TY - CONF
AB - We study two-player concurrent games on finite-state graphs played for an infinite number of rounds, where in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. The objectives are ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). While the qualitative analysis problem for concurrent parity games with infinite-memory, infinite-precision randomized strategies was studied before, we study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision, or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory, or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in (n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. Our symbolic algorithms are based on a characterization of the winning sets as μ-calculus formulas, however, our μ-calculus formulas are crucially different from the ones for concurrent parity games (without bounded rationality); and our memoryless witness strategy constructions are significantly different from the infinite-memory witness strategy constructions for concurrent parity games.
AU - Chatterjee, Krishnendu
ED - Baldan, Paolo
ED - Gorla, Daniele
ID - 2054
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Qualitative concurrent parity games: Bounded rationality
VL - 8704
ER -
TY - JOUR
AB - We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.
AU - Ganguly, Arnab
AU - Petrov, Tatjana
AU - Koeppl, Heinz
ID - 2056
IS - 3
JF - Journal of Mathematical Biology
TI - Markov chain aggregation and its applications to combinatorial reaction networks
VL - 69
ER -
TY - CONF
AB - In the past few years, a lot of attention has been devoted to multimedia indexing by fusing multimodal informations. Two kinds of fusion schemes are generally considered: The early fusion and the late fusion. We focus on late classifier fusion, where one combines the scores of each modality at the decision level. To tackle this problem, we investigate a recent and elegant well-founded quadratic program named MinCq coming from the machine learning PAC-Bayesian theory. MinCq looks for the weighted combination, over a set of real-valued functions seen as voters, leading to the lowest misclassification rate, while maximizing the voters’ diversity. We propose an extension of MinCq tailored to multimedia indexing. Our method is based on an order-preserving pairwise loss adapted to ranking that allows us to improve Mean Averaged Precision measure while taking into account the diversity of the voters that we want to fuse. We provide evidence that this method is naturally adapted to late fusion procedures and confirm the good behavior of our approach on the challenging PASCAL VOC’07 benchmark.
AU - Morvant, Emilie
AU - Habrard, Amaury
AU - Ayache, Stéphane
ID - 2057
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Majority vote of diverse classifiers for late fusion
VL - 8621
ER -
TY - CONF
AB - We present a method for smoothly blending between existing liquid animations. We introduce a semi-automatic method for matching two existing liquid animations, which we use to create new fluid motion that plausibly interpolates the input. Our contributions include a new space-time non-rigid iterative closest point algorithm that incorporates user guidance, a subsampling technique for efficient registration of meshes with millions of vertices, and a fast surface extraction algorithm that produces 3D triangle meshes from a 4D space-time surface. Our technique can be used to instantly create hundreds of new simulations, or to interactively explore complex parameter spaces. Our method is guaranteed to produce output that does not deviate from the input animations, and it generalizes to multiple dimensions. Because our method runs at interactive rates after the initial precomputation step, it has potential applications in games and training simulations.
AU - Raveendran, Karthik
AU - Wojtan, Christopher J
AU - Thuerey, Nils
AU - Türk, Greg
ID - 2058
IS - 4
T2 - ACM Transactions on Graphics
TI - Blending liquids
VL - 33
ER -
TY - JOUR
AB - Plant embryogenesis is regulated by differential distribution of the plant hormone auxin. However, the cells establishing these gradients during microspore embryogenesis remain to be identified. For the first time, we describe, using the DR5 or DR5rev reporter gene systems, the GFP- and GUS-based auxin biosensors to monitor auxin during Brassica napus androgenesis at cellular resolution in the initial stages. Our study provides evidence that the distribution of auxin changes during embryo development and depends on the temperature-inducible in vitro culture conditions. For this, microspores (mcs) were induced to embryogenesis by heat treatment and then subjected to genetic modification via Agrobacterium tumefaciens. The duration of high temperature treatment had a significant influence on auxin distribution in isolated and in vitro-cultured microspores and on microspore-derived embryo development. In the “mild” heat-treated (1 day at 32 °C) mcs, auxin localized in a polar way already at the uni-nucleate microspore, which was critical for the initiation of embryos with suspensor-like structure. Assuming a mean mcs radius of 20 μm, endogenous auxin content in a single cell corresponded to concentration of 1.01 μM. In mcs subjected to a prolonged heat (5 days at 32 °C), although auxin concentration increased dozen times, auxin polarization was set up at a few-celled pro-embryos without suspensor. Those embryos were enclosed in the outer wall called the exine. The exine rupture was accompanied by the auxin gradient polarization. Relative quantitative estimation of auxin, using time-lapse imaging, revealed that primordia possess up to 1.3-fold higher amounts than those found in the root apices of transgenic MDEs in the presence of exogenous auxin. Our results show, for the first time, which concentration of endogenous auxin coincides with the first cell division and how the high temperature interplays with auxin, by what affects delay early establishing microspore polarity. Moreover, we present how the local auxin accumulation demonstrates the apical–basal axis formation of the androgenic embryo and directs the axiality of the adult haploid plant.
