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Predicting the results of soccer matches is of great interest. This is not only due to the popularity of the sport and the joy of private "betting rounds", but also due to the large sports betting market. Where previously expert knowledge and intuition were used, today there are models that analyze large amounts of data and make predictions based on them. In addition to Poisson models, approaches that belong to the machine learning (ML) category are increasingly being used. These include, for example, neural network or random forest models, which are compared in this article with each other as well as with Poisson models with regard to single-match prediction. In each case, the match results of a season are used as the data basis. The analysis is carried out for 5 European top leagues. A statistical analysis shows that the performance levels of the teams do not change systematically during a season. In order to characterize performance levels as accurately as possible, all match results, except from the match to be predicted, can be used as features with equal weighting. It can be seen that both, the exact choice of features and the choice of model, have only a minor influence on the prediction quality. Possible improvements in match prediction are discussed., Comment: 10 pages, 1 figure

This study investigates the electrochemical behavior and decomposition pathways of four monomers, namely PMC, PMC-OH, PeMC-OH, and DEO-EA, which are potential candidates for polymer electrolytes in solid-state batteries. Density functional theory calculations were employed to determine the oxidation and reduction potentials of these monomers near different ions (Li+, TFSI-, and LiTFSI) and their corresponding reorganization energies. The results reveal notable sensitivity of the monomers to reduction in a Li+ rich regime and to oxidation in a TFSI- rich regime. Additionally, the decomposition pathways of the monomers were investigated, focusing on the cleavage of CO bonds. The findings provide insights into the stability and reactivity of these monomers in various electrochemical environments.

The hydrodynamics of thin films is typically described using phenomenological models whose connection to the microscopic particle dynamics is a subject of ongoing research. Existing methods based on density functional theory provide a good description of static thin films, but are not sufficient for understanding nonequilibrium dynamics. In this work, we present a microscopic derivation of the thin film equation using the Mori-Zwanzig projection operator formalism. This method allows to directly obtain the correct gradient dynamics structure along with microscopic expressions for the mobility and the free energy. Our results are verified against molecular dynamics simulations for both simple fluids and polymers., Comment: 14 pages, 4 figures

Exploiting physical processes for fast and energy-efficient computation bears great potential in the advancement of modern hardware components. This paper explores non-linear charge tunneling in nanoparticle networks, controlled by external voltages. The dynamics are described by a master equation, which describes the development of a distribution function over the set of charge occupation numbers. The driving force behind this evolution are charge tunneling events among nanoparticles and their associated rates. In this paper, we introduce two meanfield approximations to this master equation. By parametrization of the distribution function using its first- and second-order statistical moments, and a subsequent projection of the dynamics onto the resulting moment manifold, one can deterministically calculate expected charges and currents. Unlike a kinetic Monte Carlo approach, which extracts samples from the distribution function, this meanfield approach avoids any random elements. A comparison of results between the meanfield approximation and an already available kinetic Monte Carlo simulation demonstrates great accuracy. Our analysis also reveals that transitioning from a first-order to a second-order approximation significantly enhances the accuracy. Furthermore, we demonstrate the applicability of our approach to time-dependent simulations, using eulerian time-integration schemes.

Nonlinear behavior in the hopping transport of interacting charges enables reconfigurable logic in disordered dopant network devices, where voltages applied at control electrodes tune the relation between voltages applied at input electrodes and the current measured at an output electrode. From kinetic Monte Carlo simulations we analyze the critical nonlinear aspects of variable-range hopping transport for realizing Boolean logic gates in these devices on three levels. First, we quantify the occurrence of individual gates for random choices of control voltages. We find that linearly inseparable gates such as the XOR gate are less likely to occur than linearly separable gates such as the AND gate, despite the fact that the number of different regions in the multidimensional control voltage space for which AND or XOR gates occur is comparable. Second, we use principal component analysis to characterize the distribution of the output current vectors for the (00,10,01,11) logic input combinations in terms of eigenvectors and eigenvalues of the output covariance matrix. This allows a simple and direct comparison of the behavior of different simulated devices and a comparison to experimental devices. Third, we quantify the nonlinearity in the distribution of the output current vectors necessary for realizing Boolean functionality by introducing three nonlinearity indicators. The analysis provides a physical interpretation of the effects of changing the hopping distance and temperature and is used in a comparison with data generated by a deep neural network trained on a physical device.

