@inproceedings{3329, abstract = {We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance µ in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution shape P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. An alternative algorithm, based purely on rational arithmetic, answers the same deconstruction problem, up to an uncertainty parameter, and its running time depends on the parameter δ (in addition to the other input parameters: n, δ and the radius of the disk). If the input shape is found to be approximable, the rational-arithmetic algorithm also computes an approximate solution shape for the problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution shape P with at most one more vertex than a vertex-minimal one. Our study is motivated by applications from two different domains. However, since the offset operation has numerous uses, we anticipate that the reverse question that we study here will be still more broadly applicable. We present results obtained with our implementation of the rational-arithmetic algorithm.}, author = {Berberich, Eric and Halperin, Dan and Kerber, Michael and Pogalnikova, Roza}, booktitle = {Proceedings of the twenty-seventh annual symposium on Computational geometry}, location = {Paris, France}, pages = {187 -- 196}, publisher = {ACM}, title = {{Deconstructing approximate offsets}}, doi = {10.1145/1998196.1998225}, year = {2011}, } @inproceedings{3330, abstract = {We consider the problem of approximating all real roots of a square-free polynomial f. Given isolating intervals, our algorithm refines each of them to a width at most 2-L, that is, each of the roots is approximated to L bits after the binary point. Our method provides a certified answer for arbitrary real polynomials, only requiring finite approximations of the polynomial coefficient and choosing a suitable working precision adaptively. In this way, we get a correct algorithm that is simple to implement and practically efficient. Our algorithm uses the quadratic interval refinement method; we adapt that method to be able to cope with inaccuracies when evaluating f, without sacrificing its quadratic convergence behavior. We prove a bound on the bit complexity of our algorithm in terms of degree, coefficient size and discriminant. Our bound improves previous work on integer polynomials by a factor of deg f and essentially matches best known theoretical bounds on root approximation which are obtained by very sophisticated algorithms.}, author = {Kerber, Michael and Sagraloff, Michael}, location = {California, USA}, pages = {209 -- 216}, publisher = {Springer}, title = {{Root refinement for real polynomials}}, doi = {10.1145/1993886.1993920}, year = {2011}, } @article{3332, abstract = {Given an algebraic hypersurface O in ℝd, how many simplices are necessary for a simplicial complex isotopic to O? We address this problem and the variant where all vertices of the complex must lie on O. We give asymptotically tight worst-case bounds for algebraic plane curves. Our results gradually improve known bounds in higher dimensions; however, the question for tight bounds remains unsolved for d ≥ 3.}, author = {Kerber, Michael and Sagraloff, Michael}, journal = {Graphs and Combinatorics}, number = {3}, pages = {419 -- 430}, publisher = {Springer}, title = {{A note on the complexity of real algebraic hypersurfaces}}, doi = {10.1007/s00373-011-1020-7}, volume = {27}, year = {2011}, } @inbook{3335, abstract = {We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic. The richer information content of Betti numbers goes along the availability of fast algorithms to compute them. For continuous density fields, we determine the scale-dependence of Betti numbers by invoking the cosmologically familiar filtration of sublevel or superlevel sets defined by density thresholds. For the discrete galaxy distribution, however, the analysis is based on the alpha shapes of the particles. These simplicial complexes constitute an ordered sequence of nested subsets of the Delaunay tessellation, a filtration defined by the scale parameter, α. As they are homotopy equivalent to the sublevel sets of the distance field, they are an excellent tool for assessing the topological structure of a discrete point distribution. In order to develop an intuitive understanding for the behavior of Betti numbers as a function of α, and their relation to the morphological patterns in the Cosmic Web, we first study them within the context of simple heuristic Voronoi clustering models. These can be tuned to consist of specific morphological elements of the Cosmic Web, i.e. clusters, filaments, or sheets. To elucidate the relative prominence of the various Betti numbers in different stages of morphological evolution, we introduce the concept of alpha tracks. Subsequently, we address the topology of structures emerging in the standard LCDM scenario and in cosmological scenarios with alternative dark energy content. The evolution of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic Web. We also demonstrate that the scale-dependence of the Betti numbers yields a promising measure of cosmological parameters, with a potential to help in determining the nature of dark energy and to probe primordial non-Gaussianities. We also discuss the expected Betti numbers as a function of the density threshold for superlevel sets of a Gaussian random field. Finally, we introduce the concept of persistent homology. It measures scale levels of the mass distribution and allows us to separate small from large scale features. Within the context of the hierarchical cosmic structure formation, persistence provides a natural formalism for a multiscale topology study of the Cosmic Web.