TY - JOUR
AB - We compare the functional spectrum of protein evolution in two separate animal lineages with respect to two hypotheses: (1) rates of divergence are distributed similarly among functional classes within both lineages, indicating that selective pressure on the proteome is largely independent of organismic-level biological requirements; and (2) rates of divergence are distributed differently among functional classes within each lineage, indicating species-specific selective regimes impact genome-wide substitutional patterns. Integrating comparative genome sequence with data from tissue-specific expressed-sequence-tag (EST) libraries and detailed database annotations, we find a functional genomic signature of rapid evolution and selective constraint shared between mammalian and nematode lineages despite their extensive morphological and ecological differences and distant common ancestry. In both phyla, we find evidence of accelerated evolution among components of molecular systems involved in coevolutionary change. In mammals, lineage-specific fast evolving genes include those involved in reproduction, immunity, and possibly, maternal-fetal conflict. Likelihood ratio tests provide evidence for positive selection in these rapidly evolving functional categories in mammals. In contrast, slowly evolving genes, in terms of amino acid or insertion/deletion (indel) change, in both phyla are involved in core molecular processes such as transcription, translation, and protein transport. Thus, strong purifying selection appears to act on the same core cellular processes in both mammalian and nematode lineages, whereas positive and/or relaxed selection acts on different biological processes in each lineage.
AU - Castillo-Davis, Cristian I
AU - Fyodor Kondrashov
AU - Hartl, Daniel L
AU - Kulathinal, Rob J
ID - 902
IS - 5
JF - Genome Research
TI - The functional genomic distribution of protein divergence in two animal phyla: Coevolution, genomic conflict, and constraint
VL - 14
ER -
TY - JOUR
AB - Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Stromdnger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equal. This provides significant evidence in support of SYZ. Moreover, the examples are of great interest in their own right: they are spaces of flat SLr-connections on a smooth curve. The mirror is the corresponding space for the Langlands dual group PGLr. These examples therefore throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.
AU - Tamas Hausel
AU - Thaddeus, Michael
ID - 1457
IS - 1
JF - Inventiones Mathematicae
TI - Mirror symmetry, langlands duality, and the Hitchin system
VL - 153
ER -
TY - JOUR
AB - The moduli space of stable bundles of rank $2$ and degree $1$ on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the noncompact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance.
AU - Tamas Hausel
AU - Thaddeus, Michael
ID - 1458
IS - 2
JF - Journal of the American Mathematical Society
TI - Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles
VL - 16
ER -
TY - JOUR
AB - In this paper we explicitly calculate the analogue of the 't Hooft SU (2) Yang-Mills instantons on Gibbons-Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi-Hanson, or Ak ALE gravitational instantons and the multi-Taub-NUT spaces, or Ak ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU (2) magnetic monopole solutions of the Bogomolny equations on flat ℝ3.
AU - Etesi, Gábor
AU - Tamas Hausel
ID - 1459
IS - 2
JF - Communications in Mathematical Physics
TI - On Yang-Mills instantons over multi-centered gravitational instantons
VL - 235
ER -
TY - JOUR
AB - For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.
AU - Browning, Timothy D
AU - Swarbick Jones, M
ID - 166
JF - Proceedings of the Bonn session in analytic number theory and diophantine equations
TI - Counting rational points on del Pezzo surfaces of degree 5
VL - 360
ER -
TY - JOUR
AB - The molecular organization of bacterial NADH: ubiquinone oxidoreductase (complex I or NDH-1) is not established, apart from a rough separation into dehydrogenase, connecting and membrane domains. In this work, complex I was purified from Escherichia coli and fragmented by replacing dodecylmaltoside with other detergents. Exchange into decyl maltoside led to the removal of the hydrophobic subunit NuoL from the otherwise intact complex. Diheptanoyl phosphocholine led to the loss of NuoL and NuoM subunits, whereas other subunits remained in the complex. The presence of N,N-dimethyldodecylamine N-oxide or Triton X-100 led to further disruption of the membrane domain into fragments containing NuoL/M/N, NuoA/K/N, and NuoH/J subunits. Among the hydrophilic subunits, NuoCD was most readily dissociated from the complex, whereas NuoB was partially dissociated from the peripheral arm assembly in N,N-dimethyldodecylamine N-oxide. A model of subunit arrangement in bacterial complex I based on these data is proposed. Subunits NuoL and NuoM, which are homologous to antiporters and are implicated in proton pumping, are located at the distal end of the membrane arm, spatially separated from the redox centers of the peripheral arm. This is consistent with proposals that the mechanism of proton pumping by complex I is likely to involve long range conformational changes.
