@inbook{2705,
author = {László Erdös},
booktitle = {Spectral Theory and Mathematical Physics: a Festschrift in Honor of Barry Simon's 60th Birthday },
editor = {Gesztesy, Fritz and Deift, Percy and Galvez, Percy and Perry, Peter and Schlag, Wilhelm},
pages = {401 -- 428},
publisher = {American Mathematical Society},
title = {{Recent developments in quantum mechanics with magnetic fields}},
volume = {76},
year = {2007},
}
@article{2748,
abstract = {The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.},
author = {László Erdös and Schlein, Benjamin and Yau, Horng-Tzer},
journal = {Physical Review Letters},
number = {4},
publisher = {American Physical Society},
title = {{Rigorous derivation of the Gross-Pitaevskii equation}},
doi = {10.1103/PhysRevLett.98.040404},
volume = {98},
year = {2007},
}
@misc{2749,
abstract = {We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k. },
author = {László Erdös and Schlein, Benjamin and Yau, Horng-Tzer},
booktitle = {Inventiones Mathematicae},
number = {3},
pages = {515 -- 614},
publisher = {Springer},
title = {{Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems}},
doi = {10.1007/s00222-006-0022-1},
volume = {167},
year = {2007},
}
@article{2750,
abstract = {We consider random Schrödinger equations on ℝd for d ≥ 3 with a homogeneous Anderson-Poisson type random potential. Denote by λ the coupling constant and ψt the solution with initial data ψ0. The space and time variables scale as χ ≃λ-2-κ/2, t ≃λ-2-κ with 0 < kappa; < kappa;0(d). We prove that, in the limit λ → 0, the expectation of the Wigner distribution of ψt converges weakly to the solution of a heat equation in the space variable x for arbitrary L2 initial data. The proof is based on a rigorous analysis of Feynman diagrams. In the companion paper [10] the analysis of the non-repetition diagrams was presented. In this paper we complete the proof by estimating the recollision diagrams and showing that the main terms, i.e. the ladder diagrams with renormalized propagator, converge to the heat equation.},
author = {László Erdös and Salmhofer, Manfred and Yau, Horng-Tzer},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {1 -- 53},
publisher = {Springer},
title = {{Quantum diffusion of the random Schrödinger evolution in the scaling limit II. The recollision diagrams}},
doi = {10.1007/s00220-006-0158-2},
volume = {271},
year = {2007},
}
@article{2751,
abstract = {We consider random Schrödinger equations on ℤd for d ≥ 3 with identically distributed random potential. Denote by λ the coupling constant and ψ t the solution with initial data ψ 0. The space and time variables scale as x ∼ λ -2-κ/2,t ∼ λ-2-κ with 0 < κ < κ0(d). We prove that, in the limit λ → 0, the expectation of the Wigner distribution of ψ t converges weakly to a solution of a heat equation in the space variable x for arbitrary L 2 initial data. The diffusion coefficient is uniquely determined by the kinetic energy associated to the momentum υ. This work is an extension to the lattice case of our previous result in the continuum [8,9]. Due to the non-convexity of the level surfaces of the dispersion relation, the estimates of several Feynman graphs are more involved.},
author = {László Erdös and Salmhofer, Manfred and Yau, Horng-Tzer},
journal = {Annales Henri Poincare},
number = {4},
pages = {621 -- 685},
publisher = {Birkhäuser},
title = {{Quantum diffusion for the Anderson model in the scaling limit}},
doi = {10.1007/s00023-006-0318-0},
volume = {8},
year = {2007},
}
@article{2752,
abstract = {We prove L p -bounds on the Fourier transform of measures μ supported on two dimensional surfaces. Our method allows to consider surfaces whose Gauss curvature vanishes on a one-dimensional submanifold. Under a certain non-degeneracy condition, we prove that μ ∧ ε L 4+β, β > 0, and we give a logarithmically divergent bound on the L 4-norm. We use this latter bound to estimate almost singular integrals involving the dispersion relation, e(p)= ∑13 [1-\cos p_j]} , of the discrete Laplace operator on the cubic lattice. We briefly explain our motivation for this bound originating in the theory of random Schrödinger operators.},
author = {László Erdös and Salmhofer, Manfred},
journal = {Mathematische Zeitschrift},
number = {2},
pages = {261 -- 294},
publisher = {Springer},
title = {{Decay of the Fourier transform of surfaces with vanishing curvature}},
doi = {10.1007/s00209-007-0125-4},
volume = {257},
year = {2007},
}
@misc{2793,
