TY - JOUR AB - Recent experiments have shown that motion detection in Drosophila starts with splitting the visual input into two parallel channels encoding brightness increments (ON) or decrements (OFF). This suggests the existence of either two (ON-ON, OFF-OFF) or four (for all pairwise interactions) separate motion detectors. To decide between these possibilities, we stimulated flies using sequences of ON and OFF brightness pulses while recording from motion-sensitive tangential cells. We found direction-selective responses to sequences of same sign (ON-ON, OFF-OFF), but not of opposite sign (ON-OFF, OFF-ON), refuting the existence of four separate detectors. Based on further measurements, we propose a model that reproduces a variety of additional experimental data sets, including ones that were previously interpreted as support for four separate detectors. Our experiments and the derived model mark an important step in guiding further dissection of the fly motion detection circuit. AU - Eichner, Hubert AU - Maximilian Jösch AU - Schnell, Bettina AU - Reiff, Dierk F AU - Borst, Alexander ID - 1299 IS - 6 JF - Neuron TI - Internal structure of the fly elementary motion detector VL - 70 ER - TY - JOUR AB - We propose a general conjecture for the mixed Hodge polynomial of the generic character varieties of representations of the fundamental group of a Riemann surface of genus g to GLn(C) with fixed generic semisimple conjugacy classes at k punctures. This conjecture generalizes the Cauchy identity for Macdonald polynomials and is a common generalization of two formulas that we prove in this paper. The first is a formula for the E-polynomial of these character varieties which we obtain using the character table of GLn(Fq). We use this formula to compute the Euler characteristic of character varieties. The second formula gives the Poincaré polynomial of certain associated quiver varieties which we obtain using the character table of gln(Fq). In the last main result we prove that the Poincaré polynomials of the quiver varieties equal certain multiplicities in the tensor product of irreducible characters of GLn(Fq). As a consequence we find a curious connection between Kac-Moody algebras associated with comet-shaped, and typically wild, quivers and the representation theory of GLn(Fq). AU - Tamas Hausel AU - Letellier, Emmanuel AU - Rodríguez Villegas, Fernando ID - 1467 IS - 2 JF - Duke Mathematical Journal TI - Arithmetic harmonic analysis on character and quiver varieties VL - 160 ER - TY - JOUR AB - The emergence of differences in the arrangement of cells is the first step towards the establishment of many organs. Understanding this process is limited by the lack of systematic characterization of epithelial organisation. Here we apply network theory at the scale of individual cells to uncover patterns in cell-to-cell contacts that govern epithelial organisation. We provide an objective characterisation of epithelia using network representation, where cells are nodes and cell contacts are links. The features of individual cells, together with attributes of the cellular network, produce a defining signature that distinguishes epithelia from different organs, species, developmental stages and genetic conditions. The approach permits characterization, quantification and classification of normal and perturbed epithelia, and establishes a framework for understanding molecular mechanisms that underpin the architecture of complex tissues. AU - Escudero, Luis M AU - Costa, Luciano AU - Anna Kicheva AU - Briscoe, James AU - Freeman, Matthew AU - Babu, Madan M ID - 1723 IS - 1 JF - Nature Communications TI - Epithelial organisation revealed by a network of cellular contacts VL - 2 ER - TY - JOUR AB - Morphogens, such as Decapentaplegic (Dpp) in the fly imaginal discs, form graded concentration profiles that control patterning and growth of developing organs. In the imaginal discs, proliferative growth is homogeneous in space, posing the conundrum of how morphogen concentration gradients could control position-independent growth. To understand the mechanism of proliferation control by the Dpp gradient, we quantified Dpp concentration and signaling levels during wing disc growth. Both Dpp concentration and signaling gradients scale with tissue size during development. On average, cells divide when Dpp signaling levels have increased by 50%. Our observations are consistent with a growth control mechanism based on temporal changes of cellular morphogen signaling levels. For a scaling gradient, this mechanism generates position-independent growth rates. AU - Wartlick, Ortrud AU - Mumcu, Peer AU - Anna Kicheva AU - Bittig, Thomas AU - Seum, Carole AU - Jülicher, Frank AU - González-Gaitán, Marcos A ID - 1724 IS - 6021 JF - Science TI - Dynamics of Dpp signaling and proliferation control VL - 331 ER - TY - JOUR AB - 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. AU - Mongillo, Massimo AU - Spathis, Panayotis AU - Katsaros, Georgios AU - Gentile, Pascal AU - Sanquer, Marc AU - De Franceschi, Silvano ID - 1754 IS - 9 JF - ACS Nano TI - Joule-assisted silicidation for short-channel silicon nanowire devices VL - 5 ER - TY - JOUR AB - 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. AU - Georgios Katsaros AU - Golovach, Vitaly N AU - Spathis, Panayotis N AU - Ares, Natalia AU - Stoffel, Mathieu AU - Fournel, Frank AU - Schmidt, Oliver G AU - Glazman, Leonid I AU - De Franceschi, Silvano ID - 1755 IS - 24 JF - Physical Review Letters TI - Observation