Nanoparticles interconnected by insulating organic molecules exhibit nonlinear switching behavior at low temperatures. By assembling these switches into a network and manipulating charge transport dynamics through surrounding electrodes, the network can be reconfigurably functionalized to act as any Boolean logic gate. This work introduces a kinetic Monte Carlo-based simulation tool, applying established principles of single electronics to model charge transport dynamics in nanoparticle networks. We functionalize nanoparticle networks as Boolean logic gates and assess their quality using a fitness function. Based on the definition of fitness, we derive new metrics to quantify essential nonlinear properties of the network, including negative differential resistance and nonlinear separability. These nonlinear properties are crucial not only for functionalizing the network as Boolean logic gates but also when our networks are functionalized for brain-inspired computing applications in the future. We address fundamental questions about the dependence of fitness and nonlinear properties on system size, number of surrounding electrodes, and electrode positioning. We assert the overall benefit of having more electrodes, with proximity to the network's output being pivotal for functionality and nonlinearity. Additionally, we demonstrate a optimal system size and argue for breaking symmetry in electrode positioning to favor nonlinear properties., Comment: 15 pages, 12 figures

Understanding the properties of supercooled fluids in equilibrium, even below the calorimetric glass transition $T_g$, is an elusive challenge. This is even more true for the properties of the ideal glass, defined as the minimum of the potential energy landscape (PEL) in the non-crystalline regime. Although its existence is a mathematical necessity due to the finite range of energies, its properties, and physical relevance are still undecided. Here we combine the million-fold acceleration of Swap Monte Carlo with PEL analysis to study a non-network 2D model glass former in equilibrium for a wide range of system sizes and temperatures. We observe the transition from fragile to strong behavior and provide a generic perspective to such observations in many experimental non-network glass formers, or the saturation of structural disorder upon cooling. Furthermore, we can identify a particular system size that shows quantitative agreement with the macroscopic limit, while allowing a complete characterization of the potential energy landscape (PEL) down to its global minimum. This implies the availability of configurational entropy down to the zero temperature limit without the detour via liquid entropy, thereby quantifying the putative entropy crisis. Through appropriate system size analysis, we can identify a low-energy depletion regime, including the ideal glass, and reveal its physical relevance for equilibrium properties over a wide temperature range, including below $T_g$., Comment: 8 pages with 4 figures

We present a hydrodynamic theory describing pair diffusion in systems with periodic boundary conditions, thereby generalizing earlier work on self-diffusion [D\"unweg and Kremer, J. Chem. Phys. 1993, 99, 6983-6997; Yeh and Hummer, J. Phys. Chem. B 2004, 108, 15873-15879]. Its predictions are compared to Molecular Dynamics simulations for a liquid carbonate electrolyte and two ionic liquids, for which we characterize the correlated motion between distinct ions. Overall, we observe good agreement between theory and simulation data, highlighting that hydrodynamic interactions universally dictate ion correlations. However, when summing over all ion pairs in the system to obtain the cross-contributions to the total cationic or anionic conductivity, the hydrodynamic interactions between ions with like and unlike charges largely cancel. Consequently, significant conductivity contributions only arise from deviations from a hydrodynamic flow field of an ideal fluid, that is, from the local electrolyte structure as well as from relaxation processes in the subdiffusive regime. In case of ionic liquids, the momentum-conservation constraint additionally is vital, which we study by employing different ionic masses in the simulations. Our formalism will likely also be helpful to estimate finite-size effects of the conductivity or of Maxwell-Stefan diffusivities in simulations.

Long-term data-driven studies have become indispensable in many areas of science. Often, the data formats, structures and semantics of data change over time, the data sets evolve. Therefore, studies over several decades in particular have to consider changing database schemas. The evolution of these databases lead at some point to a large number of schemas, which have to be stored and managed, costly and time-consuming. However, in the sense of reproducibility of research data each database version must be reconstructable with little effort. So a previously published result can be validated and reproduced at any time. Nevertheless, in many cases, such an evolution can not be fully reconstructed. This article classifies the 15 most frequently used schema modification operators and defines the associated inverses for each operation. For avoiding an information loss, it furthermore defines which additional provenance information have to be stored. We define four classes dealing with dangling tuples, duplicates and provenance-invariant operators. Each class will be presented by one representative. By using and extending the theory of schema mappings and their inverses for queries, data analysis, why-provenance, and schema evolution, we are able to combine data analysis applications with provenance under evolving database structures, in order to enable the reproducibility of scientific results over longer periods of time. While most of the inverses of schema mappings used for analysis or evolution are not exact, but only quasi-inverses, adding provenance information enables us to reconstruct a sub-database of research data that is sufficient to guarantee reproducibility.

