@inproceedings{760, abstract = {A randomized implementation is given of a test-and-set register with O(log log n) individual step complexity and O(n) total step complexity against an oblivious adversary. The implementation is linearizable and multi-shot, and shows an exponential complexity improvement over previous solutions designed to work against a strong adversary.}, author = {Alistarh, Dan-Adrian and Aspnes, James}, pages = {97 -- 109}, publisher = {Springer}, title = {{Sub-logarithmic test-and-set against a weak adversary}}, doi = {10.1007/978-3-642-24100-0_7}, volume = {6950 LNCS}, year = {2011}, } @inproceedings{761, abstract = {We give two new randomized algorithms for strong renaming, both of which work against an adaptive adversary in asynchronous shared memory. The first uses repeated sampling over a sequence of arrays of decreasing size to assign unique names to each of n processes with step complexity O(log3 n). The second transforms any sorting network into a strong adaptive renaming protocol, with an expected cost equal to the depth of the sorting network. Using an AKS sorting network, this gives a strong adaptive renaming algorithm with step complexity O(log k), where k is the contention in the current execution. We show this to be optimal based on a classic lower bound of Jayanti. We also show that any such strong renaming protocol can be used to build a monotone-consistent counter with logarithmic step complexity (at the cost of adding a max register) or a linearizable fetch-and-increment register (at the cost of increasing the step complexity by a logarithmic factor).}, author = {Alistarh, Dan-Adrian and Aspnes, James and Censor Hillel, Keren and Gilbert, Seth and Zadimoghaddam, Morteza}, pages = {239 -- 248}, publisher = {ACM}, title = {{Optimal-time adaptive strong renaming, with applications to counting}}, doi = {10.1145/1993806.1993850}, year = {2011}, } @inproceedings{9943, abstract = {Segmentation is the process of partitioning digital images into meaningful regions. The analysis of biological high content images often requires segmentation as a first step. We propose ilastik as an easy-to-use tool which allows the user without expertise in image processing to perform segmentation and classification in a unified way. ilastik learns from labels provided by the user through a convenient mouse interface. Based on these labels, ilastik infers a problem specific segmentation. A random forest classifier is used in the learning step, in which each pixel's neighborhood is characterized by a set of generic (nonlinear) features. ilastik supports up to three spatial plus one spectral dimension and makes use of all dimensions in the feature calculation. ilastik provides realtime feedback that enables the user to interactively refine the segmentation result and hence further fine-tune the classifier. An uncertainty measure guides the user to ambiguous regions in the images. Real time performance is achieved by multi-threading which fully exploits the capabilities of modern multi-core machines. Once a classifier has been trained on a set of representative images, it can be exported and used to automatically process a very large number of images (e.g. using the CellProfiler pipeline). ilastik is an open source project and released under the BSD license at www.ilastik.org.}, author = {Sommer, Christoph M and Straehle, Christoph and Köthe, Ullrich and Hamprecht, Fred A.}, booktitle = {2011 IEEE International Symposium on Biomedical Imaging: from Nano to Micro}, isbn = {978-1-4244-4127-3}, issn = {1945-8452}, keywords = {image segmentation, biomedical imaging, three dimensional displays, neurons, retina, observers, image color analysis}, location = {Chicago, Illinois, USA}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Ilastik: Interactive learning and segmentation toolkit}}, doi = {10.1109/isbi.2011.5872394}, year = {2011}, } @article{3429, abstract = {Transcription factors are central to sustaining pluripotency, yet little is known about transcription factor dynamics in defining pluripotency in the early mammalian embryo. Here, we establish a fluorescence decay after photoactivation (FDAP) assay to quantitatively study the kinetic behaviour of Oct4, a key transcription factor controlling pre-implantation development in the mouse embryo. FDAP measurements reveal that each cell in a developing embryo shows one of two distinct Oct4 kinetics, before there are any morphologically distinguishable differences or outward signs of lineage patterning. The differences revealed by FDAP are due to differences in the accessibility of Oct4 to its DNA binding sites in the nucleus. Lineage tracing of the cells in the two distinct sub-populations demonstrates that the Oct4 kinetics predict lineages of the early embryo. Cells with slower Oct4 kinetics are more likely to give rise to the pluripotent cell lineage that contributes to the inner cell mass. Those with faster Oct4 kinetics contribute mostly to the extra-embryonic lineage. Our findings identify Oct4 kinetics, rather than differences in total transcription factor expression levels, as a predictive measure of developmental cell lineage patterning in the early mouse embryo.