https://structures.uni-heidelberg.de/preview_blog_may/posts/index.php Recent content in Posts on STRUCTURES Blog Hugo -- gohugo.io en-us Thu, 16 Jul 2026 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2026_07/index.php Thu, 16 Jul 2026 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2026_07/index.php If you use any modern phone gallery app, one standout feature introduced in recent years is advanced face recognition. When you tap on a photo, the app can identify the people in it and lets you browse through all the pictures on your device where that person appears. It is especially remarkable in the sense that it recognizes faces across thousands of photos, even with varying lighting, angles, and expressions, and most astoundingly, through different ages. https://structures.uni-heidelberg.de/preview_blog_may/posts/2026_02/index.php Thu, 19 Feb 2026 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2026_02/index.php Since the dawn of humanity, our ancestors have tried to predict the future by studying patterns in time. What began with Ice Age hunter-gatherers etching lunar cycles onto mammoth tusks has evolved into sophisticated algorithms that can forecast everything from the next financial market crash to disease surges weeks before hospitals feel the strain. Today’s time series forecasting, the prediction of how systems like weather or ecosystems evolve in time, represents humanity’s most successful attempt yet to peer beyond the present. https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_12/index.php Mon, 22 Dec 2025 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_12/index.php In the first part of this blog series, we explored the concept of symmetries and their foundational role in classical physics, particularly through their deep connection to conserved quantities, a link beautifully captured by Noether’s theorem. In this second part, we shift our focus to quantum field theories (QFTs), a mathematical framework that underpins numerous aspects of modern physics (and mathematics). Symmetries continue to play a central role in this context; they serve, in particular, as distinctive fingerprints that characterize a theory. https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_09/index.php Mon, 15 Sep 2025 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_09/index.php Why is energy conserved in isolated physical systems? What ensures that a planet remains in a fixed orbital plane around its star? Part of the answer lies in a simple yet profound idea: symmetry. Symmetry is one of the most fundamental and unifying principles in nature. It shapes our understanding of physical systems, from the motion of celestial bodies to the behaviour of subatomic particles. Beyond physics, symmetry has also inspired rich and elegant developments in mathematics, particularly since the 19th century. https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_07/index.php Tue, 22 Jul 2025 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_07/index.php Imagine you are trying to predict how three objects move in space – say, the Earth, the Moon, and a spacecraft. You know where they are and how fast they are moving now, but you would like to know how they will behave in a month, a year, or a century. If there were only two objects, the problem would be easy: their motion would follow simple, predictable orbits (e. https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_04/index.php Fri, 11 Apr 2025 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_04/index.php Mathematicians often face a curious dilemma: while certain concepts are elegantly defined in theory, they can be quite elusive in practice. Take, for example, the definition of π. It is given as the ratio of a circle’s circumference to its diameter. While this definition is exact, it is not very practical for use in a calculator. If we wish to use π in numerical computations, we need approximations, which yield numbers close enough to π that can be computed explicitly, like 3. https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_03/index.php Fri, 07 Mar 2025 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_03/index.php Image credit: SXS, the Simulating eXtreme Spacetimes (SXS) project. The merger of two black holes is one of the most extreme and yet fascinating events in the Cosmos. When two black holes coalesce, they release a tremendous amount of energy in the form of gravitational waves. These ripples in spacetime can be captured by high-precision detectors on Earth, and provide key insights into the nature of black holes, the galaxies they live in, and the Universe’s history. https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_02/index.php Fri, 14 Feb 2025 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2025_02/index.php When planning the activities for next weekend or for your next vacation, one of the things you probably do is check the weather forecast. In doing so, you have likely noticed that most websites show you information for the next two weeks at best and that the information changes from day to day. The further out the day you are looking at, the more uncertain the prediction. At the same time, news reports talk about how the climate on Earth will change over the next decades or even centuries. https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_11_littek/index.php Wed, 27 Nov 2024 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_11_littek/index.php A very familiar and yet fascinating sight is the collective and coherent motion of flocks of birds. Such collective behaviour is a rather ubiquitous phenomenon in nature and can be found across a variety of length scales: metres or even kilometres for animals (e.g. fish and wildebeests) or micrometres for bacteria. Seminal works by Tamás Vicsek et al. in 1995 and John Toner & Yuhai Tu in the same year led the way to understanding this phenomenon from a statistical physics and condensed matter physics point of view, which sparked interest in active matter systems. https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_09_nlp/index.php Tue, 01 Oct 2024 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_09_nlp/index.php Many real world applications repeatedly collect measurements of an object over time. Important examples are the price of a stock, sensor data in weather forecasting, and clinical measurements of patients monitored in intensive care units. The resulting data structure, called time series, can be described as ordered sets of real-valued variables, representing observations recorded sequentially over time. In this respect, time series data are similar to the way natural language is encoded for deep