}, author = {Van De Weygaert, Rien and Vegter, Gert and Edelsbrunner, Herbert and Jones, Bernard and Pranav, Pratyush and Park, Changbom and Hellwing, Wojciech and Eldering, Bob and Kruithof, Nico and Bos, Patrick and Hidding, Johan and Feldbrugge, Job and Ten Have, Eline and Van Engelen, Matti and Caroli, Manuel and Teillaud, Monique}, booktitle = {Transactions on Computational Science XIV}, editor = {Gavrilova, Marina and Tan, Kenneth and Mostafavi, Mir}, pages = {60 -- 101}, publisher = {Springer}, title = {{Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web}}, doi = {10.1007/978-3-642-25249-5_3}, volume = {6970}, year = {2011}, } @unpublished{3338, abstract = {We consider 2-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves inde- pendently and simultaneously; the current state and the two moves determine the successor state. We study concurrent games with ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respec- tively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). We study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision or infinite- precision; and in terms of memory, strategies can be memoryless, finite-memory or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as power- ful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms, that are obtained by characterization of the winning sets as μ-calculus formulas, are considerably more involved than those for turn-based games.}, author = {Chatterjee, Krishnendu}, booktitle = {arXiv}, pages = {1 -- 51}, publisher = {ArXiv}, title = {{Bounded rationality in concurrent parity games}}, year = {2011}, } @unpublished{3339, abstract = {Turn-based stochastic games and its important subclass Markov decision processes (MDPs) provide models for systems with both probabilistic and nondeterministic behaviors. We consider turn-based stochastic games with two classical quantitative objectives: discounted-sum and long-run average objectives. The game models and the quantitative objectives are widely used in probabilistic verification, planning, optimal inventory control, network protocol and performance analysis. Games and MDPs that model realistic systems often have very large state spaces, and probabilistic abstraction techniques are necessary to handle the state-space explosion. The commonly used full-abstraction techniques do not yield space-savings for systems that have many states with similar value, but does not necessarily have similar transition structure. A semi-abstraction technique, namely Magnifying-lens abstractions (MLA), that clusters states based on value only, disregarding differences in their transition relation was proposed for qualitative objectives (reachability and safety objectives). In this paper we extend the MLA technique to solve stochastic games with discounted-sum and long-run average objectives. We present the MLA technique based abstraction-refinement algorithm for stochastic games and MDPs with discounted-sum objectives. For long-run average objectives, our solution works for all MDPs and a sub-class of stochastic games where every state has the same value. }, author = {Chatterjee, Krishnendu and De Alfaro, Luca and Pritam, Roy}, booktitle = {arXiv}, pages = {17}, publisher = {ArXiv}, title = {{Magnifying lens abstraction for stochastic games with discounted and long-run average objectives}}, year = {2011}, } @inproceedings{3342, abstract = {We consider Markov decision processes (MDPs) with ω-regular specifications given as parity objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. The algorithms for the computation of the almost-sure winning set for parity objectives iteratively use the solutions for the almost-sure winning set for Büchi objectives (a special case of parity objectives). Our contributions are as follows: First, we present the first subquadratic symbolic algorithm to compute the almost-sure winning set for MDPs with Büchi objectives; our algorithm takes O(nm) symbolic steps as compared to the previous known algorithm that takes O(n 2) symbolic steps, where n is the number of states and m is the number of edges of the MDP. In practice MDPs often have constant out-degree, and then our symbolic algorithm takes O(nn) symbolic steps, as compared to the previous known O(n 2) symbolic steps algorithm. Second, we present a new algorithm, namely win-lose algorithm, with the following two properties: (a) the algorithm iteratively computes subsets of the almost-sure winning set and its complement, as compared to all previous algorithms that discover the almost-sure winning set upon termination; and (b) requires O(nK) symbolic steps, where K is the maximal number of edges of strongly connected components (scc’s) of the MDP. The win-lose algorithm requires symbolic computation of scc’s. Third, we improve the algorithm for symbolic scc computation; the previous known algorithm takes linear symbolic steps, and our new algorithm improves the constants associated with the linear number of steps. In the worst case the previous known algorithm takes 5·n symbolic steps, whereas our new algorithm takes 4 ·n symbolic steps.