AU - Dubas, Ewa
AU - Moravčíková, Jana
AU - Libantová, Jana
AU - Matušíková, Ildikó
AU - Benková, Eva
AU - Zur, Iwona
AU - Krzewska, Monika
ID - 2059
IS - 5
JF - Protoplasma
TI - The influence of heat stress on auxin distribution in transgenic B napus microspores and microspore derived embryos
VL - 251
ER -
TY - JOUR
AB - Development of cambium and its activity is important for our knowledge of the mechanism of secondary growth. Arabidopsis thaliana emerges as a good model plant for such a kind of study. Thus, this paper reports on cellular events taking place in the interfascicular regions of inflorescence stems of A. thaliana, leading to the development of interfascicular cambium from differentiated interfascicular parenchyma cells (IPC). These events are as follows: appearance of auxin accumulation, PIN1 gene expression, polar PIN1 protein localization in the basal plasma membrane and periclinal divisions. Distribution of auxin was observed to be higher in differentiating into cambium parenchyma cells compared to cells within the pith and cortex. Expression of PIN1 in IPC was always preceded by auxin accumulation. Basal localization of PIN1 was already established in the cells prior to their periclinal division. These cellular events initiated within parenchyma cells adjacent to the vascular bundles and successively extended from that point towards the middle region of the interfascicular area, located between neighboring vascular bundles. The final consequence of which was the closure of the cambial ring within the stem. Changes in the chemical composition of IPC walls were also detected and included changes of pectic epitopes, xyloglucans (XG) and extensins rich in hydroxyproline (HRGPs). In summary, results presented in this paper describe interfascicular cambium ontogenesis in terms of successive cellular events in the interfascicular regions of inflorescence stems of Arabidopsis.
AU - Mazur, Ewa
AU - Kurczyñska, Ewa
AU - Friml, Jiří
ID - 2061
IS - 5
JF - Protoplasma
TI - Cellular events during interfascicular cambium ontogenesis in inflorescence stems of Arabidopsis
VL - 251
ER -
TY - JOUR
AB - The success story of fast-spiking, parvalbumin-positive (PV+) GABAergic interneurons (GABA, γ-aminobutyric acid) in the mammalian central nervous system is noteworthy. In 1995, the properties of these interneurons were completely unknown. Twenty years later, thanks to the massive use of subcellular patch-clamp techniques, simultaneous multiple-cell recording, optogenetics, in vivo measurements, and computational approaches, our knowledge about PV+ interneurons became more extensive than for several types of pyramidal neurons. These findings have implications beyond the “small world” of basic research on GABAergic cells. For example, the results provide a first proof of principle that neuroscientists might be able to close the gaps between the molecular, cellular, network, and behavioral levels, representing one of the main challenges at the present time. Furthermore, the results may form the basis for PV+ interneurons as therapeutic targets for brain disease in the future. However, much needs to be learned about the basic function of these interneurons before clinical neuroscientists will be able to use PV+ interneurons for therapeutic purposes.
