@article{5995,
  abstract     = {Motivation
Computational prediction of the effect of mutations on protein stability is used by researchers in many fields. The utility of the prediction methods is affected by their accuracy and bias. Bias, a systematic shift of the predicted change of stability, has been noted as an issue for several methods, but has not been investigated systematically. Presence of the bias may lead to misleading results especially when exploring the effects of combination of different mutations.

Results
Here we use a protocol to measure the bias as a function of the number of introduced mutations. It is based on a self-consistency test of the reciprocity the effect of a mutation. An advantage of the used approach is that it relies solely on crystal structures without experimentally measured stability values. We applied the protocol to four popular algorithms predicting change of protein stability upon mutation, FoldX, Eris, Rosetta and I-Mutant, and found an inherent bias. For one program, FoldX, we manage to substantially reduce the bias using additional relaxation by Modeller. Authors using algorithms for predicting effects of mutations should be aware of the bias described here.},
  author       = {Usmanova, Dinara R and Bogatyreva, Natalya S and Ariño Bernad, Joan and Eremina, Aleksandra A and Gorshkova, Anastasiya A and Kanevskiy, German M and Lonishin, Lyubov R and Meister, Alexander V and Yakupova, Alisa G and Kondrashov, Fyodor and Ivankov, Dmitry},
  issn         = {1367-4811},
  journal      = {Bioinformatics},
  number       = {21},
  pages        = {3653--3658},
  publisher    = {Oxford University Press},
  title        = {{Self-consistency test reveals systematic bias in programs for prediction change of stability upon mutation}},
  doi          = {10.1093/bioinformatics/bty340},
  volume       = {34},
  year         = {2018},
}

@article{404,
  abstract     = {We construct martingale solutions to stochastic thin-film equations by introducing a (spatial) semidiscretization and establishing convergence. The discrete scheme allows for variants of the energy and entropy estimates in the continuous setting as long as the discrete energy does not exceed certain threshold values depending on the spatial grid size $h$. Using a stopping time argument to prolongate high-energy paths constant in time, arbitrary moments of coupled energy/entropy functionals can be controlled. Having established Hölder regularity of approximate solutions, the convergence proof is then based on compactness arguments---in particular on Jakubowski's generalization of Skorokhod's theorem---weak convergence methods, and recent tools on martingale convergence.

},
  author       = {Fischer, Julian L and Grün, Günther},
  journal      = {SIAM Journal on Mathematical Analysis},
  number       = {1},
  pages        = {411 -- 455},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Existence of positive solutions to stochastic thin-film equations}},
  doi          = {10.1137/16M1098796},
  volume       = {50},
  year         = {2018},
}

@article{181,
  abstract     = {We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2.},
  author       = {Erdös, László and Krüger, Torben H and Renfrew, David T},
  journal      = {SIAM Journal on Mathematical Analysis},
  number       = {3},
  pages        = {3271 -- 3290},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Power law decay for systems of randomly coupled differential equations}},
  doi          = {10.1137/17M1143125},
  volume       = {50},
  year         = {2018},
}

@article{312,
  abstract     = {Motivated by biological questions, we study configurations of equal spheres that neither pack nor cover. Placing their centers on a lattice, we define the soft density of the configuration by penalizing multiple overlaps. Considering the 1-parameter family of diagonally distorted 3-dimensional integer lattices, we show that the soft density is maximized at the FCC lattice.},
  author       = {Edelsbrunner, Herbert and Iglesias Ham, Mabel},
  issn         = {0895-4801},
  journal      = {SIAM J Discrete Math},
  number       = {1},
  pages        = {750 -- 782},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{On the optimality of the FCC lattice for soft sphere packing}},
  doi          = {10.1137/16M1097201},
  volume       = {32},
  year         = {2018},
}

