@article{251, abstract = {We study the density of varieties in a certain family which do not satisfy the Hasse principle. This work relies on results recently obtained by Colliot-Thélène [3].}, author = {de la Bretèche, Régis and Timothy Browning}, journal = {Journal de Theorie des Nombres de Bordeaux}, number = {1}, pages = {25 -- 44}, publisher = {Universite de Bordeaux I}, title = {{Counter examples to the Hasse principle among certain coflasque tori}}, doi = {10.5802/jtnb.857}, volume = {26}, year = {2013}, } @inproceedings{2517, abstract = {Traditional formal methods are based on a Boolean satisfaction notion: a reactive system satisfies, or not, a given specification. We generalize formal methods to also address the quality of systems. As an adequate specification formalism we introduce the linear temporal logic LTL[F]. The satisfaction value of an LTL[F] formula is a number between 0 and 1, describing the quality of the satisfaction. The logic generalizes traditional LTL by augmenting it with a (parameterized) set F of arbitrary functions over the interval [0,1]. For example, F may contain the maximum or minimum between the satisfaction values of subformulas, their product, and their average. The classical decision problems in formal methods, such as satisfiability, model checking, and synthesis, are generalized to search and optimization problems in the quantitative setting. For example, model checking asks for the quality in which a specification is satisfied, and synthesis returns a system satisfying the specification with the highest quality. Reasoning about quality gives rise to other natural questions, like the distance between specifications. We formalize these basic questions and study them for LTL[F]. By extending the automata-theoretic approach for LTL to a setting that takes quality into an account, we are able to solve the above problems and show that reasoning about LTL[F] has roughly the same complexity as reasoning about traditional LTL.}, author = {Almagor, Shaull and Boker, Udi and Kupferman, Orna}, location = {Riga, Latvia}, number = {Part 2}, pages = {15 -- 27}, publisher = {Springer}, title = {{Formalizing and reasoning about quality}}, doi = {10.1007/978-3-642-39212-2_3}, volume = {7966}, year = {2013}, } @inproceedings{2518, abstract = {A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. We study which classes of finite-valued languages can be solved exactly by the basic linear programming relaxation (BLP). Thapper and Živný showed [20] that if BLP solves the language then the language admits a binary commutative fractional polymorphism. We prove that the converse is also true. This leads to a necessary and a sufficient condition which can be checked in polynomial time for a given language. In contrast, the previous necessary and sufficient condition due to [20] involved infinitely many inequalities. More recently, Thapper and Živný [21] showed (using, in particular, a technique introduced in this paper) that core languages that do not satisfy our condition are NP-hard. Taken together, these results imply that a finite-valued language can either be solved using Linear Programming or is NP-hard.}, author = {Kolmogorov, Vladimir}, location = {Riga, Latvia}, number = {1}, pages = {625 -- 636}, publisher = {Springer}, title = {{The power of linear programming for finite-valued CSPs: A constructive characterization}}, doi = {10.1007/978-3-642-39206-1_53}, volume = {7965}, year = {2013}, } @article{2516, abstract = {We study the problem of object recognition for categories for which we have no training examples, a task also called zero-data or zero-shot learning. This situation has hardly been studied in computer vision research, even though it occurs frequently: the world contains tens of thousands of different object classes and for only few of them image collections have been formed and suitably annotated. To tackle the problem we introduce attribute-based classification: objects are identified based on a high-level description that is phrased in terms of semantic attributes, such as the object's color or shape. Because the identification of each such property transcends the specific learning task at hand, the attribute classifiers can be pre-learned independently, e.g. from existing image datasets unrelated to the current task. Afterwards, new classes can be detected based on their attribute representation, without the need for a new training phase. In this paper we also introduce a new dataset, Animals with Attributes, of over 30,000 images of 50 animal classes, annotated with 85 semantic attributes. Extensive experiments on this and two more datasets show that attribute-based classification indeed is able to categorize images without access to any training images of the target classes.