of spin-selective tunneling in sige nanocrystals VL - 107 ER - TY - CONF AB - Superconducting circuits have been successfully established as systems to prepare and investigate microwave light fields at the quantum level. In contrast to optical experiments where light is detected using photon counters, microwaves are usually measured with well developed linear amplifiers. This makes measurements of correlation functions - one of the important tools in optics - harder to achieve because they traditionally rely on photon counters and beam splitters. Here, we demonstrate a system where we can prepare on demand single microwave photons in a cavity and detect them at the two outputs of the cavity using linear amplifiers. Together with efficient data processing, this allows us to measure different observables of the cavity photons, including the first-order correlation function. Using these techniques we demonstrate cooling of a thermal background field in the cavity. AU - Bozyigit, Deniz AU - Lang, C AU - Steffen, L. Kraig AU - Johannes Fink AU - Eichler, Christopher AU - Baur, Matthias P AU - Bianchetti, R AU - Leek, Peter J AU - Filipp, Stefan AU - Wallraff, Andreas AU - Da Silva, Marcus P AU - Blais, Alexandre ID - 1776 IS - 1 TI - Correlation measurements of individual microwave photons emitted from a symmetric cavity VL - 264 ER - TY - JOUR AB - 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. AU - Eichler, Christopher AU - Bozyigit, Deniz AU - Lang, C AU - Steffen, L. AU - Fink, Johannes M AU - Wallraff, Andreas ID - 1777 IS - 22 JF - Physical Review Letters TI - Experimental state tomography of itinerant single microwave photons VL - 106 ER - TY - JOUR AB - 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. AU - Lang, C AU - Bozyigit, Deniz AU - Eichler, Christopher AU - Steffen, L. Kraig AU - Johannes Fink AU - Abdumalikov, Abdufarrukh A AU - Baur, Matthias P AU - Filipp, Stefan AU - Da Silva, Marcus P AU - Blais, Alexandre AU - Wallraff, Andreas ID - 1778 IS - 24 JF - Physical Review Letters TI - Observation of resonant photon blockade at microwave frequencies using correlation function measurements VL - 106 ER - TY - JOUR AB - At optical frequencies the radiation produced by a source, such as a laser, a black body or a single-photon emitter, is frequently characterized by analysing the temporal correlations of emitted photons using single-photon counters. At microwave frequencies, however, there are no efficient single-photon counters yet. Instead, well-developed linear amplifiers allow for efficient measurement of the amplitude of an electromagnetic field. Here, we demonstrate first- and second-order correlation function measurements of a pulsed microwave-frequency single-photon source integrated on the same chip with a 50/50 beam splitter followed by linear amplifiers and quadrature amplitude detectors. We clearly observe single-photon coherence in first-order and photon antibunching in second-order correlation function measurements of the propagating fields. AU - Bozyigit, Deniz AU - Lang, C AU - Steffen, L. Kraig AU - Johannes Fink AU - Eichler, Christopher AU - Baur, Matthias P AU - Bianchetti, R AU - Leek, Peter J AU - Filipp, Stefan AU - Da Silva, Marcus P AU - Blais, Alexandre AU - Wallraff, Andreas ID - 1775 IS - 2 JF - Nature Physics TI - Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors VL - 7 ER - TY - JOUR AB - Microwave cavities with high quality factors enable coherent coupling of distant quantum systems. Virtual photons lead to a transverse interaction between qubits when they are nonresonant with the cavity but resonant with each other. We experimentally investigate the inverse scaling of the interqubit coupling with the detuning from a cavity mode and its proportionality to the qubit-cavity interaction strength. We demonstrate that the enhanced coupling at higher frequencies is mediated by multiple higher-harmonic cavity modes. Moreover, we observe dark states of the coupled qubit-qubit system and analyze their relation to the symmetry of the applied driving field at different frequencies. AU - Filipp, Stefan AU - Göppl, M AU - Johannes Fink AU - Baur, Matthias P AU - Bianchetti, R AU - Steffen, L. Kraig AU - Wallraff, Andreas ID - 1781 IS - 6 JF - Physical Review A - Atomic, Molecular, and Optical Physics TI - Multimode mediated qubit-qubit coupling and dark-state symmetries in circuit quantum electrodynamics VL - 83 ER - TY - JOUR AB - Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. Here we demonstrate experiments that show the entanglement between microwave photons of different energy in a broadband squeezed beam. We use a Josephson parametric amplifier to generate the two-mode correlated state and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix, which is in good agreement with the one expected for a two-mode squeezed state. AU - Eichler, Christopher AU - Bozyigit, Deniz AU - Lang, C AU - Baur, Matthias P AU - Steffen, L. Kraig AU - Johannes Fink AU - Filipp, Stefan AU - Wallraff, Andreas ID - 1780 IS - 11 JF - Physical Review Letters TI - Observation of two-mode squeezing in the microwave frequency domain VL - 107 ER - TY - JOUR AB - 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. AU - Tamar Friedlander AU - Brenner, Naama ID - 1815 IS - 2 JF - Mathematical Biosciences and Engineering TI - Adaptive response and enlargement of dynamic range VL - 8 ER - TY - JOUR AB - The Levene model is the simplest mathematical model to describe the evolution of gene frequencies in spatially