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## Mathematics

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**1**-**20**of**23**. The race for the Kochen-Specker Theorem

A world record in solving satisfiability problems was achieved at the Vienna University of Technology - it is quite abstract, but the technology behind it is extremely important for hardware and software industries . Suppose Alice, Bob, and Carla answer a question. Each of the three answers is either correct or incorrect.

A world record in solving satisfiability problems was achieved at the Vienna University of Technology - it is quite abstract, but the technology behind it is extremely important for hardware and software industries . Suppose Alice, Bob, and Carla answer a question. Each of the three answers is either correct or incorrect.

The theory of micro-hairs

Tiny hairs on cell walls, so-called -cilia-, can move in unison to pump fluid. Now there finally is a physical theory describing these hairs' movements. They are only very simple structures, but without them we could not survive: Countless tiny hairs (cilia) are found on the outer wall of some cells, for example in our lungs or in our brain.

Tiny hairs on cell walls, so-called -cilia-, can move in unison to pump fluid. Now there finally is a physical theory describing these hairs' movements. They are only very simple structures, but without them we could not survive: Countless tiny hairs (cilia) are found on the outer wall of some cells, for example in our lungs or in our brain.

The Mathematics of Separate Things

By Birgit Baustädter Discrete mathematics is so much more than just "the language of computer science", as it is often referred to. But it is not "discrete" in the usual sense. Points are particularly discrete. Discrete mathematics derives from the Latin discernere, which means "to separate". "Discrete mathematics is about delimited or clearly separated objects - such as points, lines or sequences of integers," explains Oswin Aichholzer, a computer scientist at Graz University of Technology (TU Graz).

By Birgit Baustädter Discrete mathematics is so much more than just "the language of computer science", as it is often referred to. But it is not "discrete" in the usual sense. Points are particularly discrete. Discrete mathematics derives from the Latin discernere, which means "to separate". "Discrete mathematics is about delimited or clearly separated objects - such as points, lines or sequences of integers," explains Oswin Aichholzer, a computer scientist at Graz University of Technology (TU Graz).

From chemical Graphs To Structures

Three-dimensional (3D) configurations of atoms dictate all materials properties. Quantitative predictions of accurate equilibrium structures, 3D coordinates of all atoms, from a chemical graph, a representation of the structural formula, is a challenging and computationally expensive task which is at the beginning of practically every computational chemistry workflow.

Three-dimensional (3D) configurations of atoms dictate all materials properties. Quantitative predictions of accurate equilibrium structures, 3D coordinates of all atoms, from a chemical graph, a representation of the structural formula, is a challenging and computationally expensive task which is at the beginning of practically every computational chemistry workflow.

Computational Protein Design to Address Challenges in Biotechnology

By Gustav Oberdorfer Computational design of novel protein structures is a promising tool to make superior biological materials with tailor-made properties, new pharmaceuticals or complex fine chemicals. Over the last two years research in my group focused on developing methods to design and functionalize de novo proteins.

By Gustav Oberdorfer Computational design of novel protein structures is a promising tool to make superior biological materials with tailor-made properties, new pharmaceuticals or complex fine chemicals. Over the last two years research in my group focused on developing methods to design and functionalize de novo proteins.

From the Wild West to data security

By Cornelia Kröpfl BA MA 30 years ago, data security was a niche topic. Today, researchers at TU Graz are laying the foundations for a completely new way of thinking about security. Including future developments. Not so long ago, the mobile phone was primarily used to store contact data. Today, smartphones know where we are and what media we read.

By Cornelia Kröpfl BA MA 30 years ago, data security was a niche topic. Today, researchers at TU Graz are laying the foundations for a completely new way of thinking about security. Including future developments. Not so long ago, the mobile phone was primarily used to store contact data. Today, smartphones know where we are and what media we read.

In search of the foundations of discrete mathematics

By Birgit Baustädter Oswin Aichholzer does basic research - he doesn't invent, he discovers. The theoretical computer scientist is on the trail of basic mathematical rules which he can model and teach the computer. Oswin Aichholzer is wearing a light blue pullover, has a headset on, and is sitting in front of the computer.

