@article{1293,
abstract = {For a graph G with p vertices the closed convex cone S⪰0(G) consists of all real positive semidefinite p×p matrices whose sparsity pattern is given by G, that is, those matrices with zeros in the off-diagonal entries corresponding to nonedges of G. The extremal rays of this cone and their associated ranks have applications to matrix completion problems, maximum likelihood estimation in Gaussian graphical models in statistics, and Gauss elimination for sparse matrices. While the maximum rank of an extremal ray in S⪰0(G), known as the sparsity order of G, has been characterized for different classes of graphs, we here study all possible extremal ranks of S⪰0(G). We investigate when the geometry of the (±1)-cut polytope of G yields a polyhedral characterization of the set of extremal ranks of S⪰0(G). For a graph G without K5 minors, we show that appropriately chosen normal vectors to the facets of the (±1)-cut polytope of G specify the off-diagonal entries of extremal matrices in S⪰0(G). We also prove that for appropriately chosen scalars the constant term of the linear equation of each facet-supporting hyperplane is the rank of its corresponding extremal matrix in S⪰0(G). Furthermore, we show that if G is series-parallel then this gives a complete characterization of all possible extremal ranks of S⪰0(G). Consequently, the sparsity order problem for series-parallel graphs can be solved in terms of polyhedral geometry.},
author = {Solus, Liam T and Uhler, Caroline and Yoshida, Ruriko},
journal = {Linear Algebra and Its Applications},
pages = {247 -- 275},
publisher = {Elsevier},
title = {{Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without K5 minors}},
doi = {10.1016/j.laa.2016.07.026},
volume = {509},
year = {2016},
}
@article{1295,
abstract = {Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls.},
author = {Edelsbrunner, Herbert and Iglesias Ham, Mabel},
journal = {Electronic Notes in Discrete Mathematics},
pages = {169 -- 174},
publisher = {Elsevier},
title = {{Multiple covers with balls II: Weighted averages}},
doi = {10.1016/j.endm.2016.09.030},
volume = {54},
year = {2016},
}
@article{1303,
abstract = {In bright light, cone-photoreceptors are active and colour vision derives from a comparison of signals in cones with different visual pigments. This comparison begins in the retina, where certain retinal ganglion cells have 'colour-opponent' visual responses-excited by light of one colour and suppressed by another colour. In dim light, rod-photoreceptors are active, but colour vision is impossible because they all use the same visual pigment. Instead, the rod signals are thought to splice into retinal circuits at various points, in synergy with the cone signals. Here we report a new circuit for colour vision that challenges these expectations. A genetically identified type of mouse retinal ganglion cell called JAMB (J-RGC), was found to have colour-opponent responses, OFF to ultraviolet (UV) light and ON to green light. Although the mouse retina contains a green-sensitive cone, the ON response instead originates in rods. Rods and cones both contribute to the response over several decades of light intensity. Remarkably, the rod signal in this circuit is antagonistic to that from cones. For rodents, this UV-green channel may play a role in social communication, as suggested by spectral measurements from the environment. In the human retina, all of the components for this circuit exist as well, and its function can explain certain experiences of colour in dim lights, such as a 'blue shift' in twilight. The discovery of this genetically defined pathway will enable new targeted studies of colour processing in the brain.},
author = {Maximilian Jösch and Meister, Markus},
journal = {Nature},
number = {7598},
pages = {236 -- 239},
publisher = {Nature Publishing Group},
title = {{A neuronal circuit for colour vision based on rod-cone opponency}},
doi = {10.1038/nature17158},
volume = {532},
year = {2016},
}
@article{1306,