abstract = {Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile. Experiments on pipe flow, as well as plane Couette and plane Poiseuille flow, show that triggering turbulence depends sensitively on initial conditions, that between the laminar and the turbulent states there exists no intermediate state with simple spatial or temporal characteristics, and that turbulence is not persistent, i.e., it can decay again, if the observation time is long enough. All these features can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space. The goal of this review is to explain this concept, summarize the numerical and experimental evidence for pipe flow, and outline the consequences for related flows.},
author = {Eckhardt, Bruno and Schneider, Tobias M and Björn Hof and Westerweel, Jerry},
booktitle = {Annual Review of Fluid Mechanics},
pages = {447 -- 468},
publisher = {Annual Reviews},
title = {{Turbulence transition in pipe flow}},
doi = {10.1146/annurev.fluid.39.050905.110308},
volume = {39},
year = {2007},
}
@inproceedings{2794,
author = {Björn Hof and Tax, Wilco and Westerweel, Jerry},
pages = {556 -- 558},
publisher = {Springer},
title = {{Lifetime of turbulence in pipe flow}},
doi = {10.1007/978-3-540-72604-3_177},
volume = {117},
year = {2007},
}
@article{2893,
abstract = {Summary: Regulatory CD4+ T cells, enriched in the CD25 pool of healthy individuals, mediate natural tolerance and prevent autoimmune diseases. Despite their fundamental and potential clinical significance, regulatory T (TR) cells have not yet been incorporated in a coherent theory of the immune system. This article reviews experimental evidence and theoretical arguments supporting a model of TR cell dynamics, uncovering some of its most relevant biological implications. According to this model, the persistence and expansion of TR cell populations depend strictly on specific interactions they make with antigen-presenting cells (APCs) and conventional effector T (TE) cells. This three-partner crossregulation imposes that TR cells feed on the specific autoimmune activities they suppress, with implications ranging from their interactions with other cells to their repertoire selection in the periphery and in the thymus, and to the relationship between these cells and the innate immune system. These implications stem from the basic prediction that the peripheral dynamics sort the CD4+ T-cell repertoire into two subsets: a less diverse set of small clones of autoreactive effector and regulatory cells that regulate each other’s growth, and a more diverse set of barely autoreactive TE cell clones, whose expansion is limited only by APC availability. It is argued that such partitioning of the repertoire sets the ground for self–non-self discrimination. },
author = {Carneiro, Jorge and Leon, Kalet and Caramalho, Íris and Van Den Dool, Carline and Gardner, Rui and Oliveira, Vanessa and Bergman, Marie L and Sepúlveda, Nuno and Tiago Paixao and Faro, Jose and Demengeot, Jocelyne},
journal = {Immunological Reviews},
number = {1},
pages = {48 -- 68},
publisher = {Wiley-Blackwell},
title = {{When three is not a crowd a Crossregulation Model of the dynamics and repertoire selection of regulatory CD4 T cells}},
doi = {10.1111/j.1600-065X.2007.00487.x},
volume = {216},
year = {2007},
}
@article{2896,
abstract = {Gene expression from both parental alleles is beneficial by masking the effects of deleterious recessive mutations and by reducing the noise in gene expression in diploid organisms. However, a class of genes are expressed preferentially or strictly from a single allele. The selective advantage of avoiding biallelic expression is clear for allelic-excluded antigen receptor and odorant receptor genes, genes undergoing X-chromosome inactivation in females and parental genomic imprinted genes. In contrast, there is no clear biological rationale for the predominant and stochastic monoallelic expression of cytokine genes in the immune system, and the underlying mechanism is elusive and controversial. A clarification of the mechanism of predominant monoallelic expression would be instrumental in better understanding its eventual biological functional. This prompted the development of a quantitative framework that could describe the dynamics of the pattern of allele expression of the IL-10 gene, from which general quantitative insights could be gained. We report that the experimental observations on these patterns of allelic expression cannot be easily reconciled with a simple model of stochastic transcriptional activation, in which the two alleles are, at any time, equally competent for transcription. Instead, these observations call into action a general model of eukaryotic transcriptional regulation according to which the locus competence for transcription is dynamic, involving multiple, cooperative and stochastic modification steps. In this model, the probability that an allele becomes transcriptionally active is a function of the number of chromatin modifications that it accumulated. On the basis of the properties of this model, we argue that predominant monoallelic expression might have had no adaptive role, and may have evolved under indirect selection for low frequency of expressing cells.},