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Joglekar, Manas and Nisarg, Shah}, editor = {Gopalakrishnan, Ganesh and Qadeer, Shaz}, location = {Snowbird, USA}, pages = {260 -- 276}, publisher = {Springer}, title = {{Symbolic algorithms for qualitative analysis of Markov decision processes with Büchi objectives}}, doi = {10.1007/978-3-642-22110-1_21}, volume = {6806}, year = {2011}, } @inproceedings{3343, abstract = {We present faster and dynamic algorithms for the following problems arising in probabilistic verification: Computation of the maximal end-component (mec) decomposition of Markov decision processes (MDPs), and of the almost sure winning set for reachability and parity objectives in MDPs. We achieve the following running time for static algorithms in MDPs with graphs of n vertices and m edges: (1) O(m · min{ √m, n2/3 }) for the mec decomposition, improving the longstanding O(m·n) bound; (2) O(m·n2/3) for reachability objectives, improving the previous O(m · √m) bound for m > n4/3; and (3) O(m · min{ √m, n2/3 } · log(d)) for parity objectives with d priorities, improving the previous O(m · √m · d) bound. We also give incremental and decremental algorithms in linear time for mec decomposition and reachability objectives and O(m · log d) time for parity ob jectives.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H}, location = {San Francisco, SA, United States}, pages = {1318 -- 1336}, publisher = {SIAM}, title = {{Faster and dynamic algorithms for maximal end-component decomposition and related graph problems in probabilistic verification}}, doi = {10.1137/1.9781611973082.101}, year = {2011}, } @article{11094, abstract = {Nuclear pore complexes (NPCs) assemble at the end of mitosis during nuclear envelope (NE) reformation and into an intact NE as cells progress through interphase. Although recent studies have shown that NPC formation occurs by two different molecular mechanisms at two distinct cell cycle stages, little is known about the molecular players that mediate the fusion of the outer and inner nuclear membranes to form pores. In this paper, we provide evidence that the transmembrane nucleoporin (Nup), POM121, but not the Nup107–160 complex, is present at new pore assembly sites at a time that coincides with inner nuclear membrane (INM) and outer nuclear membrane (ONM) fusion. Overexpression of POM121 resulted in juxtaposition of the INM and ONM. Additionally, Sun1, an INM protein that is known to interact with the cytoskeleton, was specifically required for interphase assembly and localized with POM121 at forming pores. We propose a model in which POM121 and Sun1 interact transiently to promote early steps of interphase NPC assembly.}, author = {Talamas, Jessica A. and HETZER, Martin W}, issn = {1540-8140}, journal = {Journal of Cell Biology}, keywords = {Cell Biology}, number = {1}, pages = {27--37}, publisher = {Rockefeller University Press}, title = {{POM121 and Sun1 play a role in early steps of interphase NPC assembly}}, doi = {10.1083/jcb.201012154}, volume = {194}, year = {2011}, } @article{112, abstract = {Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the stream\'s macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gaslike jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams.}, author = {Waitukaitis, Scott R and Grütjen, Helge and Royer, John and Jaeger, Heinrich}, journal = {Physical Review E}, number = {5}, publisher = {American Physical Society}, title = {{Droplet and cluster formation in freely falling granular streams}}, doi = {10.1103/PhysRevE.83.051302}, volume = {83}, year = {2011}, } @article{8025, abstract = {Chandelier (axoaxonic) cells (ChCs) are a distinct group of GABAergic interneurons that innervate the axon initial segments of pyramidal cells. However, their circuit role and the function of their clearly defined anatomical specificity remain unclear. Recent work has demonstrated that chandelier cells can produce depolarizing GABAergic PSPs, occasionally driving postsynaptic targets to spike. On the other hand, other work suggests that ChCs are hyperpolarizing and may have an inhibitory role. These disparate functional effects may reflect heterogeneity among ChCs. Here, using brain slices from transgenic mouse strains, we first demonstrate that, across different neocortical areas and genetic backgrounds, upper Layer 2/3 ChCs belong to a single electrophysiologically and morphologically defined population, extensively sampling Layer 1 inputs with asymmetric dendrites. Consistent with being a single cell type, we find electrical coupling between ChCs. We then investigate the effect of chandelier cell activation on pyramidal neuron spiking in several conditions, ranging from the resting membrane potential to stimuli designed to approximate in vivo membrane potential dynamics. We find that under quiescent conditions, chandelier cells are capable of both promoting and inhibiting spike generation, depending on the postsynaptic membrane potential. However, during in vivo-like membrane potential fluctuations, the dominant postsynaptic effect was a strong inhibition. Thus, neocortical chandelier cells, even from within a homogeneous population, appear to play a dual role in the circuit, helping to activate quiescent pyramidal neurons, while at the same time inhibiting active ones.