By Birgit Baustädter Oswin Aichholzer does basic research - he doesn't invent, he discovers. The theoretical computer scientist is on the trail of basic mathematical rules which he can model and teach the computer. Oswin Aichholzer is wearing a light blue pullover, has a headset on, and is sitting in front of the computer.

Stochastic Optimisation in Financial and Insurance Mathematics

By Stefan Thonhauser Stochastic models are now indispensable for answering practical questions on finance and insurance. Their use needs to be based on a careful model validation process and an awareness of model limitations. In risk management, being able to react to negative trends is essential. Resulting questions can be directly linked to stochastic optimisation problems.

By Stefan Thonhauser Stochastic models are now indispensable for answering practical questions on finance and insurance. Their use needs to be based on a careful model validation process and an awareness of model limitations. In risk management, being able to react to negative trends is essential. Resulting questions can be directly linked to stochastic optimisation problems.

String Art - from the Hand of a Robot

String art is a technique for the creation of visual artwork where images emerge from a set of strings that are spanned between pins. Now, at TU Wien (Vienna) this work can be delegated to a robot - an example of a complex task that digital fabrication can solve. The basic idea of string art is simple: hooks distributed on a frame are connected by strings back and forth until they fuse to a perceptible image.

String art is a technique for the creation of visual artwork where images emerge from a set of strings that are spanned between pins. Now, at TU Wien (Vienna) this work can be delegated to a robot - an example of a complex task that digital fabrication can solve. The basic idea of string art is simple: hooks distributed on a frame are connected by strings back and forth until they fuse to a perceptible image.

Digital penicillin production

TU Wien and Sandoz GmbH have successfully implemented a real-time computer simulation of the complex growth behaviour of penicillin producing organisms. This simulation now helps to keep the production process under control. For thousands of years, micro-organisms have been used to facilitate chemical reactions - in beer brewing, for example.

TU Wien and Sandoz GmbH have successfully implemented a real-time computer simulation of the complex growth behaviour of penicillin producing organisms. This simulation now helps to keep the production process under control. For thousands of years, micro-organisms have been used to facilitate chemical reactions - in beer brewing, for example.

Indian Sacred Texts and the Logic of Computer Ethics

Can we teach ethical behaviour to machines' Computer Scientists in Vienna are studying ancient Sanskrit texts and using the tools of mathematical logic to describe ethical rules. The Indian sacred texts of the Vedas have been studied for millennia. But now, for the first time in history, computer scientists in Vienna analyse them by applying the methods of mathematical logic.

Can we teach ethical behaviour to machines' Computer Scientists in Vienna are studying ancient Sanskrit texts and using the tools of mathematical logic to describe ethical rules. The Indian sacred texts of the Vedas have been studied for millennia. But now, for the first time in history, computer scientists in Vienna analyse them by applying the methods of mathematical logic.

Hidden bridge between quantum experiments and graph theory uncovered using Melvin

An answer to a quantum-physical question provided by the algorithm Melvin has uncovered a hidden link between quantum experiments and the mathematical field of Graph Theory. Researchers from the Austrian Academy of Sciences and the University of Vienna found the deep connection between experimental quantum physics and this mathematical theory in the study of Melvin's unusual solutions, which lies beyond human intuition.

An answer to a quantum-physical question provided by the algorithm Melvin has uncovered a hidden link between quantum experiments and the mathematical field of Graph Theory. Researchers from the Austrian Academy of Sciences and the University of Vienna found the deep connection between experimental quantum physics and this mathematical theory in the study of Melvin's unusual solutions, which lies beyond human intuition.

The Beam of Invisibility

A new cloaking technology has been developed at TU Wien: a special kind of material is irradiated from above in such a way that another beam of light can pass completely uninhibited. The material is irradiated with a specially designed pattern, the wave from the left can pass through the object completely unperturbed.