AU - Hu, Hua
AU - Gan, Jian
AU - Jonas, Peter M
ID - 2062
IS - 6196
JF - Science
TI - Fast-spiking parvalbumin^+ GABAergic interneurons: From cellular design to microcircuit function
VL - 345
ER -
TY - CONF
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems.We focus on qualitative properties forMDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability. We introduce a new simulation relation to capture the refinement relation ofMDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.We present an automated technique for assume-guarantee style reasoning for compositional analysis ofMDPs with qualitative properties by giving a counterexample guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Daca, Przemyslaw
ID - 2063
TI - CEGAR for qualitative analysis of probabilistic systems
VL - 8559
ER -
TY - JOUR
AB - We examined the synaptic structure, quantity, and distribution of α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid (AMPA)- and N-methyl-D-aspartate (NMDA)-type glutamate receptors (AMPARs and NMDARs, respectively) in rat cochlear nuclei by a highly sensitive freeze-fracture replica labeling technique. Four excitatory synapses formed by two distinct inputs, auditory nerve (AN) and parallel fibers (PF), on different cell types were analyzed. These excitatory synapse types included AN synapses on bushy cells (AN-BC synapses) and fusiform cells (AN-FC synapses) and PF synapses on FC (PF-FC synapses) and cartwheel cell spines (PF-CwC synapses). Immunogold labeling revealed differences in synaptic structure as well as AMPAR and NMDAR number and/or density in both AN and PF synapses, indicating a target-dependent organization. The immunogold receptor labeling also identified differences in the synaptic organization of FCs based on AN or PF connections, indicating an input-dependent organization in FCs. Among the four excitatory synapse types, the AN-BC synapses were the smallest and had the most densely packed intramembrane particles (IMPs), whereas the PF-CwC synapses were the largest and had sparsely packed IMPs. All four synapse types showed positive correlations between the IMP-cluster area and the AMPAR number, indicating a common intrasynapse-type relationship for glutamatergic synapses. Immunogold particles for AMPARs were distributed over the entire area of individual AN synapses; PF synapses often showed synaptic areas devoid of labeling. The gold-labeling for NMDARs occurred in a mosaic fashion, with less positive correlations between the IMP-cluster area and the NMDAR number. Our observations reveal target- and input-dependent features in the structure, number, and organization of AMPARs and NMDARs in AN and PF synapses.
AU - Rubio, Maía
AU - Fukazawa, Yugo
AU - Kamasawa, Naomi
AU - Clarkson, Cheryl
AU - Molnár, Elek
AU - Shigemoto, Ryuichi
ID - 2064
IS - 18
JF - Journal of Comparative Neurology
TI - Target- and input-dependent organization of AMPA and NMDA receptors in synaptic connections of the cochlear nucleus
VL - 522
ER -
TY - CONF
AB - NMAC is a mode of operation which turns a fixed input-length keyed hash function f into a variable input-length function. A practical single-key variant of NMAC called HMAC is a very popular and widely deployed message authentication code (MAC). Security proofs and attacks for NMAC can typically be lifted to HMAC. NMAC was introduced by Bellare, Canetti and Krawczyk [Crypto'96], who proved it to be a secure pseudorandom function (PRF), and thus also a MAC, assuming that (1) f is a PRF and (2) the function we get when cascading f is weakly collision-resistant. Unfortunately, HMAC is typically instantiated with cryptographic hash functions like MD5 or SHA-1 for which (2) has been found to be wrong. To restore the provable guarantees for NMAC, Bellare [Crypto'06] showed its security based solely on the assumption that f is a PRF, albeit via a non-uniform reduction. - Our first contribution is a simpler and uniform proof for this fact: If f is an ε-secure PRF (against q queries) and a δ-non-adaptively secure PRF (against q queries), then NMAC f is an (ε+ℓqδ)-secure PRF against q queries of length at most ℓ blocks each. - We then show that this ε+ℓqδ bound is basically tight. For the most interesting case where ℓqδ ≥ ε we prove this by constructing an f for which an attack with advantage ℓqδ exists. This also violates the bound O(ℓε) on the PRF-security of NMAC recently claimed by Koblitz and Menezes. - Finally, we analyze the PRF-security of a modification of NMAC called NI [An and Bellare, Crypto'99] that differs mainly by using a compression function with an additional keying input. This avoids the constant rekeying on multi-block messages in NMAC and allows for a security proof starting by the standard switch from a PRF to a random function, followed by an information-theoretic analysis. We carry out such an analysis, obtaining a tight ℓq2/2 c bound for this step, improving over the trivial bound of ℓ2q2/2c. The proof borrows combinatorial techniques originally developed for proving the security of CBC-MAC [Bellare et al., Crypto'05].
