TY - JOUR
AB - We review recent results concerning the mathematical properties of the Bardeen-Cooper-Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers, partly in collaboration with R. Frank, E. Hamza, S. Naboko, and J. P. Solovej. Our discussion includes, in particular, an investigation of the critical temperature for a general class of interaction potentials, as well as a study of its dependence on external fields. We shall explain how the Ginzburg-Landau model can be derived from the BCS theory in a suitable parameter regime.
AU - Hainzl, Christian
AU - Seiringer, Robert
ID - 1486
IS - 2
JF - Journal of Mathematical Physics
TI - The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties
VL - 57
ER -
TY - JOUR
AB - Rhythms with time scales of multiple cycles per second permeate the mammalian brain, yet neuroscientists are not certain of their functional roles. One leading idea is that coherent oscillation between two brain regions facilitates the exchange of information between them. In rats, the hippocampus and the vibrissal sensorimotor system both are characterized by rhythmic oscillation in the theta range, 5–12 Hz. Previous work has been divided as to whether the two rhythms are independent or coherent. To resolve this question, we acquired three measures from rats—whisker motion, hippocampal local field potential (LFP), and barrel cortex unit firing—during a whisker-mediated texture discrimination task and during control conditions (not engaged in a whisker-mediated memory task). Compared to control conditions, the theta band of hippocampal LFP showed a marked increase in power as the rats approached and then palpated the texture. Phase synchronization between whisking and hippocampal LFP increased by almost 50% during approach and texture palpation. In addition, a greater proportion of barrel cortex neurons showed firing that was phase-locked to hippocampal theta while rats were engaged in the discrimination task. Consistent with a behavioral consequence of phase synchronization, the rats identified the texture more rapidly and with lower error likelihood on trials in which there was an increase in theta-whisking coherence at the moment of texture palpation. These results suggest that coherence between the whisking rhythm, barrel cortex firing, and hippocampal LFP is augmented selectively during epochs in which the rat collects sensory information and that such coherence enhances the efficiency of integration of stimulus information into memory and decision-making centers.
AU - Grion, Natalia
AU - Akrami, Athena
AU - Zuo, Yangfang
AU - Stella, Federico
AU - Diamond, Mathew
ID - 1487
IS - 2
JF - PLoS Biology
TI - Coherence between rat sensorimotor system and hippocampus is enhanced during tactile discrimination
VL - 14
ER -
TY - JOUR
AB - Branching morphogenesis of the epithelial ureteric bud forms the renal collecting duct system and is critical for normal nephron number, while low nephron number is implicated in hypertension and renal disease. Ureteric bud growth and branching requires GDNF signaling from the surrounding mesenchyme to cells at the ureteric bud tips, via the Ret receptor tyrosine kinase and coreceptor Gfrα1; Ret signaling up-regulates transcription factors Etv4 and Etv5, which are also critical for branching. Despite extensive knowledge of the genetic control of these events, it is not understood, at the cellular level, how renal branching morphogenesis is achieved or how Ret signaling influences epithelial cell behaviors to promote this process. Analysis of chimeric embryos previously suggested a role for Ret signaling in promoting cell rearrangements in the nephric duct, but this method was unsuited to study individual cell behaviors during ureteric bud branching. Here, we use Mosaic Analysis with Double Markers (MADM), combined with organ culture and time-lapse imaging, to trace the movements and divisions of individual ureteric bud tip cells. We first examine wild-type clones and then Ret or Etv4 mutant/wild-type clones in which the mutant and wild-type sister cells are differentially and heritably marked by green and red fluorescent proteins. We find that, in normal kidneys, most individual tip cells behave as self-renewing progenitors, some of whose progeny remain at the tips while others populate the growing UB trunks. In Ret or Etv4 MADM clones, the wild-type cells generated at a UB tip are much more likely to remain at, or move to, the new tips during branching and elongation, while their Ret−/− or Etv4−/− sister cells tend to lag behind and contribute only to the trunks. By tracking successive mitoses in a cell lineage, we find that Ret signaling has little effect on proliferation, in contrast to its effects on cell movement. Our results show that Ret/Etv4 signaling promotes directed cell movements in the ureteric bud tips, and suggest a model in which these cell movements mediate branching morphogenesis.