}, author = {Lampert, Christoph and Nickisch, Hannes and Harmeling, Stefan}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, number = {3}, pages = {453 -- 465}, publisher = {IEEE}, title = {{Attribute-based classification for zero-shot learning of object categories}}, doi = {10.1109/TPAMI.2013.140}, volume = {36}, year = {2013}, } @inproceedings{2520, abstract = {We propose a probabilistic model to infer supervised latent variables in the Hamming space from observed data. Our model allows simultaneous inference of the number of binary latent variables, and their values. The latent variables preserve neighbourhood structure of the data in a sense that objects in the same semantic concept have similar latent values, and objects in different concepts have dissimilar latent values. We formulate the supervised infinite latent variable problem based on an intuitive principle of pulling objects together if they are of the same type, and pushing them apart if they are not. We then combine this principle with a flexible Indian Buffet Process prior on the latent variables. We show that the inferred supervised latent variables can be directly used to perform a nearest neighbour search for the purpose of retrieval. We introduce a new application of dynamically extending hash codes, and show how to effectively couple the structure of the hash codes with continuously growing structure of the neighbourhood preserving infinite latent feature space.}, author = {Quadrianto, Novi and Sharmanska, Viktoriia and Knowles, David and Ghahramani, Zoubin}, booktitle = {Proceedings of the 29th conference uncertainty in Artificial Intelligence}, isbn = {9780974903996}, location = {Bellevue, WA, United States}, pages = {527 -- 536}, publisher = {AUAI Press}, title = {{The supervised IBP: Neighbourhood preserving infinite latent feature models}}, year = {2013}, } @article{253, author = {Timothy Browning}, journal = {Mathematika}, number = {1}, pages = {101 -- 107}, publisher = {Unknown}, title = {{Counting rational points on cubic hypersurfaces: Corrigendum}}, doi = {10.1112/S0025579313000132}, volume = {60}, year = {2013}, } @article{2692, abstract = {The group III metabotropic glutamate (mGlu) receptors mGlu7 and mGlu8 are receiving increased attention as potential novel therapeutic targets for anxiety disorders. The effects mediated by these receptors appear to result from a complex interplay of facilitatory and inhibitory actions at different brain sites in the anxiety/fear circuits. To better understand the effect of mGlu7 and mGlu8 receptors on extinction of contextual fear and their critical sites of action in the fear networks, we focused on the amygdala. Direct injection into the basolateral complex of the amygdala of the mGlu7 receptor agonist AMN082 facilitated extinction, whereas the mGlu8 receptor agonist (S)-3,4-DCPG sustained freezing during the extinction acquisition trial. We also determined at the ultrastructural level the synaptic distribution of these receptors in the basal nucleus (BA) and intercalated cell clusters (ITCs) of the amygdala. Both areas are thought to exert key roles in fear extinction. We demonstrate that mGlu7 and mGlu8 receptors are located in different presynaptic terminals forming both asymmetric and symmetric synapses, and that they preferentially target neurons expressing mGlu1α receptors mostly located around ITCs. In addition we show that mGlu7 and mGlu8 receptors were segregated to different inputs to a significant extent. In particular, mGlu7a receptors were primarily onto glutamatergic afferents arising from the BA or midline thalamic nuclei, but not the medial prefrontal cortex (mPFC), as revealed by combined anterograde tracing and pre-embedding electron microscopy. On the other hand, mGlu8a showed a more restricted distribution in the BA and appeared absent from thalamic, mPFC and intrinsic inputs. This segregation of mGlu7 and mGlu8 receptors in different neuronal pathways of the fear circuit might explain the distinct effects on fear extinction training observed with mGlu7 and mGlu8 receptor agonists.}, author = {Dobi, Alice and Sartori, Simone B and Busti, Daniela and Van Der Putten, Herman V and Singewald, Nicolas and Ryuichi Shigemoto and Ferraguti, Francesco}, journal = {Neuropharmacology}, pages = {274 -- 289}, publisher = {Elsevier}, title = {{Neural substrates for the distinct effects of presynaptic group III metabotropic glutamate receptors on extinction of contextual fear conditioning in mice}}, doi = {10.1016/j.neuropharm.2012.05.025}, volume = {66}, year = {2013}, } @article{2691, abstract = {P/Q-type voltage-dependent calcium channels play key roles in transmitter release, integration of dendritic signals, generation of dendritic spikes, and gene expression. High intracellular calcium concentration transient produced by these channels is restricted to tens to hundreds of nanometers from the channels. Therefore, precise localization of these channels along the plasma membrane was long sought to decipher how each neuronal cell function is controlled. Here, we analyzed the distribution of Cav2.1 subunit of the P/Q-type channel using highly sensitive SDS-digested freeze-fracture replica labeling in the rat cerebellar Purkinje cells. The labeling efficiency was such that the number of