@article{73,
abstract = {We consider the space of probability measures on a discrete set X, endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset Y⊆X, it is natural to ask whether they can be connected by a constant speed geodesic with support in Y at all times. Our main result answers this question affirmatively, under a suitable geometric condition on Y introduced in this paper. The proof relies on an extension result for subsolutions to discrete Hamilton-Jacobi equations, which is of independent interest.},
author = {Erbar, Matthias and Maas, Jan and Wirth, Melchior},
issn = {09442669},
journal = {Calculus of Variations and Partial Differential Equations},
number = {1},
publisher = {Springer},
title = {{On the geometry of geodesics in discrete optimal transport}},
doi = {10.1007/s00526-018-1456-1},
volume = {58},
year = {2019},
}
@article{7140,
abstract = {The cerebral cortex contains multiple areas with distinctive cytoarchitectonical patterns, but the cellular mechanisms underlying the emergence of this diversity remain unclear. Here, we have investigated the neuronal output of individual progenitor cells in the developing mouse neocortex using a combination of methods that together circumvent the biases and limitations of individual approaches. Our experimental results indicate that progenitor cells generate pyramidal cell lineages with a wide range of sizes and laminar configurations. Mathematical modelling indicates that these outcomes are compatible with a stochastic model of cortical neurogenesis in which progenitor cells undergo a series of probabilistic decisions that lead to the specification of very heterogeneous progenies. Our findings support a mechanism for cortical neurogenesis whose flexibility would make it capable to generate the diverse cytoarchitectures that characterize distinct neocortical areas.},
author = {Llorca, Alfredo and Ciceri, Gabriele and Beattie, Robert J and Wong, Fong Kuan and Diana, Giovanni and Serafeimidou-Pouliou, Eleni and Fernández-Otero, Marian and Streicher, Carmen and Arnold, Sebastian J and Meyer, Martin and Hippenmeyer, Simon and Maravall, Miguel and Marin, Oscar},
issn = {2050-084X},
journal = {eLife},
publisher = {eLife Sciences Publications},
title = {{A stochastic framework of neurogenesis underlies the assembly of neocortical cytoarchitecture}},
doi = {10.7554/elife.51381},
volume = {8},
year = {2019},
}
@article{7145,
abstract = {End-to-end correlated bound states are investigated in superconductor-semiconductor hybrid nanowires at zero magnetic field. Peaks in subgap conductance are independently identified from each wire end, and a cross-correlation function is computed that counts end-to-end coincidences, averaging over thousands of subgap features. Strong correlations in a short, 300-nm device are reduced by a factor of 4 in a long, 900-nm device. In addition, subgap conductance distributions are investigated, and correlations between the left and right distributions are identified based on their mutual information.},
author = {Anselmetti, G. L. R. and Martinez, E. A. and Ménard, G. C. and Puglia, D. and Malinowski, F. K. and Lee, J. S. and Choi, S. and Pendharkar, M. and Palmstrøm, C. J. and Marcus, C. M. and Casparis, L. and Higginbotham, Andrew P},
issn = {2469-9969},
journal = {Physical Review B},
number = {20},
publisher = {APS},
title = {{End-to-end correlated subgap states in hybrid nanowires}},
doi = {10.1103/physrevb.100.205412},
volume = {100},
year = {2019},
}
@book{7171,
editor = {Kersting, Kristian and Lampert, Christoph and Rothkopf, Constantin},
isbn = {9783658267629},
pages = {245},
publisher = {Springer Nature},
title = {{Wie Maschinen lernen}},
doi = {10.1007/978-3-658-26763-6},
year = {2019},
}
@inproceedings{7183,
abstract = {A probabilistic vector addition system with states (pVASS) is a finite state Markov process augmented with non-negative integer counters that can be incremented or decremented during each state transition, blocking any behaviour that would cause a counter to decrease below zero. The pVASS can be used as abstractions of probabilistic programs with many decidable properties. The use of pVASS as abstractions requires the presence of nondeterminism in the model. In this paper, we develop techniques for checking fast termination of pVASS with nondeterminism. That is, for every initial configuration of size n, we consider the worst expected number of transitions needed to reach a configuration with some counter negative (the expected termination time). We show that the problem whether the asymptotic expected termination time is linear is decidable in polynomial time for a certain natural class of pVASS with nondeterminism. Furthermore, we show the following dichotomy: if the asymptotic expected termination time is not linear, then it is at least quadratic, i.e., in Ω(n2).},
author = {Brázdil, Tomás and Chatterjee, Krishnendu and Kučera, Antonín and Novotný, Petr and Velan, Dominik},
booktitle = {International Symposium on Automated Technology for Verification and Analysis},
isbn = {9783030317836},
issn = {16113349},
location = {Taipei, Taiwan},
pages = {462--478},
publisher = {Springer Nature},
title = {{Deciding fast termination for probabilistic VASS with nondeterminism}},
doi = {10.1007/978-3-030-31784-3_27},
volume = {11781},
year = {2019},
}
@article{6972,
abstract = {We give fault-tolerant algorithms for establishing synchrony in distributed systems in which each of thennodes has its own clock. Our algorithms operate in a very strong fault model: we require self-stabilisation, i.e.,the initial state of the system may be arbitrary, and there can be up to f0 one can find a simple 1-dimensional constant coefficient linear equation whose solution at the boundary is not α-Hölder continuous.We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on C1 domains are proved to be α-Hölder continuous up to the boundary with some α>0.},
author = {Gerencser, Mate},
issn = {00911798},
journal = {Annals of Probability},
number = {2},
pages = {804--834},
publisher = {Institute of Mathematical Statistics},
title = {{Boundary regularity of stochastic PDEs}},
doi = {10.1214/18-AOP1272},
volume = {47},
year = {2019},
}