}, author = {Plachta, Nicolas and Bollenbach, Mark Tobias and Pease, Shirley and Fraser, Scott and Pantazis, Periklis}, journal = {Nature Cell Biology}, number = {2}, pages = {117 -- 123}, publisher = {Nature Publishing Group}, title = {{Oct4 kinetics predict cell lineage patterning in the early mammalian embryo}}, doi = {10.1038/ncb2154}, volume = {13}, year = {2011}, } @article{3505, abstract = {Cell migration on two-dimensional (2D) substrates follows entirely different rules than cell migration in three-dimensional (3D) environments. This is especially relevant for leukocytes that are able to migrate in the absence of adhesion receptors within the confined geometry of artificial 3D extracellular matrix scaffolds and within the interstitial space in vivo. Here, we describe in detail a simple and economical protocol to visualize dendritic cell migration in 3D collagen scaffolds along chemotactic gradients. This method can be adapted to other cell types and may serve as a physiologically relevant paradigm for the directed locomotion of most amoeboid cells.}, author = {Sixt, Michael K and Lämmermann, Tim}, journal = {Cell Migration}, pages = {149 -- 165}, publisher = {Springer}, title = {{In vitro analysis of chemotactic leukocyte migration in 3D environments}}, doi = {10.1007/978-1-61779-207-6_11}, volume = {769}, year = {2011}, } @inbook{3724, abstract = {Small photochromic molecules are widespread in nature and serve as switches for a plethora of light-controlled processes. In a typical photoreceptor, the different geometries and polarities of the photochrome isomers are tightly coupled to functionally relevant conformational changes in the proteins. The past decade has seen extensive efforts to mimic nature and create proteins controlled by synthetic photochromes in the laboratory. Here, we discuss the role of molecular modeling to gain a structural understanding of photochromes and to design light-controlled peptides and proteins. We address several fundamental questions: What are the molecular structures of photochromes, particularly for metastable isomers that cannot be addressed experimentally? How are the structures of bistable photoisomers coupled to the conformational states of peptides and proteins? Can we design light-controlled proteins rapidly and reliably? After an introduction to the principles of molecular modeling, we answer these questions by examining systems that range from the size of isolated photochromes, to that of peptides and large cell surface receptors, each from its unique computational perspective.}, author = {Harald Janovjak and Isacoff, Ehud Y}, booktitle = {Photosensitive Molecules for the Control of Biological Function}, pages = {233 -- 266}, publisher = {Springer}, title = {{Structure-based design of light-controlled proteins}}, doi = {10.1007/978-1-61779-031-7_13}, volume = {55}, year = {2011}, } @article{3770, abstract = {The pink dolphin (Inia geoffrensis) is widely distributed along the Amazon and Orinoco basins, covering an area of approximately 7 million km2. Previous morphological and genetic studies have proposed the existence of at least two evolutionary significant units: one distributed across the Orinoco and Amazon basins and another confined to the Bolivian Amazon. The presence of barriers in the riverine environment has been suggested to play a significant role in shaping present-day patterns of ecological and genetic structure for this species. In the present study, we examined the phylogeographic structure, lineage divergence time and historical demography using mitochondrial (mt)DNA sequences in different pink dolphin populations distributed in large and small spatial scales, including two neighbouring Brazilian Amazon populations. mtDNA control region (CR) analysis revealed that the Brazilian haplotypes occupy an intermediate position compared to three previously studied geographic locations: the Colombian Amazon, the Colombian Orinoco, and the Bolivian Amazon. On a local scale, we have identified a pattern of maternal isolation between two neighbouring populations from Brazil. Six mtDNA CR haplotypes were identified in Brazil with no sharing between the two populations, as well as specific cytochrome b (cyt b) haplotypes identified in each locality. In addition, we analyzed autosomal microsatellites to investigate male-mediated gene flow and demographic changes within the study area in Brazil. Data analysis of 14 microsatellite loci failed to detect significant population subdivision, suggesting that male-mediated gene flow may maintain homogeneity between these two locations. Moreover, both mtDNA and microsatellite data indicate a major demographic collapse within Brazil in the late Pleistocene. Bayesian skyline plots (BSP) of mtDNA data revealed a stable population for Colombian and Brazilian Amazon lineages through time, whereas a population decline was demonstrated in the Colombian Orinoco lineage. Moreover, BSP and Tajima's D and Fu's Fs tests revealed a recent population expansion exclusively in the Bolivian sample. Finally, we estimated that the diversification of the Inia sp. lineage began in the Late Pliocene (approximately 3.1 Mya) and continued throughout the Pleistocene.