@article{18411, abstract = {Recent works have shown the use of diffusion geometry for various pattern recognition applications, including nonrigid shape analysis. In this paper, we introduce spectral shape distance as a general framework for distribution-based shape similarity and show that two recent methods for shape similarity due to Rustamov and Mahmoudi and Sapiro are particular cases thereof.}, author = {Bronstein, Michael M and Bronstein, Alexander}, issn = {0162-8828}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, number = {5}, pages = {1065--1071}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Shape recognition with spectral distances}}, doi = {10.1109/tpami.2010.210}, volume = {33}, year = {2011}, } @article{18433, abstract = {The computer vision and pattern recognition communities have recently witnessed a surge of feature-based methods in object recognition and image retrieval applications. These methods allow representing images as collections of “visual words” and treat them using text search approaches following the “bag of features” paradigm. In this article, we explore analogous approaches in the 3D world applied to the problem of nonrigid shape retrieval in large databases. Using multiscale diffusion heat kernels as “geometric words,” we construct compact and informative shape descriptors by means of the “bag of features” approach. We also show that considering pairs of “geometric words” (“geometric expressions”) allows creating spatially sensitive bags of features with better discriminative power. Finally, adopting metric learning approaches, we show that shapes can be efficiently represented as binary codes. Our approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.}, author = {Bronstein, Alexander and Bronstein, Michael M. and Guibas, Leonidas J. and Ovsjanikov, Maks}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {1}, pages = {1--20}, publisher = {Association for Computing Machinery}, title = {{Shape google: Geometric words and expressions for invariant shape retrieval}}, doi = {10.1145/1899404.1899405}, volume = {30}, year = {2011}, } @article{22061, abstract = {We consider the defocusing nonlinear wave equation utt − Δu + |u| pu = 0 with spherically-symmetric initial data in the regime 4 d−2 4 d−2 . The principal result is that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalent formulation is that maximal-lifespan solutions with bounded critical Sobolev norm are global and scatter}, author = {Killip, Rowan and Visan, Monica}, issn = {1088-6826}, journal = {Proceedings of the American Mathematical Society}, number = {5}, pages = {1805--1817}, publisher = {American Mathematical Society}, title = {{The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions}}, doi = {10.1090/s0002-9939-2010-10615-9}, volume = {139}, 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 for Computational Logic}, title = {{Timed parity games: Complexity and robustness}}, doi = {10.2168/LMCS-7(4:8)2011}, volume = {7}, year = {2011}, } @inproceedings{3302, abstract = {Cloud computing aims to give users virtually unlimited pay-per-use computing resources without the burden of managing the underlying infrastructure. We present a new job execution environment Flextic that exploits scal- able static scheduling techniques to provide the user with a flexible pricing model, such as a tradeoff between dif- ferent degrees of execution speed and execution price, and at the same time, reduce scheduling overhead for the cloud provider. We have evaluated a prototype of Flextic on Amazon EC2 and compared it against Hadoop. For various data parallel jobs from machine learning, im- age processing, and gene sequencing that we considered, Flextic has low scheduling overhead and reduces job du- ration by up to 15% compared to Hadoop, a dynamic cloud scheduler.}, author = {Henzinger, Thomas A and Singh, Anmol and Singh, Vasu and Wies, Thomas and Zufferey, Damien}, booktitle = {3rd USENIX Workshop on Hot Topics in Cloud Computing}, location = {Portland, OR, United States}, pages = {1 -- 6}, publisher = {Usenix Association}, title = {{Static scheduling in clouds}}, year = {2011}, } @inproceedings{3356, abstract = {There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with "controlled-accumulation", allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.}, author = {Boker, Udi and Chatterjee, Krishnendu and Henzinger, Thomas A and Kupferman, Orna}, location = {Toronto, Canada}, publisher = {IEEE}, title = {{Temporal specifications with accumulative values}}, doi = {10.1109/LICS.2011.33}, year = {2011}, } @misc{5385, abstract = {There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with “controlled-accumulation”, allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.