@article{22,
  abstract     = {Conventional ultra-high sensitivity detectors in the millimeter-wave range are usually cooled as their own thermal noise at room temperature would mask the weak received radiation. The need for cryogenic systems increases the cost and complexity of the instruments, hindering the development of, among others, airborne and space applications. In this work, the nonlinear parametric upconversion of millimeter-wave radiation to the optical domain inside high-quality (Q) lithium niobate whispering-gallery mode (WGM) resonators is proposed for ultra-low noise detection. We experimentally demonstrate coherent upconversion of millimeter-wave signals to a 1550 nm telecom carrier, with a photon conversion efficiency surpassing the state-of-the-art by 2 orders of magnitude. Moreover, a theoretical model shows that the thermal equilibrium of counterpropagating WGMs is broken by overcoupling the millimeter-wave WGM, effectively cooling the upconverted mode and allowing ultra-low noise detection. By theoretically estimating the sensitivity of a correlation radiometer based on the presented scheme, it is found that room-temperature radiometers with better sensitivity than state-of-the-art high-electron-mobility transistor (HEMT)-based radiometers can be designed. This detection paradigm can be used to develop room-temperature instrumentation for radio astronomy, earth observation, planetary missions, and imaging systems.},
  author       = {Botello, Gabriel and Sedlmeir, Florian and Rueda Sanchez, Alfredo R and Abdalmalak, Kerlos and Brown, Elliott and Leuchs, Gerd and Preu, Sascha and Segovia Vargas, Daniel and Strekalov, Dmitry and Munoz, Luis and Schwefel, Harald},
  issn         = {2334-2536},
  journal      = {Optica},
  number       = {10},
  pages        = {1210--1219},
  publisher    = {Optica Publishing Group},
  title        = {{Sensitivity limits of millimeter-wave photonic radiometers based on efficient electro-optic upconverters}},
  doi          = {10.1364/OPTICA.5.001210},
  volume       = {5},
  year         = {2018},
}

@techreport{5686,
  abstract     = {In the working paper I describe in detail the approach for Open Access definitions which was presented in the Workshop "Open Access Monitoring - Approaches and Perspectives" in Vienna. It defines five criteria on which are the definitions build. Each criteria can be out of 4 classes. The minimum classes for the criteria which are used in a Open Access definition can be presented as the Classification of Open Access Tuples e.g. Open Access (Berlin Declaration) (1,1,1,1,3) this methods allows much easier to distinguish between different Open Access definitions. This is needed if the Open Access Universe should be measured in studies or monitoring approaches and the results should become more comparable.     },
  author       = {Danowski, Patrick},
  pages        = {5},
  publisher    = {Zenodo},
  title        = {{An Austrian proposal for the Classification of Open Access Tuples (COAT) - Distinguish different Open Access types beyond colors}},
  doi          = {10.5281/zenodo.1244154},
  year         = {2018},
}

@article{58,
  abstract     = {Inside a two-dimensional region (``cake&quot;&quot;), there are m nonoverlapping tiles of a certain kind (``toppings&quot;&quot;). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,&quot;&quot; such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks.},
  author       = {Akopyan, Arseniy and Segal Halevi, Erel},
  journal      = {SIAM Journal on Discrete Mathematics},
  number       = {3},
  pages        = {2242 -- 2257},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Counting blanks in polygonal arrangements}},
  doi          = {10.1137/16M110407X},
  volume       = {32},
  year         = {2018},
}

@article{427,
  abstract     = {We investigate the quantum interference induced shifts between energetically close states in highly charged ions, with the energy structure being observed by laser spectroscopy. In this work, we focus on hyperfine states of lithiumlike heavy-Z isotopes and quantify how much quantum interference changes the observed transition frequencies. The process of photon excitation and subsequent photon decay for the transition 2s→2p→2s is implemented with fully relativistic and full-multipole frameworks, which are relevant for such relativistic atomic systems. We consider the isotopes Pb79+207 and Bi80+209 due to experimental interest, as well as other examples of isotopes with lower Z, namely Pr56+141 and Ho64+165. We conclude that quantum interference can induce shifts up to 11% of the linewidth in the measurable resonances of the considered isotopes, if interference between resonances is neglected. The inclusion of relativity decreases the cross section by 35%, mainly due to the complete retardation form of the electric dipole multipole. However, the contribution of the next higher multipoles (e.g., magnetic quadrupole) to the cross section is negligible. This makes the contribution of relativity and higher-order multipoles to the quantum interference induced shifts a minor effect, even for heavy-Z elements.},
  author       = {Amaro, Pedro and Loureiro, Ulisses and Safari, Laleh and Fratini, Filippo and Indelicato, Paul and Stöhlker, Thomas and Santos, José},
  journal      = {Physical Review A},
  number       = {2},
  publisher    = {American Physical Society},
  title        = {{Quantum interference in laser spectroscopy of highly charged lithiumlike ions}},
  doi          = {10.1103/PhysRevA.97.022510},
  volume       = {97},
  year         = {2018},
}