learning. https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_06_noel/index.php Fri, 14 Jun 2024 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_06_noel/index.php What is Thermal Equilibrium in Physics? Imagine there is a late-night party. At the beginning of the night, people are all at different temperatures – some hot from dancing, others cooler from having just arrived. As the party goes on, people interact, mingle and dance together. Eventually, everyone reaches a similar temperature – they have thermalised. In the world of physics, thermalisation is a bit like this party. It is the process where particles within a system that are at different energies or temperatures interact and settle into a uniform state, a state which we refer to as thermal equilibrium. https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_04_jf/index.php Thu, 04 Apr 2024 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_04_jf/index.php Jellyfish galaxies have a main luminous, stellar body with tails of gas stemming out in one direction. On the left is an image of a simulated jellyfish galaxy in IllustrisTNG, which resembles the jellyfish galaxies we observe in the real Universe, such as ESO 137-001 (NASA) on the right (Credit: NASA/ESA/CXC/UAH/M.Sun, Hubble Heritage Team, STScI/AURA). What Are Jellyfish Galaxies? Galaxies, like our own Milky Way, come in all shapes, sizes, and colours, and exploring their evolution is key to understanding how our Universe formed. https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_03_womens_day/index.php Fri, 08 Mar 2024 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_03_womens_day/index.php A century ago, the pioneering work of astronomer Henrietta Swan Leavitt revolutionized astronomy. Her work was crucial and changed our picture of the universe. What does this have to do with the mysterious property of pulsating variable stars? “Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space. https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_02_schaefer/index.php Tue, 06 Feb 2024 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_02_schaefer/index.php Deduction and Inference In science, truth can take two forms. First, there is mathematical truth, where statements are deemed true if they’re derived in a logically consistent way from fundamental axioms – and if these axioms are free of contradiction. Second, things can be true empirically, meaning that they are consistent with an experiment and that the experiment is reproducible. The process of deriving statements from axioms is referred to as deduction, and making statements about physical laws based on experimental data is called inference. https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_01_costa/index.php Wed, 10 Jan 2024 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2024_01_costa/index.php What's that structure? Do you enjoy a game of pool or billiards? I certainly do; I find it very satisfying to pocket a ball with a complicated shot following several bounces. I’m not a very skilled player, though, so I miss a lot of shots. Luckily, I can blame these failures on friction and inelasticity in the collisions, or on the unexpected interference of a different ball. You can imagine my relief when I learned of the existence of mathematical billiards! https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_11_kimmig/index.php Tue, 07 Nov 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_11_kimmig/index.php Observation of a protoplanetary disk around the young star HL Tau. Credit: ALMA (ESO/NAOJ/NRAO), CC-BY. The above image shows beautiful structures such as rings and gaps in an astrophysical object – a truly remarkable image. But what is it? A part of this question is answered easily: it’s an observation of a young star called HL Tau, surrounded by a disk out of gas and dust. But the further part, the question about the rings and gaps and where they come from, is much more difficult to answer. https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_10_koppe/index.php Wed, 04 Oct 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_10_koppe/index.php Perhaps you can relate to situations in which you may have caught yourself pondering excessively about something unpleasant, and, although deliberately shifting attention to something else, your mind repeatedly kept wandering back to those thoughts. Or, you may have felt so emotional (or angry) that - in that very moment – you were unable to accept any other but your own perspective, unfit to detach from your own thoughts and judgments, or control your anger. https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_09_brandstetter_lunt/index.php Wed, 06 Sep 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_09_brandstetter_lunt/index.php Editor’s note: This blog post is based on the talk “Eins, zwei, viele – Die kleinste Flüssigkeit der Welt” given by Sandra Brandstetter & Philipp Lunt at the public lecture series event “Akademische Mittagspause 2023: Strukturen in der Welt” (German). The content was edited by the authors together with the STRUCTURES Blog Team, after the transcript has been auto-generated and edited with the support of artificial intelligence tools. The natural world never ceases to fascinate us with its myriad of complex patterns and phenomena, one of which is collective behaviour. https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_07_schwarz/index.php Wed, 12 Jul 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_07_schwarz/index.php This blog post is based on a transcript of the talk “Strukturbildung auf Kommando in biologischen Zellen” given by Prof Ulrich Schwarz at the public lecture series event “Akademische Mittagspause 2023: Strukturen in der Welt”, and published with kind permission. Parts of the transcript have been edited with the help of the artificial intelligence (AI) tools DeepL and ChatGPT before the text was finally copy-edited by the STRUCTURES Blog Editorial Board together with Ulrich Schwarz. https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_06_radev/index.php Tue, 06 Jun 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_06_radev/index.php This is the first part of a series of blog posts on the topics of Bayesian models and statistical inference with neural networks. The series is a simplified summary of a scientific overview article, and intended to provide a glimpse into some of our recent conceptual and methodological work on bridging the gap between “classical” statistics and artificial intelligence (AI) research. With the surge of probabilistic modeling, more and more branches of science subscribe to the use of Bayesian models. https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_05_sorrenson/index.php Tue, 02 May 