@article{2198, abstract = {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.}, author = {Mikhail Lemeshko}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {5}, publisher = {American Physical Society}, title = {{Shaping interactions between polar molecules with far-off-resonant light}}, doi = {10.1103/PhysRevA.83.051402}, volume = {83}, year = {2011}, } @article{2199, abstract = {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.}, author = {Mikhail Lemeshko and Mustafa, Mustafa K and Kais, Sabre and Friedrich, Břetislav}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {4}, publisher = {American Physical Society}, title = {{Supersymmetric factorization yields exact solutions to the molecular Stark-effect problem for "stretched" states}}, doi = {10.1103/PhysRevA.83.043415}, volume = {83}, year = {2011}, } @article{2200, abstract = {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.}, author = {Mikhail Lemeshko and Mustafa, Mustafa K and Kais, Sabre and Friedrich, Břetislav}, journal = {New Journal of Physics}, publisher = {IOP Publishing Ltd.}, title = {{Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically}}, doi = {10.1088/1367-2630/13/6/063036}, volume = {13}, year = {2011}, } @misc{2312, abstract = {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.}, author = {Gaia Novarino and Akizu, Naiara and Gleeson, Joseph G}, booktitle = {Cell}, number = {1}, pages = {70 -- 79}, publisher = {Cell Press}, title = {{Modeling human disease in humans: The ciliopathies}}, doi = {10.1016/j.cell.2011.09.014}, volume = {147}, year = {2011}, } @inproceedings{2320, abstract = {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.}, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer and Thomas, Lawrence E}, pages = {21 -- 32}, publisher = {World Scientific Publishing}, title = {{Binding, stability, and non-binding of multi-polaron systems}}, doi = {10.1142/9789814350365_0002}, year = {2011}, } @inproceedings{2321, abstract = {We derive a sharp bound on the location of non-positive eigenvalues of Schrödinger operators on the half-line with complex-valued potentials.}, author = {Frank, Rupert L and Laptev, Ari and Robert Seiringer}, pages = {39 -- 44}, publisher = {Springer}, title = {{ A sharp bound on eigenvalues of Schrödinger operators on the halfline with complex-valued potentials}}, doi = {10.1007/978-3-7643-9994-8_3}, volume = {214}, year = {2011}, } @article{233, abstract = {For an irreducible polynomial in at most two variables the problem of representing power-free integers is investigated. }, author = {Timothy Browning}, journal = {Archiv der Mathematik}, number = {2}, pages = {139 -- 150}, publisher = {Birkhäuser}, title = {{Power-free values of polynomials}}, doi = {10.1007/s00013-011-0224-7}, volume = {96}, year = {2011}, } @article{234, abstract = {We investigate the average order of the divisor function at values of binary cubic forms that are reducible over Q and discuss some applications.}, author = {Timothy Browning}, journal = {Journal de Theorie des Nombres de Bordeaux}, number = {3}, pages = {579 -- 602}, publisher = {Universite de Bordeaux}, title = {{The divisor problem for binary cubic forms}}, doi = {10.5802/jtnb.778}, volume = {23}, year = {2011}, } @article{235, abstract = {For given positive integers m and n, we consider the frequency of representations of m/n as a sum of unit fractions.}, author = {Browning, Timothy D and Elsholtz, Christian}, journal = {Illinois Journal of Mathematics}, number = {2}, pages = {685 -- 696}, publisher = {University of Illinois Press}, title = {{The number of representations of rationals as a sum of unit fractions}}, volume = {55}, year = {2011}, } @article{236, abstract = {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.}, author = {de la Bretèche, Régis and Timothy Browning}, journal = {Duke Mathematical Journal}, number = {1}, pages = {1 -- 69}, publisher = {Duke University Press}, title = {{Manin's conjecture for quartic Del Pezzo surfaces with a conic fibration}}, doi = {10.1215/00127094-1443466}, volume = {160}, year = {2011}, } @article{239, abstract = {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.