@article{307,
  abstract     = {Spontaneous emission spectra of two initially excited closely spaced identical atoms are very sensitive to the strength and the direction of the applied magnetic field. We consider the relevant schemes that ensure the determination of the mutual spatial orientation of the atoms and the distance between them by entirely optical means. A corresponding theoretical description is given accounting for the dipole-dipole interaction between the two atoms in the presence of a magnetic field and for polarizations of the quantum field interacting with magnetic sublevels of the two-atom system. },
  author       = {Redchenko, Elena and Makarov, Alexander and Yudson, Vladimir},
  journal      = {Physical Review A},
  number       = {4},
  publisher    = {American Physical Society},
  title        = {{Nanoscopy of pairs of atoms by fluorescence in a magnetic field}},
  doi          = {10.1103/PhysRevA.97.043812},
  volume       = {97},
  year         = {2018},
}

@inproceedings{34,
  abstract     = {Partially observable Markov decision processes (POMDPs) are widely used in probabilistic planning problems in which an agent interacts with an environment using noisy and imprecise sensors. We study a setting in which the sensors are only partially defined and the goal is to synthesize “weakest” additional sensors, such that in the resulting POMDP, there is a small-memory policy for the agent that almost-surely (with probability 1) satisfies a reachability objective. We show that the problem is NP-complete, and present a symbolic algorithm by encoding the problem into SAT instances. We illustrate trade-offs between the amount of memory of the policy and the number of additional sensors on a simple example. We have implemented our approach and consider three classical POMDP examples from the literature, and show that in all the examples the number of sensors can be significantly decreased (as compared to the existing solutions in the literature) without increasing the complexity of the policies.},
  author       = {Chatterjee, Krishnendu and Chemlík, Martin and Topcu, Ufuk},
  booktitle    = {28th International Conference on Automated Planning and Scheduling},
  location     = {Delft, Netherlands},
  pages        = {47 -- 55},
  publisher    = {AAAI Press},
  title        = {{Sensor synthesis for POMDPs with reachability objectives}},
  doi          = {10.1609/icaps.v28i1.13875},
  volume       = {2018},
  year         = {2018},
}

@inproceedings{35,
  abstract     = {We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set; and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs, and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs and for the sequential reachability problem games on graphs are harder than MDPs and graphs; and (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.},
  author       = {Chatterjee, Krishnendu and Dvorák, Wolfgang and Henzinger, Monika H and Svozil, Alexander},
  booktitle    = {28th International Conference on Automated Planning and Scheduling},
  location     = {Delft, Netherlands},
  publisher    = {AAAI Press},
  title        = {{Algorithms and conditional lower bounds for planning problems}},
  year         = {2018},
}

