Projects, scientific reflection, and poetry
In many time series — particularly financial returns — the variance is not constant over time. Some periods are calm, while others display intense volatility. This article introduces ARCH and GARCH models, which allow us to model conditional variance and the phenomenon known as volatility clustering.
Read the article →Many time series contain periodic components imposed by physics (seasonal temperature, ECG rhythms, communications signals). This post introduces the random-phase harmonic model, derives the autocorrelation, explains why the spectrum has “lines” at fixed frequencies, and extends to the realistic signal + noise setting with a clear link to ARMA approximations.
Read the articleBetween divine knowledge and acquired wisdom: a reflection on learning in the age of artificial intelligence. From the medieval origins of "infused knowledge" to our modern ocean of information, this text explores the tension between instant knowledge and knowledge gained through effort. Science is not beautiful because it knows everything, but because it pushes us to search, to explore, to fail certainly but to bounce back.
Read the articleThis article presents a principled construction of symmetric encryption schemes from pseudorandom generators. Starting from the analogy with the one-time pad, it explains how pseudorandomness enables indistinguishable encryptions in the presence of an eavesdropper. The discussion then extends to variable-length messages, stream ciphers, and shows why deterministic encryption and naive keystream reuse fail under multiple-message security.
Read the articleRecurrent networks introduce a key idea: a hidden state updated at every timestep. This post explains why vanilla RNNs struggle with long sequences (vanishing gradients), then shows how GRUs and LSTMs use gating mechanisms to control forgetting and memory. The focus is forecasting intuition, practical model choice, and a compact math view.
Read the articleModern cryptography relies on a subtle idea: a system can appear random without being truly random. This article introduces pseudorandomness, perfect secrecy, the limits of concrete security guarantees, and explains why the asymptotic, complexity-theoretic approach has become central to defining cryptographic security.
Read articlePerfect secrecy formalizes an extreme (and elegant) security guarantee: the ciphertext should reveal absolutely nothing about the message. This article introduces the information-theoretic definition, the indistinguishability experiment, the one-time pad, and Shannon's theorem explaining why perfect secrecy requires keys at least as large as the message space.
Read articleTime series forecasting is often presented as a specialized discipline, yet it naturally fits within the supervised learning framework. This article explains how forecasting problems are structured, how multi-step predictions are constructed, and why classical statistical models should always be compared with machine learning approaches in practice.
Read articleKerckhoffs' principle is a foundational concept in modern cryptography. It states that a cryptographic system must remain secure even if the encryption algorithm is fully known to the adversary, as long as the secret key remains unknown.
Read articleVigenère weakens simple frequency attacks but remains vulnerable. This article explains Kasiski's insight—repeated patterns reveal the key length—and connects classical cryptanalysis to the emergence of modern cryptographic definitions and security proofs.
Read articlePresentation of OpenSpot (FindSpot), a computer vision project for detecting and classifying parking spaces from images. The article compares several CNN architectures (MobileNetV3, EfficientNet, ResNet) with respect to accuracy, inference speed, and real-world deployment constraints.
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In the darkness looming over me,
I see nothing but shadows.
Despair and melancholy overwhelm me.
Who will save me from the abyss?
What is this light?
What is this faint glimmer?
Is it an escape or a cruel snare?
Symmetry, my savior.
You, master of structures and forms.
You, devoted steward of Nature.
You, who tame fields and time.
You, said to be local or global.
How better to show you my gratitude
Than by offering myself as a faithful disciple,
By submitting to your divine critique?
From now on, your laws shall be my shelter,
Your principles, a source of hope.
Welcome me to your lofty realms.
I will study your geometry,
I will confront your nemeses: asymmetries.
A poem inspired by the TRUTH , structure, and order.