}, author = {Woodruff, A. R. and McGarry, L. M. and Vogels, Tim P and Inan, M. and Anderson, S. A. and Yuste, R.}, issn = {0270-6474}, journal = {Journal of Neuroscience}, number = {49}, pages = {17872--17886}, publisher = {Society for Neuroscience}, title = {{State-dependent function of neocortical chandelier cells}}, doi = {10.1523/jneurosci.3894-11.2011}, volume = {31}, year = {2011}, } @article{1754, abstract = {We report on a technique enabling electrical control of the contact silicidation process in silicon nanowire devices. Undoped silicon nanowires were contacted by pairs of nickel electrodes and each contact was selectively silicided by means of the Joule effect. By a realtime monitoring of the nanowire electrical resistance during the contact silicidation process we were able to fabricate nickel-silicide/silicon/nickel- silicide devices with controlled silicon channel length down to 8 nm. }, author = {Mongillo, Massimo and Spathis, Panayotis and Katsaros, Georgios and Gentile, Pascal and Sanquer, Marc and De Franceschi, Silvano}, journal = {ACS Nano}, number = {9}, pages = {7117 -- 7123}, publisher = {American Chemical Society}, title = {{Joule-assisted silicidation for short-channel silicon nanowire devices}}, doi = {10.1021/nn202524j}, volume = {5}, year = {2011}, } @article{1755, abstract = {Spin-selective tunneling of holes in SiGe nanocrystals contacted by normal-metal leads is reported. The spin selectivity arises from an interplay of the orbital effect of the magnetic field with the strong spin-orbit interaction present in the valence band of the semiconductor. We demonstrate both experimentally and theoretically that spin-selective tunneling in semiconductor nanostructures can be achieved without the use of ferromagnetic contacts. The reported effect, which relies on mixing the light and heavy holes, should be observable in a broad class of quantum-dot systems formed in semiconductors with a degenerate valence band.}, author = {Georgios Katsaros and Golovach, Vitaly N and Spathis, Panayotis N and Ares, Natalia and Stoffel, Mathieu and Fournel, Frank and Schmidt, Oliver G and Glazman, Leonid I and De Franceschi, Silvano}, journal = {Physical Review Letters}, number = {24}, publisher = {American Physical Society}, title = {{Observation of spin-selective tunneling in sige nanocrystals}}, doi = {10.1103/PhysRevLett.107.246601}, volume = {107}, year = {2011}, } @article{1777, abstract = {A wide range of experiments studying microwave photons localized in superconducting cavities have made important contributions to our understanding of the quantum properties of radiation. Propagating microwave photons, however, have so far been studied much less intensely. Here we present measurements in which we reconstruct the quantum state of itinerant single photon Fock states and their superposition with the vacuum by analyzing moments of the measured amplitude distribution up to fourth order. Using linear amplifiers and quadrature amplitude detectors, we have developed efficient methods to separate the detected single photon signal from the noise added by the amplifier. From our measurement data we have also reconstructed the corresponding Wigner function.}, author = {Eichler, Christopher and Bozyigit, Deniz and Lang, C and Steffen, L. and Fink, Johannes M and Wallraff, Andreas}, journal = {Physical Review Letters}, number = {22}, publisher = {American Physical Society}, title = {{Experimental state tomography of itinerant single microwave photons}}, doi = {10.1103/PhysRevLett.106.220503}, volume = {106}, year = {2011}, } @article{1778, abstract = {Creating a train of single photons and monitoring its propagation and interaction is challenging in most physical systems, as photons generally interact very weakly with other systems. However, when confining microwave frequency photons in a transmission line resonator, effective photon-photon interactions can be mediated by qubits embedded in the resonator. Here, we observe the phenomenon of photon blockade through second-order correlation function measurements. The experiments clearly demonstrate antibunching in a continuously pumped source of single microwave photons measured by using microwave beam splitters, linear amplifiers, and quadrature amplitude detectors. We also investigate resonance fluorescence and Rayleigh scattering in Mollow-triplet-like spectra.