abstract = {Resolving patterns of synaptic connectivity in neural circuits currently requires serial section electron microscopy. However, complete circuit reconstruction is prohibitively slow and may not be necessary for many purposes such as comparing neuronal structure and connectivity among multiple animals. Here, we present an alternative strategy, targeted reconstruction of specific neuronal types. We used viral vectors to deliver peroxidase derivatives, which catalyze production of an electron-dense tracer, to genetically identify neurons, and developed a protocol that enhances the electron-density of the labeled cells while retaining the quality of the ultrastructure. The high contrast of the marked neurons enabled two innovations that speed data acquisition: targeted high-resolution reimaging of regions selected from rapidly-acquired lower resolution reconstruction, and an unsupervised segmentation algorithm. This pipeline reduces imaging and reconstruction times by two orders of magnitude, facilitating directed inquiry of circuit motifs.},
author = {Maximilian Jösch and Mankus, David and Yamagata, Masahito and Shahbazi, Ali and Schalek, Richard L and Suissa-Peleg, Adi and Meister, Markus and Lichtman, Jeff W and Scheirer, Walter J and Sanes, Joshua R},
journal = {eLife},
number = {2016JULY},
publisher = {eLife Sciences Publications},
title = {{Reconstruction of genetically identified neurons imaged by serial-section electron microscopy}},
doi = {10.7554/eLife.15015},
volume = {5},
year = {2016},
}
@article{1315,
abstract = {We prove optimal second order convergence of a modified lowest-order Brezzi-Douglas-Marini (BDM1) mixed finite element scheme for advection-diffusion problems in divergence form. If advection is present, it is known that the total flux is approximated only with first-order accuracy by the classical BDM1 mixed method, which is suboptimal since the same order of convergence is obtained if the computationally less expensive Raviart-Thomas (RT0) element is used. The modification that was first proposed by Brunner et al. [Adv. Water Res., 35 (2012),pp. 163-171] is based on the hybrid problem formulation and consists in using the Lagrange multipliers for the discretization of the advective term instead of the cellwise constant approximation of the scalar unknown.},
author = {Brunner, Fabian and Julian Fischer and Knabner, Peter},
journal = {SIAM Journal on Numerical Analysis},
number = {4},
pages = {2359 -- 2378},
publisher = {Society for Industrial and Applied Mathematics },
title = {{Analysis of a modified second-order mixed hybrid BDM1 finite element method for transport problems in divergence form}},
doi = {10.1137/15M1035379},
volume = {54},
year = {2016},
}
@article{1317,
abstract = {We analyze the behaviour of free boundaries in thin-film flow in the regime of strong slippage n∈[1,2) and in the regime of very weak slippage n∈,3) qualitatively and quantitatively. In the regime of strong slippage, we construct initial data which are bounded from above by the steady state but for which nevertheless instantaneous forward motion of the free boundary occurs. This shows that the initial behaviour of the free boundary is not determined just by the growth of the initial data at the free boundary. Note that this is a new phenomenon for degenerate parabolic equations which is specific for higher-order equations. Furthermore, this result resolves a controversy in the literature over optimality of sufficient conditions for the occurrence of a waiting time phenomenon. In contrast, in the regime of very weak slippage we derive lower bounds on free boundary propagation which are optimal in the sense that they coincide up to a constant factor with the known upper bounds. In particular, in this regime the growth of the initial data at the free boundary fully determines the initial behaviour of the interface.},
author = {Julian Fischer},
journal = {Annales de l'Institut Henri Poincare (C) Non Linear Analysis},
number = {5},
pages = {1301 -- 1327},
publisher = {Elsevier},
title = {{Behaviour of free boundaries in thin-film flow: The regime of strong slippage and the regime of very weak slippage}},
doi = {10.1016/j.anihpc.2015.05.001},
volume = {33},
year = {2016},
}
@article{1318,
abstract = {We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coefficient case. This result can be seen as the qualitative side of a large-scale Ck,α-regularity theory, which in the present work is developed in the form of a corresponding Ck,α-“excess decay” estimate: For a given a-harmonic function u on a ball BR, its energy distance on some ball Br to the above space of a-harmonic functions that grow at most like a polynomial of degree k has the natural decay in the radius r above some minimal radius r0. Though motivated by stochastic homogenization, the contribution of this paper is of purely deterministic nature: We work under the assumption that for the given realization a of the coefficient field, the couple (φ, σ) of scalar and vector potentials of the harmonic coordinates, where φ is the usual corrector, grows sublinearly in a mildly quantified way. We then construct “kth-order correctors” and thereby the space of a-harmonic functions that grow at most like a polynomial of degree k, establish the above excess decay, and then the corresponding Liouville principle.},