@article{12,
  abstract     = {Molding is a popular mass production method, in which the initial expenses for the mold are offset by the low per-unit production cost. However, the physical fabrication constraints of the molding technique commonly restrict the shape of moldable objects. For a complex shape, a decomposition of the object into moldable parts is a common strategy to address these constraints, with plastic model kits being a popular and illustrative example. However, conducting such a decomposition requires considerable expertise, and it depends on the technical aspects of the fabrication technique, as well as aesthetic considerations. We present an interactive technique to create such decompositions for two-piece molding, in which each part of the object is cast between two rigid mold pieces. Given the surface description of an object, we decompose its thin-shell equivalent into moldable parts by first performing a coarse decomposition and then utilizing an active contour model for the boundaries between individual parts. Formulated as an optimization problem, the movement of the contours is guided by an energy reflecting fabrication constraints to ensure the moldability of each part. Simultaneously, the user is provided with editing capabilities to enforce aesthetic guidelines. Our interactive interface provides control of the contour positions by allowing, for example, the alignment of part boundaries with object features. Our technique enables a novel workflow, as it empowers novice users to explore the design space, and it generates fabrication-ready two-piece molds that can be used either for casting or industrial injection molding of free-form objects.},
  author       = {Nakashima, Kazutaka and Auzinger, Thomas and Iarussi, Emmanuel and Zhang, Ran and Igarashi, Takeo and Bickel, Bernd},
  journal      = {ACM Transactions on Graphics},
  number       = {4},
  publisher    = {ACM},
  title        = {{CoreCavity: Interactive shell decomposition for fabrication with two-piece rigid molds}},
  doi          = {10.1145/3197517.3201341},
  volume       = {37},
  year         = {2018},
}

@article{4,
  abstract     = {We present a data-driven technique to instantly predict how fluid flows around various three-dimensional objects. Such simulation is useful for computational fabrication and engineering, but is usually computationally expensive since it requires solving the Navier-Stokes equation for many time steps. To accelerate the process, we propose a machine learning framework which predicts aerodynamic forces and velocity and pressure fields given a threedimensional shape input. Handling detailed free-form three-dimensional shapes in a data-driven framework is challenging because machine learning approaches usually require a consistent parametrization of input and output. We present a novel PolyCube maps-based parametrization that can be computed for three-dimensional shapes at interactive rates. This allows us to efficiently learn the nonlinear response of the flow using a Gaussian process regression. We demonstrate the effectiveness of our approach for the interactive design and optimization of a car body.},
  author       = {Umetani, Nobuyuki and Bickel, Bernd},
  journal      = {ACM Transactions on Graphics},
  number       = {4},
  publisher    = {ACM},
  title        = {{Learning three-dimensional flow for interactive aerodynamic design}},
  doi          = {10.1145/3197517.3201325},
  volume       = {37},
  year         = {2018},
}

@article{13,
  abstract     = {We propose a new method for fabricating digital objects through reusable silicone molds. Molds are generated by casting liquid silicone into custom 3D printed containers called metamolds. Metamolds automatically define the cuts that are needed to extract the cast object from the silicone mold. The shape of metamolds is designed through a novel segmentation technique, which takes into account both geometric and topological constraints involved in the process of mold casting. Our technique is simple, does not require changing the shape or topology of the input objects, and only requires off-the- shelf materials and technologies. We successfully tested our method on a set of challenging examples with complex shapes and rich geometric detail. © 2018 Association for Computing Machinery.},
  author       = {Alderighi, Thomas and Malomo, Luigi and Giorgi, Daniela and Pietroni, Nico and Bickel, Bernd and Cignoni, Paolo},
  journal      = {ACM Transactions on Graphics},
  number       = {4},
  publisher    = {ACM},
  title        = {{Metamolds: Computational design of silicone molds}},
  doi          = {10.1145/3197517.3201381},
  volume       = {37},
  year         = {2018},
}

@inproceedings{6589,
  abstract     = {Distributed training of massive machine learning models, in particular deep neural networks, via Stochastic Gradient Descent (SGD) is becoming commonplace. Several families of communication-reduction methods, such as quantization, large-batch methods, and gradient sparsification, have been proposed. To date, gradient sparsification methods--where each node sorts gradients by magnitude, and only communicates a subset of the components, accumulating the rest locally--are known to yield some of the largest practical gains. Such methods can reduce the amount of communication per step by up to \emph{three orders of magnitude}, while preserving model accuracy. Yet, this family of methods currently has no theoretical justification. This is the question we address in this paper. We prove that, under analytic assumptions, sparsifying gradients by magnitude with local error correction provides convergence guarantees, for both convex and non-convex smooth objectives, for data-parallel SGD. The main insight is that sparsification methods implicitly maintain bounds on the maximum impact of stale updates, thanks to selection by magnitude. Our analysis and empirical validation also reveal that these methods do require analytical conditions to converge well, justifying existing heuristics.},
  author       = {Alistarh, Dan-Adrian and Hoefler, Torsten and Johansson, Mikael and Konstantinov, Nikola H and Khirirat, Sarit and Renggli, Cedric},
  booktitle    = {32nd Conference on Neural Information Processing Systems},
  issn         = {1049-5258},
  location     = {Montreal, Canada},
  pages        = {5973--5983},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{The convergence of sparsified gradient methods}},
  year         = {2018},
}

