@article{1328,
  abstract     = {Hole spins have gained considerable interest in the past few years due to their potential for fast electrically controlled qubits. Here, we study holes confined in Ge hut wires, a so-far unexplored type of nanostructure. Low-temperature magnetotransport measurements reveal a large anisotropy between the in-plane and out-of-plane g-factors of up to 18. Numerical simulations verify that this large anisotropy originates from a confined wave function of heavy-hole character. A light-hole admixture of less than 1% is estimated for the states of lowest energy, leading to a surprisingly large reduction of the out-of-plane g-factors compared with those for pure heavy holes. Given this tiny light-hole contribution, the spin lifetimes are expected to be very long, even in isotopically nonpurified samples.},
  author       = {Watzinger, Hannes and Kloeffel, Christoph and Vukusic, Lada and Rossell, Marta and Sessi, Violetta and Kukucka, Josip and Kirchschlager, Raimund and Lausecker, Elisabeth and Truhlar, Alisha and Glaser, Martin and Rastelli, Armando and Fuhrer, Andreas and Loss, Daniel and Katsaros, Georgios},
  journal      = {Nano Letters},
  number       = {11},
  pages        = {6879 -- 6885},
  publisher    = {American Chemical Society},
  title        = {{Heavy-hole states in germanium hut wires}},
  doi          = {10.1021/acs.nanolett.6b02715},
  volume       = {16},
  year         = {2016},
}

@article{1329,
  abstract     = {Daphnia species have become models for ecological genomics and exhibit interesting features, such as high phenotypic plasticity and a densely packed genome with many lineage-specific genes. They are also cyclic parthenogenetic, with alternating asexual and sexual cycles and environmental sex determination. Here, we present a de novo transcriptome assembly of over 32,000 D. galeata genes and use it to investigate gene expression in females and spontaneously produced males of two clonal lines derived from lakes in Germany and the Czech Republic. We find that only a low percentage (18%) of genes shows sex-biased expression and that there are many more female-biased gene (FBG) than male-biased gene (MBG). Furthermore, FBGs tend to be more conserved between species than MBGs in both sequence and expression. These patterns may be a consequence of cyclic parthenogenesis leading to a relaxation of purifying selection on MBGs. The two clonal lines show considerable differences in both number and identity of sex-biased genes, suggesting that they may have reproductive strategies differing in their investment in sexual reproduction. Orthologs of key genes in the sex determination and juvenile hormone pathways, which are thought to be important for the transition from asexual to sexual reproduction, are present in D. galeata and highly conserved among Daphnia species.},
  author       = {Huylmans, Ann K and López Ezquerra, Alberto and Parsch, John and Cordellier, Mathilde},
  journal      = {Genome Biology and Evolution},
  number       = {10},
  pages        = {3120 -- 3139},
  publisher    = {Oxford University Press},
  title        = {{De novo transcriptome assembly and sex-biased gene expression in the cyclical parthenogenetic Daphnia galeata}},
  doi          = {10.1093/gbe/evw221},
  volume       = {8},
  year         = {2016},
}

@article{1330,
  abstract     = {In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K.},
  author       = {Akopyan, Arseniy and Balitskiy, Alexey},
  journal      = {Israel Journal of Mathematics},
  number       = {2},
  pages        = {833 -- 845},
  publisher    = {Springer},
  title        = {{Billiards in convex bodies with acute angles}},
  doi          = {10.1007/s11856-016-1429-z},
  volume       = {216},
  year         = {2016},
}