subdivided populations. It provides insight into how locally varying selection promotes a population’s genetic diversity. Despite its simplicity, interesting problems have remained unsolved even in the diallelic case. In this paper we answer an open problem by establishing that for two alleles at one locus and J demes, up to 2J−1 polymorphic equilibria may coexist. We first present a proof for the case of stable monomorphisms and then show that the result also holds for protected alleles. These findings allow us to prove that any odd number (up to 2J−1) of equilibria is possible, before we extend the proof to even numbers. We conclude with some numerical results and show that for J>2, the proportion of parameter space affording this maximum is extremely small. AU - Sebastian Novak ID - 1863 IS - 3 JF - Theoretical Population Biology TI - The number of equilibria in the diallelic Levene model with multiple demes VL - 79 ER - TY - JOUR AB - Modern α-proteobacteria are thought to be closely related to the ancient symbiont of eukaryotes, an ancestor of mitochondria. Respiratory complex I from α-proteobacteria and mitochondria is well conserved at the level of the 14 "core" subunits, consistent with that notion. Mitochondrial complex I contains the core subunits, present in all species, and up to 31 "supernumerary" subunits, generally thought to have originated only within eukaryotic lineages. However, the full protein composition of an α-proteobacterial complex I has not been established previously. Here, we report the first purification and characterization of complex I from the α-proteobacterium Paracoccus denitrificans. Single particle electron microscopy shows that the complex has a well defined L-shape. Unexpectedly, in addition to the 14 core subunits, the enzyme also contains homologues of three supernumerary mitochondrial subunits as follows: B17.2, AQDQ/18, and 13 kDa (bovine nomenclature). This finding suggests that evolution of complex I via addition of supernumerary or "accessory" subunits started before the original endosymbiotic event that led to the creation of the eukaryotic cell. It also provides further confirmation that α-proteobacteria are the closest extant relatives of mitochondria. AU - Yip, Chui Y AU - Harbour, Michael E AU - Jayawardena, Kamburapola G AU - Fearnley, Ian M AU - Leonid Sazanov ID - 1975 IS - 7 JF - Journal of Biological Chemistry TI - Evolution of respiratory complex I "Supernumerary" subunits are present in the α-proteobacterial enzyme VL - 286 ER - TY - JOUR AB - Complex I is the first and largest enzyme of the respiratory chain, coupling electron transfer between NADH and ubiquinone to the translocation of four protons across the membrane. It has a central role in cellular energy production and has been implicated in many human neurodegenerative diseases. The L-shaped enzyme consists of hydrophilic and membrane domains. Previously, we determined the structure of the hydrophilic domain. Here we report the crystal structure of the Esherichia coli complex I membrane domain at 3.0 Ã. resolution. It includes six subunits, NuoL, NuoM, NuoN, NuoA, NuoJ and NuoK, with 55 transmembrane helices. The fold of the homologous antiporter-like subunits L, M and N is novel, with two inverted structural repeats of five transmembrane helices arranged, unusually, face-to-back. Each repeat includes a discontinuous transmembrane helix and forms half of a channel across the membrane. A network of conserved polar residues connects the two half-channels, completing the proton translocation pathway. Unexpectedly, lysines rather than carboxylate residues act as the main elements of the proton pump in these subunits. The fourth probable proton-translocation channel is at the interface of subunits N, K, J and A. The structure indicates that proton translocation in complex I, uniquely, involves coordinated conformational changes in six symmetrical structural elements. AU - Efremov, Rouslan G AU - Leonid Sazanov ID - 1973 IS - 7361 JF - Nature TI - Structure of the membrane domain of respiratory complex i VL - 476 ER - TY - JOUR AB - Complex I is the first enzyme of the respiratory chain and plays a central role in cellular energy production. It has been implicated in many human neurodegenerative diseases, as well as in ageing. One of the biggest membrane protein complexes, it is an L-shaped assembly consisting of hydrophilic and membrane domains. Previously, we have determined structures of the hydrophilic domain in several redox states. Last year was marked by fascinating breakthroughs in the understanding of the complete structure. We described the architecture of the membrane domain and of the entire bacterial complex I. X-ray analysis of the larger mitochondrial enzyme has also been published. The core subunits of the bacterial and mitochondrial enzymes have remarkably similar structures. The proposed mechanism of coupling between electron transfer and proton translocation involves long-range conformational changes, coordinated in part by a long α-helix, akin to the coupling rod of a steam engine. AU - Efremov, Rouslan G AU - Leonid Sazanov ID - 1974 IS - 4 JF - Current Opinion in Structural Biology TI - Respiratory complex I: 'steam engine' of the cell? VL - 21 ER - TY - JOUR AB - In Escherichia coli, the pole-to-pole oscillation of the Min proteins directs septum formation to midcell, which is required for symmetric cell division. In vitro, protein waves emerge from the self-organization of MinD, a membrane-binding ATPase, and