}, author = {Hollatz, Claudia and Vilaça, Sibelle and Fernandes Redondo, Rodrigo A and Marmontel, Míriam and Baker, Cyndi and Santos, Fabrício}, journal = {Biological Journal of the Linnean Society}, number = {4}, pages = {812 -- 827}, publisher = {Wiley}, title = {{The Amazon River system as an ecological barrier driving genetic differentiation of the pink dolphin (Inia geoffrensis)}}, doi = {10.1111/j.1095-8312.2011.01616.x}, volume = {102}, year = {2011}, } @article{3771, abstract = {The small-sized frugivorous bat Carollia perspicillata is an understory specialist and occurs in a wide range of lowland habitats, tending to be more common in tropical dry or moist forests of South and Central America. Its sister species, Carollia brevicauda, occurs almost exclusively in the Amazon rainforest. A recent phylogeographic study proposed a hypothesis of origin and subsequent diversification for C. perspicillata along the Atlantic coastal forest of Brazil. Additionally, it also found two allopatric clades for C. brevicauda separated by the Amazon Basin. We used cytochrome b gene sequences and a more extensive sampling to test hypotheses related to the origin and diversification of C. perspicillata plus C. brevicauda clade in South America. The results obtained indicate that there are two sympatric evolutionary lineages within each species. In C. perspicillata, one lineage is limited to the Southern Atlantic Forest, whereas the other is widely distributed. Coalescent analysis points to a simultaneous origin for C. perspicillata and C. brevicauda, although no place for the diversification of each species can be firmly suggested. The phylogeographic pattern shown by C. perspicillata is also congruent with the Pleistocene refugia hypothesis as a likely vicariant phenomenon shaping the present distribution of its intraspecific lineages.}, author = {Pavan, Ana and Martins, Felipe and Santos, Fabrício and Ditchfield, Albert and Fernandes Redondo, Rodrigo A}, journal = {Biological Journal of the Linnean Society}, number = {3}, pages = {527 -- 539}, publisher = {Wiley-Blackwell}, title = {{Patterns of diversification in two species of short-tailed bats (Carollia Gray, 1838): the effects of historical fragmentation of Brazilian rainforests.}}, doi = {10.1111/j.1095-8312.2010.01601.x}, volume = {102}, year = {2011}, } @article{3778, author = {Barton, Nicholas H}, journal = {Heredity}, number = {2}, pages = {205 -- 206}, publisher = {Nature Publishing Group}, title = {{Estimating linkage disequilibria}}, doi = {10.1038/hdy.2010.67}, volume = {106}, year = {2011}, } @article{3784, abstract = {Advanced stages of Scyllarus phyllosoma larvae were collected by demersal trawling during fishery research surveys in the western Mediterranean Sea in 2003–2005. Nucleotide sequence analysis of the mitochondrial 16S rDNA gene allowed the final-stage phyllosoma of Scyllarus arctus to be identified among these larvae. Its morphology is described and illustrated. This constitutes the second complete description of a Scyllaridae phyllosoma with its specific identity being validated by molecular techniques (the first was S. pygmaeus). These results also solved a long lasting taxonomic anomaly of several species assigned to the ancient genus Phyllosoma Leach, 1814. Detailed examination indicated that the final-stage phyllosoma of S. arctus shows closer affinities with the American scyllarid Scyllarus depressus or with the Australian Scyllarus sp. b (sensu Phillips et al., 1981) than to its sympatric species S. pygmaeus.}, author = {Palero, Ferran and Guerao, Guillermo and Clark, Paul and Abello, Pere}, journal = {Journal of the Marine Biological Association of the United Kingdom}, number = {2}, pages = {485 -- 492}, publisher = {Cambridge University Press}, title = {{Scyllarus arctus (Crustacea: Decapoda: Scyllaridae) final stage phyllosoma identified by DNA analysis, with morphological description}}, doi = {10.1017/S0025315410000287}, volume = {91}, year = {2011}, } @inbook{3791, abstract = {During the development of multicellular organisms, cell fate specification is followed by the sorting of different cell types into distinct domains from where the different tissues and organs are formed. Cell sorting involves both the segregation of a mixed population of cells with different fates and properties