AU - Gazi, Peter
AU - Pietrzak, Krzysztof Z
AU - Rybar, Michal
ED - Garay, Juan
ED - Gennaro, Rosario
ID - 2082
IS - 1
TI - The exact PRF-security of NMAC and HMAC
VL - 8616
ER -
TY - JOUR
AB - Understanding the effects of sex and migration on adaptation to novel environments remains a key problem in evolutionary biology. Using a single-cell alga Chlamydomonas reinhardtii, we investigated how sex and migration affected rates of evolutionary rescue in a sink environment, and subsequent changes in fitness following evolutionary rescue. We show that sex and migration affect both the rate of evolutionary rescue and subsequent adaptation. However, their combined effects change as the populations adapt to a sink habitat. Both sex and migration independently increased rates of evolutionary rescue, but the effect of sex on subsequent fitness improvements, following initial rescue, changed with migration, as sex was beneficial in the absence of migration but constraining adaptation when combined with migration. These results suggest that sex and migration are beneficial during the initial stages of adaptation, but can become detrimental as the population adapts to its environment.
AU - Lagator, Mato
AU - Morgan, Andrew
AU - Neve, Paul
AU - Colegrave, Nick
ID - 2083
IS - 8
JF - Evolution
TI - Role of sex and migration in adaptation to sink environments
VL - 68
ER -
TY - JOUR
AB - Receptor tyrosine kinases (RTKs) are a large family of cell surface receptors that sense growth factors and hormones and regulate a variety of cell behaviours in health and disease. Contactless activation of RTKs with spatial and temporal precision is currently not feasible. Here, we generated RTKs that are insensitive to endogenous ligands but can be selectively activated by low-intensity blue light. We screened light-oxygen-voltage (LOV)-sensing domains for their ability to activate RTKs by light-activated dimerization. Incorporation of LOV domains found in aureochrome photoreceptors of stramenopiles resulted in robust activation of the fibroblast growth factor receptor 1 (FGFR1), epidermal growth factor receptor (EGFR) and rearranged during transfection (RET). In human cancer and endothelial cells, light induced cellular signalling with spatial and temporal precision. Furthermore, light faithfully mimicked complex mitogenic and morphogenic cell behaviour induced by growth factors. RTKs under optical control (Opto-RTKs) provide a powerful optogenetic approach to actuate cellular signals and manipulate cell behaviour.
AU - Grusch, Michael
AU - Schelch, Karin
AU - Riedler, Robert
AU - Gschaider-Reichhart, Eva
AU - Differ, Christopher
AU - Berger, Walter
AU - Inglés Prieto, Álvaro
AU - Janovjak, Harald L
ID - 2084
IS - 15
JF - EMBO Journal
TI - Spatio-temporally precise activation of engineered receptor tyrosine kinases by light
VL - 33
ER -
TY - JOUR
AB - Pathogens may gain a fitness advantage through manipulation of the behaviour of their hosts. Likewise, host behavioural changes can be a defence mechanism, counteracting the impact of pathogens on host fitness. We apply harmonic radar technology to characterize the impact of an emerging pathogen - Nosema ceranae (Microsporidia) - on honeybee (Apis mellifera) flight and orientation performance in the field. Honeybees are the most important commercial pollinators. Emerging diseases have been proposed to play a prominent role in colony decline, partly through sub-lethal behavioural manipulation of their hosts. We found that homing success was significantly reduced in diseased (65.8%) versus healthy foragers (92.5%). Although lost bees had significantly reduced continuous flight times and prolonged resting times, other flight characteristics and navigational abilities showed no significant difference between infected and non-infected bees. Our results suggest that infected bees express normal flight characteristics but are constrained in their homing ability, potentially compromising the colony by reducing its resource inputs, but also counteracting the intra-colony spread of infection. We provide the first high-resolution analysis of sub-lethal effects of an emerging disease on insect flight behaviour. The potential causes and the implications for both host and parasite are discussed.