its activator MinE. For wave propagation, the proteins need to cycle through states of collective membrane binding and unbinding. Although MinD presumably undergoes cooperative membrane attachment, it is unclear how synchronous detachment is coordinated. We used confocal and single-molecule microscopy to elucidate the order of events during Min wave propagation. We propose that protein detachment at the rear of the wave, and the formation of the E-ring, are accomplished by two complementary processes: first, local accumulation of MinE due to rapid rebinding, leading to dynamic instability; and second, a structural change induced by membrane-interaction of MinE in an equimolar MinD-MinE (MinDE) complex, which supports the robustness of pattern formation. AU - Martin Loose AU - Fischer-Friedrich, Elisabeth AU - Herold, Christoph AU - Kruse, Karsten AU - Schwille, Petra ID - 1985 IS - 5 JF - Nature Structural and Molecular Biology TI - Min protein patterns emerge from rapid rebinding and membrane interaction of MinE VL - 18 ER - TY - JOUR AB - One of the most fundamental features of biological systems is probably their ability to self-organize in space and time on different scales. Despite many elaborate theoretical models of how molecular self-organization can come about, only a few experimental systems of biological origin have so far been rigorously described, due mostly to their inherent complexity. The most promising strategy of modern biophysics is thus to identify minimal biological systems showing self-organized emergent behavior. One of the best-understood examples of protein self-organization, which has recently been successfully reconstituted in vitro, is represented by the oscillations of the Min proteins in Escherichia coli. In this review, we summarize the current understanding of the mechanism of Min protein self-organization in vivo and in vitro. We discuss the potential of the Min oscillations to sense the geometry of the cell and suggest that spontaneous protein waves could be a general means of intracellular organization. We hypothesize that cooperative membrane binding and unbinding, e.g., as an energy-dependent switch, may act as an important regulatory mechanism for protein oscillations and pattern formation in the cell. AU - Martin Loose AU - Kruse, Karsten AU - Schwille, Petra ID - 1986 IS - 1 JF - Annual Review of Biophysics TI - Protein self-organization: Lessons from the min system VL - 40 ER - TY - JOUR AB - 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. AU - Vicoso, Beatriz AU - Bachtrog, Doris ID - 2072 IS - 1 JF - Genome Biology and Evolution TI - Lack of global dosage compensation in Schistosoma mansoni, a female-heterogametic parasite VL - 3 ER - TY - JOUR AB - We present a new technique for passive and markerless facial performance capture based on anchor frames. Our method starts with high resolution per-frame geometry acquisition using state-of-theart stereo reconstruction, and proceeds to establish a single triangle mesh that is propagated through the entire performance. Leveraging the fact that facial performances often contain repetitive subsequences, we identify anchor frames as those which contain similar facial expressions to a manually chosen reference expression. Anchor frames are automatically computed over one or even multiple performances. We introduce a robust image-space tracking method that computes pixel matches directly from the reference frame to all anchor frames, and thereby to the remaining frames in the sequence via sequential matching. This allows us to propagate one reconstructed frame to an entire sequence in parallel, in contrast to previous sequential methods. Our anchored reconstruction approach also limits tracker drift and robustly handles occlusions and motion blur. The parallel tracking and mesh propagation offer low computation times. Our technique will even automatically match anchor frames across different sequences captured on different occasions, propagating a single mesh to all performances. AU - Beeler, Thabo AU - Hahn, Fabian AU - Bradley, Derek J AU - Bernd Bickel AU - Beardsley, Paul A AU - Gotsman, Craig AU - Sumner, Robert W AU - Groß, Markus S ID - 2099 IS - 4 JF - ACM Transactions on Graphics TI - High-quality passive facial performance capture using anchor frames VL - 30 ER - TY - CHAP AB - This chapter presents a method for real-time animation of highly detailed facial expressions based on sparse motion captures data and a limited set of static example poses. The method for real-time animation of highly detailed facial expressions decomposes geometry into large-scale motion and fine-scale details, such as expression wrinkles. Both large- and fine-scale deformation algorithms run entirely on the GPU, and our implementation based on CUDA achieves an overall performance of about 30 fps. The face conveys the most relevant visual characteristics of human identity and expression. Hence, realistic facial animations or interactions with virtual avatars are important for storytelling and gameplay. However, current approaches are either computationally expensive, require very specialized capture hardware, or are extremely labor intensive. At runtime, given an arbitrary facial expression, the algorithm computes the skin strain from the relative distance between marker points and derives fine-scale corrections for the largescale deformation. During gameplay only the sparse set of marker-point positions is transmitted to the GPU. The face animation is entirely computed