We present an extensive molecular dynamics (MD) simulation study of poly(ethylene oxide) (PEO) based densely cross-linked polymers, focussing on structural properties as well as the systems dynamics in the presence of lithium salt. Motivated by experimental findings for networks with short PEO strands we employ a combination of LiTFSI (Lithium bis(trifluoromethanesulfonyl)imide) and LiDFOB (Lithium difluoro(oxalato)borate). Recently, it has been shown that such multi-salt systems outperform classical single salt systems (Shaji et al., Energy Storage Materials, 2022, 44, 263). To analyse the microscopic scenario we employ an analytical model, originally developed for non-cross-linked polymer electrolytes or blends (Maitra et al., Phys. Rev. Lett., 2007, 98, 227802 and Diddens et al., J. Electrochem. Soc., 2017, 164, E3225-E3231). Excluding very short PEO strands, the local dynamics is only slightly restricted compared to linear PEO and is not significantly dependent on the network structure. The transfer of lithium ions between PEO chains and the motion along the polymer backbone may be controlled through the employed salt., Comment: 19 pages, 9 figures Supplementary Information: 20 pages, 18 figures

Cholesterol (CHOL) is one of the most important components of plasma membranes of higher cells and one of the main factors for the formation of (nano)domains. In this work, molecular dynamics simulations of mixtures of CHOL with DPPC (saturated lipid) and DLiPC (unsaturated lipid) as standard phospholipids (PLs) are presented in a wide range of CHOL concentrations. The key idea is to systematically extract all structural and enthalpic properties relevant to the formulation of a lattice model of these systems and express them in dependence of the acyl chain order parameters. Detailed interpretation is simplified by the observation that, to a good approximation, the interaction effects do not depend on the total CHOL concentration, but only on the local CHOL arrangement. The resulting information can be used to motivate the agglomeration of CHOL molecules, the relevance of entropic rather than enthalpic effects for understanding the stronger influence of CHOL on DPPC compared to DLiPC, or the thermodynamic background of raft formation. It is verified that the interaction functions hardly change during the transition from binary to ternary mixtures, suggesting the applicability of the concepts to more complex mixtures.

Lithium salts with low coordinating anions like bis(trifluoromethanesulfonyl)imide (TFSI) have been the state-of-the-art for PEO-based 'dry' polymer electrolytes for three decades. Plasticizing PEO with TFSI-based ionic liquids (ILs) to form ternary solid polymer electrolytes (TSPEs) increases conductivity and Li$^+$ diffusivity. However, the Li$^+$ transport mechanism is unaffected compared to their 'dry' counterpart and essentially coupled to the dynamics of the polymer host matrix, which limits Li$^+$ transport improvement. Thus, a paradigm shift is hereby suggested: The utilization of more coordinating anions such as trifluoromethanesulfonyl-N-cyanoamide (TFSAM), able to compete with PEO for Li$^+$ solvation to accelerate the Li$^+$ transport and reach higher Li$^+$ transference number. The Li-TFSAM interaction in binary and ternary TFSAM-based electrolytes was probed by experimental methods and discussed in the context of recent computational results. In PEO-based TSPEs, TFSAM drastically accelerates the Li$^+$ transport (increased Li$^+$ transference number by 600$\%$ and Li$^+$ conductivity by 200-300$\%$) and computer simulations reveal that lithium dynamics are effectively re-coupled from polymer to anion dynamics. Finally, this concept of coordinating anions in TSPEs was successfully applied in LFP$||$Li metal cells leading to enhanced capacity retention (86$\%$ after 300 cycles) and an improved rate performance at 2C., Comment: 33 pages, 10 Figures

The main cause of the fragile-to-strong crossover of 3D silica was previously attributed to the presence of a low energy cutoff in the potential energy landscape. The important question emerges about the microscopic origin of this crossover and the generalizibility to other glass-formers. In this work, the fragile-to-strong crossover of a model 2D glassy system is analyzed via molecular dynamics simulation, which represents 2D-silica. By separating the sampled defect and defect-free inherent structures, we are able to identify their respective density of state distributions with respect to energy. A low energy cutoff is found in both distributions. It is shown that the fragile-to-strong crossover can be quantitatively related to the parameters of the energy landscape, involving in particular the low-energy cutoff of the energy distribution. It is also shown that the low-energy cutoff of the defect-states is determined by the formation energy of a specific defect configuration, involving two silicon and no oxygen defect. The low-temperature behavior of 2D silica is quantitatively compared with that of 3D silica, showing surprisingly similar behavior., Comment: 11 pages, 7 figures