AU - Riccio, Paul
AU - Cebrián, Cristina
AU - Zong, Hui
AU - Hippenmeyer, Simon
AU - Costantini, Frank
ID - 1488
IS - 2
JF - PLoS Biology
TI - Ret and Etv4 promote directed movements of progenitor cells during renal branching morphogenesis
VL - 14
ER -
TY - JOUR
AB - We prove optimal local law, bulk universality and non-trivial decay for the off-diagonal elements of the resolvent for a class of translation invariant Gaussian random matrix ensembles with correlated entries.
AU - Ajanki, Oskari H
AU - Erdös, László
AU - Krüger, Torben H
ID - 1489
IS - 2
JF - Journal of Statistical Physics
TI - Local spectral statistics of Gaussian matrices with correlated entries
VL - 163
ER -
TY - JOUR
AB - To induce adaptive immunity, dendritic cells (DCs) migrate through afferent lymphatic vessels (LVs) to draining lymph nodes (dLNs). This process occurs in several consecutive steps. Upon entry into lymphatic capillaries, DCs first actively crawl into downstream collecting vessels. From there, they are next passively and rapidly transported to the dLN by lymph flow. Here, we describe a role for the chemokine CCL21 in intralymphatic DC crawling. Performing time-lapse imaging in murine skin, we found that blockade of CCL21-but not the absence of lymph flow-completely abolished DC migration from capillaries toward collecting vessels and reduced the ability of intralymphatic DCs to emigrate from skin. Moreover, we found that in vitro low laminar flow established a CCL21 gradient along lymphatic endothelial monolayers, thereby inducing downstream-directed DC migration. These findings reveal a role for intralymphatic CCL21 in promoting DC trafficking to dLNs, through the formation of a flow-induced gradient.
AU - Russo, Erica
AU - Teijeira, Alvaro
AU - Vaahtomeri, Kari
AU - Willrodt, Ann
AU - Bloch, Joël
AU - Nitschké, Maximilian
AU - Santambrogio, Laura
AU - Kerjaschki, Dontscho
AU - Sixt, Michael K
AU - Halin, Cornelia
ID - 1490
IS - 7
JF - Cell Reports
TI - Intralymphatic CCL21 promotes tissue egress of dendritic cells through afferent lymphatic vessels
VL - 14
ER -
TY - JOUR
AB - We study the ground state of a trapped Bose gas, starting from the full many-body Schrödinger Hamiltonian, and derive the non-linear Schrödinger energy functional in the limit of a large particle number, when the interaction potential converges slowly to a Dirac delta function. Our method is based on quantitative estimates on the discrepancy between the full many-body energy and its mean-field approximation using Hartree states. These are proved using finite dimensional localization and a quantitative version of the quantum de Finetti theorem. Our approach covers the case of attractive interactions in the regime of stability. In particular, our main new result is a derivation of the 2D attractive non-linear Schrödinger ground state.
AU - Lewin, Mathieu
AU - Nam, Phan
AU - Rougerie, Nicolas
ID - 1491
IS - 9
JF - Transactions of the American Mathematical Society
TI - The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases
VL - 368
ER -
TY - JOUR
AB - To sustain a lifelong ability to initiate organs, plants retain pools of undifferentiated cells with a preserved prolif eration capacity. The root pericycle represents a unique tissue with conditional meristematic activity, and its tight control determines initiation of lateral organs. Here we show that the meristematic activity of the pericycle is constrained by the interaction with the adjacent endodermis. Release of these restraints by elimination of endo dermal cells by single-cell ablation triggers the pericycle to re-enter the cell cycle. We found that endodermis removal substitutes for the phytohormone auxin-dependent initiation of the pericycle meristematic activity. However, auxin is indispensable to steer the cell division plane orientation of new organ-defining divisions. We propose a dual, spatiotemporally distinct role for auxin during lateral root initiation. In the endodermis, auxin releases constraints arising from cell-to-cell interactions that compromise the pericycle meristematic activity, whereas, in the pericycle, auxin defines the orientation of the cell division plane to initiate lateral roots.
AU - Marhavy, Peter
AU - Montesinos López, Juan C
AU - Abuzeineh, Anas
AU - Van Damme, Daniël
AU - Vermeer, Joop
AU - Duclercq, Jérôme
AU - Rakusova, Hana
AU - Marhavá, Petra
AU - Friml, Jirí
AU - Geldner, Niko
AU - Benková, Eva
ID - 1492
IS - 4
JF - Genes and Development
TI - Targeted cell elimination reveals an auxin-guided biphasic mode of lateral root initiation
VL - 30
ER -
TY - JOUR
AB - We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151–164 2011) for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence.