@article{1331,
  abstract     = {Cytokinin is a phytohormone that is well known for its roles in numerous plant growth and developmental processes, yet it has also been linked to abiotic stress response in a less defined manner. Arabidopsis (Arabidopsis thaliana) Cytokinin Response Factor 6 (CRF6) is a cytokinin-responsive AP2/ERF-family transcription factor that, through the cytokinin signaling pathway, plays a key role in the inhibition of dark-induced senescence. CRF6 expression is also induced by oxidative stress, and here we show a novel function for CRF6 in relation to oxidative stress and identify downstream transcriptional targets of CRF6 that are repressed in response to oxidative stress. Analysis of transcriptomic changes in wild-type and crf6 mutant plants treated with H2O2 identified CRF6-dependent differentially expressed transcripts, many of which were repressed rather than induced. Moreover, many repressed genes also show decreased expression in 35S:CRF6 overexpressing plants. Together, these findings suggest that CRF6 functions largely as a transcriptional repressor. Interestingly, among the H2O2 repressed CRF6-dependent transcripts was a set of five genes associated with cytokinin processes: (signaling) ARR6, ARR9, ARR11, (biosynthesis) LOG7, and (transport) ABCG14. We have examined mutants of these cytokinin-associated target genes to reveal novel connections to oxidative stress. Further examination of CRF6-DNA interactions indicated that CRF6 may regulate its targets both directly and indirectly. Together, this shows that CRF6 functions during oxidative stress as a negative regulator to control this cytokinin-associated module of CRF6- dependent genes and establishes a novel connection between cytokinin and oxidative stress response.},
  author       = {Zwack, Paul and De Clercq, Inge and Howton, Timothy and Hallmark, H Tucker and Hurny, Andrej and Keshishian, Erika and Parish, Alyssa and Benková, Eva and Mukhtar, M Shahid and Van Breusegem, Frank and Rashotte, Aaron},
  issn         = {1532-2548},
  journal      = {Plant Physiology},
  number       = {2},
  pages        = {1249 -- 1258},
  publisher    = {American Society of Plant Biologists},
  title        = {{Cytokinin response factor 6 represses cytokinin-associated genes during oxidative stress}},
  doi          = {10.1104/pp.16.00415},
  volume       = {172},
  year         = {2016},
}

@article{1332,
  abstract     = {Antibiotic-sensitive and -resistant bacteria coexist in natural environments with low, if detectable, antibiotic concentrations. Except possibly around localized antibiotic sources, where resistance can provide a strong advantage, bacterial fitness is dominated by stresses unaffected by resistance to the antibiotic. How do such mixed and heterogeneous conditions influence the selective advantage or disadvantage of antibiotic resistance? Here we find that sub-inhibitory levels of tetracyclines potentiate selection for or against tetracycline resistance around localized sources of almost any toxin or stress. Furthermore, certain stresses generate alternating rings of selection for and against resistance around a localized source of the antibiotic. In these conditions, localized antibiotic sources, even at high strengths, can actually produce a net selection against resistance to the antibiotic. Our results show that interactions between the effects of an antibiotic and other stresses in inhomogeneous environments can generate pervasive, complex patterns of selection both for and against antibiotic resistance.},
  author       = {Chait, Remy P and Palmer, Adam and Yelin, Idan and Kishony, Roy},
  journal      = {Nature Communications},
  publisher    = {Nature Publishing Group},
  title        = {{Pervasive selection for and against antibiotic resistance in inhomogeneous multistress environments}},
  doi          = {10.1038/ncomms10333},
  volume       = {7},
  year         = {2016},
}

@article{1333,
  abstract     = {Social dilemmas force players to balance between personal and collective gain. In many dilemmas, such as elected governments negotiating climate-change mitigation measures, the decisions are made not by individual players but by their representatives. However, the behaviour of representatives in social dilemmas has not been investigated experimentally. Here inspired by the negotiations for greenhouse-gas emissions reductions, we experimentally study a collective-risk social dilemma that involves representatives deciding on behalf of their fellow group members. Representatives can be re-elected or voted out after each consecutive collective-risk game. Selfish players are preferentially elected and are hence found most frequently in the "representatives" treatment. Across all treatments, we identify the selfish players as extortioners. As predicted by our mathematical model, their steadfast strategies enforce cooperation from fair players who finally compensate almost completely the deficit caused by the extortionate co-players. Everybody gains, but the extortionate representatives and their groups gain the most.},
  author       = {Milinski, Manfred and Hilbe, Christian and Semmann, Dirk and Sommerfeld, Ralf and Marotzke, Jochem},
  journal      = {Nature Communications},
  publisher    = {Nature Publishing Group},
  title        = {{Humans choose representatives who enforce cooperation in social dilemmas through extortion}},
  doi          = {10.1038/ncomms10915},
  volume       = {7},
  year         = {2016},
}