@article{131,
  abstract     = {XY systems usually show chromosome-wide compensation of X-linked genes, while in many ZW systems, compensation is restricted to a minority of dosage-sensitive genes. Why such differences arose is still unclear. Here, we combine comparative genomics, transcriptomics and proteomics to obtain a complete overview of the evolution of gene dosage on the Z-chromosome of Schistosoma parasites. We compare the Z-chromosome gene content of African (Schistosoma mansoni and S. haematobium) and Asian (S. japonicum) schistosomes and describe lineage-specific evolutionary strata. We use these to assess gene expression evolution following sex-linkage. The resulting patterns suggest a reduction in expression of Z-linked genes in females, combined with upregulation of the Z in both sexes, in line with the first step of Ohno’s classic model of dosage compensation evolution. Quantitative proteomics suggest that post-transcriptional mechanisms do not play a major role in balancing the expression of Z-linked genes. },
  author       = {Picard, Marion A and Cosseau, Celine and Ferré, Sabrina and Quack, Thomas and Grevelding, Christoph and Couté, Yohann and Vicoso, Beatriz},
  journal      = {eLife},
  publisher    = {eLife Sciences Publications},
  title        = {{Evolution of gene dosage on the Z-chromosome of schistosome parasites}},
  doi          = {10.7554/eLife.35684},
  volume       = {7},
  year         = {2018},
}

@misc{5586,
  abstract     = {Input files and scripts from "Evolution of gene dosage on the Z-chromosome of schistosome parasites" by Picard M.A.L., et al (2018).},
  author       = {Vicoso, Beatriz},
  keywords     = {schistosoma, Z-chromosome, gene expression},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Input files and scripts from "Evolution of gene dosage on the Z-chromosome of schistosome parasites" by Picard M.A.L., et al (2018)}},
  doi          = {10.15479/AT:ISTA:109},
  year         = {2018},
}

@article{5996,
  abstract     = {In pipes, turbulence sets in despite the linear stability of the laminar Hagen–Poiseuille flow. The Reynolds number ( ) for which turbulence first appears in a given experiment – the ‘natural transition point’ – depends on imperfections of the set-up, or, more precisely, on the magnitude of finite amplitude perturbations. At onset, turbulence typically only occupies a certain fraction of the flow, and this fraction equally is found to differ from experiment to experiment. Despite these findings, Reynolds proposed that after sufficiently long times, flows may settle to steady conditions: below a critical velocity, flows should (regardless of initial conditions) always return to laminar, while above this velocity, eddying motion should persist. As will be shown, even in pipes several thousand diameters long, the spatio-temporal intermittent flow patterns observed at the end of the pipe strongly depend on the initial conditions, and there is no indication that different flow patterns would eventually settle to a (statistical) steady state. Exploiting the fact that turbulent puffs do not age (i.e. they are memoryless), we continuously recreate the puff sequence exiting the pipe at the pipe entrance, and in doing so introduce periodic boundary conditions for the puff pattern. This procedure allows us to study the evolution of the flow patterns for arbitrary long times, and we find that after times in excess of advective time units, indeed a statistical steady state is reached. Although the resulting flows remain spatio-temporally intermittent, puff splitting and decay rates eventually reach a balance, so that the turbulent fraction fluctuates around a well-defined level which only depends on . In accordance with Reynolds’ proposition, we find that at lower (here 2020), flows eventually always resume to laminar, while for higher ( ), turbulence persists. The critical point for pipe flow hence falls in the interval of $2020 , which is in very good agreement with the recently proposed value of . The latter estimate was based on single-puff statistics and entirely neglected puff interactions. Unlike in typical contact processes where such interactions strongly affect the percolation threshold, in pipe flow, the critical point is only marginally influenced. Interactions, on the other hand, are responsible for the approach to the statistical steady state. As shown, they strongly affect the resulting flow patterns, where they cause ‘puff clustering’, and these regions of large puff densities are observed to travel across the puff pattern in a wave-like fashion.},
  author       = {Vasudevan, Mukund and Hof, Björn},
  issn         = {1469-7645},
  journal      = {Journal of Fluid Mechanics},
  pages        = {76--94},
  publisher    = {Cambridge University Press},
  title        = {{The critical point of the transition to turbulence in pipe flow}},
  doi          = {10.1017/jfm.2017.923},
  volume       = {839},
  year         = {2018},
}

