@unpublished{14703,
  abstract     = {We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton-Jacobi equation.},
  author       = {Ishida, Sadashige and Lavenant, Hugo},
  booktitle    = {arXiv},
  keywords     = {Optimal transport, Hamilton-Jacobi equation, convex optimization},
  title        = {{Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation}},
  doi          = {10.48550/arXiv.2312.12213},
  year         = {2023},
}

@article{12984,
  abstract     = {Tattoos are a highly popular medium, with both artistic and medical applications. Although the mechanical process of tattoo application has evolved historically, the results are reliant on the artisanal skill of the artist. This can be especially challenging for some skin tones, or in cases where artists lack experience. We provide the first systematic overview of tattooing as a computational fabrication technique. We built an automated tattooing rig and a recipe for the creation of silicone sheets mimicking realistic skin tones, which allowed us to create an accurate model predicting tattoo appearance. This enables several exciting applications including tattoo previewing, color retargeting, novel ink spectra optimization, color-accurate prosthetics, and more.},
  author       = {Piovarci, Michael and Chapiro, Alexandre and Bickel, Bernd},
  issn         = {1557-7368},
  journal      = {Transactions on Graphics},
  keywords     = {appearance, modeling, reproduction, tattoo, skin color, gamut mapping, ink-optimization, prosthetic},
  location     = {Los Angeles, CA, United States},
  number       = {4},
  publisher    = {Association for Computing Machinery},
  title        = {{Skin-Screen: A computational fabrication framework for color tattoos}},
  doi          = {10.1145/3592432},
  volume       = {42},
  year         = {2023},
}

@article{9817,
  abstract     = {Elastic bending of initially flat slender elements allows the realization and economic fabrication of intriguing curved shapes. In this work, we derive an intuitive but rigorous geometric characterization of the design space of plane elastic rods with variable stiffness. It enables designers to determine which shapes are physically viable with active bending by visual inspection alone. Building on these insights, we propose a method for efficiently designing the geometry of a flat elastic rod that realizes a target equilibrium curve, which only requires solving a linear program. We implement this method in an interactive computational design tool that gives feedback about the feasibility of a design, and computes the geometry of the structural elements necessary to realize it within an instant. The tool also offers an iterative optimization routine that improves the fabricability of a model while modifying it as little as possible. In addition, we use our geometric characterization to derive an algorithm for analyzing and recovering the stability of elastic curves that would otherwise snap out of their unstable equilibrium shapes by buckling. We show the efficacy of our approach by designing and manufacturing several physical models that are assembled from flat elements.},
  author       = {Hafner, Christian and Bickel, Bernd},
  issn         = {1557-7368},
  journal      = {ACM Transactions on Graphics},
  keywords     = {Computing methodologies, shape modeling, modeling and simulation, theory of computation, computational geometry, mathematics of computing, mathematical optimization},
  location     = {Virtual},
  number       = {4},
  publisher    = {Association for Computing Machinery},
  title        = {{The design space of plane elastic curves}},
  doi          = {10.1145/3450626.3459800},
  volume       = {40},
  year         = {2021},
}

@article{7130,
  abstract     = {We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify the frequency with which different outcomes occur in a sample, as the variable carrying useful information on the generative process. The entropy of the frequency, that we call relevance, provides an upper bound to the number of informative bits. This differs from the entropy of the data, that we take as a measure of resolution. Samples that maximise relevance at a given resolution—that we call maximally informative samples—exhibit statistical criticality. In particular, Zipf's law arises at the optimal trade-off between resolution (i.e. compression) and relevance. As a byproduct, we derive a bound of the maximal number of parameters that can be estimated from a dataset, in the absence of prior knowledge on the generative model.

Furthermore, we relate criticality to the statistical properties of the representation of the data generating process. We show that, as a consequence of the concentration property of the asymptotic equipartition property, representations that are maximally informative about the data generating process are characterised by an exponential distribution of energy levels. This arises from a principle of minimal entropy, that is conjugate of the maximum entropy principle in statistical mechanics. This explains why statistical criticality requires no parameter fine tuning in maximally informative samples.},
  author       = {Cubero, Ryan J and Jo, Junghyo and Marsili, Matteo and Roudi, Yasser and Song, Juyong},
  issn         = {1742-5468},
  journal      = {Journal of Statistical Mechanics: Theory and Experiment},
  keywords     = {optimization under uncertainty, source coding, large deviation},
  number       = {6},
  publisher    = {IOP Publishing},
  title        = {{Statistical criticality arises in most informative representations}},
  doi          = {10.1088/1742-5468/ab16c8},
  volume       = {2019},
  year         = {2019},
}

@article{11683,
  abstract     = {The vertex connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding separator. The time for a digraph having n vertices and m edges is O(min{κ3 + n, κn}m); for an undirected graph the term m can be replaced by κn. A randomized algorithm finds κ with error probability 1/2 in time O(nm). If the vertices have nonnegative weights the weighted vertex connectivity is found in time O(κ1nmlog(n2/m)) where κ1 ≤ m/n is the unweighted vertex connectivity or in expected time O(nmlog(n2/m)) with error probability 1/2. The main algorithm combines two previous vertex connectivity algorithms and a generalization of the preflow-push algorithm of Hao and Orlin (1994, J. Algorithms17, 424–446) that computes edge connectivity.},
  author       = {Henzinger, Monika H and Rao, Satish and Gabow, Harold N.},
  issn         = {0196-6774},
  journal      = {Journal of Algorithms},
  keywords     = {Computational Theory and Mathematics, Computational Mathematics, Control and Optimization},
  number       = {2},
  pages        = {222--250},
  publisher    = {Elsevier},
  title        = {{Computing vertex connectivity: New bounds from old techniques}},
  doi          = {10.1006/jagm.1999.1055},
  volume       = {34},
  year         = {2000},
}