@article{1334,
  abstract     = {Hippocampal neurons encode a cognitive map of space. These maps are thought to be updated during learning and in response to changes in the environment through activity-dependent synaptic plasticity. Here we examine how changes in activity influence spatial coding in rats using halorhodopsin-mediated, spatially selective optogenetic silencing. Halorhoposin stimulation leads to light-induced suppression in many place cells and interneurons; some place cells increase their firing through disinhibition, whereas some show no effect. We find that place fields of the unaffected subpopulation remain stable. On the other hand, place fields of suppressed place cells were unstable, showing remapping across sessions before and after optogenetic inhibition. Disinhibited place cells had stable maps but sustained an elevated firing rate. These findings suggest that place representation in the hippocampus is constantly governed by activity-dependent processes, and that disinhibition may provide a mechanism for rate remapping.},
  author       = {Schönenberger, Philipp and O'Neill, Joseph and Csicsvari, Jozsef L},
  journal      = {Nature Communications},
  publisher    = {Nature Publishing Group},
  title        = {{Activity dependent plasticity of hippocampal place maps}},
  doi          = {10.1038/ncomms11824},
  volume       = {7},
  year         = {2016},
}

@inproceedings{1335,
  abstract     = {In this paper we review various automata-theoretic formalisms for expressing quantitative properties. We start with finite-state Boolean automata that express the traditional regular properties. We then consider weighted ω-automata that can measure the average density of events, which finite-state Boolean automata cannot. However, even weighted ω-automata cannot express basic performance properties like average response time. We finally consider two formalisms of weighted ω-automata with monitors, where the monitors are either (a) counters or (b) weighted automata themselves. We present a translation result to establish that these two formalisms are equivalent. Weighted ω-automata with monitors generalize weighted ω-automata, and can express average response time property. They present a natural, robust, and expressive framework for quantitative specifications, with important decidable properties.},
  author       = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
  location     = {Edinburgh, United Kingdom},
  pages        = {23 -- 38},
  publisher    = {Springer},
  title        = {{Quantitative monitor automata}},
  doi          = {10.1007/978-3-662-53413-7_2},
  volume       = {9837},
  year         = {2016},
}

@inproceedings{8094,
  abstract     = {With the accelerated development of robot technologies, optimal control becomes one of the central themes of research. In traditional approaches, the controller, by its internal functionality, finds appropriate actions on the basis of the history of sensor values, guided by the goals, intentions, objectives, learning schemes, and so forth. The idea is that the controller controls the world---the body plus its environment---as reliably as possible. This paper focuses on new lines of self-organization for developmental robotics. We apply the recently developed differential extrinsic synaptic plasticity to a muscle-tendon driven arm-shoulder system from the Myorobotics toolkit. In the experiments, we observe a vast variety of self-organized behavior patterns: when left alone, the arm realizes pseudo-random sequences of different poses. By applying physical forces, the system can be entrained into definite motion patterns like wiping a table. Most interestingly, after attaching an object, the controller gets in a functional resonance with the object's internal dynamics, starting to shake spontaneously bottles half-filled with water or sensitively driving an attached pendulum into a circular mode. When attached to the crank of a wheel the neural system independently discovers how to rotate it. In this way, the robot discovers affordances of objects its body is interacting with.},
  author       = {Martius, Georg S and Hostettler, Rafael and Knoll, Alois and Der, Ralf},
  booktitle    = {Proceedings of the Artificial Life Conference 2016},
  isbn         = {9780262339360},
  location     = {Cancun, Mexico},
  pages        = {142--143},
  publisher    = {MIT Press},
  title        = {{Self-organized control of an tendon driven arm by differential extrinsic plasticity}},
  doi          = {10.7551/978-0-262-33936-0-ch029},
  volume       = {28},
  year         = {2016},
}