AU - Petrat, Sören P
AU - Pickl, Peter
ID - 1493
IS - 1
JF - Mathematical Physics, Analysis and Geometry
TI - A new method and a new scaling for deriving fermionic mean-field dynamics
VL - 19
ER -
TY - JOUR
AB - The two-photon 1s2 2s 2p 3P0 1s22s2 1S0 transition in berylliumlike ions is theoretically investigated within a fully relativistic framework and a second-order perturbation theory. We focus our analysis on how electron correlation, as well as the negative-energy spectrum, can affect the forbidden E1M1 decay rate. For this purpose, we include the electronic correlation via an effective local potential and within a single configuration-state model. Due to its experimental interest, evaluations of decay rates are performed for berylliumlike xenon and uranium. We find that the negative-energy contribution can be neglected at the present level of accuracy in the evaluation of the decay rate. On the other hand, if contributions of electronic correlation are not carefully taken into account, it may change the lifetime of the metastable state by up to 20%. By performing a full-relativistic jj-coupling calculation, we found a decrease of the decay rate by two orders of magnitude compared to non-relativistic LS-coupling calculations, for the selected heavy ions.
AU - Amaro, Pedro
AU - Fratini, Filippo
AU - Safari, Laleh
AU - Machado, Jorge
AU - Guerra, Mauro
AU - Indelicato, Paul
AU - Santos, José
ID - 1496
IS - 3
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Relativistic evaluation of the two-photon decay of the metastable 1s22s2p3P0 state in berylliumlike ions with an effective-potential model
VL - 93
ER -
TY - JOUR
AB - The inference of demographic history from genome data is hindered by a lack of efficient computational approaches. In particular, it has proved difficult to exploit the information contained in the distribution of genealogies across the genome. We have previously shown that the generating function (GF) of genealogies can be used to analytically compute likelihoods of demographic models from configurations of mutations in short sequence blocks (Lohse et al. 2011). Although the GF has a simple, recursive form, the size of such likelihood calculations explodes quickly with the number of individuals and applications of this framework have so far been mainly limited to small samples (pairs and triplets) for which the GF can be written by hand. Here we investigate several strategies for exploiting the inherent symmetries of the coalescent. In particular, we show that the GF of genealogies can be decomposed into a set of equivalence classes that allows likelihood calculations from nontrivial samples. Using this strategy, we automated blockwise likelihood calculations for a general set of demographic scenarios in Mathematica. These histories may involve population size changes, continuous migration, discrete divergence, and admixture between multiple populations. To give a concrete example, we calculate the likelihood for a model of isolation with migration (IM), assuming two diploid samples without phase and outgroup information. We demonstrate the new inference scheme with an analysis of two individual butterfly genomes from the sister species Heliconius melpomene rosina and H. cydno.
AU - Lohse, Konrad
AU - Chmelik, Martin
AU - Martin, Simon
AU - Barton, Nicholas H
ID - 1518
IS - 2
JF - Genetics
TI - Efficient strategies for calculating blockwise likelihoods under the coalescent
VL - 202
ER -
TY - JOUR
AB - We classify smooth Brunnian (i.e., unknotted on both components) embeddings (S2 × S1) ⊔ S3 → ℝ6. Any Brunnian embedding (S2 × S1) ⊔ S3 → ℝ6 is isotopic to an explicitly constructed embedding fk,m,n for some integers k, m, n such that m ≡ n (mod 2). Two embeddings fk,m,n and fk′ ,m′,n′ are isotopic if and only if k = k′, m ≡ m′ (mod 2k) and n ≡ n′ (mod 2k). We use Haefliger’s classification of embeddings S3 ⊔ S3 → ℝ6 in our proof. The relation between the embeddings (S2 × S1) ⊔ S3 → ℝ6 and S3 ⊔ S3 → ℝ6 is not trivial, however. For example, we show that there exist embeddings f: (S2 ×S1) ⊔ S3 → ℝ6 and g, g′ : S3 ⊔ S3 → ℝ6 such that the componentwise embedded connected sum f # g is isotopic to f # g′ but g is not isotopic to g′.
