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 - 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 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 - 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 -
TY - JOUR
AB - 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.
AU - László Erdös
AU - Schlein, Benjamin
AU - Yau, Horng-Tzer
ID - 2764
IS - 1
JF - Inventiones Mathematicae
TI - Universality of random matrices and local relaxation flow
VL - 185
ER -