immunogold particles in each parallel fiber active zone was comparable to that of functional channels calculated from previous reports. Two distinct patterns of Cav2.1 distribution, scattered and clustered, were found in Purkinje cells. The scattered Cav2.1 had a somatodendritic gradient with the density of immunogold particles increasing 2.5-fold from soma to distal dendrites. The other population with 74-fold higher density than the scattered particles was found within clusters of intramembrane particles on the P-face of soma and primary dendrites. Both populations of Cav2.1 were found as early as P3 and increased in the second postnatal week to a mature level. Using double immunogold labeling, we found that virtually all of the Cav2.1 clusters were colocalized with two types of calcium-activated potassium channels, BK and SK2, with the nearest neighbor distance of 40∼nm. Calcium nanodomain created by the opening of Cav2.1 channels likely activates the two channels that limit the extent of depolarization.}, author = {Indriati, Dwi Wahyu and Kamasawa, Naomi and Matsui, Ko and Meredith, Andrea L and Watanabe, Masahiko and Ryuichi Shigemoto}, journal = {Journal of Neuroscience}, number = {8}, pages = {3668 -- 3678}, publisher = {Society for Neuroscience}, title = {{Quantitative localization of Cav2.1 (P/Q-Type) voltage-dependent calcium channels in Purkinje cells: Somatodendritic gradient and distinct somatic coclustering with calcium-activated potassium channels}}, doi = {10.1523/JNEUROSCI.2921-12.2013}, volume = {33}, year = {2013}, } @article{2690, abstract = {Establishing the spatiotemporal concentration profile of neurotransmitter following synaptic vesicular release is essential for our understanding of inter-neuronal communication. Such profile is a determinant of synaptic strength, short-term plasticity and inter-synaptic crosstalk. Synaptically released glutamate has been suggested to reach a few millimolar in concentration and last for <1 ms. The synaptic cleft is often conceived as a single concentration compartment, whereas a huge gradient likely exists. Modelling studies have attempted to describe this gradient, but two key parameters, the number of glutamate in a vesicle (NGlu) and its diffusion coefficient (DGlu) in the extracellular space, remained unresolved. To determine this profile, the rat calyx of Held synapse at postnatal day 12-16 was studied where diffusion of glutamate occurs two-dimensionally and where quantification of AMPA receptor distribution on individual postsynaptic specialization on medial nucleus of the trapezoid body principal cells is possible using SDS-digested freeze-fracture replica labelling. To assess the performance of these receptors as glutamate sensors, a kinetic model of the receptors was constructed from outside-out patch recordings. From here, we simulated synaptic responses and compared them with the EPSC recordings. Combinations of NGlu and DGlu with an optimum of 7000 and 0.3 μm2 ms-1 reproduced the data, suggesting slow diffusion. Further simulations showed that a single vesicle does not saturate the synaptic receptors, and that glutamate spillover does not affect the conductance amplitude at this synapse. Using the estimated profile, we also evaluated how the number of multiple vesicle releases at individual active zones affects the amplitude of postsynaptic signals.}, author = {Budisantoso, Timotheus and Harumi Harada and Kamasawa, Naomi and Fukazawa, Yugo and Ryuichi Shigemoto and Matsui, Ko}, journal = {Journal of Physiology}, number = {1}, pages = {219 -- 239}, publisher = {Wiley-Blackwell}, title = {{Evaluation of glutamate concentration transient in the synaptic cleft of the rat calyx of Held}}, doi = {10.1113/jphysiol.2012.241398}, volume = {591}, year = {2013}, } @article{2693, abstract = {Inhibitory parvalbumin-containing interneurons (PVIs) control neuronal discharge and support the generation of theta- and gammafrequency oscillations in cortical networks. Fast GABAergic input onto PVIs is crucial for their synchronization and oscillatory entrainment, but the role of metabotropic GABAB receptors (GABABRs) in mediating slow presynaptic and postsynaptic inhibition remains unknown. In this study, we have combined high-resolution immunoelectron microscopy, whole-cell patch-clamp recording, and computational modeling to investigate the subcellular distribution and effects of GABABRs and their postsynaptic effector Kir3 channels in rat hippocampal PVIs. Pre-embedding immunogold labeling revealed that the receptors and channels localize at high levels to the extrasynaptic membrane of parvalbumin-immunoreactive dendrites. Immunoreactivity forGABABRs was also present at lower levels on PVI axon terminals. Whole-cell recordings further showed that synaptically released GABA in response to extracellular stimulation evokes large GABABR-mediated slow IPSCs in perisomatic-targeting (PT) PVIs, but only small or no currents in dendrite-targeting (DT) PVIs. In contrast, paired recordings demonstrated that GABABR activation results in presynaptic inhibition at the output synapses of both PT and DT PVIs, but more strongly in the latter. Finally, computational analysis indicated that GABAB IPSCs can phasically modulate the discharge of PT interneurons at theta frequencies. In summary, our results show that GABABRs differentially mediate slow presynaptic and postsynaptic inhibition in PVIs and can contribute to the dynamic modulation of their activity during oscillations. Furthermore, these data provide evidence for a compartment-specific molecular divergence of hippocampal PVI subtypes, suggesting that activation of GABABRs may shift the balance between perisomatic and dendritic inhibition.