author = {Julian Fischer and Otto, Felix},
journal = {Communications in Partial Differential Equations},
number = {7},
pages = {1108 -- 1148},
publisher = {Taylor & Francis},
title = {{A higher-order large scale regularity theory for random elliptic operators}},
doi = {10.1080/03605302.2016.1179318},
volume = {41},
year = {2016},
}
@inproceedings{1319,
abstract = {We present a novel optimization-based algorithm for the design and fabrication of customized, deformable input devices, capable of continuously sensing their deformation. We propose to embed piezoresistive sensing elements into flexible 3D printed objects. These sensing elements are then utilized to recover rich and natural user interactions at runtime. Designing such objects is a challenging and hard problem if attempted manually for all but the simplest geometries and deformations. Our method simultaneously optimizes the internal routing of the sensing elements and computes a mapping from low-level sensor readings to user-specified outputs in order to minimize reconstruction error. We demonstrate the power and flexibility of the approach by designing and fabricating a set of flexible input devices. Our results indicate that the optimization-based design greatly outperforms manual routings in terms of reconstruction accuracy and thus interaction fidelity.},
author = {Bächer, Moritz and Hepp, Benjamin and Pece, Fabrizio and Kry, Paul and Bickel, Bernd and Thomaszewski, Bernhard and Hilliges, Otmar},
location = {San Jose, California, USA},
pages = {3806 -- 3816},
publisher = {ACM},
title = {{DefSense: computational design of customized deformable input devices}},
doi = {10.1145/2858036.2858354},
year = {2016},
}
@inproceedings{1320,
abstract = {In recent years, several biomolecular systems have been shown to be scale-invariant (SI), i.e. to show the same output dynamics when exposed to geometrically scaled input signals (u → pu, p > 0) after pre-adaptation to accordingly scaled constant inputs. In this article, we show that SI systems-as well as systems invariant with respect to other input transformations-can realize nonlinear differential operators: when excited by inputs obeying functional forms characteristic for a given class of invariant systems, the systems' outputs converge to constant values directly quantifying the speed of the input.},
author = {Lang, Moritz and Sontag, Eduardo},
location = {Boston, MA, USA},
publisher = {IEEE},
title = {{Scale-invariant systems realize nonlinear differential operators}},
doi = {10.1109/ACC.2016.7526722},
volume = {2016-July},
year = {2016},
}
@article{1323,
abstract = {Mossy fiber synapses on CA3 pyramidal cells are 'conditional detonators' that reliably discharge postsynaptic targets. The 'conditional' nature implies that burst activity in dentate gyrus granule cells is required for detonation. Whether single unitary excitatory postsynaptic potentials (EPSPs) trigger spikes in CA3 neurons remains unknown. Mossy fiber synapses exhibit both pronounced short-term facilitation and uniquely large post-tetanic potentiation (PTP). We tested whether PTP could convert mossy fiber synapses from subdetonator into detonator mode, using a recently developed method to selectively and noninvasively stimulate individual presynaptic terminals in rat brain slices. Unitary EPSPs failed to initiate a spike in CA3 neurons under control conditions, but reliably discharged them after induction of presynaptic short-term plasticity. Remarkably, PTP switched mossy fiber synapses into full detonators for tens of seconds. Plasticity-dependent detonation may be critical for efficient coding, storage, and recall of information in the granule cell–CA3 cell network.},
author = {Vyleta, Nicholas and Borges Merjane, Carolina and Jonas, Peter M},
journal = {eLife},
publisher = {eLife Sciences Publications},
title = {{Plasticity-dependent, full detonation at hippocampal mossy fiber–CA3 pyramidal neuron synapses}},
doi = {10.7554/eLife.17977},
volume = {5},
year = {2016},
}