into distinct domains, and the active maintenance of their segregated state. Because of its biological importance and apparent resemblance to fluid segregation in physics, cell sorting was extensively studied by both biologists and physicists over the last decades. Different theories were developed that try to explain cell sorting on the basis of the physical properties of the constituent cells. However, only recently the molecular and cellular mechanisms that control the physical properties driving cell sorting, have begun to be unraveled. In this review, we will provide an overview of different cell-sorting processes in development and discuss how these processes can be explained by the different sorting theories, and how these theories in turn can be connected to the molecular and cellular mechanisms driving these processes.}, author = {Krens, Gabriel and Heisenberg, Carl-Philipp J}, booktitle = {Forces and Tension in Development}, editor = {Labouesse, Michel}, pages = {189 -- 213}, publisher = {Elsevier}, title = {{Cell sorting in development}}, doi = {10.1016/B978-0-12-385065-2.00006-2}, volume = {95}, year = {2011}, } @inbook{3796, abstract = {We address the problem of covering ℝ n with congruent balls, while minimizing the number of balls that contain an average point. Considering the 1-parameter family of lattices defined by stretching or compressing the integer grid in diagonal direction, we give a closed formula for the covering density that depends on the distortion parameter. We observe that our family contains the thinnest lattice coverings in dimensions 2 to 5. We also consider the problem of packing congruent balls in ℝ n , for which we give a closed formula for the packing density as well. Again we observe that our family contains optimal configurations, this time densest packings in dimensions 2 and 3.}, author = {Edelsbrunner, Herbert and Kerber, Michael}, booktitle = {Rainbow of Computer Science}, editor = {Calude, Cristian and Rozenberg, Grzegorz and Salomaa, Arto}, pages = {20 -- 35}, publisher = {Springer}, title = {{Covering and packing with spheres by diagonal distortion in R^n}}, doi = {10.1007/978-3-642-19391-0_2}, volume = {6570}, year = {2011}, } @article{386, abstract = {We present a detailed study of the local density of states (LDOS) associated with the surface-state band near a step edge of the strong topological insulator Bi2Te3 and reveal a one-dimensional bound state that runs parallel to the step edge and is bound to it at some characteristic distance. This bound state is clearly observed in the bulk gap region, while it becomes entangled with the oscillations of the warped surface band at high energy, and with the valence-band states near the Dirac point. We obtain excellent fits to theoretical predictions [Alpichshev, 2011] that properly incorporate the three-dimensional nature of the problem to the surface state. Fitting the data at different energies, we can recalculate the LDOS originating from the Dirac band without the contribution of the bulk bands or incoherent tunneling effects. }, author = {Alpichshev, Zhanybek and Analytis, J G and Chu, J H and Fisher, I R and Kapitulnik, A}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {4}, publisher = {American Physical Society}, title = {{STM imaging of a bound state along a step on the surface of the topological insulator Bi2Te3}}, doi = {10.1103/PhysRevB.84.041104}, volume = {84}, year = {2011}, } @article{3965, abstract = {The elevation function on a smoothly embedded 2-manifold in R-3 reflects the multiscale topography of cavities and protrusions as local maxima. The function has been useful in identifying coarse docking configurations for protein pairs. Transporting the concept from the smooth to the piecewise linear category, this paper describes an algorithm for finding all local maxima. While its worst-case running time is the same as of the algorithm used in prior work, its performance in practice is orders of magnitudes superior. We cast light on this improvement by relating the running time to the total absolute Gaussian curvature of the 2-manifold.}, author = {Wang, Bei and Edelsbrunner, Herbert and Morozov, Dmitriy}, journal = {Journal of Experimental Algorithmics}, number = {2.2}, pages = {1 -- 13}, publisher = {ACM}, title = {{Computing elevation maxima by searching the Gauss sphere}}, doi = {10.1145/1963190.1970375}, volume = {16}, year = {2011}, } @phdthesis{3275, abstract = {Chemokines organize immune cell trafficking by inducing either directed (tactic) or random (kinetic) migration and by activating integrins in order to support surface adhesion (haptic). Beyond that the same chemokines can establish clearly defined functional areas in secondary lymphoid organs. Until now it is unclear how chemokines can fulfill such diverse functions. One decisive prerequisite to explain these capacities is to know how chemokines are presented in