The von Neumann algebra generated by t-gaussians

We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ sufficiently close to 1, then these algebras do not depend on $t$. In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness

Using Virtual Reality to increase technical performance during rowing workouts

Technology is advancing rapidly in virtual reality (VR) and sensors, gathering feedback from our body and the environment we are interacting in. Combining the two technologies gives us the opportunity to create personalized and reactive immersive environments. These environments can be used e.g. for training in dangerous situations (e.g. fire, crashes, etc), or to improve skills with less distraction than regular natural environments would have. The pilot study described in this thesis puts an athlete who is rowing on a stationary rowing machine into a virtual environment. The VR takes movement from several sensors of the ergo-meter and displays those in VR. In addition, metrics on technique are being derived from the sensor data and physiological data. All this is used to investigate if, and to which extent, VR may improve the technical skills of the athlete during the complex sport of rowing. Furthermore, athletes are giving subjective feedback about their experience comparing a standard rowing workout, with the workout using VR. First results indicate better performance and an enhanced experience by the athlete

Smallness of Invisible Dictators

Fishburn (1970) showed that in an infinite society Arrow's axioms for a preference aggregation rule do not necessarily imply a dictator. Kirman and Sondermann (1972) showed that, in this case, nondictatorial rules imply an invisible dictator that, whenever the agent set is an atomless finite measure space, can be viewed as the limit of coalitions of arbitrarily small size. We show first that, when admissible coalitions are restricted to an algebra, there are two sorts of invisible dictators. We next show that, in most cases of interest, we do not need to resort to measures on the agent space to give a precise meaning to the statement that invisible dictators are the limit of arbitrarily small decisive coalitions.Preference aggregation, Arrow´s Theorem, Invisible Dictators, Ultrafilter Property, Strict Neutrality

Some remarks on noncommutative Khintchine inequalities

Normalized free semi-circular random variables satisfy an upper Khintchine inequality in $L_\infty$. We show that this implies the corresponding upper Khintchine inequality in any noncommutative Banach function space. As applications, we obtain a very simple proof of a well-known interpolation result for row and column operator spaces and, moreover, answer an open question on noncommutative moment inequalities concerning a paper by Bekjan and Chen

Nonequilibrium entropic bounds for Darwinian replicators

Life evolved on our planet by means of a combination of Darwinian selection and innovations leading to higher levels of complexity. The emergence and selection of replicating entities is a central problem in prebiotic evolution. Theoretical models have shown how populations of different types of replicating entities exclude or coexist with other classes of replicators. Models are typically kinetic, based on standard replicator equations. On the other hand, the presence of thermodynamical constrains for these systems remain an open question. This is largely due to the lack of a general theory of out of statistical methods for systems far from equilibrium. Nonetheless, a first approach to this problem has been put forward in a series of novel developements in non-equilibrium physics, under the rubric of the extended second law of thermodynamics. The work presented here is twofold: firstly, we review this theoretical framework and provide a brief description of the three fundamental replicator types in prebiotic evolution: parabolic, malthusian and hyperbolic. Finally, we employ these previously mentioned techinques to explore how replicators are constrained by thermodynamics.Comment: 12 Pages, 5 Figure