author = {Tiago Paixao and Carvalho, Tiago P and Calado, Dinis P and Carneiro, Jorge},
journal = {Immunology and Cell Biology},
number = {4},
pages = {315 -- 322},
publisher = {Nature Publishing Group},
title = {{Quantitative insights into stochastic monoallelic expression of cytokine genes}},
doi = {10.1038/sj.icb.7100057},
volume = {85},
year = {2007},
}
@inproceedings{2933,
author = {Kumar, M Pawan and Vladimir Kolmogorov and Torr, Philip H},
publisher = {Neural Information Processing Systems},
title = {{An Analysis of Convex Relaxations for MAP Estimation}},
year = {2007},
}
@article{8027,
abstract = {Gating deficits and hallucinatory sensations are prominent symptoms of schizophrenia. Comparing these abnormalities with the failure modes of network models is an interesting way to explore how they arise. We present a network model that can both propagate and gate signals. The model exhibits effects reminiscent of clinically observed pathologies when the balance between excitation and inhibition that it requires is not properly maintained.},
author = {Vogels, Tim P and Abbott, L.},
issn = {0176-3679},
journal = {Pharmacopsychiatry},
number = {S 1},
pages = {S73--S77},
publisher = {Thieme},
title = {{Gating deficits in model networks: A path to schizophrenia?}},
doi = {10.1055/s-2007-992130},
volume = {40},
year = {2007},
}
@article{8483,
abstract = {Atom-resolved real-time studies of kinetic processes in proteins have been hampered in the past by the lack of experimental techniques that yield sufficient temporal and atomic resolution. Here we present band-selective optimized flip-angle short transient (SOFAST) real-time 2D NMR spectroscopy, a method that allows simultaneous observation of reaction kinetics for a large number of nuclear sites along the polypeptide chain of a protein with an unprecedented time resolution of a few seconds. SOFAST real-time 2D NMR spectroscopy combines fast NMR data acquisition techniques with rapid sample mixing inside the NMR magnet to initiate the kinetic event. We demonstrate the use of SOFAST real-time 2D NMR to monitor the conformational transition of α-lactalbumin from a molten globular to the native state for a large number of amide sites along the polypeptide chain. The kinetic behavior observed for the disappearance of the molten globule and the appearance of the native state is monoexponential and uniform along the polypeptide chain. This observation confirms previous findings that a single transition state ensemble controls folding of α-lactalbumin from the molten globule to the native state. In a second application, the spontaneous unfolding of native ubiquitin under nondenaturing conditions is characterized by amide hydrogen exchange rate constants measured at high pH by using SOFAST real-time 2D NMR. Our data reveal that ubiquitin unfolds in a gradual manner with distinct unfolding regimes.},
author = {Schanda, Paul and Forge, V. and Brutscher, B.},
issn = {1091-6490},
journal = {Proceedings of the National Academy of Sciences},
keywords = {Multidisciplinary},
number = {27},
pages = {11257--11262},
publisher = {National Academy of Sciences},
title = {{Protein folding and unfolding studied at atomic resolution by fast two-dimensional NMR spectroscopy}},
doi = {10.1073/pnas.0702069104},
volume = {104},
year = {2007},
}
@article{8484,
abstract = {A series of sequential, intra-residue, and bi-directional BEST H–N–CA, H–N–CO, and H–N–CB pulse sequences is presented that extends the BEST concept introduced recently for fast multidimensional protein NMR [Schanda et al., J. Am. Chem. Soc. 128 (2006) 9042] to the complete set of experiments required for sequential resonance assignment. We demonstrate for the protein ubiquitin that 3D BEST H–N–C correlation spectra can be recorded on a 600 MHz NMR spectrometer equipped with a cryogenic probe in only a few minutes of acquisition time with sufficient sensitivity to detect all expected cross peaks.},
author = {Lescop, Ewen and Schanda, Paul and Brutscher, Bernhard},
issn = {1090-7807},
journal = {Journal of Magnetic Resonance},
number = {1},
pages = {163--169},
publisher = {Elsevier},
title = {{A set of BEST triple-resonance experiments for time-optimized protein resonance assignment}},
doi = {10.1016/j.jmr.2007.04.002},
volume = {187},
year = {2007},
}
@article{8485,