What do applications like semantic optimization, data exchange and integration, answering queries under dependencies, query reformulation with constraints, and data cleaning have in common? All these applications can be processed by the Chase, a family of algorithms for reasoning with constraints. While the theory of the Chase is well understood, existing implementations are confined to specific use cases and application scenarios, making it difficult to reuse them in other settings. ChaTEAU overcomes this limitation: It takes the logical core of the Chase, generalizes it, and provides a software library for different Chase applications in a single toolkit.

The development of substrates with a switchable wettability is on a fast pace. The limit of switching frequencies and contact angle differences between substrate states are steadily pushed further. We investigate the behavior of a droplet on a homogeneous substrate, which is switched between two wettabilities for a large range of switching frequencies. Here, we are particularly interested in the dependence of the wetting behavior on the switching frequency. We show, that results obtained on the particle level via molecular dynamics simulations and on the continuum level via the thin-film model are consistent. Predictions of simple models as the molecular theory of wetting (MKT) and analytical calculations based on the MKT also show good agreement and offer deeper insights into the underlying mechanisms.

The molecular self-assembly of various structures such as micelles and vesicles has been the subject of comprehensive studies. Recently, a new approach to design these structures, the frame-guided assembly, has been developed to progress towards fabrics of predefined shape and size, following an initially provided frame of guiding elements. Here we study frame-guided assembly into a two-dimensional membrane via computer simulations, based on a single-bead coarse grained surfactant model in continuous space. In agreement with the experiment the assembly process already starts for surfactant concentrations below the critical micelle concentration. Furthermore, upon decreasing temperature the formation process gets more localized. Additionally, we consider a lattice gas model of the membrane plane including guiding elements where the particle concentration is varied via a chemical potential. It behaves similar to the continuous model and additionally allows the formulation of analytical mean-field predictions which provide a fundamental understanding of frame-guided assembly.

In this work, we report the results from molecular dynamics simulations of lithium salt-ionic liquid electrolytes (ILEs) based either on the symmetric bis[(trifluoromethyl)sulfonyl]imide ($\text{TFSI}^-$) anion or its asymmetric analog 2,2,2-(trifluoromethyl)sulfonyl-N-cyanoamide ($\text{TFSAM}^-$). Relating lithium's coordination environment to anion mean residence times and diffusion constants confirms the remarkable transport behaviour of the $\text{TFSAM}^-$-based ILEs that has been observed in recent experiments: For increased salt doping, the lithium ions must compete for the more attractive cyano over oxygen coordination and a fragmented landscape of solvation geometries emerges, in which lithium appears to be less strongly bound. We present a novel, yet statistically straightforward methodology to quantify the extent to which lithium and its solvation shell are dynamically coupled. By means of a Lithium Coupling Factor (LCF) we demonstrate that the shell anions do not constitute a stable lithium vehicle, which suggests for this electrolyte material the commonly termed "vehicular" lithium transport mechanism could be more aptly pictured as a correlated, flow-like motion of lithium and its neighbourhood. Our analysis elucidates two separate causes why lithium and shell dynamics progressively decouple with higher salt content: On the one hand, an increased sharing of anions between lithium limits the achievable LCF of individual lithium-anion pairs. On the other hand, weaker binding configurations naturally entail a lower dynamic stability of the lithium-anion complex, which is particularly relevant for the $\text{TFSAM}^-$-containing ILEs., Comment: Main manuscript: 13 pages, 10 Figures and 2 Schemes; Supplementary Information: 52 pages and 32 Figures

To understand the non-equilibrium relaxation dynamics of a liquid droplet on a switchable substrate the interplay of different length- and time-scales needs to be understood. We present a method to map the microscopic information, resulting from a molecular dynamics simulation, to a mesoscopic scale, reflected by a thin film model. After a discussion of the mapping procedure we first analyze the relaxation of a liquid droplet upon switching the wettability of the substrate. Further, we show that a nearly identical mapping procedure can be used for the description of two coalescing droplets. With our procedure we take a first step to extend the mapping from the equilibrium case to non-equilibrium wetting dynamics, thus allowing for a quantitative multi-scale analysis., Comment: 34 pages, 15 figures