on the GPU where the resulting mesh can directly be used as input for the rendering stages. This data can be easily obtained by traditional capture hardware. The proposed in-game algorithm is fast. It also is easy to implement and maps well onto programmable GPUs. AU - Bernd Bickel AU - Lang, Manuel ID - 2098 T2 - GPU Computing Gems Emerald Edition TI - From sparse mocap to highly detailed facial animation ER - TY - CONF AB - Acquiring panoramic images using stitching takes a lot of time and moving objects may cause ghosting. It is also difficult to obtain a full spherical panorama, because the downward picture cannot be captured while the camera is mounted on the tripod. AU - Pfeil, Jonas AU - Hildebrand, Kristian AU - Gremzow, Carsten AU - Bernd Bickel AU - Alexa, Marc ID - 2100 TI - Throwable panoramic ball camera ER - TY - CHAP AB - 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. AU - Jan Maas AU - Van Neerven, Jan ID - 2116 T2 - Parabolic Problems TI - Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators VL - 80 ER - TY - JOUR AB - 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. AU - Jan Maas AU - van Neerven, Jan M AU - Portal, Pierre ID - 2122 IS - 2 JF - Publicacions Matemàtiques TI - Conical square functions and non-tangential maximal functions with respect to the Gaussian measure VL - 55 ER - TY - JOUR AB - 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. AU - Clément, Philippe AU - Maas, Jan ID - 2123 IS - 2 JF - Journal of Evolution Equations TI - A Trotter product formula for gradient flows in metric spaces VL - 11 ER - TY - JOUR AB - Let K be an irreducible and reversible Markov kernel on a finite set X. We construct a metric W on the set of probability measures on X and show that with respect to this metric, the law of the continuous time Markov chain evolves as the gradient flow of the entropy. This result is a discrete counterpart of the Wasserstein gradient flow interpretation of the heat flow in Rn by Jordan, Kinderlehrer and Otto (1998). The metric W is similar to, but different from, the L2-Wasserstein metric, and is defined via a discrete variant of the Benamou–Brenier formula. AU - Jan Maas ID - 2126 IS - 8 JF - Journal of Functional Analysis TI - Gradient flows of the entropy for finite Markov chains VL - 261 ER - TY - GEN AB - A (diatomic) shape resonance is a metastable state of a pair of colliding atoms quasi-bound by the centrifugal barrier imposed by the angular momentum involved in the collision. The temporary trapping of the atoms' scattering wavefunction corresponds to an enhanced atom pair density at low interatomic separations. This leads to larger overlap of the wavefunctions involved in a molecule formation process such as photoassociation, rendering the process more efficient. However, for an ensemble of atoms, the atom pair density will only be enhanced if the energy of the resonance comes close to the temperature of the atomic ensemble. Herein we explore the possibility of controlling the energy of a shape resonance by shifting it toward the temperature of atoms confined in a trap. The shifts are imparted by the interaction of non-resonant light with the anisotropic polarizability of the atom pair, which affects both the centrifugal barrier and the pair's rotational and vibrational levels. We find that at laser intensities of up to 5×109 W/cm2 the pair density is increased by one order of magnitude for 87Rb atoms at 100μK and by two orders of magnitude for 88Sr atoms at 20μK. AU - Ağanoğlu, Ruzin AU - Mikhail Lemeshko AU - Friedrich, Břetislav AU - González-Férez, Rosario AU - Koch, Christiane P ID - 2138 T2 - Unknown TI - Controlling a diatomic shape resonance with non-resonant light ER - TY - JOUR AB - We made use of supersymmetric (SUSY) quantum mechanics to find the condition under which the Stark effect problem for a polar and polarizable closed-shell diatomic molecule subjected to collinear electrostatic and nonresonant radiative fields becomes exactly solvable. The condition Δω = ω2/4(m+1)2 connects values of the dimensionless parameters ω and Δω that characterize the strengths of the permanent and induced dipole interactions of the molecule with the respective fields. The exact solutions are obtained for the \J̃ = m, m; ω, Δω) family of 'stretched' states. The field-free and strong-field limits of the combined-fields problem were found to exhibit supersymmetry and shape invariance, which is indeed the reason why they are analytically solvable. By making use of the analytic form of the \J̃ = m,m; ω, Δω) wavefunctions, we obtained simple formulae for the expectation values of the space-fixed electric dipole moment, the alignment cosine and the angular momentum squared, and derived a 'sum rule' that combines the above expectation values into a formula for the eigenenergy. The analytic expressions for the characteristics of the strongly oriented and aligned states provide direct access to the values of the interaction parameters required for creating such states in the laboratory. AU - Mikhail Lemeshko AU - Mustafa, Mustafa K AU - Kais, Sabre AU - Friedrich, Břetislav ID - 2200 JF - New Journal of Physics TI - Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically VL - 13 ER - TY - JOUR AB - By invoking supersymmetry, we found a condition under which the Stark-effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable for the family of stretched states. The analytic expressions for the wave function and eigenenergy and other expectation values allow one to readily