}, author = {Lang, C and Bozyigit, Deniz and Eichler, Christopher and Steffen, L. Kraig and Johannes Fink and Abdumalikov, Abdufarrukh A and Baur, Matthias P and Filipp, Stefan and Da Silva, Marcus P and Blais, Alexandre and Wallraff, Andreas}, journal = {Physical Review Letters}, number = {24}, publisher = {American Physical Society}, title = {{Observation of resonant photon blockade at microwave frequencies using correlation function measurements}}, doi = {10.1103/PhysRevLett.106.243601}, volume = {106}, year = {2011}, } @article{1815, abstract = {Many membrane channels and receptors exhibit adaptive, or desensitized, response to a strong sustained input stimulus, often supported by protein activity-dependent inactivation. Adaptive response is thought to be related to various cellular functions such as homeostasis and enlargement of dynamic range by background compensation. Here we study the quantitative relation between adaptive response and background compensation within a modeling framework. We show that any particular type of adaptive response is neither sufficient nor necessary for adaptive enlargement of dynamic range. In particular a precise adaptive response, where system activity is maintained at a constant level at steady state, does not ensure a large dynamic range neither in input signal nor in system output. A general mechanism for input dynamic range enlargement can come about from the activity-dependent modulation of protein responsiveness by multiple biochemical modification, regardless of the type of adaptive response it induces. Therefore hierarchical biochemical processes such as methylation and phosphorylation are natural candidates to induce this property in signaling systems.}, author = {Tamar Friedlander and Brenner, Naama}, journal = {Mathematical Biosciences and Engineering}, number = {2}, pages = {515 -- 526}, publisher = {Arizona State University}, title = {{Adaptive response and enlargement of dynamic range}}, doi = {10.3934/mbe.2011.8.515}, volume = {8}, year = {2011}, } @article{2072, abstract = {Many species have morphologically and genetically differentiated sex chromosomes, such as the XY pair of mammals. Y chromosomes are often highly degenerated and carry few functional genes, so that XY males have only one copy of most Xlinked genes (whereas females have two). As a result, chromosome-wide mechanisms of dosage compensation, such as the mammalian X-inactivation, often evolve to reestablish expression balance. A similar phenomenon is expected in femaleheterogametic species, where ZW females should suffer from imbalances due to W-chromosome degeneration. However, no global dosage compensation mechanisms have been detected in the two independent ZW systems that have been studied systematically (birds and silkworm), leading to the suggestion that lack of global dosage compensation may be a general feature of female-heterogametic species. However, analyses of other independently evolved ZW systems are required to test if this is the case. In this study, we use published genomic and expression data to test for the presence of global dosage compensation in Schistosoma mansoni, a trematode parasite that causes schistosomiasis in humans. We find that Z-linked expression is reduced relative to autosomal expression in females but not males, consistent with incomplete or localized dosage compensation. This gives further support to the theory that female-heterogametic species may not require global mechanisms of dosage compensation.}, author = {Vicoso, Beatriz and Bachtrog, Doris}, journal = {Genome Biology and Evolution}, number = {1}, pages = {230 -- 235}, publisher = {Oxford University Press}, title = {{Lack of global dosage compensation in Schistosoma mansoni, a female-heterogametic parasite}}, doi = {10.1093/gbe/evr010}, volume = {3}, year = {2011}, } @inbook{2116, abstract = {Let P be the Ornstein-Uhlenbeck semigroup associated with the stochastic Cauchy problem dU(t)=AU(t)dt+dWH(t), where A is the generator of a C 0-semigroup S on a Banach space E, H is a Hilbert subspace of E, and W H is an H-cylindrical Brownian motion. Assuming that S restricts to a C 0-semigroup on H, we obtain L p -bounds for D H P(t). We show that if P is analytic, then the invariance assumption is fulfilled. As an application we determine the L p -domain of the generator of P explicitly in the case where S restricts to a C 0-semigroup on H which is similar to an analytic contraction semigroup. The results are applied to the 1D stochastic heat equation driven by additive space-time white noise.}, author = {Jan Maas and Van Neerven, Jan}, booktitle = {Parabolic Problems}, pages = {463 -- 477}, publisher = {Birkhäuser}, title = {{Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators}}, doi = {10.1007/978-3-0348-0075-4_24}, volume = {80}, year = {2011}, } @article{2122, abstract = {We study, in L1(R̃n; γ) with respect to the gaussian measure, non- tangential maximal functions and conical square functions associ- ated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in L1-norm by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda.}, author = {Jan Maas and van Neerven, Jan M and Portal, Pierre}, journal = {Publicacions Matemàtiques}, number = {2}, pages = {313 -- 341}, publisher = {Universitat Autònoma de Barcelona, Departament de Matemàtique}, title = {{Conical square functions and non-tangential maximal functions with respect to the Gaussian measure}}, doi = {10.5565/PUBLMAT_55211_03 }, volume = {55}, year = {2011}, } @article{2123, abstract = {We prove a Trotter product formula for gradient flows in metric spaces. This result is applied to establish convergence in the L 2-Wasserstein metric of the splitting method for some Fokker-Planck equations and porous medium type equations perturbed by a potential.}, author = {Clément, Philippe and Maas, Jan}, journal = {Journal of Evolution Equations}, number = {2}, pages = {405 -- 427}, publisher = {Birkhäuser}, title = {{A Trotter product formula for gradient flows in metric spaces}}, doi = {10.1007/s00028-010-0096-5}, volume = {11}, year = {2011}, }