Cholesterol (CHOL) drives lipid segregation and is thus a key player for the formation of lipid rafts and followingly for the ability of a cell to, e.g., enable selective agglomeration of proteins. The lipid segregation is driven by cholesterol's affinity for saturated lipids, which stands directly in relation to the ability of cholesterol to order the individual phospholipid (PL) acyl chains. In this work, Molecular Dynamics simulations of DPPC (Dipalmitoylphosphatidylcholine, saturated lipid) and DLiPC (Dilineoylphosphatidylcholine, unsaturated lipid) mixtures with cholesterol are used to elucidate the underlying mechanisms of the cholesterol ordering effect. To this end, all enthalpic contributions, experienced by the PL molecules, are recorded as a function of the PL's acyl chain order. This involves, the PL-PL, the PL-cholesterol interaction, the interaction of the PLs with water, and the interleaflet interaction. This systematic analysis allows one to unravel differences of saturated and unsaturated lipids in terms of the different interaction factors. It turns out that cholesterol's impact on chain ordering stems not only from direct interactions with the PLs but is also indirectly present in the other energy contributions. Furthermore, the analysis sheds light on the relevance of the entropic contributions, related to the degrees of freedom of the acyl chain., Comment: 14 pages (2-column, rsc style), 21 figures (including SI)

Given a query result of a big database, why-provenance can be used to calculate the necessary part of this database, consisting of so-called witnesses. If this database consists of personal data, privacy protection has to prevent the publication of these witnesses. This implies a natural conflict of interest between publishing original data (provenance) and protecting these data (privacy). In this paper, privacy goes beyond the concept of personal data protection. The paper gives an extended definition of privacy as intellectual property protection. If the provenance information is not sufficient to reconstruct a query result, additional data such as witnesses or provenance polynomials have to be published to guarantee traceability. Nevertheless, publishing this provenance information might be a problem if (significantly) more tuples than necessary can be derived from the original database. At this point, it is already possible to violate privacy policies, provided that quasi identifiers are included in this provenance information. With this poster, we point out fundamental problems and discuss first proposals for solutions., Comment: Accepted at ProvenanceWeek 2020 ( https://iitdbgroup.github.io/ProvenanceWeek2020/ )

Polymer electrolytes are intensely investigated for use as solid electrolytes in next generation lithium-ion and lithium-metal batteries. However, little is known about the structural and dynamical properties of polymer electrolytes close to electrode surfaces. Here, a PEO-LiTFSI polymer electrolyte, confined between two oppositely charged graphite-like electrodes, is studied via molecular dynamics simulations. Three different surface charges of $\sigma_S = 0$, $\pm 0.5$ and $\pm 1$ $e$/nm$^2$ are considered. Upon charging, a very strong and component-specific layering is observed. Only for the highest surface charge, lithium ions get desolvated and come into direct contact with the negative electrode. The layer structure goes along with the emergence of free energy barriers, which lead to a reduction of the lithium-ion dynamics, as quantified by spatially resolved mean square displacements, corrected for a drift component. Interchain transfers that are known to be very important for long-range lithium-ion transport in polymer electrolytes play no significant role for transitions of lithium ions between different layers., Comment: Main paper: 19 pages, 11 figures, 0 tables; Supplementary information: 31 pages, 17 figures, 6 tables; Version 2: Entirely re-written!; Submitted to The Journal of Physical Chemistry C; Version 3: Incorporated changes from the review process; Accepted by The Journal of Physical Chemistry C

Block-copolymer electrolytes with lamellar microstructure show promising results regarding the ion transport in experiments. Motivated by these observations we study block-copolymers consisting of a polystyrene (PS) block and a poly(ethylene oxide) (PEO) block which were assembled in a lamellar structure. The lamella was doped with various amounts of lithium-bis(trifluoromethane)sulfonimide (LiTFSI) until very high loadings with ratios of EO monomers to cations up to 1:1 were reached. We present insights into the structure and ion transport from extensive Molecular Dynamics simulations. For high salt concentrations most cations are not coordinated by PEO but rather by TFSI and THF. More specifically, LiTFSI partially separates from the PEO domain and forms a network-like structure in the middle of the lamella. This central salt-rich layer plays a decisive role to enable remarkably good cationic mobilities as well as high transport numbers in agreement with the experimental results., Comment: 30 pages, 22 figures (including Supporting Information)