reverse-engineer the problem of finding the values of the interaction parameters required for creating quantum states with preordained characteristics. The method also allows the construction of families of isospectral potentials, realizable with combined fields. AU - Mikhail Lemeshko AU - Mustafa, Mustafa K AU - Kais, Sabre AU - Friedrich, Břetislav ID - 2199 IS - 4 JF - Physical Review A - Atomic, Molecular, and Optical Physics TI - Supersymmetric factorization yields exact solutions to the molecular Stark-effect problem for "stretched" states VL - 83 ER - TY - JOUR AB - We show that dressing polar molecules with a far-off-resonant optical field leads to new types of intermolecular potentials, which undergo a crossover from the inverse power to oscillating behavior depending on the intermolecular distance, and whose parameters can be tuned by varying the laser intensity and wavelength. We present analytic expressions for the potential energy surfaces, thereby providing direct access to the parameters of an optical field required to design intermolecular interactions experimentally. AU - Mikhail Lemeshko ID - 2198 IS - 5 JF - Physical Review A - Atomic, Molecular, and Optical Physics TI - Shaping interactions between polar molecules with far-off-resonant light VL - 83 ER - TY - GEN AB - Soon, the genetic basis of most human Mendelian diseases will be solved. The next challenge will be to leverage this information to uncover basic mechanisms of disease and develop new therapies. To understand how this transformation is already beginning to unfold, we focus on the ciliopathies, a class of multi-organ diseases caused by disruption of the primary cilium. Through a convergence of data involving mutant gene discovery, proteomics, and cell biology, more than a dozen phenotypically distinguishable conditions are now united as ciliopathies. Sitting at the interface between simple and complex genetic conditions, these diseases provide clues to the future direction of human genetics. AU - Gaia Novarino AU - Akizu, Naiara AU - Gleeson, Joseph G ID - 2312 IS - 1 T2 - Cell TI - Modeling human disease in humans: The ciliopathies VL - 147 ER - TY - CONF AB - The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U = 2α, where U is the electronic Coulomb repulsion and α is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large α. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross. AU - Frank, Rupert L AU - Lieb, Élliott H AU - Robert Seiringer AU - Thomas, Lawrence E ID - 2320 TI - Binding, stability, and non-binding of multi-polaron systems ER - TY - CONF AB - We derive a sharp bound on the location of non-positive eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. AU - Frank, Rupert L AU - Laptev, Ari AU - Robert Seiringer ID - 2321 TI - A sharp bound on eigenvalues of Schrödinger operators on the halfline with complex-valued potentials VL - 214 ER - TY - JOUR AB - For an irreducible polynomial in at most two variables the problem of representing power-free integers is investigated. AU - Timothy Browning ID - 233 IS - 2 JF - Archiv der Mathematik TI - Power-free values of polynomials VL - 96 ER - TY - JOUR AB - We investigate the average order of the divisor function at values of binary cubic forms that are reducible over Q and discuss some applications. AU - Timothy Browning ID - 234 IS - 3 JF - Journal de Theorie des Nombres de Bordeaux TI - The divisor problem for binary cubic forms VL - 23 ER - TY - JOUR AB - For given positive integers m and n, we consider the frequency of representations of m/n as a sum of unit fractions. AU - Browning, Timothy D AU - Elsholtz, Christian ID - 235 IS - 2 JF - Illinois Journal of Mathematics TI - The number of representations of rationals as a sum of unit fractions VL - 55 ER - TY - JOUR AB - An asymptotic formula is established for the number of Q-rational points of bounded height on a nonsingular quartic Del Pezzo surface with a conic bundle structure. AU - de la Bretèche, Régis AU - Timothy Browning ID - 236 IS - 1 JF - Duke Mathematical Journal TI - Manin's conjecture for quartic Del Pezzo surfaces with a conic fibration VL - 160 ER - TY - JOUR AB - We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N≥2 polarons. Fröhlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling √α, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2α, stability of matter does hold for U>2α, that is, the ground state energy per particle has a finite limit as N→∞. (ii) There is no binding of any kind if U exceeds a critical value that depends on α but not on N. The same results are shown to hold for the Pekar-Tomasevich model. AU - Frank, Rupert L AU - Lieb, Élliott H AU - Robert Seiringer AU - Thomas, Lawrence E ID - 2390 IS - 1 JF - Publications Mathematiques de l Institut des Hautes Etudes Scientifiques TI - Stability and absence of binding for multi-polaron systems VL - 113 ER - TY - JOUR AB - The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condensed matter physics. We show that they can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation. AU - Frank, Rupert L AU - Lewin, Mathieu AU - Lieb, Élliott H AU - Robert Seiringer ID - 2391 IS - 15 JF - Physical Review Letters TI - Energy cost to make a hole in the fermi sea VL - 106 ER - TY - JOUR AB - An effective search bound is established for the least non-trivial integer zero of an arbitrary cubic form C ε ℤ[X 1,...,X n], provided that n ≥ 17. AU - Timothy Browning AU - Dietmann, Rainer AU - Elliott, Peter ID - 239 IS - 3 JF - Mathematische Annalen