@article{1208,
abstract = {We study parameter estimation in linear Gaussian covariance models, which are p-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex optimization problem which typically has many local maxima. Using recent results on the asymptotic distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient conditions for any hill climbing method to converge to the global maximum. Although we are primarily interested in the case in which n≫p, the proofs of our results utilize large sample asymptotic theory under the scheme n/p→γ>1. Remarkably, our numerical simulations indicate that our results remain valid for p as small as 2. An important consequence of this analysis is that, for sample sizes n≃14p, maximum likelihood estimation for linear Gaussian covariance models behaves as if it were a convex optimization problem. © 2016 The Royal Statistical Society and Blackwell Publishing Ltd.},
author = {Zwiernik, Piotr and Uhler, Caroline and Richards, Donald},
issn = {13697412},
journal = {Journal of the Royal Statistical Society. Series B: Statistical Methodology},
number = {4},
pages = {1269 -- 1292},
publisher = {Wiley-Blackwell},
title = {{Maximum likelihood estimation for linear Gaussian covariance models}},
doi = {10.1111/rssb.12217},
volume = {79},
year = {2017},
}
@article{1211,
abstract = {Systems such as fluid flows in channels and pipes or the complex Ginzburg–Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial reflections or complex conjugation. The simplest, and very common symmetry of this type is the equivariance of the defining equations under the orthogonal group O(2). We formulate a novel symmetry reduction scheme for such systems by combining the method of slices with invariant polynomial methods, and show how it works by applying it to the Kuramoto–Sivashinsky system in one spatial dimension. As an example, we track a relative periodic orbit through a sequence of bifurcations to the onset of chaos. Within the symmetry-reduced state space we are able to compute and visualize the unstable manifolds of relative periodic orbits, their torus bifurcations, a transition to chaos via torus breakdown, and heteroclinic connections between various relative periodic orbits. It would be very hard to carry through such analysis in the full state space, without a symmetry reduction such as the one we present here.},
author = {Budanur, Nazmi B and Cvitanović, Predrag},
journal = {Journal of Statistical Physics},
number = {3-4},
pages = {636--655},
publisher = {Springer},
title = {{Unstable manifolds of relative periodic orbits in the symmetry reduced state space of the Kuramoto–Sivashinsky system}},
doi = {10.1007/s10955-016-1672-z},
volume = {167},
year = {2017},
}
@article{1228,
abstract = {Since 2006, reprogrammed cells have increasingly been used as a biomedical research technique in addition to neuro-psychiatric methods. These rapidly evolving techniques allow for the generation of neuronal sub-populations, and have sparked interest not only in monogenetic neuro-psychiatric diseases, but also in poly-genetic and poly-aetiological disorders such as schizophrenia (SCZ) and bipolar disorder (BPD). This review provides a summary of 19 publications on reprogrammed adult somatic cells derived from patients with SCZ, and five publications using this technique in patients with BPD. As both disorders are complex and heterogeneous, there is a plurality of hypotheses to be tested in vitro. In SCZ, data on alterations of dopaminergic transmission in vitro are sparse, despite the great explanatory power of the so-called DA hypothesis of SCZ. Some findings correspond to perturbations of cell energy metabolism, and observations in reprogrammed cells suggest neuro-developmental alterations. Some studies also report on the efficacy of medicinal compounds to revert alterations observed in cellular models. However, due to the paucity of replication studies, no comprehensive conclusions can be drawn from studies using reprogrammed cells at the present time. In the future, findings from cell culture methods need to be integrated with clinical, epidemiological, pharmacological and imaging data in order to generate a more comprehensive picture of SCZ and BPD.},
author = {Sauerzopf, Ulrich and Sacco, Roberto and Novarino, Gaia and Niello, Marco and Weidenauer, Ana and Praschak Rieder, Nicole and Sitte, Harald and Willeit, Matthaeus},
journal = {European Journal of Neuroscience},
number = {1},
pages = {45 -- 57},
publisher = {Wiley-Blackwell},
title = {{Are reprogrammed cells a useful tool for studying dopamine dysfunction in psychotic disorders? A review of the current evidence}},
doi = {10.1111/ejn.13418},
volume = {45},
year = {2017},
}
@article{123,
abstract = {The Leidenfrost effect occurs when an object near a hot surface vaporizes rapidly enough to lift itself up and hover. Although well understood for liquids and stiff sublimable solids, nothing is known about the effect with materials whose stiffness lies between these extremes. Here we introduce a new phenomenon that occurs with vaporizable soft solids - the elastic Leidenfrost effect. By dropping hydrogel spheres onto hot surfaces we find that, rather than hovering, they energetically bounce several times their diameter for minutes at a time. With high-speed video during a single impact, we uncover high-frequency microscopic gap dynamics at the sphere/substrate interface. We show how these otherwise-hidden agitations constitute work cycles that harvest mechanical energy from the vapour and sustain the bouncing. Our findings suggest a new strategy for injecting mechanical energy into a widely used class of soft materials, with potential relevance to fields such as active matter, soft robotics and microfluidics.},
author = {Waitukaitis, Scott R and Zuiderwijk, Antal and Souslov, Anton and Coulais, Corentin and Van Hecke, Martin},
journal = {Nature Physics},
number = {11},
pages = {1095 -- 1099},
publisher = {Nature Publishing Group},
title = {{Coupling the Leidenfrost effect and elastic deformations to power sustained bouncing}},
doi = {10.1038/nphys4194},
volume = {13},
year = {2017},
}
@article{909,
abstract = {We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor ½ cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.},
author = {Akopyan, Arseniy and Vysotsky, Vladislav},
issn = {00029890},
journal = {The American Mathematical Monthly},
number = {7},
pages = {588 -- 596},
publisher = {Mathematical Association of America},
title = {{On the lengths of curves passing through boundary points of a planar convex shape}},
doi = {10.4169/amer.math.monthly.124.7.588},
volume = {124},
year = {2017},
}