}, author = {Booker, Sam A and Gross, Anna and Althof, Daniel and Ryuichi Shigemoto and Bettler, Bernhard and Frotscher, Michael and Hearing, Matthew C and Wickman, Kevin D and Watanabe, Masahiko and Kulik, Ákos and Vida, Imre}, journal = {Journal of Neuroscience}, number = {18}, pages = {7961 -- 7974}, publisher = {Society for Neuroscience}, title = {{Differential GABAB-receptor-mediated effects in perisomatic- and dendrite-targeting parvalbumin interneurons}}, doi = {10.1523/JNEUROSCI.1186-12.2013}, volume = {33}, year = {2013}, } @article{2698, abstract = {We consider non-interacting particles subject to a fixed external potential V and a self-generated magnetic field B. The total energy includes the field energy β∫B2 and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter β tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical asymptotics, h→0, of the total ground state energy E(β,h,V). The relevant parameter measuring the field strength in the semiclassical limit is κ=βh. We are not able to give the exact leading order semiclassical asymptotics uniformly in κ or even for fixed κ. We do however give upper and lower bounds on E with almost matching dependence on κ. In the simultaneous limit h→0 and κ→∞ we show that the standard non-magnetic Weyl asymptotics holds. The same result also holds for the spinless case, i.e. where the Pauli operator is replaced by the Schrödinger operator.}, author = {Erdös, László and Fournais, Søren and Solovej, Jan}, journal = {Journal of the European Mathematical Society}, number = {6}, pages = {2093 -- 2113}, publisher = {European Mathematical Society}, title = {{Stability and semiclassics in self-generated fields}}, doi = {10.4171/JEMS/416}, volume = {15}, year = {2013}, } @article{2697, abstract = {We consider Hermitian and symmetric random band matrices H = (h xy ) in d⩾1 d ⩾ 1 dimensions. The matrix entries h xy , indexed by x,y∈(Z/LZ)d x , y ∈ ( Z / L Z ) d , are independent, centred random variables with variances sxy=E|hxy|2 s x y = E | h x y | 2 . We assume that s xy is negligible if |x − y| exceeds the band width W. In one dimension we prove that the eigenvectors of H are delocalized if W≫L4/5 W ≫ L 4 / 5 . We also show that the magnitude of the matrix entries |Gxy|2 | G x y | 2 of the resolvent G=G(z)=(H−z)−1 G = G ( z ) = ( H - z ) - 1 is self-averaging and we compute E|Gxy|2 E | G x y | 2 . We show that, as L→∞ L → ∞ and W≫L4/5 W ≫ L 4 / 5 , the behaviour of E|Gxy|2 E | G x y | 2 is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions.}, author = {László Erdös and Knowles, Antti and Yau, Horng-Tzer and Yin, Jun}, journal = {Communications in Mathematical Physics}, number = {1}, pages = {367 -- 416}, publisher = {Springer}, title = {{Delocalization and diffusion profile for random band matrices}}, doi = {10.1007/s00220-013-1773-3}, volume = {323}, year = {2013}, } @inproceedings{2718, abstract = {Even though both population and quantitative genetics, and evolutionary computation, deal with the same questions, they have developed largely independently of each other. I review key results from each field, emphasising those that apply independently of the (usually unknown) relation between genotype and phenotype. The infinitesimal model provides a simple framework for predicting the response of complex traits to selection, which in biology has proved remarkably successful. This allows one to choose the schedule of population sizes and selection intensities that will maximise the response to selection, given that the total number of individuals realised, C = ∑t Nt, is constrained. This argument shows that for an additive trait (i.e., determined by the sum of effects of the genes), the optimum population size and the maximum possible response (i.e., the total change in trait mean) are both proportional to √C.}, author = {Barton, Nicholas H and Paixao, Tiago}, booktitle = {Proceedings of the 15th annual conference on Genetic and evolutionary computation}, location = {Amsterdam, Netherlands}, pages = {1573 -- 1580}, publisher = {ACM}, title = {{Can quantitative and population genetics help us understand evolutionary computation?