mathematical Parade
http://ctsan.github.io/other/mathematical-market/
Sun, 01 Jan 2023 15:43:48 +0800http://ctsan.github.io/other/mathematical-market/Mathematical River
http://ctsan.github.io/other/mathematical-river/
Sun, 01 Jan 2023 15:43:48 +0800http://ctsan.github.io/other/mathematical-river/Mathematical Tapestry
http://ctsan.github.io/other/mathematical-tapestry/
Sun, 01 Jan 2023 15:43:48 +0800http://ctsan.github.io/other/mathematical-tapestry/ Enable Dark Mode The Hidden Simplicity Principle: Discovering the Underlying Reality
http://ctsan.github.io/post/hidden-simplicity-principle/
Thu, 07 May 2020 19:00:00 +0800http://ctsan.github.io/post/hidden-simplicity-principle/The Hidden Simplicity Principle posits that our limited perception of the world can result in complicated models of a simpler underlying reality. Many concepts, notions, or phenomena we encounter, analyze, and contemplate may be simplified manifestations of broader, more general ideas when presented in specific contexts. By recognizing this principle and striving for the simplest possible explanation, we can avoid overfitting and develop more accurate models of the world around us.Modelling and Simulating a Pandemic
http://ctsan.github.io/post/modeling-and-simulating-a-pandemic/
Sun, 29 Mar 2020 14:47:48 +0800http://ctsan.github.io/post/modeling-and-simulating-a-pandemic/Adjust the Parameters below to explore the spread of the disease under different scenarios. Bear in Mind that some parameters might lead to poor performance depending on your device. If you don’t understand what is happening, there is an explanation below the simulation environment.
Warning: It’s recommended to use a large enough screen (for example a tablet or a desktop). Some information is omitted in smaller screens.
Population Density Town Size Connections Radius Connectivity Chance Infection Chance Mean Days Sick Can you get Reinfected?Effective Learning: Generalizing, Exploring, and Relating Concepts
http://ctsan.github.io/post/learn-by-generalizing/
Sun, 04 Feb 2018 17:50:48 +0800http://ctsan.github.io/post/learn-by-generalizing/In the pursuit of personal growth, it’s essential to develop an effective learning strategy to navigate the vast world of information and new concepts. This blog post will focus on three key principles for mastering learning: generalizing, exploring, and relating concepts. By employing these techniques, you can not only absorb more information but also apply it in practical and meaningful ways.
Generalizing, Exploring, and Relating Concepts Consider the following learning principles:How to make a profitable virtual football betting game
http://ctsan.github.io/post/creating-a-football-betting-game/
Fri, 22 Dec 2017 15:43:48 +0800http://ctsan.github.io/post/creating-a-football-betting-game/I have already dedicated a previous post on the simulation of the doubling method. In this post I will walk you through steps that can be taken for the creation of a virtual betting game. In particular we will examine a football betting game, similar to one currently found in the market.
Design decisions Initially, before we develop the simulation, we can discuss two different possible methods to create such a game.A functional approach for solving equations
http://ctsan.github.io/post/functional-approach-for-solving-equations/
Tue, 05 Dec 2017 15:43:48 +0800http://ctsan.github.io/post/functional-approach-for-solving-equations/Solving or interpreting equations is a fundamental topic, usually taught in young ages, when students are not very eager to capture the essence of the equations or do not know some more advanced concepts that can reinforce their understanding of them.
When students are presented with an equation $x+4=13$, usually they are asked about the value of $x$. As a student I was shown a number of manipulations that I had to learn in isolation, making the task cumbersome initially but then mechanic.The Enlightened Gambler: A Sobering Simulation of the Doubling Method
http://ctsan.github.io/post/gambler-enlightened-doubling-method/
Sat, 19 Aug 2017 15:43:48 +0800http://ctsan.github.io/post/gambler-enlightened-doubling-method/In conversations about gambling, I frequently encounter a dangerous cocktail of misinformation and misunderstanding. The average person, quite understandably, grapples with comprehending how probabilities can guarantee long-term losses. This challenge is further exacerbated by fallacies and complicated games that intentionally obscure the underlying truth: the house always wins.
To illustrate this point, I’ve chosen to simulate the gambling process and present the average outcomes rather than diving into a potentially confusing sea of probabilities.Counting the number of elements in sequences through compression
http://ctsan.github.io/post/counting-insight/
Sun, 13 Aug 2017 15:43:48 +0800http://ctsan.github.io/post/counting-insight/Counting the elements in a sequence is a common problem in mathematics, computer science, and programming. Although in many cases this appears tricky, there’s a simple method to make the task straightforward, requiring only basic math skills.
Examples Before Theory Let’s dive into a few examples before explaining the method precisely.
Example 1: {5, 6, 7, …, 100} First, find a function that maps integers (ideally starting from 0) to the elements above.Athens mini-markets Voronoi
http://ctsan.github.io/project/greek-mini-markets/
Mon, 19 Jun 2017 16:01:23 +0800http://ctsan.github.io/project/greek-mini-markets/The process followed was the following:
Download data containing the addresses of 1404 mini markets in athens.