AU - Avvakumov, Serhii
ID - 1522
IS - 1
JF - Moscow Mathematical Journal
TI - The classification of certain linked 3-manifolds in 6-space
VL - 16
ER -
TY - JOUR
AB - For random graphs, the containment problem considers the probability that a binomial random graph G(n, p) contains a given graph as a substructure. When asking for the graph as a topological minor, i.e., for a copy of a subdivision of the given graph, it is well known that the (sharp) threshold is at p = 1/n. We consider a natural analogue of this question for higher-dimensional random complexes Xk(n, p), first studied by Cohen, Costa, Farber and Kappeler for k = 2. Improving previous results, we show that p = Θ(1/ √n) is the (coarse) threshold for containing a subdivision of any fixed complete 2-complex. For higher dimensions k > 2, we get that p = O(n−1/k) is an upper bound for the threshold probability of containing a subdivision of a fixed k-dimensional complex.
AU - Gundert, Anna
AU - Wagner, Uli
ID - 1523
IS - 4
JF - Proceedings of the American Mathematical Society
TI - On topological minors in random simplicial complexes
VL - 144
ER -
TY - CONF
AB - When designing genetic circuits, the typical primitives used in major existing modelling formalisms are gene interaction graphs, where edges between genes denote either an activation or inhibition relation. However, when designing experiments, it is important to be precise about the low-level mechanistic details as to how each such relation is implemented. The rule-based modelling language Kappa allows to unambiguously specify mechanistic details such as DNA binding sites, dimerisation of transcription factors, or co-operative interactions. Such a detailed description comes with complexity and computationally costly executions. We propose a general method for automatically transforming a rule-based program, by eliminating intermediate species and adjusting the rate constants accordingly. To the best of our knowledge, we show the first automated reduction of rule-based models based on equilibrium approximations.
Our algorithm is an adaptation of an existing algorithm, which was designed for reducing reaction-based programs; our version of the algorithm scans the rule-based Kappa model in search for those interaction patterns known to be amenable to equilibrium approximations (e.g. Michaelis-Menten scheme). Additional checks are then performed in order to verify if the reduction is meaningful in the context of the full model. The reduced model is efficiently obtained by static inspection over the rule-set. The tool is tested on a detailed rule-based model of a λ-phage switch, which lists 92 rules and 13 agents. The reduced model has 11 rules and 5 agents, and provides a dramatic reduction in simulation time of several orders of magnitude.
AU - Beica, Andreea
AU - Guet, Calin C
AU - Petrov, Tatjana
ID - 1524
TI - Efficient reduction of kappa models by static inspection of the rule-set
VL - 9271
ER -
TY - CONF
AB - We present the first study of robustness of systems that are both timed as well as reactive (I/O). We study the behavior of such timed I/O systems in the presence of uncertain inputs and formalize their robustness using the analytic notion of Lipschitz continuity: a timed I/O system is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation using similarity functions over timed words such as the timed version of the Manhattan distance and the Skorokhod distance. We consider two models of timed I/O systems — timed transducers and asynchronous sequential circuits. We show that K-robustness of timed transducers can be decided in polynomial space under certain conditions. For asynchronous sequential circuits, we reduce K-robustness w.r.t. timed Manhattan distances to K-robustness of discrete letter-to-letter transducers and show PSpace-completeness of the problem.
AU - Henzinger, Thomas A
AU - Otop, Jan
AU - Samanta, Roopsha
ID - 1526
TI - Lipschitz robustness of timed I/O systems
VL - 9583
ER -
TY - JOUR
AB - We consider partially observable Markov decision processes (POMDPs) with a set of target states and an integer cost associated with every transition. The optimization objective we study asks to minimize the expected total cost of reaching a state in the target set, while ensuring that the target set is reached almost surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost, both double exponential in the POMDP state space size; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst-case running time of our algorithm is double exponential, we also present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples of interest.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 1529
JF - Artificial Intelligence
TI - Optimal cost almost-sure reachability in POMDPs
VL - 234
ER -
TY - JOUR
AB - We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our sufficient conditions are optimal in the sense that they become necessary when the relevant one-body operators commute.