We present the results from an extensive atomistic molecular dynamics simulation study of poly(ethylene oxide) (PEO) doped with various amounts of lithium-bis(trifluoromethane)sulfonimide (LiTFSI) salt under the influence of external electric field strengths up to $1\,$V/nm. The motivation stems from recent experimental reports on the nonlinear response of mobilities to the application of an electric field in such electrolyte systems and arising speculations on field-induced alignment of the polymer chains, creating channel-like structures that facilitate ion passage. Hence, we systematically examine the electric field impact on the lithium coordination environment, polymer structure as well as ionic transport properties and further present a procedure to quantify the susceptibility of both structural and dynamical observables to the external field. Our investigation reveals indeed a coiled-to-stretched transformation of the PEO strands along with a concurrent nonlinear behavior of the dynamic properties. However, from studying the temporal response of the unperturbed electrolyte system to field application we are able to exclude a structurally conditioned enhancement of ion transport and surprisingly observe a slowing down. A microscopic understanding is supplied., Comment: Main manuscript comprises 30 pages and 13 figures, supplementary information section comprises 30 pages and 28 figures

Sterols have been ascribed a major role in the organization of biological membranes, in particular for the formation of liquid ordered domains in complex lipid mixtures. Here, we employed molecular dynamics simulations to compare the effects of cholesterol and ergosterol as the major sterol of mammalian and fungal cells, respectively, on binary mixtures with 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) as a proxy for saturated lipids. In agreement with previous work, we observe that the addition of sterol molecules modifies the order of DPPC both in the gel phase and in the liquid phase. When disentangling the overall tilt angle and the structure of the tail imposed by trans/gauche configurations of torsion angles in the tail, respectively, a more detailed picture of the impact of sterols can be formulated, revealing, e.g., an approximate temperature-concentration superposition ranging from the liquid to the gel phase. Furthermore, a new quantitative measure to identify the presence of collective sterol effects is discussed. Moreover, when comparing both types of sterols, addition of cholesterol has a noticeably stronger impact on phospholipid properties than of ergosterol. The observed differences can be attributed to higher planarity of the cholesterol ring system. This planarity combined with an inherent asymmetry in its molecular interactions leads to better alignment and hence stronger interaction with saturated acyl chains. Our results suggest that the high order demonstrated for ergosterol in fungal plasma membranes must therefore be generated via additional mechanisms.

The forecasting of sports events is of broad interest from the applied but also from the theoretical perspective. In this work the question is addressed for the example of the German soccer Bundesliga how a theoretically optimum forecast of the goal difference of a match can be characterized. This involves a careful analysis of the random contributions in a match and its disentanglement from the informative contributions, resulting from the individual team strengths. An important aspect is the consideration of the time dependence of the team strength which turns out to mainly fluctuate around a team-specific value during the course of a season. Two types of time-dependent properties have to be distinguished, one being uncorrelated between different match-days, the other being correlated and thus accessible by an appropriate correlation analysis. For some performance indicators, which may be used to estimate the team strength, the quality of the respective forecast is compared to the theoretical optimum. Knowledge of the informative contribution allows one to conclude that the offensive team strength is more important than the defensive team strength for the final success.

A myriad of different data are generated to characterize a soccer match. Here we discuss which performance indicators are particularly helpful to forecast the future results of a team via an estimation of the underlying team strengths with minimum statistical uncertainty. We introduce an appropriate statistical framework and exemplify it for different performance indicators for the German premier soccer league. Two aspects are involved: (i) It is quantified how well the estimation process would work if no statistical noise due to finite information is present. The related score directly expresses to which degree the chosen performance indicator reflects the underlying team strength. (ii) Additionally, the reduction of the forecasting quality due to statistical noise is determined. From both pieces of information a normalized value can be constructed which is a direct measure of the overall forecasting quality. It turns out that the so-called packing rate works best. New perspectives of performance indicators enter when trying to understand the outcome of single matches based on match-specific observations from the same match. Implications for the purpose of forecasting as well as consequences for the interpretation of team strengths are discussed.