Use google API to query the latitude and longitude of the addresses, given the information of the location (area and address).
Convert latitude and longitude to cartesian coordinates, assuming linearity with small error due to the restricted range.
Use google maps api to keep a white simplified map of Athens.
Create the voronoi diagram using the coordinates of the points.Turkey to Greece missile range
http://ctsan.github.io/project/turkey-greece-range/
Sat, 27 May 2017 16:01:23 +0800http://ctsan.github.io/project/turkey-greece-range/It was announced in Greek media that Turkey achieved a new maximum range with modern missiles in its disposal. I was instantly curious: what targets in Greece can be hit by Turkey now?
This experiment is created for fun. The author is optimistic about the relations of the two countries.
scroll down for the results to see the resulting images
Problem Setting Hit Area Let $\mathcal{T}$ be the set of points that are in Turkey.Unified Terminal Experience, BACU
http://ctsan.github.io/project/bacu/
Fri, 10 Feb 2017 16:01:23 +0800http://ctsan.github.io/project/bacu/Motivation In this page I am going to demonstrate an idea of a unified terminal experience. To substantiate it, I created an application for SQL, using ncurses and python, but the concept is to apply the same principle in any hierarchical tree structure, aiding the development by an underlying library.
The interaction we have each day with computers varies from application to application. This is also the case for terminal experience.Blind Hunter
http://ctsan.github.io/project/blind-hunter/
Sun, 06 Nov 2016 16:01:23 +0800http://ctsan.github.io/project/blind-hunter/Suppose you are a hunter that doesn’t have information about the distance from the prey. For instance a blind dog with very precise smelling which can be mapped to a distance from the potential prey. How can this dog locate and eventually reach its prey?
The algorithms are not documented yet, but a simulation is provided. If you are interested contact me for more information.
Demo simulation parameters:
\( V_{prey} \approx V_{predator} \) Prey changes direction with small probability Predator adopts the strategy we have assigned it (not explained here).Black Scholes
http://ctsan.github.io/project/black-scholes/
Fri, 19 Feb 2016 16:01:23 +0800http://ctsan.github.io/project/black-scholes/ Demonstration Heat Equation PDE Simulation
http://ctsan.github.io/project/heat-equation/
Fri, 19 Feb 2016 16:01:23 +0800http://ctsan.github.io/project/heat-equation/Heat equation The heat equation is a partial differential equation, that is, it involves both derivatives of the time and of spatial variables.
$$\frac {\partial u} {\partial t} - \alpha \frac {\partial^2 u}{\partial x^2} = 0 $$
Where the parameter \(\alpha\) determines how much conductive the material is.
This is the case for one variable, and thus one dimension. You can imagine that as a long but very thin wire. Of course in reality there is no such thing as 1 Dimension material, but from physicists and mostly engineers we know that this can be approximated when the long side is much bigger than the radius of the wire.Exploring Logarithmic Counting: A Thought Experiment on Human Capabilities
http://ctsan.github.io/post/hierarchies/
Sat, 02 Jan 2016 15:43:48 +0800http://ctsan.github.io/post/hierarchies/This essay considers the problem of counting a large number of objects by a human. While counting large quantities of objects may not be an everyday necessity (unless you are a poker player), it is an intriguing thought experiment to explore how we can design approaches around human limitations. Logarithmic counting offer a lens through which we can examine our cognitive abilities and devise methods that cater to our strengths and weaknesses.Mice Make Art!
http://ctsan.github.io/project/mice-make-art/
Mon, 23 Nov 2015 16:01:23 +0800http://ctsan.github.io/project/mice-make-art/Concept The concept is the following: Drop $N$ mice randomly in a rectangular area. Each mouse targets exactly one other mouse forming a circle of targets.
$$M_1 \rightarrow M_2 \rightarrow … \rightarrow M_N \rightarrow M_1$$
All mice have equal velocity. The simulation follows. After clicking on the simulation, press (i) to increase the number of mice, and press (d) to decrease it.
Simulation Emerging Behaviors Each mouse \(M_i\) is confined in the rectangular area.Regex Experimenting Platform
http://ctsan.github.io/project/regex-experimenter/
Sun, 09 Mar 2014 16:01:23 +0800http://ctsan.github.io/project/regex-experimenter/This is an experimenting platform I’ve created for people who are learning regular expressions. Javascript Regular Expressions are used.
The platform allows you to experiment by entering a regular expression, and then highlighting the matching parts. Match and replace is also available, with special regex replacing syntax available. You can either use the reload button or edit the text yourself in the platform.
Experiment with the platform yourself
Demonstration Warcraft 3 Mod - Pimp my Peon
http://ctsan.github.io/project/warcraft-game/
Wed, 10 Jun 2009 16:01:23 +0800http://ctsan.github.io/project/warcraft-game/Pimp my Peon was the first contact I had with programming at the age of 15-16 and very influential to the later developed interests. Alternatively you might consider it as an early indication of an innate fascination for the art of “creation” using technology.
It is documented here for historical reasons.
It was a mod for Warcraft 3, like the famous Dota 1, which had begun as an open source project and was then “forked” by young me.