@phdthesis{197,
  abstract     = {Modern computer vision systems heavily rely on statistical machine learning models, which typically require large amounts of labeled data to be learned reliably. Moreover, very recently computer vision research widely adopted techniques for representation learning, which further increase the demand for labeled data. However, for many important practical problems there is relatively small amount of labeled data available, so it is problematic to leverage full potential of the representation learning methods. One way to overcome this obstacle is to invest substantial resources into producing large labelled datasets. Unfortunately, this can be prohibitively expensive in practice. In this thesis we focus on the alternative way of tackling the aforementioned issue. We concentrate on methods, which make use of weakly-labeled or even unlabeled data. Specifically, the first half of the thesis is dedicated to the semantic image segmentation task. We develop a technique, which achieves competitive segmentation performance and only requires annotations in a form of global image-level labels instead of dense segmentation masks. Subsequently, we present a new methodology, which further improves segmentation performance by leveraging tiny additional feedback from a human annotator. By using our methods practitioners can greatly reduce the amount of data annotation effort, which is required to learn modern image segmentation models. In the second half of the thesis we focus on methods for learning from unlabeled visual data. We study a family of autoregressive models for modeling structure of natural images and discuss potential applications of these models. Moreover, we conduct in-depth study of one of these applications, where we develop the state-of-the-art model for the probabilistic image colorization task.},
  author       = {Kolesnikov, Alexander},
  issn         = {2663-337X},
  pages        = {113},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Weakly-supervised segmentation and unsupervised modeling of natural images}},
  doi          = {10.15479/AT:ISTA:th_1021},
  year         = {2018},
}

@phdthesis{201,
  abstract     = {We describe arrangements of three-dimensional spheres from a geometrical and topological point of view. Real data (fitting this setup) often consist of soft spheres which show certain degree of deformation while strongly packing against each other. In this context, we answer the following questions: If we model a soft packing of spheres by hard spheres that are allowed to overlap, can we measure the volume in the overlapped areas? Can we be more specific about the overlap volume, i.e. quantify how much volume is there covered exactly twice, three times, or k times? What would be a good optimization criteria that rule the arrangement of soft spheres while making a good use of the available space? Fixing a particular criterion, what would be the optimal sphere configuration? The first result of this thesis are short formulas for the computation of volumes covered by at least k of the balls. The formulas exploit information contained in the order-k Voronoi diagrams and its closely related Level-k complex. The used complexes lead to a natural generalization into poset diagrams, a theoretical formalism that contains the order-k and degree-k diagrams as special cases. In parallel, we define different criteria to determine what could be considered an optimal arrangement from a geometrical point of view. Fixing a criterion, we find optimal soft packing configurations in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools from computational topology on real physical data, to show the potentials of higher-order diagrams in the description of melting crystals. The results of the experiments leaves us with an open window to apply the theories developed in this thesis in real applications.},
  author       = {Iglesias Ham, Mabel},
  issn         = {2663-337X},
  pages        = {171},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Multiple covers with balls}},
  doi          = {10.15479/AT:ISTA:th_1026},
  year         = {2018},
}