}}, doi = {10.1145/2463372.2463568}, year = {2013}, } @article{2720, abstract = {Knowledge of the rate and fitness effects of mutations is essential for understanding the process of evolution. Mutations are inherently difficult to study because they are rare and are frequently eliminated by natural selection. In the ciliate Tetrahymena thermophila, mutations can accumulate in the germline genome without being exposed to selection. We have conducted a mutation accumulation (MA) experiment in this species. Assuming that all mutations are deleterious and have the same effect, we estimate that the deleterious mutation rate per haploid germline genome per generation is U = 0.0047 (95% credible interval: 0.0015, 0.0125), and that germline mutations decrease fitness by s = 11% when expressed in a homozygous state (95% CI: 4.4%, 27%). We also estimate that deleterious mutations are partially recessive on average (h = 0.26; 95% CI: –0.022, 0.62) and that the rate of lethal mutations is <10% of the deleterious mutation rate. Comparisons between the observed evolutionary responses in the germline and somatic genomes and the results from individual-based simulations of MA suggest that the two genomes have similar mutational parameters. These are the first estimates of the deleterious mutation rate and fitness effects from the eukaryotic supergroup Chromalveolata and are within the range of those of other eukaryotes.}, author = {Long, Hongan and Paixao, Tiago and Azevedo, Ricardo and Zufall, Rebecca}, journal = {Genetics}, number = {2}, pages = {527--540}, publisher = {Genetics Society of America}, title = {{Accumulation of spontaneous mutations in the ciliate Tetrahymena thermophila}}, doi = {10.1534/genetics.113.153536}, volume = {195}, year = {2013}, } @inproceedings{2719, abstract = {Prediction of the evolutionary process is a long standing problem both in the theory of evolutionary biology and evolutionary computation (EC). It has long been realized that heritable variation is crucial to both the response to selection and the success of genetic algorithms. However, not all variation contributes in the same way to the response. Quantitative genetics has developed a large body of work trying to estimate and understand how different components of the variance in fitness in the population contribute to the response to selection. We illustrate how to apply some concepts of quantitative genetics to the analysis of genetic algorithms. In particular, we derive estimates for the short term prediction of the response to selection and we use variance decomposition to gain insight on local aspects of the landscape. Finally, we propose a new population based genetic algorithm that uses these methods to improve its operation.}, author = {Paixao, Tiago and Barton, Nicholas H}, booktitle = {Proceedings of the 15th annual conference on Genetic and evolutionary computation}, location = {Amsterdam, Netherlands}, pages = {845 -- 852}, publisher = {ACM}, title = {{A variance decomposition approach to the analysis of genetic algorithms}}, doi = {10.1145/2463372.2463470}, year = {2013}, } @article{2782, abstract = {We consider random n×n matrices of the form (XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2}, where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are known as MANOVA matrices and which have joint eigenvalue density given by the third classical ensemble, the Jacobi ensemble. We show that, away from the spectral edge, the eigenvalue density converges to the limiting density of the Jacobi ensemble even on the shortest possible scales of order 1/n (up to log n factors). This result is the analogue of the local Wigner semicircle law and the local Marchenko-Pastur law for general MANOVA matrices.}, author = {Erdös, László and Farrell, Brendan}, journal = {Journal of Statistical Physics}, number = {6}, pages = {1003 -- 1032}, publisher = {Springer}, title = {{Local eigenvalue density for general MANOVA matrices}}, doi = {10.1007/s10955-013-0807-8}, volume = {152}, year = {2013}, } @article{2781, abstract = {We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, that is, graphs on N vertices where every edge is chosen independently and with probability p = p(N). We rescale the matrix so that its bulk eigenvalues are of order one. We prove that, as long as pN→∞(with a speed at least logarithmic in N), the density of eigenvalues of the Erdős-Rényi ensemble is given by the Wigner semicircle law for spectral windows of length larger than N-1 (up to logarithmic corrections). As a consequence, all eigenvectors are proved to be completely delocalized in the sense that the ℓ∞-norms of the ℓ2-normalized eigenvectors are at most of order N-1/2 with a very high probability. The estimates in this paper will be used in the companion paper [Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues (2011) Preprint] to prove the universality of eigenvalue distributions both in the bulk and at the spectral edges under the further restriction that pN »N2/3.