Research issues in data modeling for scientific visualization

This article summarizes some topics of modeling as they impinge on the future development of scientific data visualization. The benefits from visualization techniques in analyzing data are well established, but to build on these pioneering efforts, one must recognize modeling as a distinct structural component in the larger context of visualization and problem-solving systems. Volume modeling is the entry way to this arena of future development, and model-based rendering describes how scientists will view the results. Important side developments such as multiresolution modeling and model-based segmentation will contribute structural capability to these systems. All of these components ultimately depend on the mathematical foundations of scattered data modeling and on model validation and standards to incorporate this modeling methodology into effective tools for scientific inquiry.Postprint (published version

How Coaches Can Improve Their Teams’ Match Performance—The Influence of In-Game Changes of Tactical Formation in Professional Soccer

The tactical formation has been shown to influence the match performance of professional soccer players. This study aimed to examine the effects of in-game changes in tactical formation on match performance and to analyze coach-specific differences. We investigated three consecutive seasons of an elite team in the German Bundesliga which were managed by three different coaches, respectively. For every season, the formation changes that occurred during games were recorded. The match performance was measured on a team level using the variables ‘goals’, ‘chances’, and ‘last plane’ entries (≙successful attacking sequence) for the own/opposing team. Non-parametric tests were used to compare the ten minutes before with the ten minutes after the formation change, as well as games with and without formation change. In the ten minutes after the formation change, the team achieved more goals/chances/last plane entries than in the ten minutes before the formation change (mean ES=0.52). Similarly, the team conceded fewer opposing goals/chances/last plane entries in the ten minutes after the formation change (mean ES=0.35). Furthermore, the results indicate that the success of the respective formation change was dependent on the responsible coach. Depending on the season, the extent of the impacts varied (season 1: mean ES=0.71; season 2: mean ES=0.26; season 3: mean ES=0.22). Over all three seasons, the formation changes had a positive effect on the match performance of the analyzed team, highlighting their importance in professional soccer. Depending on the season, formation changes had varying impacts on the performance, indicating coach-specific differences. The provided information can support coaches in understanding the effects of their in-game decisions

Three loop renormalization of the SU(N_c) non-abelian Thirring model

We renormalize to three loops a version of the Thirring model where the fermion fields not only lie in the fundamental representation of a non-abelian colour group SU(N_c) but also depend on the number of flavours, N_f. The model is not multiplicatively renormalizable in dimensional regularization due to the generation of evanescent operators which emerge at each loop order. Their effect in the construction of the true wave function, mass and coupling constant renormalization constants is handled by considering the projection technique to a new order. Having constructed the MSbar renormalization group functions we consider other massless independent renormalization schemes to ensure that the renormalization is consistent with the equivalence of the non-abelian Thirring model with other models with a four-fermi interaction. One feature to emerge from the computation is the establishment of the fact that the SU(N_f) Gross Neveu model is not multiplicatively renormalizable in dimensional regularization. An evanescent operator arises first at three loops and we determine its associated renormalization constant explicitly.Comment: 40 latex pages, 14 postscript figure

Does Technical Match Performance in Professional Soccer Depend on the Positional Role or the Individuality of the Player?

The aim of the study was to examine the impact of the positional role and the individuality on the technical match performance in professional soccer players. From official match data of the Bundesliga season 2018/19, technical performance (short[30 m] passes, dribblings, ball possessions) of all players who played during the season were analyzed (normative data). Five playing positions (center back, full back, central midfielder, wide midfielder, forward) were distinguished. As the contextual factor tactical formation is known to influence match performance, this parameter was controlled for. Further, those players who played at minimum four games in at least two different playing positions were included in the study sample (n = 13). The technical match performance of the players was analyzed in relation to the normative data regarding the extent to which the players either adapted or maintained their performance when changing the playing position. When switching playing positions, positional role could explain 3-6% of the variance in short passes and ball possessions and 27-44% of the variance in dribblings, medium passes, and long passes. Moreover, we observed large interindividual differences in the extent to which a player changed, adapted, or maintained his performance. In detail, five players clearly adapted their technical performance when changing playing positions, while five players maintained their performance. Coaches can use these findings to better understand the technical match performance of single players and, further, to estimate the impact of a change in the positional role on the technical performance of the respective player

Four loop wave function renormalization in the non-abelian Thirring model

We compute the anomalous dimension of the fermion field with N_f flavours in the fundamental representation of a general Lie colour group in the non-abelian Thirring model at four loops. The implications on the renormalization of the two point Green's function through the loss of multiplicative renormalizability of the model in dimensional regularization due to the appearance of evanescent four fermi operators are considered at length. We observe the appearance of one new colour group Casimir, d_F^{abcd} d_F^{abcd}, in the final four loop result and discuss its consequences for the relation of the Knizhnik-Zamolodchikov critical exponents in the Wess Zumino Witten Novikov model to the non-abelian Thirring model. Renormalization scheme changes are also considered to ensure that the underlying Fierz symmetry broken by dimensional regularization is restored.Comment: 25 latex pages with 9 postscript figure

Phase Transition in Anyon Superconductivity at Finite Temperature

The magnetic response of the charged anyon fluid at temperatures larger than the fermion energy gap is investigated in the self-consistent field approximation. In this temperature region a new phase, characterized by an inhomogeneous magnetic penetration, is found. The inhomogeneity is linked to the existence of an imaginary magnetic mass which increases with the temperature. The system stability in the new phase is proved by investigating the electromagnetic field rest-energy spectrum.Comment: 18 pages, revte

The generalized chiral Schwinger model on the two-sphere

A family of theories which interpolate between vector and chiral Schwinger models is studied on the two--sphere $S^{2}$. The conflict between the loss of gauge invariance and global geometrical properties is solved by introducing a fixed background connection. In this way the generalized Dirac--Weyl operator can be globally defined on $S^{2}$. The generating functional of the Green functions is obtained by taking carefully into account the contribution of gauge fields with non--trivial topological charge and of the related zero--modes of the Dirac determinant. In the decompactification limit, the Green functions of the flat case are recovered; in particular the fermionic condensate in the vacuum vanishes, at variance with its behaviour in the vector Schwinger model.Comment: 39 pages, latex, no figure

The fate of conformal symmetry in the non-linear Schr\"{o}dinger theory

The free Schroedinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in particular for the Phi^4-theory in d = 2. We compute the full quantum corrections to the 4-point function to show that the symmetry is broken by an anomalous contribution proportional to the exact beta-functionComment: 22 pages, 5 figures. v3: version to be published; reference added; imaginary part of 4-point function corrected, unitarity checke

Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing \beta-function. As main application we prove that Euclidean \phi^4-quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for N->\infty the same spectrum as the Laplace operator in 4 dimensions. Using the theory of singular integral equations of Carleman type we compute (for N->\infty and after renormalisation of E,\lambda) the free energy density (1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae and vanishing of \beta-function hold for general quartic matrix models. v3: We add the existence proof for a solution of the non-linear integral equation. A rescaling of matrix indices was necessary. v2: We provide Schwinger-Dyson equations for all correlation functions and prove an algebraic recursion formula for their solutio