}, author = {Timothy Browning and Dietmann, Rainer and Elliott, Peter}, journal = {Mathematische Annalen}, number = {3}, pages = {745 -- 778}, publisher = {Springer}, title = {{Least zero of a cubic form}}, doi = {10.1007/s00208-011-0651-6}, volume = {352}, year = {2011}, } @article{2390, abstract = {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.}, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer and Thomas, Lawrence E}, journal = {Publications Mathematiques de l Institut des Hautes Etudes Scientifiques}, number = {1}, pages = {39 -- 67}, publisher = {Springer}, title = {{Stability and absence of binding for multi-polaron systems}}, doi = {10.1007/s10240-011-0031-5}, volume = {113}, year = {2011}, } @article{2391, abstract = {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.}, author = {Frank, Rupert L and Lewin, Mathieu and Lieb, Élliott H and Robert Seiringer}, journal = {Physical Review Letters}, number = {15}, publisher = {American Physical Society}, title = {{Energy cost to make a hole in the fermi sea}}, doi = {10.1103/PhysRevLett.106.150402}, volume = {106}, year = {2011}, } @article{2393, abstract = {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.}, author = {Robert Seiringer}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {565 -- 578}, publisher = {Springer}, title = {{The excitation spectrum for weakly interacting Bosons}}, doi = {10.1007/s00220-011-1261-6}, volume = {306}, year = {2011}, } @article{2436, 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 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. }, author = {Matoušek, Jiří and Martin Tancer and Uli Wagner}, journal = {Journal of the European Mathematical Society}, number = {2}, pages = {259 -- 295}, publisher = {European Mathematical Society}, title = {{Hardness of embedding simplicial complexes in Rd}}, doi = {10.4171/JEMS/252}, volume = {13}, year = {2011}, } @inproceedings{2437, abstract = {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.}, author = {Uli Wagner}, pages = {351 -- 360}, publisher = {ACM}, title = {{Minors in random and expanding hypergraphs}}, doi = {10.1145/1998196.1998256}, year = {2011}, } @article{2454, abstract = {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.}, author = {Hongjiang Li and Lin, Deshu and Dhonukshe, Pankaj B and Nagawa, Shingo and Chen, Dandan and Jirí Friml and Scheres, Ben and Guo, Hongwei and Yang, Zhenbiao}, journal = {Cell Research}, number = {6}, pages = {970 -- 978}, publisher = {Nature Publishing Group}, title = {{Phosphorylation switch modulates the interdigitated pattern of PIN1 localization and cell expansion in Arabidopsis leaf epidermis}}, doi = {10.1038/cr.2011.49}, volume = {21}, year = {2011}, } @article{2460, abstract = {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.}, author = {Dettmer, Jan and Friml, Jirí}, journal = {Current Opinion in Cell Biology}, number = {6}, pages = {686 -- 696}, publisher = {Elsevier}, title = {{Cell polarity in plants: When two do the same, it is not the same...}}, doi = {10.1016/j.ceb.2011.09.006}, volume = {23}, year = {2011}, } @article{2511, abstract = {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.}, author = {Chan, Savio and Glajch, Kelly E and Gertler, Tracy S and Guzmán, Jaime N and Mercer, Jeff N and Lewis, Alan S and Goldberg, Alan B and Tkatch, Tatiana and Ryuichi Shigemoto and Fleming, Sheila M and Chetkovich, Dane M and Osten, Pavel and Kita, Hitoshi and Surmeier, James D}, journal = {Nature Neuroscience}, number = {1}, pages = {85 -- 94}, publisher = {Nature Publishing Group}, title = {{HCN channelopathy in external globus pallidus neurons in models of Parkinson s disease}}, doi = {10.1038/nn.2692}, volume = {14}, year = {2011}, } @article{2512, abstract = {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.}, author = {Szabadits, Eszter and Cserép, Csaba and Szonyi, András and Fukazawa, Yugo and Ryuichi Shigemoto and Watanabe, Masahiko and Itohara, Shigeyoshi and Freund, Tamás F and Nyíri, Gábor}, journal = {Journal of Neuroscience}, number = {16}, pages = {5893 -- 5904}, publisher = {Society for Neuroscience}, title = {{NMDA receptors in hippocampal GABAergic synapses and their role in nitric oxide signaling}}, doi = {10.1523/JNEUROSCI.5938-10.2011}, volume = {31}, year = {2011}, }