AU - Holt, Peter J
AU - Morgan, David J
AU - Leonid Sazanov
ID - 1959
IS - 44
JF - Journal of Biological Chemistry
TI - The location of NuoL and NuoM subunits in the membrane domain of the Escherichia coli Complex I: implications for the mechanism of proton pumping
VL - 278
ER -
TY - JOUR
AB - NADH-ubiquinone oxidoreductase (complex I or NDH-1) was purified from the BL21 strain of Escherichia coli using an improved procedure. The complex was effectively stabilized by addition of divalent cations and lipids, making the preparation suitable for structural studies. The ubiquinone reductase activity of the enzyme was fully restored by addition of native E. coli lipids. Two different two-dimensional crystal forms, with p2 and p3 symmetry, were obtained using lipids containing native E. coli extracts. Analysis of the crystals showed that they are formed by fully intact complex I in an L-shaped conformation. Activity assays and single particle analysis indicated that complex I maintains this structure in detergent solution and does not adopt a different conformation in the active state. Thus, we provide the first experimental evidence that complex I from E. coli has an L-shape in a lipid bilayer and confirm that this is also the case for the active enzyme in solution. This suggests strongly that bacterial complex I exists in an L-shaped conformation in vivo. Our results also indicate that native lipids play an important role in the activation, stabilization and, as a consequence, crystallization of purified complex I from E. coli.
AU - Leonid Sazanov
AU - Carroll, Joe D
AU - Holt, Peter J
AU - Toime, Laurence J
AU - Fearnley, Ian M
ID - 1960
IS - 21
JF - Journal of Biological Chemistry
TI - A role for native lipids in the stabilization and two dimensional crystallization of the Escherichia coli NADH ubiquinone oxidoreductase (complex I)
VL - 278
ER -
TY - JOUR
AU - Timothy Browning
ID - 205
IS - 3
JF - Acta Arithmetica
TI - Counting rational points on cubic and quartic surfaces
VL - 108
ER -
TY - JOUR
AB - Let T ⊂ ℙ 4 be a non-singular threefold of degree at least four. Then we show that the number of points in T(ℚ), with height at most B, is o(B 3) or B → ∞.
AU - Timothy Browning
ID - 206
IS - 1
JF - Quarterly Journal of Mathematics
TI - A note on the distribution of rational points on threefolds
VL - 54
ER -
TY - JOUR
AU - Browning, Timothy D
ID - 207
IS - 3
JF - Mathematical Proceedings of the Cambridge Philosophical Society
TI - Sums of four biquadrates
VL - 134
ER -
TY - JOUR
AB - For any ε > 0 and any diagonal quadratic form Q ∈ ℤ[x 1, x 2, x 3, x 4] with a square-free discriminant of modulus Δ Q ≠ 0, we establish the uniform estimate ≪ε B 3/2+ε + B 2+ε/Δ Q 1/6 for the number of rational points of height at most B lying in the projective surface Q = 0.
AU - Timothy Browning
ID - 208
IS - 1
JF - Quarterly Journal of Mathematics
TI - Counting rational points on diagonal quadratic surfaces
VL - 54
ER -
TY - CONF
AU - Lieb, Élliott H
AU - Robert Seiringer
ED - Karpeshina, Yulia
ED - Weikard, Rudi
ED - Zeng, Yanni
ID - 2337
TI - Bose-Einstein condensation of dilute gases in traps
VL - 327
ER -
TY - JOUR
AB - We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the Gross-Pitaevskii (GP) limit of a dilute gas. Analysing both the absolute and the bosonic ground states of the system, we show, in particular, their different behaviour for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.
AU - Robert Seiringer
ID - 2354
IS - 37
JF - Journal of Physics A: Mathematical and Theoretical
TI - Ground state asymptotics of a dilute, rotating gas
VL - 36
ER -
TY - JOUR
AB - The classic Poincaré inequality bounds the L q-norm of a function f in a bounded domain Ω ⊂ ℝ n in terms of some L p-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Τ from Ω and concentrate our attention on Λ = Ω \ Τ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it might have a very bad constant. This is so even if the volume of Τ is arbitrarily small. A Poincaré inequality does hold, however, if one makes the additional assumption that f has a finite L p gradient norm on the whole of Ω, not just on Λ. The important point is that the Poincaré inequality thus obtained bounds the L q-norm of f in terms of the L p gradient norm on Λ (not Ω) plus an additional term that goes to zero as the volume of Τ goes to zero. This error term depends on Τ only through its volume. Apart from this additive error term, the constant in the inequality remains that of the 'nice' domain Ω. In the second generalization we are given a vector field A and replace ∇ by ∇ + iA(x) (geometrically, a connection on a U(1) bundle). Unlike the A = 0 case, the infimum of ∥(∇ + iA)f∥ p over all f with a given ∥f∥ q is in general not zero. This permits an improvement of the inequality by the addition of a term whose sharp value we derive. We describe some open problems that arise from these generalizations.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2357
IS - 3
JF - Annals of Mathematics
TI - Poincaré inequalities in punctured domains
VL - 158
ER -
TY - JOUR
AB - A study was conducted on the one-dimensional (1D) bosons in three-dimensional (3D) traps. A rigorous analysis was carried out on the parameter regions in which various types of 1D or 3D behavior occurred in the ground state. The four parameter regions include density, transverse, longitudinal dimensions and scattering length.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2358
IS - 15
JF - Physical Review Letters
TI - One-dimensional Bosons in three-dimensional traps
VL - 91
ER -
TY - THES
AU - Uli Wagner
ID - 2414
TI - On k-Sets and Their Applications
ER -
TY - CONF
AB - We prove a lower bound of 0.3288(4 n) for the rectilinear crossing number cr̄(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadrilaterals in any set of n points in general position in the Euclidean plane. As we see it, the main contribution of this paper is not so much the concrete numerical improvement over earlier bounds, as the novel method of proof, which is not based on bounding cr̄(Kn) for some small n.
