@article{2119, abstract = {Let (E, H, μ) be an abstract Wiener space and let DV : = V D, where D denotes the Malliavin derivative and V is a closed and densely defined operator from H into another Hilbert space under(H, {combining low line}). Given a bounded operator B on under(H, {combining low line}), coercive on the range over(R (V), -), we consider the operators A : = V* B V in H and under(A, {combining low line}) : = V V* B in under(H, {combining low line}), as well as the realisations of the operators L : = DV* B DV and under(L, {combining low line}) : = DV DV* B in Lp (E, μ) and Lp (E, μ ; under(H, {combining low line})) respectively, where 1 < p < ∞. Our main result asserts that the following four assertions are equivalent: (1)D (sqrt(L)) = D (DV) with {norm of matrix} sqrt(L) f {norm of matrix}p {minus tilde} {norm of matrix} DV f {norm of matrix}p for f ∈ D (sqrt(L));(2)under(L, {combining low line}) admits a bounded H∞-functional calculus on over(R (DV), -);(3)D (sqrt(A)) = D (V) with {norm of matrix} sqrt(A) h {norm of matrix} {minus tilde} {norm of matrix} V h {norm of matrix} for h ∈ D (sqrt(A));(4)under(A, {combining low line}) admits a bounded H∞-functional calculus on over(R (V), -). Moreover, if these conditions are satisfied, then D (L) = D (DV2) ∩ D (DA). The equivalence (1)-(4) is a non-symmetric generalisation of the classical Meyer inequalities of Malliavin calculus (where under(H, {combining low line}) = H, V = I, B = frac(1, 2) I). A one-sided version of (1)-(4), giving Lp-boundedness of the Riesz transform DV / sqrt(L) in terms of a square function estimate, is also obtained. As an application let -A generate an analytic C0-contraction semigroup on a Hilbert space H and let -L be the Lp-realisation of the generator of its second quantisation. Our results imply that two-sided bounds for the Riesz transform of L are equivalent with the Kato square root property for A. The boundedness of the Riesz transform is used to obtain an Lp-domain characterisation for the operator L.}, author = {Jan Maas and van Neerven, Jan M}, journal = {Journal of Functional Analysis}, number = {8}, pages = {2410 -- 2475}, publisher = {Academic Press}, title = {{Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces}}, doi = {10.1016/j.jfa.2009.07.001}, volume = {257}, year = {2009}, } @article{2137, abstract = {Relying on the quantization rule of Raab and Friedrich [Phys. Rev. A (2009) in press], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecular ion. We also provide analytic estimates of the rotational constants of any such levels up to threshold for dissociation and obtain a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential.}, author = {Mikhail Lemeshko and Frierich, Bretislav}, journal = {Journal of Atomic and Molecular Sciences}, number = {1}, pages = {41 -- 47}, publisher = {Global Science Press}, title = {{Rotational structure of weakly bound molecular ions}}, doi = {10.4208/jams.101009.110209a}, volume = {1}, year = {2009}, } @article{2149, abstract = {We investigate the effects of a magnetic field on the dynamics of rotationally inelastic collisions of open-shell molecules (Σ2, Σ3, and Π2) with closed-shell atoms. Our treatment makes use of the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric [M. Lemeshko and B. Friedrich, J. Chem. Phys. 129, 024301 (2008)] and radiative fields [M. Lemeshko and B. Friedrich, Int. J. Mass. Spec. 280, 19 (2009)]. A magnetic field aligns the molecule in the space-fixed frame and thereby alters the effective shape of the diffraction target. This significantly affects the differential and integral scattering cross sections. We exemplify our treatment by evaluating the magnetic-field-dependent scattering characteristics of the He-CaH (XΣ+2), He-O2 (XΣ–3), and He-OH (XΠΩ2) systems at thermal collision energies. Since the cross sections can be obtained for different orientations of the magnetic field with respect to the relative velocity vector, the model also offers predictions about the frontal-versus-lateral steric asymmetry of the collisions. The steric asymmetry is found to be almost negligible for the He-OH system, weak for the He-CaH collisions, and strong for the He-O2. While odd ΔM transitions dominate the He-OH [J=3/2,f→J′,e/f] integral cross sections in a magnetic field parallel to the relative velocity vector, even ΔM transitions prevail in the case of the He-CaH (X2Σ+) and He-O2 (XΣ−3) collision systems. For the latter system, the magnetic field opens inelastic channels that are closed in the absence of the field. These involve the transitions N=1,J=0→N′, J′ with J′=N′.