@article{1479,
  abstract     = {Most entropy notions H(.) like Shannon or min-entropy satisfy a chain rule stating that for random variables X,Z, and A we have H(X|Z,A)≥H(X|Z)−|A|. That is, by conditioning on A the entropy of X can decrease by at most the bitlength |A| of A. Such chain rules are known to hold for some computational entropy notions like Yao’s and unpredictability-entropy. For HILL entropy, the computational analogue of min-entropy, the chain rule is of special interest and has found many applications, including leakage-resilient cryptography, deterministic encryption, and memory delegation. These applications rely on restricted special cases of the chain rule. Whether the chain rule for conditional HILL entropy holds in general was an open problem for which we give a strong negative answer: we construct joint distributions (X,Z,A), where A is a distribution over a single bit, such that the HILL entropy H HILL (X|Z) is large but H HILL (X|Z,A) is basically zero.

Our counterexample just makes the minimal assumption that NP⊈P/poly. Under the stronger assumption that injective one-way function exist, we can make all the distributions efficiently samplable.

Finally, we show that some more sophisticated cryptographic objects like lossy functions can be used to sample a distribution constituting a counterexample to the chain rule making only a single invocation to the underlying object.},
  author       = {Krenn, Stephan and Pietrzak, Krzysztof Z and Wadia, Akshay and Wichs, Daniel},
  journal      = {Computational Complexity},
  number       = {3},
  pages        = {567 -- 605},
  publisher    = {Springer},
  title        = {{A counterexample to the chain rule for conditional HILL entropy}},
  doi          = {10.1007/s00037-015-0120-9},
  volume       = {25},
  year         = {2016},
}

@article{1480,
  abstract     = {Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses of symmetric matrices satisfying linear constraints. This class includes Gaussian graphical models. We develop a general theory of exponential varieties. These are derived from hyperbolic polynomials and their integral representations. We compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials. },
  author       = {Michałek, Mateusz and Sturmfels, Bernd and Uhler, Caroline and Zwiernik, Piotr},
  journal      = {Proceedings of the London Mathematical Society},
  number       = {1},
  pages        = {27 -- 56},
  publisher    = {Oxford University Press},
  title        = {{Exponential varieties}},
  doi          = {10.1112/plms/pdv066},
  volume       = {112},
  year         = {2016},
}

@article{1482,
  abstract     = {Plants have the ability to continously generate new organs by maintaining populations of stem cells throught their lives. The shoot apical meristem (SAM) provides a stable environment for the maintenance of stem cells. All cells inside the SAM divide, yet boundaries and patterns are maintained. Experimental evidence indicates that patterning is independent of cell lineage, thus a dynamic self-regulatory mechanism is required. A pivotal role in the organization of the SAM is played by the WUSCHEL gene (WUS). An important question in this regard is that how WUS expression is positioned in the SAM via a cell-lineage independent signaling mechanism. In this study we demonstrate via mathematical modeling that a combination of an inhibitor of the Cytokinin (CK) receptor, Arabidopsis histidine kinase 4 (AHK4) and two morphogens originating from the top cell layer, can plausibly account for the cell lineage-independent centering of WUS expression within SAM. Furthermore, our laser ablation and microsurgical experiments support the hypothesis that patterning in SAM occurs at the level of CK reception and signaling. The model suggests that the interplay between CK signaling, WUS/CLV feedback loop and boundary signals can account for positioning of the WUS expression, and provides directions for further experimental investigation.},
  author       = {Adibi, Milad and Yoshida, Saiko and Weijers, Dolf and Fleck, Christian},
  journal      = {PLoS One},
  number       = {2},
  publisher    = {Public Library of Science},
  title        = {{Centering the organizing center in the Arabidopsis thaliana shoot apical meristem by a combination of cytokinin signaling and self-organization}},
  doi          = {10.1371/journal.pone.0147830},
  volume       = {11},
  year         = {2016},
}

@article{1484,
  author       = {Chen, Xu and Wu, Shuang and Liu, Zengyu and Friml, Jiřĺ},
  journal      = {Trends in Cell Biology},
  number       = {6},
  pages        = {409 -- 419},
  publisher    = {Cell Press},
  title        = {{Environmental and endogenous control of cortical microtubule orientation}},
  doi          = {10.1016/j.tcb.2016.02.003},
  volume       = {26},
  year         = {2016},
}