The formation of self assembled structures such as micelles has been intensively studied and is well understood. The ability of a solution of amphiphilic molecules to develop micelles is depending on the concentration and characterized by the critical micelle concentration (cmc), above which micelle formation does occur. Recent studies use a lattice approach in order to determine cmc and show that the correct modelling and analysis of cluster formations is highly non-trivial. We developed a minimalistic coarse grained model for amphiphilic molecules in the continuum and simulated the time evolution via dynamic Monte Carlo simulations in the canonical (NVT) ensemble. Starting from a homogeneous system we observed and characterized how the initial fluctuations, yielding small aggregates of amphiphilic molecules, end up in the growth of complete micelles. Our model is sufficiently versatile to account for different structures of surfactant systems such as membranes, micelles of variable radius and tubes at high particle densities by adjusting particle density and potential properties. Particle densities and micellization rates are investigated and an order parameter is introduced, so that the dependence of the micellization process on temperature and surfactant density can be studied. The constant density of free particles for concentrations above cmc, e. g. as expected from theoretical considerations, can be reproduced when choosing a careful definition of free volumes. In the cmc regime at low temperatures different non-equilibrium effects are reported, occurring even for very long time-scales., Comment: This article has been accepted by the Journal of Chemical Physics

Recently, it became possible to experimentally generate and characterize a very thin silica system on a substrate which can be basically described as a 2D random network. The key structural properties, in particular related to the ring statistics, could be numerically reproduced by performing molecular dynamics simulations with an appropriately chosen 2D force field. Using a maximum entropy formulation it is shown that the probability distribution of the individual rings and triplets can be related to the ring and triplet energies, respectively, obtained from the simulations. Using additional Lagrange parameters, the correct average properties of random networks are guaranteed. In agreement with previous work, based on distributions of complementary rings and triplets, respectively, one finds a Boltzmann-type relation albeit with an effective temperature which largely deviates from the bath temperature. Furthermore, it is shown that the ring and triplet energies can be estimated based on the properties of their average inner angles. This calculation supports, on a quantitative level, the previously suggested angle mismatch theory. It suggests that correlations among adjacent rings originate from the net mismatch in the inner ring angles in a triplet of rings. By taking into account an average effect from the surrounding rings of a triplet, an even better estimate of the correlations can be provided. That approach is also applied to estimate of the Aboav-Wearie parameter., Comment: 22 pages, 13 figures

The thermodynamic properties of subsystems in strong interaction with the neighborhood can largely differ from the standard behavior. Here we study the thermodynamic properties of rings and triplets in equilibrated disordered 2D-silica. Their statistics follows a Boltzmann behavior, albeit with a strongly reduced temperature. This effective temperature strongly depends on the length scale of the chosen subsystem. From a systematic analysis of the 1D Ising model and an analytically solvable model we suggest that these observations reflect the presence of strong local positive energy correlations., Comment: 10 pages, 3 figures, letter

Understanding the yielding of glass-forming systems upon shearing is notoriously difficult since it is a strong non-equilibrium effect. Here we show that the concept of the potential energy landscape (PEL), developed for the quiescent state, can be extended to shearing. When introducing an appropriate coarse graining of the extended PEL for sheared systems, one can distinguish two fundamentally different types of plastic events, namely inherent structures (IS) vs. minimized structure (MS) transitions. We apply these concepts to non-cyclic and cyclic shearing of small systems, which allow us to characterize the properties of elementary plastic events. Whereas the general properties of the stress-strain curves are similar to larger systems, a closer analysis reveals significantly different properties. This allows one to identify the impact of the elastic coupling in larger systems. The concept of MS enables us to relate the stress overshoot of a single trajectory to the emergence of an MS transition. Furthermore, the occurrence of limit cycles can be characterized in great detail for the small systems and connections to the properties of the PEL can be formulated. Possible implications of our small-system results for the macroscopic limit are discussed.

The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential $g(h)$ which is an excess free energy per unit area that depends on the liquid film height $h$. Given a microscopic theory for the liquid, to determine $g(h)$ one must calculate the free energy for liquid films of any given value of $h$; i.e. one needs to create and analyze out-of-equilibrium states, since at equilibrium there is a unique value of $h$, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate $g(h)$ and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We show too that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed., Comment: 5 pages, 2 figures

The gain of free energy upon unmixing is determined via application of Markov state modeling (MSM), using an Ising model with a fixed number of up- and down-spins. MSM yields reasonable estimates of the free energies. However, a closer look reveals significant differences which point to residual non-Markovian effects. These non-Markovian effects are rather unexpected since the typical criteria to study the quality of Markovianity indicate complete Markovian behavior. We identify the sparse connectivity between different Markov states as a likely reason for the observed bias. By studying a simple five state model system we can analytically elucidate different sources of the bias and thus explain the different deviations that were observed for the Ising model. Based on this insight we can modify the determination of the count matrix in the MSM approach. In this way, the estimation of the free energy is significantly improved.

