Jekyll2026-05-12T13:28:15+00:00https://mikel-zhobro.github.io/feed.xmlMikel ZhobroI’m a PhD student with Prof. [Georg Martius](https://uni-tuebingen.de/fakultaeten/mathematisch-naturwissenschaftliche-fakultaet/fachbereiche/informatik/lehrstuehle/distributed-intelligence/team/prof-dr-georg-martius/) and since November 2023, I've been part of the Autonomous Learning Group at the University of Tübingen and MPI‑IS. Previously, I spent some time at the [EV](https://is.mpg.de/ev) under Jorg Stückler and [LDS](https://is.mpg.de/lds) under [Michael Muehlebach](https://sites.google.com/view/mmuehlebach). Not so long ago, I earned an M.Sc. in Electrical Engineering from RWTH Aachen and an M.Sc. in Computer Science from KTH Royal Institute of Technology. My main focus is on spatial intelligence. In particular, I am developing temporal world models with inherent 3D spatial consistency both for generation and downstream robotics tasks. In the long term, I aim to scale these models to videos in the wild in a morphology‑agnostic way, from humans to robotic arms and beyond. Outside of my research, I am fascinated by open-ended learning and keep an eye on the latest developments in the field.3d-world-sim2025-12-27T19:43:14+00:002025-12-27T19:43:14+00:00https://mikel-zhobro.github.io/2025/12/27/3d-world-simSources:

  • openAI joining world-sim: http://adityaramesh.com/
]]>Understanding Fourier Series2025-12-27T12:00:00+00:002025-12-27T12:00:00+00:00https://mikel-zhobro.github.io/2025/12/27/fourier-seriesThe Fourier Series is a way to represent a function as the sum of simple sine waves1. More formally, it decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines.

The Definition

Let $f(x)$ be a periodic function with period $2L$. The Fourier series of $f(x)$ is given by:

\[f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} \left[ a_n \cos\left(\frac{n\pi x}{L}\right) + b_n \sin\left(\frac{n\pi x}{L}\right) \right]\]

Where the coefficients are defined as:

\[a_n = \frac{1}{L} \int_{-L}^{L} f(x) \cos\left(\frac{n\pi x}{L}\right) dx\] \[b_n = \frac{1}{L} \int_{-L}^{L} f(x) \sin\left(\frac{n\pi x}{L}\right) dx\]

Visualization

Here is a visual representation of how adding more terms approximates a square wave:

Fourier Series Approximation

Figure 1: Approximation of a square wave using Fourier Series.

Applications

Fourier series are used in:

  1. Signal Processing: Filtering and compression.
  2. Heat Distribution: Solving the heat equation1.
  3. Quantum Mechanics: Wave functions.

References

  1. Fourier, J. (1822). Théorie analytique de la chaleur. Firmin Didot. ↩ ↩2

]]>Video Embedding Demo2024-01-10T00:00:00+00:002024-01-10T00:00:00+00:00https://mikel-zhobro.github.io/2024/01/10/video-demoThis post demonstrates how to embed videos in your blog posts.

Local Video

You can embed a local video using the video.html include. Make sure to place your video file in the images or assets folder.


{% include video.html path="/images/sample_video.mp4" caption="A sample local video" %}

(Note: Since we don’t have a real video file at that path, this will show the player but won’t play anything. Please add a valid .mp4 file to your images folder and update the path.)

A sample local video

YouTube Video

You can also embed YouTube videos using the youtube.html include and the video ID.


{% include youtube.html id="M7lc1UVf-VE" caption="YouTube Developers Example" %}

YouTube Developers Example

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