@article{1485,
  abstract     = {In this article the notion of metabolic turnover is revisited in the light of recent results of out-of-equilibrium thermodynamics. By means of Monte Carlo methods we perform an exact sampling of the enzymatic fluxes in a genome scale metabolic network of E. Coli in stationary growth conditions from which we infer the metabolites turnover times. However the latter are inferred from net fluxes, and we argue that this approximation is not valid for enzymes working nearby thermodynamic equilibrium. We recalculate turnover times from total fluxes by performing an energy balance analysis of the network and recurring to the fluctuation theorem. We find in many cases values one of order of magnitude lower, implying a faster picture of intermediate metabolism.},
  author       = {De Martino, Daniele},
  journal      = {Physical Biology},
  number       = {1},
  publisher    = {IOP Publishing Ltd.},
  title        = {{Genome-scale estimate of the metabolic turnover of E. Coli from the energy balance analysis}},
  doi          = {10.1088/1478-3975/13/1/016003},
  volume       = {13},
  year         = {2016},
}

@article{1486,
  abstract     = {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.},
  author       = {Hainzl, Christian and Seiringer, Robert},
  journal      = {Journal of Mathematical Physics},
  number       = {2},
  publisher    = {American Institute of Physics},
  title        = {{The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties}},
  doi          = {10.1063/1.4941723},
  volume       = {57},
  year         = {2016},
}

@article{1487,
  abstract     = {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.},
  author       = {Grion, Natalia and Akrami, Athena and Zuo, Yangfang and Stella, Federico and Diamond, Mathew},
  journal      = {PLoS Biology},
  number       = {2},
  publisher    = {Public Library of Science},
  title        = {{Coherence between rat sensorimotor system and hippocampus is enhanced during tactile discrimination}},
  doi          = {10.1371/journal.pbio.1002384},
  volume       = {14},
  year         = {2016},
}

@article{1488,
  abstract     = {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.},
  author       = {Riccio, Paul and Cebrián, Cristina and Zong, Hui and Hippenmeyer, Simon and Costantini, Frank},
  journal      = {PLoS Biology},
  number       = {2},
  publisher    = {Public Library of Science},
  title        = {{Ret and Etv4 promote directed movements of progenitor cells during renal branching morphogenesis}},
  doi          = {10.1371/journal.pbio.1002382},
  volume       = {14},
  year         = {2016},
}

@article{1489,
  abstract     = {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. },
  author       = {Ajanki, Oskari H and Erdös, László and Krüger, Torben H},
  journal      = {Journal of Statistical Physics},
  number       = {2},
  pages        = {280 -- 302},
  publisher    = {Springer},
  title        = {{Local spectral statistics of Gaussian matrices with correlated entries}},
  doi          = {10.1007/s10955-016-1479-y},
  volume       = {163},
  year         = {2016},
}

@article{1490,
  abstract     = {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.},
  author       = {Russo, Erica and Teijeira, Alvaro and Vaahtomeri, Kari and Willrodt, Ann and Bloch, Joël and Nitschké, Maximilian and Santambrogio, Laura and Kerjaschki, Dontscho and Sixt, Michael K and Halin, Cornelia},
  journal      = {Cell Reports},
  number       = {7},
  pages        = {1723 -- 1734},
  publisher    = {Cell Press},
  title        = {{Intralymphatic CCL21 promotes tissue egress of dendritic cells through afferent lymphatic vessels}},
  doi          = {10.1016/j.celrep.2016.01.048},
  volume       = {14},
  year         = {2016},
}

@article{1491,
  abstract     = {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.},
  author       = {Lewin, Mathieu and Nam, Phan and Rougerie, Nicolas},
  journal      = {Transactions of the American Mathematical Society},
  number       = {9},
  pages        = {6131 -- 6157},
  publisher    = {American Mathematical Society},
  title        = {{The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases}},
  doi          = {10.1090/tran/6537},
  volume       = {368},
  year         = {2016},
}