A new cloaking technology has been developed at TU Wien: a special kind of material is irradiated from above in such a way that another beam of light can pass completely uninhibited. The material is irradiated with a specially designed pattern, the wave from the left can pass through the object completely unperturbed.

Who can find the fish that makes the best sound?

Using new computer algorithms, it is possible to adjust specific properties of three-dimensional objects, such as the sounds they produce or how stable they are. The thickness of a piece of metal made into different animal shapes - including a giraffe and a fish - is adjusted by using a computer algorithm in such a way that a specific sound spectrum is exhibited when the objects are struck.

Using new computer algorithms, it is possible to adjust specific properties of three-dimensional objects, such as the sounds they produce or how stable they are. The thickness of a piece of metal made into different animal shapes - including a giraffe and a fish - is adjusted by using a computer algorithm in such a way that a specific sound spectrum is exhibited when the objects are struck.

The demise of the Maya civilisation: water shortage can destroy cultures

Mathematical models analysing the interplay between society and hydrological effects have been developed at TU Wien (Vienna).

Mathematical models analysing the interplay between society and hydrological effects have been developed at TU Wien (Vienna).

Solving Hard Quantum Problems: Everything is Connected

Quantum objects cannot just be understood as the sum of their parts. This is what makes quantum calculations so complicated. Scientists at TU Wien (Vienna) have now calculated Bose-Einstein-condensates, revealing the secrets of the particles? collective behaviour. Quantum systems are extremely hard to analyse if they consist of more than just a few parts.

Quantum objects cannot just be understood as the sum of their parts. This is what makes quantum calculations so complicated. Scientists at TU Wien (Vienna) have now calculated Bose-Einstein-condensates, revealing the secrets of the particles? collective behaviour. Quantum systems are extremely hard to analyse if they consist of more than just a few parts.

Paving the way for a faster quantum computer

A team of physicists from the University of Vienna and the Austrian Academy of Sciences have demonstrated a new quantum computation scheme in which operations occur without a well-defined order. The researchers led by Philip Walther and Caslav Brukner used this effect to accomplish a task more efficiently than a standard quantum computer.

A team of physicists from the University of Vienna and the Austrian Academy of Sciences have demonstrated a new quantum computation scheme in which operations occur without a well-defined order. The researchers led by Philip Walther and Caslav Brukner used this effect to accomplish a task more efficiently than a standard quantum computer.

Carrot or stick?

What motivates people to cooperate in collaborative endeavors? "First carrot, then stick". Tatsuya Sasaki, mathematician from the University of Vienna, has put forth for the first time ever a mathematical proof of this process. The study is recently published online in the "Journal of the Royal Society Interface".

What motivates people to cooperate in collaborative endeavors? "First carrot, then stick". Tatsuya Sasaki, mathematician from the University of Vienna, has put forth for the first time ever a mathematical proof of this process. The study is recently published online in the "Journal of the Royal Society Interface".

Logic is Like Abstract Art

Modern logic unleashed new areas of mathematics. Even when language and intuition fail, conclusive theories can be constructed with the help of logic. When little children share chocolates, they already have to deal with numbers. Even complicated mathematical objects can often be grasped intuitively.

Modern logic unleashed new areas of mathematics. Even when language and intuition fail, conclusive theories can be constructed with the help of logic. When little children share chocolates, they already have to deal with numbers. Even complicated mathematical objects can often be grasped intuitively.

This Sentence is Wrong

The great Viennese logician Kurt Gödel studied statements which refer to themselves - and his results shook the foundations of mathematics. "All Cretans are liars", said Epimenides, a Cretan. But this means that his statement must be a lie too. But then it is false that Cretans are liars and the statement must be true.

The great Viennese logician Kurt Gödel studied statements which refer to themselves - and his results shook the foundations of mathematics. "All Cretans are liars", said Epimenides, a Cretan. But this means that his statement must be a lie too. But then it is false that Cretans are liars and the statement must be true.