We employ kinetic Monte Carlo (KMC) simulations and a thin-film continuum model to comparatively study the transverse (i.e., Plateau-Rayleigh) instability of ridges formed by molecules on pre-patterned substrates. It is demonstrated that the evolution of the occurring instability qualitatively agrees between the two models for a single ridge as well as for two weakly interacting ridges. In particular, it is shown for both models that the instability occurs on well defined length and time scales which are, for the KMC model, significantly larger than the intrinsic scales of thermodynamic fluctuations. This is further evidenced by the similarity of dispersion relations characterising the linear instability modes., Comment: 9 pages, 5 figures

We analyse the interaction of charged Janus particles including screening effects. The explicit interaction is mapped via a least square method on a variable number $n$ of systematically generated tensors that reflect the angular dependence of the potential. For $n = 2$ we show that the interaction is equivalent to a model previously described by Erdmann, Kr\"oger and Hess (EKH). Interestingly, this mapping is not able to capture the subtleties of the interaction for small screening lengths. Rather, a larger number of tensors has to be used. We find that the characteristics of the Janus type interaction plays an important role for the aggregation behaviour. We obtained cluster structures up to the size of $13$ particles for $n = 2$ and $36$ and screening lengths $\kappa^{-1} = 0.1$ and $1.0$ via Monte Carlo simulations. The influence of the screening length is analysed and the structures are compared to results for an electrostatic-type potential and for multipole-expanded Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. We find that a dipole-like potential (EKH or dipole DLVO approximation) is not able to sufficiently reproduce the anisotropy effects of the potential. Instead, a higher order expansion has to be used to obtain clusters structures that are identical to experimental results for up to $N = 8$ particles. The resulting minimum-energy clusters are compared to those of sticky hard sphere systems. Janus particles with a short-range screened interaction resemble sticky hard sphere clusters for all considered particle numbers, whereas for long-range screening even very small clusters are structurally different.

The pre-patterning of a substrate to create energetically more attractive or repulsive regions allows one to generate a variety of structures in physical vapor deposition experiments. A particular interesting structure is generated if the energetically attractive region is forming a rectangular grid. For specific combinations of the particle flux, the substrate temperature and the lattice size it is possible to generate exactly one cluster per cell, giving rise to nucleation control. Here, we show that the experimental observations of nucleation control can be very well understood from a theoretical perspective. For this purpose we perform, on the one hand, kinetic Monte Carlo simulations and, on the other hand, use analytical scaling arguments to rationalize the observed behavior. For several observables, characterizing nucleation control, a very good agreement is found between experiment and theory. This underlines the generality of the presented mechanism to control the deposition of material by manipulation of the direct environment., Comment: 9 pages (two-columned), 11 figures (updated), Phys. Chem. Chem. Phys. (2018)

We report an experimental approach to control the position of molecular aggregates on surfaces by vacuum deposition. The control is accomplished by regulating the molecular density on the surface in a confined area. The diffusing molecules are concentrated at the centre of the confined area, producing a stable cluster when reaching the critical density for nucleation. Mechanistic aspects of that control are obtained from kinetic Monte Carlo simulations. The dimensions of the position can further be controlled by varying the beam flux and the substrate temperature., Comment: 6 pages, 5 figures

In active microrheology the mechanical properties of a material are tested by adding probe particles which are pulled by an external force. In case of supercooled liquids, strong forcing leads to a thinning of the host material which becomes more pronounced as the system approaches the glass transition. In this work we provide a quantitative theoretical description of this thinning behavior based on the properties of the Potential Energy Landscape (PEL) of a model glass-former. A key role plays the trap-like nature of the PEL. We find that the mechanical properties in the strongly driven system behave the same as in a quiescent system at an enhanced temperature, giving rise to a well-characterized effective temperature. Furthermore, this effective temperature turns out to be independent of the chosen observable and individually shows up in the thermodynamic and dynamic properties of the system. Based on this underlying theoretical understanding, we can estimate its dependence on temperature and force by the PEL-properties of the quiescent system. We furthermore critically discuss the relevance of effective temperatures obtained by scaling relations for the description of out-of-equilibrium situations.