}, author = {Mikhail Lemeshko and Friedrich, Břetislav}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {1}, publisher = {American Physical Society}, title = {{Collisions of paramagnetic molecules in magnetic fields: An analytic model based on Fraunhofer diffraction of matter waves}}, doi = {10.1103/PhysRevA.79.012718}, volume = {79}, year = {2009}, } @article{2150, abstract = {We examine the effects of a linearly polarized nonresonant radiative field on the dynamics of rotationally inelastic Na+ + N2 collisions at eV collision energies. Our treatment is based on the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric fields [M. Lemeshko, B. Friedrich, J. Chem. Phys. 129 (2008) 024301]. The nonresonant radiative field changes the effective shape of the target molecule by aligning it in the space-fixed frame. This markedly alters the differential and integral scattering cross-sections. As the cross-sections can be evaluated for a polarization of the radiative field collinear or perpendicular to the relative velocity vector, the model also offers predictions about steric asymmetry of the collisions.}, author = {Mikhail Lemeshko and Friedrich, Břetislav}, journal = {International Journal of Mass Spectrometry}, number = {1-3}, pages = {19 -- 25}, publisher = {Elsevier}, title = {{The effect of a nonresonant radiative field on low-energy rotationally inelastic Na+ + N2 collisions}}, doi = {10.1016/j.ijms.2008.06.010 }, volume = {280}, year = {2009}, } @article{2191, abstract = {By making use of the quantization rule of Raab and Friedrich [Phys. Rev. A 78, 022707 (2008)], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecule and the rotational constants of any such levels up to the threshold, and provide a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential and are applicable to halo molecules. }, author = {Mikhail Lemeshko and Friedrich, Břetislav}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {5}, publisher = {American Physical Society}, title = {{Rotational and rotationless states of weakly bound molecules}}, doi = {10.1103/PhysRevA.79.050501}, volume = {79}, year = {2009}, } @article{2192, abstract = {We develop an analytic model of thermal state-to-state rotationally inelastic collisions of asymmetric-top molecules with closed-shell atoms in electric fields and apply it to the Ar-H2O collision system. The predicted cross sections as well as the steric asymmetry of the collisions show at fields up to 150 kV/cm characteristic field-dependent features which can be experimentally tested. Particularly suitable candidates for such tests are the 000 → 220 and 101→ 221 channels, arising from the relaxation of the field-free selection rules due to the hybridization of J states by the field. Averaging over the M' product channels is found to largely obliterate the orientation effects brought about by the field.}, author = {Mikhail Lemeshko and Friedrich, Břetislav}, journal = {Journal of Physical Chemistry A}, number = {52}, pages = {15055 -- 15063}, publisher = {American Chemical Society}, title = {{Model analysis of rotationally inelastic Ar + H2O scattering in an electric field}}, doi = {10.1021/jp9051598}, volume = {113}, year = {2009}, } @article{2193, abstract = {We show that weakly bound molecules can be probed by "shaking" in a pulsed nonresonant laser field. The field introduces a centrifugal term which expels the highest vibrational level from the potential that binds it. Our numerical simulations applied to the Rb2 and KRb Feshbach molecules indicate that shaking by feasible laser pulses can be used to accurately recover the square of the vibrational wave function and, by inversion, also the long-range part of the molecular potential.}, author = {Mikhail Lemeshko and Friedrich, Břetislav}, journal = {Physical Review Letters}, number = {5}, publisher = {American Physical Society}, title = {{Probing weakly bound molecules with nonresonant light}}, doi = {10.1103/PhysRevLett.103.053003}, volume = {103}, year = {2009}, } @article{228, abstract = {Let X be a projective non-singular quartic hypersurface of dimension 39 or more, which is defined over . We show that X() is non-empty provided that X() is non-empty and X has p-adic points for every prime p.}, author = {Timothy Browning and Heath-Brown, Roger}, journal = {Journal fur die Reine und Angewandte Mathematik}, number = {629}, pages = {37 -- 88}, publisher = {Walter de Gruyter}, title = {{Rational points on quartic hypersurfaces}}, doi = {10.1515/CRELLE.2009.026}, year = {2009}, } @article{229, abstract = {An upper bound of the expected order of magnitude is established for the number of ℚ-rational points of bounded height on Châtelet surfaces defined over ℚ.}, author = {Timothy Browning}, journal = {Mathematische Annalen}, number = {1}, pages = {41 -- 50}, publisher = {Springer Nature}, title = {{Linear growth for Châtelet surfaces}}, doi = {10.1007/s00208-009-0383-z}, volume = {346}, year = {2009}, } @article{2384, abstract = {We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the Bogoliubov approximation is exact in an appropriate parameter regime, as far as the ground state energy is concerned.