abstract = {High signal to noise is a necessity for the quantification of NMR spectral parameters to be translated into accurate and precise restraints on protein structure and dynamics. An important source of long-range structural information is obtained from 1H–1H residual dipolar couplings (RDCs) measured for weakly aligned molecules. For sensitivity reasons, such measurements are generally performed on highly deuterated protein samples. Here we show that high sensitivity is also obtained for protonated protein samples if the pulse schemes are optimized in terms of longitudinal relaxation efficiency and J-mismatch compensated coherence transfer. The new sensitivity-optimized quantitative J-correlation experiment yields important signal gains reaching factors of 1.5 to 8 for individual correlation peaks when compared to previously proposed pulse schemes.},
author = {Schanda, Paul and Lescop, Ewen and Falge, Mirjam and Sounier, Rémy and Boisbouvier, Jérôme and Brutscher, Bernhard},
issn = {0925-2738},
journal = {Journal of Biomolecular NMR},
keywords = {Spectroscopy, Biochemistry},
pages = {47--55},
publisher = {Springer Nature},
title = {{Sensitivity-optimized experiment for the measurement of residual dipolar couplings between amide protons}},
doi = {10.1007/s10858-006-9138-2},
volume = {38},
year = {2007},
}
@article{8486,
abstract = {A technique is described that allows reducing acquisition times of multidimensional NMR experiments by extensive spectral folding. The method is simple and has many interesting applications for NMR studies of molecular structure, dynamics, and kinetics.},
author = {Lescop, Ewen and Schanda, Paul and Rasia, Rodolfo and Brutscher, Bernhard},
issn = {0002-7863},
journal = {Journal of the American Chemical Society},
keywords = {Colloid and Surface Chemistry, Biochemistry, General Chemistry, Catalysis},
number = {10},
pages = {2756--2757},
publisher = {American Chemical Society},
title = {{Automated spectral compression for fast multidimensional NMR and increased time resolution in real-time NMR spectroscopy}},
doi = {10.1021/ja068949u},
volume = {129},
year = {2007},
}
@article{8487,
abstract = {Following unidirectional biophysical events such as the folding of proteins or the equilibration of binding interactions, requires experimental methods that yield information at both atomic-level resolution and at high repetition rates. Toward this end a number of different approaches enabling the rapid acquisition of 2D NMR spectra have been recently introduced, including spatially encoded “ultrafast” 2D NMR spectroscopy and SOFAST HMQC NMR. Whereas the former accelerates acquisitions by reducing the number of scans that are necessary for completing arbitrary 2D NMR experiments, the latter operates by reducing the delay between consecutive scans while preserving sensitivity. Given the complementarities between these two approaches it seems natural to combine them into a single tool, enabling the acquisition of full 2D protein NMR spectra at high repetition rates. We demonstrate here this capability with the introduction of “ultraSOFAST” HMQC NMR, a spatially encoded and relaxation-optimized approach that can provide 2D protein correlation spectra at ∼1 s repetition rates for samples in the ∼2 mM concentration range. The principles, relative advantages, and current limitations of this new approach are discussed, and its application is exemplified with a study of the fast hydrogen−deuterium exchange characterizing amide sites in Ubiquitin.},
author = {Gal, Maayan and Schanda, Paul and Brutscher, Bernhard and Frydman, Lucio},
issn = {0002-7863},
journal = {Journal of the American Chemical Society},
keywords = {Colloid and Surface Chemistry, Biochemistry, General Chemistry, Catalysis},
number = {5},
pages = {1372--1377},
publisher = {American Chemical Society},
title = {{UltraSOFAST HMQC NMR and the repetitive acquisition of 2D protein spectra at Hz rates}},
doi = {10.1021/ja066915g},
volume = {129},
year = {2007},
}
@article{8511,
abstract = {Here we study an amazing phenomenon discovered by Newhouse [S. Newhouse, Non-density of Axiom A(a) on S2, in: Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., 1970, pp. 191–202; S. Newhouse,
Diffeomorphisms with infinitely many sinks, Topology 13 (1974) 9–18; S. Newhouse, The abundance of
wild hyperbolic sets and nonsmooth stable sets of diffeomorphisms, Publ. Math. Inst. Hautes Études Sci.
50 (1979) 101–151]. It turns out that in the space of Cr smooth diffeomorphisms Diffr(M) of a compact
surface M there is an open set U such that a Baire generic diffeomorphism f ∈ U has infinitely many coexisting sinks. In this paper we make a step towards understanding “how often does a surface diffeomorphism
have infinitely many sinks.” Our main result roughly says that with probability one for any positive D a
surface diffeomorphism has only finitely many localized sinks either of cyclicity bounded by D or those
whose period is relatively large compared to its cyclicity. It verifies a particular case of Palis’ Conjecture
saying that even though diffeomorphisms with infinitely many coexisting sinks are Baire generic, they have
probability zero.