}, author = {László Erdös and Knowles, Antti and Yau, Horng-Tzer and Yin, Jun}, journal = {Annals of Probability}, number = {3 B}, pages = {2279 -- 2375}, publisher = {Institute of Mathematical Statistics}, title = {{Spectral statistics of Erdős-Rényi graphs I: Local semicircle law}}, doi = {10.1214/11-AOP734}, volume = {41}, year = {2013}, } @article{2780, abstract = {We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix entries. Our results generalize the previous results of Erdős et al. (Ann Probab, arXiv:1103.1919, 2013; Commun Math Phys, arXiv:1103.3869, 2013; J Combin 1(2):15-85, 2011) which constituted a key step in the proof of the local semicircle law with optimal error bound in mean-field random matrix models. Our bounds apply to random band matrices and improve previous estimates from order 2 to order 4 in the cases relevant to applications. In particular, they lead to a proof of the diffusion approximation for the magnitude of the resolvent of random band matrices. This, in turn, implies new delocalization bounds on the eigenvectors. The applications are presented in a separate paper (Erdős et al., arXiv:1205.5669, 2013).}, author = {László Erdös and Knowles, Antti and Yau, Horng-Tzer}, journal = {Annales Henri Poincare}, number = {8}, pages = {1837 -- 1926}, publisher = {Birkhäuser}, title = {{Averaging fluctuations in resolvents of random band matrices}}, doi = {10.1007/s00023-013-0235-y}, volume = {14}, year = {2013}, } @inproceedings{2807, abstract = {We consider several basic problems of algebraic topology, with connections to combinatorial and geometric questions, from the point of view of computational complexity. The extension problem asks, given topological spaces X; Y , a subspace A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X → Y . For computational purposes, we assume that X and Y are represented as finite simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map. In this generality the problem is undecidable, as follows from Novikov's result from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected; informally, this means that Y has \no holes up to dimension k-1" (a basic example of such a Y is the sphere Sk). We prove that, on the one hand, this problem is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2, we obtain an algorithm that solves the extension problem in polynomial time assuming Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides a classification of all extensions up to homotopy (continuous deformation). This relies on results of our SODA 2012 paper, and the main new ingredient is a machinery of objects with polynomial-time homology, which is a polynomial-time analog of objects with effective homology developed earlier by Sergeraert et al. We also consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected Y . Their computability was established by Brown in 1957; we show that πk(Y ) can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where Y is a cell complex with certain rather compact encoding. We strengthen his result to #P-hardness for Y given as a simplicial complex. }, author = {Čadek, Martin and Krcál, Marek and Matoušek, Jiří and Vokřínek, Lukáš and Wagner, Uli}, booktitle = {45th Annual ACM Symposium on theory of computing}, location = {Palo Alto, CA, United States}, pages = {595 -- 604}, publisher = {ACM}, title = {{Extending continuous maps: Polynomiality and undecidability}}, doi = {10.1145/2488608.2488683}, year = {2013}, } @article{2808, abstract = {In order to establish a reference for analysis of the function of auxin and the auxin biosynthesis regulators SHORT INTERNODE/ STYLISH (SHI/STY) during Physcomitrella patens reproductive development, we have described male (antheridial) and female (archegonial) development in detail, including temporal and positional information of organ initiation. This has allowed us to define discrete stages of organ morphogenesis and to show that reproductive organ development in P. patens is highly organized and that organ phyllotaxis differs between vegetative and reproductive development. Using the PpSHI1 and PpSHI2 reporter and knockout lines, the auxin reporters GmGH3pro:GUS and PpPINApro:GFP-GUS, and the auxin-conjugating transgene PpSHI2pro:IAAL, we could show that the PpSHI genes, and by inference also auxin, play important roles for reproductive organ development in moss. The PpSHI genes are required for the apical opening of the reproductive organs, the final differentiation of the egg cell, and the progression of canal cells into a cell death program. The apical cells of the archegonium, the canal cells, and the egg cell are also sites of auxin responsiveness and are affected by reduced levels of active auxin, suggesting that auxin mediates PpSHI function in the reproductive organs.}, author = {Landberg, Katarina and Pederson, Eric and Viaene, Tom and Bozorg, Behruz and Friml, Jirí and Jönsson, Henrik and Thelander, Mattias and Sundberg, Eva}, journal = {Plant Physiology}, number = {3}, pages = {1406 -- 1419}, publisher = {American Society of Plant Biologists}, title = {{The moss physcomitrella patens reproductive organ development is highly organized, affected by the two SHI/STY genes and by the level of active auxin in the SHI/STY expression domain}}, doi = {10.1104/pp.113.214023}, volume = {162}, year = {2013}, }