AU - Uli Wagner
ID - 2422
TI - On the rectilinear crossing number of complete graphs
ER -
TY - CONF
AB - A finite set N ⊃ Rd is a weak ε-net for an n-point set X ⊃ Rd (with respect to convex sets) if N intersects every convex set K with |K ∩ X| ≥ εn. We give an alternative, and arguably simpler, proof of the fact, first shown by Chazelle et al. [7], that every point set X in Rd admits a weak ε-net of cardinality O(ε-d polylog(1/ε)). Moreover, for a number of special point sets (e.g., for points on the moment curve), our method gives substantially better bounds. The construction yields an algorithm to construct such weak ε-nets in time O(n ln(1/ε)). We also prove, by a different method, a near-linear upper bound for points uniformly distributed on the (d - 1)-dimensional sphere.
AU - Matoušek, Jiří
AU - Uli Wagner
ID - 2423
TI - New constructions of weak epsilon-nets
ER -
TY - CONF
AB - We introduce the adaptive neighborhood graph as a data structure for modeling a smooth manifold M embedded in some (potentially very high-dimensional) Euclidean space ℝd. We assume that M is known to us only through a finite sample P ⊂ M, as it is often the case in applications. The adaptive neighborhood graph is a geometric graph on P. Its complexity is at most min{2O(k)(n, n2}, where n = |P| and k = dim M, as opposed to the n⌈d/2⌉ complexity of the Delaunay triangulation, which is often used to model manifolds. We show that we can provably correctly infer the connectivity of M and the dimension of M from the adaptive neighborhood graph provided a certain standard sampling condition is fulfilled. The running time of the dimension detection algorithm is d2O(k7 log k) for each connected component of M. If the dimension is considered constant, this is a constant-time operation, and the adaptive neighborhood graph is of linear size. Moreover, the exponential dependence of the constants is only on the intrinsic dimension k, not on the ambient dimension d. This is of particular interest if the co-dimension is high, i.e., if k is much smaller than d, as is the case in many applications. The adaptive neighborhood graph also allows us to approximate the geodesic distances between the points in P.
AU - Giesen, Joachim
AU - Uli Wagner
ID - 2424
TI - Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
ER -
TY - JOUR
AB - Patients with Hodgkin's disease can develop paraneoplastic cerebellar ataxia because of the generation of autoantibodies against mGluR1 (mGluR1-Abs). Yet, the pathophysiological mechanisms underlying their motor coordination deficits remain to be elucidated. Here, we show that application of IgG purified from the patients' serum to cerebellar slices of mice acutely reduces the basal activity of Purkinje cells, whereas application to the flocculus of mice in vivo evokes acute disturbances in the performance of their compensatory eye movements. In addition, the mGluR1-Abs block induction of long-term depression in cultured mouse Purkinje cells, whereas the cerebellar motor learning behavior of the patients is affected in that they show impaired adaptation of their saccadic eye movements. Finally, postmortem analysis of the cerebellum of a paraneoplastic cerebellar ataxia patient showed that the number of Purkinje cells was significantly reduced by approximately two thirds compared with three controls. We conclude that autoantibodies against mGluR1 can cause cerebellar motor coordination deficits caused by a combination of rapid effects on both acute and plastic responses of Purkinje cells and chronic degenerative effects.
AU - Coesmans, Michiel P
AU - Sillevis-Smitt, Peter A
AU - Linden, David J
AU - Ryuichi Shigemoto
AU - Hirano, Tomoo
AU - Yamakawa, Yoshinori
AU - Van Alphen, Adriaan M
AU - Luo, Chongde
AU - Van Der Geest, Jos N
AU - Kros, Johan M
AU - Gaillard, Carlo A
AU - Frens, Maarten A
AU - De Zeeuw, Chris I
ID - 2623
IS - 3
JF - Annals of Neurology
TI - Mechanisms underlying cerebellar motor deficits due to mGluR1-autoantibodies
VL - 53
ER -