AU - Nam, Phan
AU - Napiórkowski, Marcin M
AU - Solovej, Jan
ID - 1545
IS - 11
JF - Journal of Functional Analysis
TI - Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
VL - 270
ER -
TY - JOUR
AB - Antibiotic resistance carries a fitness cost that must be overcome in order for resistance to persist over the long term. Compensatory mutations that recover the functional defects associated with resistance mutations have been argued to play a key role in overcoming the cost of resistance, but compensatory mutations are expected to be rare relative to generally beneficial mutations that increase fitness, irrespective of antibiotic resistance. Given this asymmetry, population genetics theory predicts that populations should adapt by compensatory mutations when the cost of resistance is large, whereas generally beneficial mutations should drive adaptation when the cost of resistance is small. We tested this prediction by determining the genomic mechanisms underpinning adaptation to antibiotic-free conditions in populations of the pathogenic bacterium Pseudomonas aeruginosa that carry costly antibiotic resistance mutations. Whole-genome sequencing revealed that populations founded by high-cost rifampicin-resistant mutants adapted via compensatory mutations in three genes of the RNA polymerase core enzyme, whereas populations founded by low-cost mutants adapted by generally beneficial mutations, predominantly in the quorum-sensing transcriptional regulator gene lasR. Even though the importance of compensatory evolution in maintaining resistance has been widely recognized, our study shows that the roles of general adaptation in maintaining resistance should not be underestimated and highlights the need to understand how selection at other sites in the genome influences the dynamics of resistance alleles in clinical settings.
AU - Qi, Qin
AU - Toll Riera, Macarena
AU - Heilbron, Karl
AU - Preston, Gail
AU - Maclean, R Craig
ID - 1552
IS - 1822
JF - Proceedings of the Royal Society of London Series B Biological Sciences
TI - The genomic basis of adaptation to the fitness cost of rifampicin resistance in Pseudomonas aeruginosa
VL - 283
ER -
TY - JOUR
AB - The addition of polysialic acid to N- and/or O-linked glycans, referred to as polysialylation, is a rare posttranslational modification that is mainly known to control the developmental plasticity of the nervous system. Here we show that CCR7, the central chemokine receptor controlling immune cell trafficking to secondary lymphatic organs, carries polysialic acid. This modification is essential for the recognition of the CCR7 ligand CCL21. As a consequence, dendritic cell trafficking is abrogated in polysialyltransferase-deficient mice, manifesting as disturbed lymph node homeostasis and unresponsiveness to inflammatory stimuli. Structure-function analysis of chemokine-receptor interactions reveals that CCL21 adopts an autoinhibited conformation, which is released upon interaction with polysialic acid. Thus, we describe a glycosylation-mediated immune cell trafficking disorder and its mechanistic basis.
AU - Kiermaier, Eva
AU - Moussion, Christine
AU - Veldkamp, Christopher
AU - Gerardy Schahn, Rita
AU - De Vries, Ingrid
AU - Williams, Larry
AU - Chaffee, Gary
AU - Phillips, Andrew
AU - Freiberger, Friedrich
AU - Imre, Richard
AU - Taleski, Deni
AU - Payne, Richard
AU - Braun, Asolina
AU - Förster, Reinhold
AU - Mechtler, Karl
AU - Mühlenhoff, Martina
AU - Volkman, Brian
AU - Sixt, Michael K
ID - 1599
IS - 6269
JF - Science
TI - Polysialylation controls dendritic cell trafficking by regulating chemokine recognition
VL - 351
ER -
TY - JOUR
AB - We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional structure allowing a description through transfer matrices which involve some Schur complement. For such operators we introduce the notion of having one propagating channel and extend theorems from the theory of one-dimensional Jacobi operators that relate the behavior of transfer matrices with the spectrum. These theorems are then applied to the considered model. In essence, in a certain energy region the kinetic part averages the random potentials along shells and the transfer matrices behave similar as for a one-dimensional operator with random potential of decaying variance. At d dimensional growth for d>2 this effective decay is strong enough to obtain absolutely continuous spectrum, whereas for some uniform d dimensional growth with d<2 one has pure point spectrum in this energy region. At exactly uniform 2 dimensional growth also some singular continuous spectrum appears, at least at small disorder. As a corollary we also obtain a change from singular spectrum (d≤2) to absolutely continuous spectrum (d≥3) for random operators of the type rΔdr+λ on ℤd, where r is an orthogonal radial projection, Δd the discrete adjacency operator (Laplacian) on ℤd and λ a random potential.
AU - Sadel, Christian
ID - 1608
IS - 7
JF - Annales Henri Poincare
TI - Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel
VL - 17
ER -
TY - JOUR
AB - We prove that whenever A is a 3-conservative relational structure with only binary and unary relations,then the algebra of polymorphisms of A either has no Taylor operation (i.e.,CSP(A)is NP-complete),or it generates an SD(∧) variety (i.e.,CSP(A)has bounded width).
AU - Kazda, Alexandr
ID - 1612
IS - 1
JF - Algebra Universalis
TI - CSP for binary conservative relational structures
VL - 75
ER -