AU - Wolf, Stephan
AU - Mcmahon, Dino
AU - Lim, Ka
AU - Pull, Christopher
AU - Clark, Suzanne
AU - Paxton, Robert
AU - Osborne, Juliet
ID - 2086
IS - 8
JF - PLoS One
TI - So near and yet so far: Harmonic radar reveals reduced homing ability of Nosema infected honeybees
VL - 9
ER -
TY - JOUR
AB - The computation of the winning set for Büchi objectives in alternating games on graphs is a central problem in computer-aided verification with a large number of applications. The long-standing best known upper bound for solving the problem is Õ(n ⋅ m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the Õ(n ⋅ m) boundary by presenting a new technique that reduces the running time to O(n2). This bound also leads to O(n2)-time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of Õ(n ⋅ m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n3)), and (3) in Markov decision processes (improving for m>n4/3 an earlier bound of O(m ⋅ √m)). We then show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. Our algorithms are the first dynamic algorithms for this problem. We then consider another core graph theoretic problem in verification of probabilistic systems, namely computing the maximal end-component decomposition of a graph. We present two improved static algorithms for the maximal end-component decomposition problem. Our first algorithm is an O(m ⋅ √m)-time algorithm, and our second algorithm is an O(n2)-time algorithm which is obtained using the same technique as for alternating Büchi games. Thus, we obtain an O(min &lcu;m ⋅ √m,n2})-time algorithm improving the long-standing O(n ⋅ m) time bound. Finally, we show how to maintain the maximal end-component decomposition of a graph under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per edge deletion, and O(m) worst-case time per edge insertion. Again, our algorithms are the first dynamic algorithms for this problem.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
ID - 2141
IS - 3
JF - Journal of the ACM
TI - Efficient and dynamic algorithms for alternating Büchi games and maximal end-component decomposition
VL - 61
ER -
TY - CONF
AB - We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Copyright is held by the owner/author(s).
AU - Bauer, Ulrich
AU - Lesnick, Michael
ID - 2153
T2 - Proceedings of the Annual Symposium on Computational Geometry
TI - Induced matchings of barcodes and the algebraic stability of persistence
ER -
TY - JOUR
AB - A result of Boros and Füredi (d = 2) and of Bárány (arbitrary d) asserts that for every d there exists cd > 0 such that for every n-point set P ⊂ ℝd, some point of ℝd is covered by at least (Formula presented.) of the d-simplices spanned by the points of P. The largest possible value of cd has been the subject of ongoing research. Recently Gromov improved the existing lower bounds considerably by introducing a new, topological proof method. We provide an exposition of the combinatorial component of Gromov's approach, in terms accessible to combinatorialists and discrete geometers, and we investigate the limits of his method. In particular, we give tighter bounds on the cofilling profiles for the (n - 1)-simplex. These bounds yield a minor improvement over Gromov's lower bounds on cd for large d, but they also show that the room for further improvement through the cofilling profiles alone is quite small. We also prove a slightly better lower bound for c3 by an approach using an additional structure besides the cofilling profiles. We formulate a combinatorial extremal problem whose solution might perhaps lead to a tight lower bound for cd.
AU - Matoušek, Jiří
AU - Wagner, Uli
ID - 2154
IS - 1
JF - Discrete & Computational Geometry
TI - On Gromov's method of selecting heavily covered points
VL - 52
ER -
TY - CONF
AB - Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s).
AU - Bauer, Ulrich
AU - Edelsbrunner, Herbert
ID - 2155
T2 - Proceedings of the Annual Symposium on Computational Geometry
TI - The morse theory of Čech and Delaunay filtrations
ER -
TY - CONF
AB - We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).
AU - Bauer, Ulrich
AU - Ge, Xiaoyin
AU - Wang, Yusu
ID - 2156
T2 - Proceedings of the Annual Symposium on Computational Geometry
TI - Measuring distance between Reeb graphs
ER -
TY - CONF
AB - We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in ℝ3? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold X into the 3-sphere S3. The main step, which allows us to simplify X and recurse, is in proving that if X can be embedded in S3, then there is also an embedding in which X has a short meridian, i.e., an essential curve in the boundary of X bounding a disk in S3 nX with length bounded by a computable function of the number of tetrahedra of X.
AU - Matoušek, Jiří
AU - Sedgwick, Eric
AU - Tancer, Martin
AU - Wagner, Uli
ID - 2157
T2 - Proceedings of the Annual Symposium on Computational Geometry
TI - Embeddability in the 3 sphere is decidable
ER -
TY - JOUR
AB - Directional guidance of migrating cells is relatively well explored in the reductionist setting of cell culture experiments. Here spatial gradients of chemical cues as well as gradients of mechanical substrate characteristics prove sufficient to attract single cells as well as their collectives. How such gradients present and act in the context of an organism is far less clear. Here we review recent advances in understanding how guidance cues emerge and operate in the physiological context.
AU - Majumdar, Ritankar
AU - Sixt, Michael K
AU - Parent, Carole
ID - 2158
IS - 1
JF - Current Opinion in Cell Biology
TI - New paradigms in the establishment and maintenance of gradients during directed cell migration
VL - 30
ER -