tissue. In theory chemokines could occur either soluble or immobilized, and could be distributed either homogenously or as a concentration gradient. To dissect if and how the presenting mode of chemokines influences immune cells, I tested the response of dendritic cells (DCs) to differentially displayed chemokines. DCs are antigen presenting cells that reside in the periphery and migrate into draining lymph nodes (LNs) once exposed to inflammatory stimuli to activate naïve T cells. DCs are guided to and within the LN by the chemokine receptor CCR7, which has two ligands, the chemokines CCL19 and CCL21. Both CCR7 ligands are expressed by fibroblastic reticular cells in the LN, but differ in their ability to bind to heparan sulfate residues. CCL21 has a highly charged C-terminal extension, which mediates binding to anionic surfaces, whereas CCL19 is lacking such residues and likely distributes as a soluble molecule. This study shows that surface-bound CCL21 causes random, haptokinetic DC motility, which is confined to the chemokine coated area by insideout activation of β2 integrins that mediate cell binding to the surface. CCL19 on the other hand forms concentration gradients which trigger directional, chemotactic movement, but no surface adhesion. In addition DCs can actively manipulate this system by recruiting and activating serine proteases on their surfaces, which create - by proteolytically removing the adhesive C-terminus - a solubilized variant of CCL21 that functionally resembles CCL19. By generating a CCL21 concentration gradient DCs establish a positive feedback loop to recruit further DCs from the periphery to the CCL21 coated region. In addition DCs can sense chemotactic gradients as well as immobilized haptokinetic fields at the same time and integrate these signals. The result is chemotactically biased haptokinesis - directional migration confined to a chemokine coated track or area - which could explain the dynamic but spatially tightly controlled swarming leukocyte locomotion patterns that have been observed in lymphatic organs by intravital microscopists. The finding that DCs can approach soluble cues in a non-adhesive manner while they attach to surfaces coated with immobilized cues raises the question how these cells transmit intracellular forces to the environment, especially in the non-adherent migration mode. In order to migrate, cells have to generate and transmit force to the extracellular substrate. Force transmission is the prerequisite to procure an expansion of the leading edge and a forward motion of the whole cell body. In the current conceptions actin polymerization at the leading edge is coupled to extracellular ligands via the integrin family of transmembrane receptors, which allows the transmission of intracellular force. Against the paradigm of force transmission during migration, leukocytes, like DCs, are able to migrate in threedimensional environments without using integrin transmembrane receptors (Lämmermann et al., 2008). This reflects the biological function of leukocytes, as they can invade almost all tissues, whereby their migration has to be independent from the extracellular environment. How the cells can achieve this is unclear. For this study I examined DC migration in a defined threedimensional environment and highlighted actin-dynamics with the probe Lifeact-GFP. The result was that chemotactic DCs can switch between integrin-dependent and integrin- independent locomotion and can thereby adapt to the adhesive properties of their environment. If the cells are able to couple their actin cytoskeleton to the substrate, actin polymerization is entirely converted into protrusion. Without coupling the actin cortex undergoes slippage and retrograde actin flow can be observed. But retrograde actin flow can be completely compensated by higher actin polymerization rate keeping the migration velocity and the shape of the cells unaltered. Mesenchymal cells like fibroblast cannot balance the loss of adhesive interaction, cannot protrude into open space and, therefore, strictly depend on integrinmediated force coupling. This leukocyte specific phenomenon of “adaptive force transmission” endows these cells with the unique ability to transit and invade almost every type of tissue. }, author = {Schumann, Kathrin}, issn = {2663-337X}, pages = {141}, publisher = {Institute of Science and Technology Austria}, title = {{The role of chemotactic gradients in dendritic cell migration}}, year = {2011}, } @phdthesis{3273, author = {Maître, Jean-Léon}, issn = {2663-337X}, publisher = {Institute of Science and Technology Austria}, title = {{Mechanics of adhesion and de‐adhesion in zebrafish germ layer progenitors}}, year = {2011}, } @inproceedings{9648, abstract = {In this paper, we establish a correspondence between the incremental algorithm for computing AT-models [8,9] and the one for computing persistent homology [6,14,15]. We also present a decremental algorithm for computing AT-models that allows to extend the persistence computation to a wider setting. Finally, we show how to combine incremental and decremental techniques for persistent homology computation.