@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}, } @article{2513, abstract = {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. }, author = {Allen, Duane H and Bond, Chris T and Luján, Rafael and Ballesteros-Merino, Carmen and Lin, Michael T and Wang, Kang and Klett, Nathan and Watanabe, Masahiko and Ryuichi Shigemoto and Stackman, Robert W and Maylie, James G and Adelman, John P}, journal = {Nature Neuroscience}, number = {6}, pages = {744 -- 749}, publisher = {Nature Publishing Group}, title = {{The SK2-long isoform directs synaptic localization and function of SK2-containing channels}}, doi = {10.1038/nn.2832}, volume = {14}, year = {2011}, } @article{2717, abstract = {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. }, author = {László Erdös and Knowles, Antti}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {509 -- 554}, publisher = {Springer}, title = {{Quantum diffusion and eigenfunction delocalization in a random band matrix model}}, doi = {10.1007/s00220-011-1204-2}, volume = {303}, year = {2011}, } @article{2764, abstract = {Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds to the eigenvalue flows for the eigenvalues of symmetric, hermitian and quaternion self-dual ensembles. For any β≥1, we prove that the relaxation time to local equilibrium for the Dyson Brownian motion is bounded above by N -ζ for some ζ> 0. The proof is based on an estimate of the entropy flow of the Dyson Brownian motion w. r. t. a "pseudo equilibrium measure". As an application of this estimate, we prove that the eigenvalue spacing statistics in the bulk of the spectrum for N×N symmetric Wigner ensemble is the same as that of the Gaussian Orthogonal Ensemble (GOE) in the limit N→∞. The assumptions on the probability distribution of the matrix elements of the Wigner ensemble are a subexponential decay and some minor restriction on the support.}, author = {László Erdös and Schlein, Benjamin and Yau, Horng-Tzer}, journal = {Inventiones Mathematicae}, number = {1}, pages = {75 -- 119}, publisher = {Springer}, title = {{Universality of random matrices and local relaxation flow}}, doi = {10.1007/s00222-010-0302-7}, volume = {185}, year = {2011}, } @misc{2765, abstract = {This is a study of the universality of spectral statistics for large random matrices. Considered are N×N symmetric, Hermitian, or quaternion self-dual random matrices with independent identically distributed entries (Wigner matrices), where the probability distribution of each matrix element is given by a measure v with zero expectation and with subexponential decay. The main result is that the correlation functions of the local eigenvalue statistics in the bulk of the spectrum coincide with those of the Gaussian Orthogonal Ensemble (GOE), the Gaussian Unitary Ensemble (GUE), and the Gaussian Symplectic Ensemble (GSE), respectively, in the limit as N → ∞. This approach is based on a study of the Dyson Brownian motion via a related new dynamics, the local relaxation flow. As a main input, it is established that the density of the eigenvalues converges to the Wigner semicircle law, and this holds even down to the smallest possible scale. Moreover, it is shown that the eigenvectors are completely delocalized. These results hold even without the condition that the matrix elements are identically distributed: only independence is used. In fact, for the matrix elements of the Green function strong estimates are given that imply that the local statistics of any two ensembles in the bulk are identical if the first four moments of the matrix elements match. Universality at the spectral edges requires matching only two moments. A Wigner-type estimate is also proved, and it is shown that the eigenvalues repel each other on arbitrarily small scales.}, author = {László Erdös}, booktitle = {Russian Mathematical Surveys}, number = {3}, pages = {507 -- 626}, publisher = {IOP Publishing Ltd.}, title = {{Universality of Wigner random matrices: A survey of recent results}}, doi = {10.1070/RM2011v066n03ABEH004749}, volume = {66}, year = {2011}, }