One of the key points of the proof is an application of Newton Interpolation Polynomials to study the dynamics initiated in [V. Kaloshin, B. Hunt, A stretched exponential bound on the rate of growth of the number
of periodic points for prevalent diffeomorphisms I, Ann. of Math., in press, 92 pp.; V. Kaloshin, A stretched
exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II,
preprint, 85 pp.].},
author = {Gorodetski, A. and Kaloshin, Vadim},
issn = {0001-8708},
journal = {Advances in Mathematics},
keywords = {General Mathematics},
number = {2},
pages = {710--797},
publisher = {Elsevier},
title = {{How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency}},
doi = {10.1016/j.aim.2006.03.012},
volume = {208},
year = {2007},
}
@article{8512,
abstract = {For diffeomorphisms of smooth compact finite-dimensional manifolds, we consider the problem of how fast the number of periodic points with period n grows as a function of n. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the first author has shown that arbitrarily fast growth is topologically (Baire) generic for C2 or smoother diffeomorphisms. In the present work we show that, by contrast, for a measure-theoretic notion of genericity we call “prevalence”, the growth is not much faster than exponential. Specifically, we show that for each ρ,δ>0, there is a prevalent set of C1+ρ (or smoother) diffeomorphisms for which the number of periodic n points is bounded above by exp(Cn1+δ) for some C independent of n. We also obtain a related bound on the decay of hyperbolicity of the periodic points as a function of n, and obtain the same results for 1-dimensional endomorphisms. The contrast between topologically generic and measure-theoretically generic behavior for the growth of the number of periodic points and the decay of their hyperbolicity show this to be a subtle and complex phenomenon, reminiscent of KAM theory. Here in Part I we state our results and describe the methods we use. We complete most of the proof in the 1-dimensional C2-smooth case and outline the remaining steps, deferred to Part II, that are needed to establish the general case.
The novel feature of the approach we develop in this paper is the introduction of Newton Interpolation Polynomials as a tool for perturbing trajectories of iterated maps.},
author = {Kaloshin, Vadim and Hunt, Brian},
issn = {0003-486X},
journal = {Annals of Mathematics},
number = {1},
pages = {89--170},
publisher = {Princeton University Press},
title = {{Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I}},
doi = {10.4007/annals.2007.165.89},
volume = {165},
year = {2007},
}
@article{860,
abstract = {We identified a mutation in the CRYGD gene (P23S) of the γ-crystallin gene cluster that is associated with a polymorphic congenital cataract that occurs with frequency of ∼0.3% in a human population. To gain insight into the molecular mechanism of the pathogenesis of γ-crystallin isoforms, we undertook an evolutionary analysis of the available mammalian and newly obtained primate sequences of the γ-crystallin genes. The cataract-associated serine at site 23 corresponds to the ancestral state, since it was found in CRYGD of a lower primate and all the surveyed nonprimate mammals. Crystallin proteins include two structurally similar domains, and substitutions in mammalian CRYGD protein at site 23 of the first domain were always associated with substitutions in the structurally reciprocal sites 109 and 136 of the second domain. These data suggest that the cataractogenic effect of serine at site 23 in the N-terminal domain of CRYGD may be compensated indirectly by amino acid changes in a distal domain. We also found that gene conversion was a factor in the evolution of the γ-crystallin gene cluster throughout different mammalian clades. The high rate of gene conversion observed between the functional CRYGD gene and two primate γ-crystallin pseudogenes (CRYGEP1 and CRYGFP1) coupled with a surprising finding of apparent negative selection in primate pseudogenes suggest a deleterious impact of recently derived pseudogenes involved in gene conversion in the γ-crystallin gene cluster.},
author = {Plotnikova, Olga V and Fyodor Kondrashov and Vlasov, Peter K and Grigorenko, Anastasia P and Ginter, Evgeny K and Rogaev, Evgeny I},
journal = {American Journal of Human Genetics},
number = {1},
pages = {32 -- 43},
publisher = {Cell Press},
title = {{Conversion and compensatory evolution of the γ-crystallin genes and identification of a cataractogenic mutation that reverses the sequence of the human CRYGD gene to an ancestral state}},
doi = {10.1086/518616},
volume = {81},
year = {2007},
}