}, author = {Gonzalez-Diaz, Rocio and Ion, Adrian and Jimenez, Maria Jose and Poyatos, Regina}, booktitle = {Computer Analysis of Images and Patterns}, isbn = {9783642236716}, issn = {1611-3349}, location = {Seville, Spain}, pages = {286--293}, publisher = {Springer Nature}, title = {{Incremental-decremental algorithm for computing AT-models and persistent homology}}, doi = {10.1007/978-3-642-23672-3_35}, volume = {6854}, year = {2011}, } @article{3315, abstract = {We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are concurrent in that at each turn, both players independently propose a time delay and an action, and the action with the shorter delay is chosen. To prevent a player from winning by blocking time, we restrict each player to play strategies that ensure that the player cannot be responsible for causing a zeno run. First, we present an efficient reduction of these games to turn-based (i.e., not concurrent) finite-state (i.e., untimed) parity games. Our reduction improves the best known complexity for solving timed parity games. Moreover, the rich class of algorithms for classical parity games can now be applied to timed parity games. The states of the resulting game are based on clock regions of the original game, and the state space of the finite game is linear in the size of the region graph. Second, we consider two restricted classes of strategies for the player that represents the controller in a real-time synthesis problem, namely, limit-robust and bounded-robust winning strategies. Using a limit-robust winning strategy, the controller cannot choose an exact real-valued time delay but must allow for some nonzero jitter in each of its actions. If there is a given lower bound on the jitter, then the strategy is bounded-robust winning. We show that exact strategies are more powerful than limit-robust strategies, which are more powerful than bounded-robust winning strategies for any bound. For both kinds of robust strategies, we present efficient reductions to standard timed automaton games. These reductions provide algorithms for the synthesis of robust real-time controllers.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Prabhu, Vinayak}, journal = {Logical Methods in Computer Science}, number = {4}, publisher = {International Federation of Computational Logic}, title = {{Timed parity games: Complexity and robustness}}, doi = {10.2168/LMCS-7(4:8)2011}, volume = {7}, year = {2011}, } @article{2701, abstract = {We consider N × N Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order 1/ N. Under suitable assumptions on the distribution of the single matrix element, we first prove that, away from the spectral edges, the empirical density of eigenvalues concentrates around the Wigner semicircle law on energy scales η ≫ N -1. This result establishes the semicircle law on the optimal scale and it removes a logarithmic factor from our previous result [6]. We then show a Wegner estimate, i.e., that the averaged density of states is bounded. Finally, we prove that the eigenvalues of a Wigner matrix repel each other, in agreement with the universality conjecture.}, author = {László Erdös and Schlein, Benjamin and Yau, Horng-Tzer}, journal = {International Mathematics Research Notices}, number = {3}, pages = {436 -- 479}, publisher = {Oxford University Press}, title = {{Wegner estimate and level repulsion for Wigner random matrices}}, doi = {10.1093/imrn/rnp136}, year = {2010}, } @article{2704, abstract = {Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N2V(N(xi-xj)), where x = (x1, ..., xN) denotes the positions of the particles. Let HN, denote the Hamiltonian of the system and let ψN,t be the solution to the Schrödinger equation. Suppose that the initial data ψN,0 satisfies the energy condition 〈 ψ N,0,Hk N ψN,0〉 ≤ CkNk for k =1, 2, ....We also assume that the k-particle density matrices of the initial state are asymptotically factorized as N →∞1. We prove that the k-particle density matrices of ψN,t are also asymptotically factorized and the one particle orbital wave function solves the Gross-Pitaevskii equation, a cubic nonlinear Schrödinger equation with the coupling constant given by the scattering length of the potential V. We also prove the same conclusion if the energy condition holds only for k=1 but the factorization of ψN,0 is assumed in a stronger sense.}, author = {László Erdös and Schlein, Benjamin and Yau, Horng-Tzer}, journal = {Annals of Mathematics}, number = {1}, pages = {291 -- 370}, publisher = {Princeton University Press}, title = {{Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate}}, doi = {10.4007/annals.2010.172.291}, volume = {172}, year = {2010}, }