TI - Least zero of a cubic form VL - 352 ER - TY - JOUR AB - We investigate the low energy excitation spectrum of a Bose gas with weak, long range repulsive interactions. In particular, we prove that the Bogoliubov spectrum of elementary excitations with linear dispersion relation for small momentum becomes exact in the mean-field limit. AU - Robert Seiringer ID - 2393 IS - 2 JF - Communications in Mathematical Physics TI - The excitation spectrum for weakly interacting Bosons VL - 306 ER - TY - JOUR AB - Let EMBEDk→d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k, does there exist a (piecewise linear) embedding of K into Rd? Known results easily imply the polynomiality of EMBEDk→2 (k = 1; 2; the case k = 1, d = 2 is graph planarity) and of EMBEDk→2k for all k ≥ 3. We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that EMBEDd→d and EMBED (d-1)→d are undecidable for each d ≥ 5. Our main result is the NP-hardness of EMBED2→4 and, more generally, of EMBED k→d for all k; d with d ≥ 4 and d ≥ k ≥ (2d - 2)/3. These dimensions fall outside the metastable range of a theorem of Haefliger and Weber, which characterizes embeddability using the deleted product obstruction. Our reductions are based on examples, due to Segal, Spież, Freedman, Krushkal, Teichner, and Skopenkov, showing that outside the metastable range the deleted product obstruction is not sufficient to characterize embeddability. AU - Matoušek, Jiří AU - Martin Tancer AU - Uli Wagner ID - 2436 IS - 2 JF - Journal of the European Mathematical Society TI - Hardness of embedding simplicial complexes in Rd VL - 13 ER - TY - CONF AB - We introduce a new notion of minors for simplicial complexes (hypergraphs), so-called homological minors. Our motivation is to propose a general approach to attack certain extremal problems for sparse simplicial complexes and the corresponding threshold problems for random complexes. In this paper, we focus on threshold problems. The basic model for random complexes is the Linial-Meshulam model Xk(n, p). By definition, such a complex has n vertices, a complete (k -1)-dimensional skeleton, and every possible k-dimensional simplex is chosen independently with probability p. We show that for every k, t≥ 1, there is a constant C = C(k, t) such that for p≥ C/n, the random complex Xk(n, p) asymptotically almost surely contains K tk (the complete k-dimensional complex on t vertices) as a homological minor. As corollary, the threshold for (topological) embeddability of Xk(n, p) into R2k is at p = θ(1/n). The method can be extended to other models of random complexes (for which the lower skeleta are not necessarily complete) and also to more general Tverberg-type problems, where instead of continuous maps without doubly covered image points (embeddings), we consider maps without qfold covered image points. AU - Uli Wagner ID - 2437 TI - Minors in random and expanding hypergraphs ER - TY - JOUR AB - Within a multicellular tissue cells may coordinately form a singular or multiple polar axes, but it is unclear whether a common mechanism governs different types of polar axis formation. The phosphorylation status of PIN proteins, which is directly affected by the PINOID (PID) protein kinase and the PP2A protein phosphatase, is known to regulate the apical-basal polarity of PIN localization in bipolar cells of roots and shoot apices. Here, we provide evidence that the phosphorylation status-mediated PIN polarity switch is widely used to modulate cellular processes in Arabidopsis including multipolar pavement cells (PC) with interdigitated lobes and indentations. The degree of PC interdigitation was greatly reduced either when the FYPP1 gene, which encodes a PP2A called phytochrome-associated serine/threonine protein phosphatase, was knocked out or when the PID gene was overexpressed (35S:PID). These genetic modifications caused PIN1 localization to switch from lobe to indentation regions. The PP2A and PID mediated switching of PIN1 localization is strikingly similar to their regulation of the apical-basal polarity switch of PIN proteins in other cells. Our findings suggest a common mechanism for the regulation of PIN1 polarity formation, a fundamental cellular process that is crucial for pattern formation both at the tissue/organ and cellular levels. AU - Hongjiang Li AU - Lin, Deshu AU - Dhonukshe, Pankaj B AU - Nagawa, Shingo AU - Chen, Dandan AU - Jirí Friml AU - Scheres, Ben AU - Guo, Hongwei AU - Yang, Zhenbiao ID - 2454 IS - 6 JF - Cell Research TI - Phosphorylation switch modulates the interdigitated pattern of PIN1 localization and cell expansion in Arabidopsis leaf epidermis VL - 21 ER - TY - JOUR AB - In unicellular and multicellular organisms, cell polarity is essential for a wide range of biological processes. An important feature of cell polarity is the asymmetric distribution of proteins in or at the plasma membrane. In plants such polar localized proteins play various specific roles ranging from organizing cell morphogenesis, asymmetric cell division, pathogen defense, nutrient transport and establishment of hormone gradients for developmental patterning. Moreover, flexible respecification of cell polarities enables plants to adjust their physiology and development to environmental changes. Having evolved multicellularity independently and lacking major cell polarity mechanisms of animal cells, plants came up with alternative solutions to generate and respecify cell polarity as well as to regulate polar domains at the plasma membrane. AU - Dettmer, Jan