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_05_sorrenson/index.php Generative Models: The Art of Data Mimicry Picture a talented artist, able to skillfully imitate the style of famous works of art. This artist can study the works of Van Gogh or Monet and produce never-before-seen paintings that have the same look and feel. Maybe you’ve heard of Midjourney, DALL-E or Stable Diffusion? They do something similar, turning a prompt of simple text into richly detailed images, spanning widely across the range of human creativity. https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_04_ksoll/index.php Mon, 03 Apr 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_04_ksoll/index.php Image credits: NASA, ESA, CSA, STScI, Webb ERO Production Team. Stars are fundamental building blocks of our Universe. They bring light into the galaxies and are the very furnaces that forge most of the elements heavier than hydrogen through nuclear fusion, in particular during the late stages of their lives or, in the case of the most massive stars, their ultimate explosive demise as supernovae. Understanding the origin of stars themselves is, therefore, among the central questions of astronomical research. https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_03_hegl/index.php Mon, 06 Mar 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_03_hegl/index.php This post was originally published by the Heidelberg Experimental Geometry Lab (HEGL, see the HEGL Blog) and is featured as a guest article with kind permission by the authors. Topology and geometry are important concepts in mathematics and physics. Especially in theories like general relativity, they have a direct impact, as the spacetime description of a system is already quite geometrical. To highlight the difference between the two concepts, let’s look at a simple two-dimensional disc first. https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_02_ants_ads/index.php Mon, 13 Feb 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_02_ants_ads/index.php There is a well-known riddle that can be stated as follows: suppose you have a stick of length $L$ with a number of $N$ ants placed on it. The ants can move with constant speed $v$ either to the left or the right. If two ants collide, they each change their direction instantaneously and if an ant reaches the end of the stick, it falls down and is never to be seen again. https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_01_palace_crystallographic/index.php Mon, 09 Jan 2023 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2023_01_palace_crystallographic/index.php I first learned about tilings during my last year of the bachelor’s program. At the time Dr. Pellicer was in charge of the class on Selected Topics in Combinatorics, and from then on, tilings held a very special place in my mathematical heart. A tiling (or tessellation) is a covering of the plane by copies of pieces of the plane that don’t overlap. More precisely, one starts with a collection of subsets $ \{ T_1, T_2, \dots \} $ (not necessarily finite, although for this post, it doesn’t hurt to assume the set is finite) of the plane called tiles, and a tiling consists of an arrangement of copies of $T_i$ in $\mathbb R^2$ so that: https://structures.uni-heidelberg.de/preview_blog_may/posts/2022_12_cw/index.php Mon, 05 Dec 2022 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/2022_12_cw/index.php The observable universe is rich in structures and patterns. From atomic nuclei to huge clusters of galaxies, it hosts a vast variety of shapes and complex phenomena. In many cases complex structures emerge from the collective action of simple physical processes as soon as many interacting constituents join to form a system. An example is the hexagonal geometry of snow crystals, which reflects the internal order of water molecules forming six-sided arrangements due to fundamental electric dipole-dipole interactions. https://structures.uni-heidelberg.de/preview_blog_may/posts/gaussian-random-fields/index.php Mon, 07 Nov 2022 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/gaussian-random-fields/index.php How do scientists describe and predict complex patterns and structures emerging in nature, signals or data? Is there a straightforward method to reduce the complexity even of systems as big and complex as the entire universe itself, without losing information we might be interested in? Remarkably, several such methods exist and are frequently used by physicists and mathematicians. Today we want to look at one particularly simple, yet powerful method: Gaussian Random Fields. https://structures.uni-heidelberg.de/preview_blog_may/posts/triangles_integer/index.php Mon, 10 Oct 2022 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/triangles_integer/index.php Triangles are probably the simplest geometric objects in the two dimensional world. Draw three lines, hope they are not parallel (or go all through one point), and you end up with a structure which has so many intriguing properties that it is impossible to count them all. From congruence (which is comparing triangles as geometric objects) to trigonometry (which is comparing the intrinsic values such as angles and side lengths) and the list goes on and on. https://structures.uni-heidelberg.de/preview_blog_may/posts/sphere_packing/index.php Mon, 05 Sep 2022 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/sphere_packing/index.php To the layman mathematics often is an obscure and inscrutable exercise of sheer abstraction. The truth is, however, that a lot of deep and advanced mathematics is born out of very simple and down-to-earth problems. The sphere packing problem is one of these. Suppose that a vendor has a certain quantity of oranges to be arranged in a box. What is the arrangement that maximizes the number of oranges that fit the box? https://structures.uni-heidelberg.de/preview_blog_may/posts/can_you_tell_a_cup_from_a_doughnut/index.php Mon, 08 Aug 2022 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/can_you_tell_a_cup_from_a_doughnut/index.php https://structures.uni-heidelberg.de/preview_blog_may/posts/struc_logo/index.php Mon, 01 Aug 2022 00:00:00 +0000 https://structures.uni-heidelberg.de/preview_blog_may/posts/struc_logo/index.php This structure arises in a visualisation of connections between entities (such as people or countries). It is useful when the individual entities can be associated to groups. Every individual may belong to more than one group. Being in the same group means being connected. We then draw a polygon with corners associated to the individuals that are in the same group. We all know polygons in the Euclidian plane: triangles, quadrangles, pentagons, hexagons, etc.