}, author = {Giuliani, Alessandro and Robert Seiringer}, journal = {Journal of Statistical Physics}, number = {5-6}, pages = {915 -- 934}, publisher = {Springer}, title = {{The ground state energy of the weakly interacting Bose gas at high density}}, doi = {10.1007/s10955-009-9718-0}, volume = {135}, year = {2009}, } @article{2385, abstract = {We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity, so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii energy functional accurately describes the ground-state energy of the corresponding N -body Hamiltonian with contact interaction provided the total angular momentum L is much less than N2. While the Gross-Pitaevskii energy is always an obvious variational upper bound to the ground-state energy, a more refined analysis is needed to establish it as an exact lower bound. We also discuss the question of Bose-Einstein condensation in the parameter range considered. Coherent states together with inequalities in spaces of analytic functions are the main technical tools.}, author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {6}, publisher = {American Physical Society}, title = {{Yrast line of a rapidly rotating Bose gas: Gross-Pitaevskii regime}}, doi = {10.1103/PhysRevA.79.063626}, volume = {79}, year = {2009}, } @article{2386, abstract = {We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a2 ρ is small and the temperature T satisfies T> 4πρ ln | ln (a2 ρ) |. Here, a is the scattering length of the repulsive interaction potential and ρ is the density. To the leading order in a2 ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when T- Tc (0) Tc (0) >5 a ρ1/3, where Tc (0) is the critical temperature of the ideal gas. While this condition is not expected to be sharp, it gives a rigorous upper bound on the critical temperature for Bose-Einstein condensation.}, author = {Robert Seiringer and Ueltschi, Daniel}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {1}, publisher = {American Physical Society}, title = {{Rigorous upper bound on the critical temperature of dilute Bose gases}}, doi = {10.1103/PhysRevB.80.014502}, volume = {80}, year = {2009}, } @article{2387, abstract = {We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.}, author = {Lewin, Mathieu and Robert Seiringer}, journal = {Journal of Statistical Physics}, number = {5}, pages = {1040 -- 1062}, publisher = {Springer}, title = {{Strongly correlated phases in rapidly rotating Bose gases}}, doi = {10.1007/s10955-009-9833-y}, volume = {137}, year = {2009}, } @article{2388, abstract = {This paper provides self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifies the connection of coherence and proper scoring rules to Bregman divergence.}, author = {Predd, Joel B and Robert Seiringer and Lieb, Élliott H and Osherson, Daniel N and Poor, Harold V and Kulkarni, Sanjeev R}, journal = {IEEE Transactions on Information Theory}, number = {10}, pages = {4786 -- 4792}, publisher = {IEEE}, title = {{Probabilistic coherence and proper scoring rules}}, doi = {10.1109/TIT.2009.2027573}, volume = {55}, year = {2009}, } @inproceedings{2433, abstract = {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 polynomiality of EMBEDk→2 (k = 1, 2; the case k = 1, d = 2 is graph planarity) and of EMBEDk→2k for all k ≥ 3 (even if k is not considered fixed). We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that EMBED d→d and EMBED(d-1)→d are undecidable for each d ≥ 5. Our main result is NP-hardness of EMBED2→4 and, more generally, of EMBEDk→d for all k, d with d ≥ 4 and d ≥ k ≥ (2d - 2)/3.}, author = {Matoušek, Jiří and Martin Tancer and Uli Wagner}, pages = {855 -- 864}, publisher = {SIAM}, title = {{Hardness of embedding simplicial complexes in ℝd}}, year = {2009}, } @article{2499, abstract = {G protein-coupled receptors (GPCRs) have critical functions in intercellular communication. Although a wide range of different receptors have been identified in the same cells, the mechanism by which signals are integrated remains elusive. The ability of GPCRs to form dimers or larger hetero-oligomers is thought to generate such signal integration. We examined the molecular mechanisms responsible for the GABAB receptor-mediated potentiation of the mGlu receptor signalling reported in Purkinje neurons. We showed that this effect does not require a physical interaction between both receptors. Instead, it is the result of a more general mechanism in which the βγ subunits produced by the Gi-coupled GABAB receptor enhance the mGlu-mediated Gq response. Most importantly, this mechanism could be generally applied to other pairs of Gi- and Gq-coupled receptors and the signal integration varied depending on the time delay between activation of each receptor. Such a mechanism helps explain specific properties of cells expressing two different Gi- and Gq-coupled receptors activated by a single transmitter, or properties of GPCRs naturally coupled to both types of the G protein.