AU - Friml, Jirí ID - 2460 IS - 6 JF - Current Opinion in Cell Biology TI - Cell polarity in plants: When two do the same, it is not the same... VL - 23 ER - TY - JOUR AB - Parkinson's disease is a common neurodegenerative disorder characterized by a profound motor disability that is traceable to the emergence of synchronous, rhythmic spiking in neurons of the external segment of the globus pallidus (GPe). The origins of this pathophysiology are poorly defined for the generation of pacemaking. After the induction of a parkinsonian state in mice, there was a progressive decline in autonomous GPe pacemaking, which normally serves to desynchronize activity. The loss was attributable to the downregulation of an ion channel that is essential in pacemaking, the hyperpolarization and cyclic nucleotide-gated (HCN) channel. Viral delivery of HCN2 subunits restored pacemaking and reduced burst spiking in GPe neurons. However, the motor disability induced by dopamine (DA) depletion was not reversed, suggesting that the loss of pacemaking was a consequence, rather than a cause, of key network pathophysiology, a conclusion that is consistent with the ability of L-type channel antagonists to attenuate silencing after DA depletion. AU - Chan, Savio AU - Glajch, Kelly E AU - Gertler, Tracy S AU - Guzmán, Jaime N AU - Mercer, Jeff N AU - Lewis, Alan S AU - Goldberg, Alan B AU - Tkatch, Tatiana AU - Ryuichi Shigemoto AU - Fleming, Sheila M AU - Chetkovich, Dane M AU - Osten, Pavel AU - Kita, Hitoshi AU - Surmeier, James D ID - 2511 IS - 1 JF - Nature Neuroscience TI - HCN channelopathy in external globus pallidus neurons in models of Parkinson s disease VL - 14 ER - TY - JOUR AB - GABAergic inhibition plays a central role in the control of pyramidal cell ensemble activities; thus, any signaling mechanism that regulates inhibition is able to fine-tune network patterns. Here, we provide evidence that the retrograde nitric oxide (NO)- cGMP cascade triggered by NMDA receptor (NMDAR) activation plays a role in the control of hippocampal GABAergic transmission in mice. GABAergic synapses express neuronal nitric oxide synthase (nNOS) postsynaptically and NO receptors (NO-sensitive guanylyl cyclase) in the presynaptic terminals. We hypothesized that-similar to glutamatergic synapses-the Ca 2+ transients required to activate nNOS were provided by NMDA receptor activation. Indeed, administration of 5 μm NMDA induced a robust nNOS-dependent cGMP production in GABAergic terminals, selectively in the CA1 and CA3c areas. Furthermore, using preembedding, postembedding, and SDS-digested freeze-fracture replica immunogold labeling, we provided quantitative immunocytochemical evidence that NMDAR subunits GluN1, GluN2A, and GluN2B were present in most somatic GABAergic synapses postsynaptically. These data indicate that NMDARs can modulate hippocampal GABAergic inhibition via NO- cGMP signaling in an activity-dependent manner and that this effect is subregion specific in the mouse hippocampus. AU - Szabadits, Eszter AU - Cserép, Csaba AU - Szonyi, András AU - Fukazawa, Yugo AU - Ryuichi Shigemoto AU - Watanabe, Masahiko AU - Itohara, Shigeyoshi AU - Freund, Tamás F AU - Nyíri, Gábor ID - 2512 IS - 16 JF - Journal of Neuroscience TI - NMDA receptors in hippocampal GABAergic synapses and their role in nitric oxide signaling VL - 31 ER - TY - JOUR AB - SK2-containing channels are expressed in the postsynaptic density (PSD) of dendritic spines on mouse hippocampal area CA1 pyramidal neurons and influence synaptic responses, plasticity and learning. The Sk2 gene (also known as Kcnn2) encodes two isoforms that differ only in the length of their N-terminal domains. SK2-long (SK2-L) and SK2-short (SK2-S) are coexpressed in CA1 pyramidal neurons and likely form heteromeric channels. In mice lacking SK2-L (SK2-S only mice), SK2-S-containing channels were expressed in the extrasynaptic membrane, but were excluded from the PSD. The SK channel contribution to excitatory postsynaptic potentials was absent in SK2-S only mice and was restored by SK2-L re-expression. Blocking SK channels increased the amount of long-term potentiation induced in area CA1 in slices from wild-type mice but had no effect in slices from SK2-S only mice. Furthermore, SK2-S only mice outperformed wild-type mice in the novel object recognition task. These results indicate that SK2-L directs synaptic SK2-containing channel expression and is important for normal synaptic signaling, plasticity and learning. AU - Allen, Duane H AU - Bond, Chris T AU - Luján, Rafael AU - Ballesteros-Merino, Carmen AU - Lin, Michael T AU - Wang, Kang AU - Klett, Nathan AU - Watanabe, Masahiko AU - Ryuichi Shigemoto AU - Stackman, Robert W AU - Maylie, James G AU - Adelman, John P ID - 2513 IS - 6 JF - Nature Neuroscience TI - The SK2-long isoform directs synaptic localization and function of SK2-containing channels VL - 14 ER - TY - JOUR AB - We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H xy, indexed by, are independent, uniformly distributed random variables if {pipe}x-y{pipe} is less than the band width W, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales. We also show that the localization length of the eigenvectors of H is larger than a factor W d/6 times the band width. All results are uniform in the size of the matrix. AU - László Erdös AU - Knowles, Antti ID - 2717 IS - 2 JF - Communications in Mathematical Physics TI - Quantum diffusion and eigenfunction delocalization in a random band matrix model VL - 303 ER -