}, author = {Rives, Marie L and Vol, Claire and Fukazawa, Yugo and Tinel, Norbert and Trinquet, Eric and Ayoub, Mohammed A and Ryuichi Shigemoto and Pin, Jean-Philippe and Prezèau, Laurent}, journal = {EMBO Journal}, number = {15}, pages = {2195 -- 2208}, publisher = {Wiley-Blackwell}, title = {{Crosstalk between GABAB and mGlu1a receptors reveals new insight into GPCR signal integration}}, doi = {10.1038/emboj.2009.177}, volume = {28}, year = {2009}, } @article{3051, author = {Weijers, Dolf and Friml, Jirí}, journal = {Cell}, number = {6}, pages = {1172 -- 1172}, publisher = {Cell Press}, title = {{SnapShot: Auxin signaling and transport}}, doi = {10.1016/j.cell.2009.03.009}, volume = {136}, year = {2009}, } @article{3052, abstract = {The dynamic, differential distribution of the hormone auxin within plant tissues controls an impressive variety of developmental processes, which tailor plant growth and morphology to environmental conditions. Various environmental and endogenous signals can be integrated into changes in auxin distribution through their effects on local auxin biosynthesis and intercellular auxin transport. Individual cells interpret auxin largely by a nuclear signaling pathway that involves the F box protein TIR1 acting as an auxin receptor. Auxin-dependent TIR1 activity leads to ubiquitination-based degradation of transcriptional repressors and complex transcriptional reprogramming. Thus, auxin appears to be a versatile trigger of preprogrammed developmental changes in plant cells.}, author = {Vanneste, Steffen and Friml, Jirí}, journal = {Cell}, number = {6}, pages = {1005 -- 1016}, publisher = {Cell Press}, title = {{Auxin: A trigger for change in plant development}}, doi = {10.1016/j.cell.2009.03.001}, volume = {136}, year = {2009}, } @article{3057, abstract = {The differential distribution of the plant signaling molecule auxin is required for many aspects of plant development. Local auxin maxima and gradients arise as a result of local auxin metabolism and, predominantly, from directional cell-to-cell transport. In this primer, we discuss how the coordinated activity of several auxin influx and efflux systems, which transport auxin across the plasma membrane, mediates directional auxin flow. This activity crucially contributes to the correct setting of developmental cues in embryogenesis, organogenesis, vascular tissue formation and directional growth in response to environmental stimuli.}, author = {Petrášek, Jan and Friml, Jirí}, journal = {Development}, number = {16}, pages = {2675 -- 2688}, publisher = {Company of Biologists}, title = {{Auxin transport routes in plant development}}, doi = {10.1242/dev.030353}, volume = {136}, year = {2009}, } @article{3061, abstract = {The PIN-FORMED (PIN) proteins are secondary transporters acting in the efflux of the plant signal molecule auxin from cells. They are asymmetrically localized within cells and their polarity determines the directionality of intercellular auxin flow. PIN genes are found exclusively in the genomes of multicellular plants and play an important role in regulating asymmetric auxin distribution in multiple developmental processes, including embryogenesis, organogenesis, tissue differentiation and tropic responses. All PIN proteins have a similar structure with amino- and carboxy-terminal hydrophobic, membrane-spanning domains separated by a central hydrophilic domain. The structure of the hydrophobic domains is well conserved. The hydrophilic domain is more divergent and it determines eight groups within the protein family. The activity of PIN proteins is regulated at multiple levels, including transcription, protein stability, subcellular localization and transport activity. Different endogenous and environmental signals can modulate PIN activity and thus modulate auxin-distribution-dependent development. A large group of PIN proteins, including the most ancient members known from mosses, localize to the endoplasmic reticulum and they regulate the subcellular compartmentalization of auxin and thus auxin metabolism. Further work is needed to establish the physiological importance of this unexpected mode of auxin homeostasis regulation. Furthermore, the evolution of PIN-based transport, PIN protein structure and more detailed biochemical characterization of the transport function are important topics for further studies.}, author = {Křeček, Pavel and Skůpa, Petr and Libus, Jiří and Naramoto, Satoshi and Tejos, Ricardo and Friml, Jirí and Zažímalová, Eva}, journal = {Genome Biology}, number = {12}, publisher = {BioMed Central}, title = {{The PIN-FORMED (PIN) protein family of auxin transporters}}, doi = {10.1186/gb-2009-10-12-249}, volume = {10}, year = {2009}, }