}, author = {Boker, Udi and Chatterjee, Krishnendu and Henzinger, Thomas A and Kupferman, Orna}, issn = {2664-1690}, pages = {14}, publisher = {IST Austria}, title = {{Temporal specifications with accumulative values}}, doi = {10.15479/AT:IST-2011-0003}, year = {2011}, } @misc{5381, abstract = {In two-player finite-state stochastic games of partial obser- vation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distri- bution over the successor states. The game is played for infinitely many rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1) or pos- itively (i.e., with positive probability), no matter the strategy of the second player. We classify such games according to the information and to the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two- sided with (c) both players having partial observation. On the basis of randomization, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. Our main results for pure strategies are as follows: (1) For one-sided games with player 2 perfect observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strate- gies are not sufficient, and present an exponential upper bound on mem- ory both for almost-sure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete and present symbolic algo- rithms that avoid the explicit exponential construction. (2) For one-sided games with player 1 perfect observation we show that non-elementary memory is both necessary and sufficient for both almost-sure and posi- tive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least non-elementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence re- sult exhibit serious flaws in previous results in the literature: we show a non-elementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, issn = {2664-1690}, pages = {43}, publisher = {IST Austria}, title = {{Partial-observation stochastic games: How to win when belief fails}}, doi = {10.15479/AT:IST-2011-0007}, year = {2011}, } @article{3353, abstract = {Compositional theories are crucial when designing large and complex systems from smaller components. In this work we propose such a theory for synchronous concurrent systems. Our approach follows so-called interface theories, which use game-theoretic interpretations of composition and refinement. These are appropriate for systems with distinct inputs and outputs, and explicit conditions on inputs that must be enforced during composition. Our interfaces model systems that execute in an infinite sequence of synchronous rounds. At each round, a contract must be satisfied. The contract is simply a relation specifying the set of valid input/output pairs. Interfaces can be composed by parallel, serial or feedback composition. A refinement relation between interfaces is defined, and shown to have two main properties: (1) it is preserved by composition, and (2) it is equivalent to substitutability, namely, the ability to replace an interface by another one in any context. Shared refinement and abstraction operators, corresponding to greatest lower and least upper bounds with respect to refinement, are also defined. Input-complete interfaces, that impose no restrictions on inputs, and deterministic interfaces, that produce a unique output for any legal input, are discussed as special cases, and an interesting duality between the two classes is exposed. A number of illustrative examples are provided, as well as algorithms to compute compositions, check refinement, and so on, for finite-state interfaces.}, author = {Tripakis, Stavros and Lickly, Ben and Henzinger, Thomas A and Lee, Edward}, journal = {ACM Transactions on Programming Languages and Systems}, number = {4}, publisher = {ACM}, title = {{A theory of synchronous relational interfaces}}, doi = {10.1145/1985342.1985345}, volume = {33}, year = {2011}, } @article{3354, abstract = {We consider two-player games played on a finite state space for an infinite number of rounds. The games are concurrent: 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. We consider ω-regular winning conditions specified as parity objectives. Both players are allowed to use randomization when choosing their moves. We study the computation of the limit-winning set of states, consisting of the states where the sup-inf value of the game for player 1 is 1: in other words, a state is limit-winning if player 1 can ensure a probability of winning arbitrarily close to 1. We show that the limit-winning set can be computed in O(n2d+2) time, where n is the size of the game structure and 2d is the number of priorities (or colors). The membership problem of whether a state belongs to the limit-winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms are considerably more involved than those for turn-based games. This is because concurrent games do not satisfy two of the most fundamental properties of turn-based parity games. First, in concurrent games limit-winning strategies require randomization; and second, they require infinite memory.}, author = {Chatterjee, Krishnendu and De Alfaro, Luca and Henzinger, Thomas A}, journal = {ACM Transactions on Computational Logic}, number = {4}, publisher = {ACM}, title = {{Qualitative concurrent parity games}}, doi = {10.1145/1970398.1970404}, volume = {12}, year = {2011}, } @article{3396, abstract = {Facial branchiomotor neurons (FBMNs) in zebrafish and mouse embryonic hindbrain undergo a characteristic tangential migration from rhombomere (r) 4, where they are born, to r6/7. Cohesion among neuroepithelial cells (NCs) has been suggested to function in FBMN migration by inhibiting FBMNs positioned in the basal neuroepithelium such that they move apically between NCs towards the midline of the neuroepithelium instead of tangentially along the basal side of the neuroepithelium towards r6/7. However, direct experimental evaluation of this hypothesis is still lacking. Here, we have used a combination of biophysical cell adhesion measurements and high-resolution time-lapse microscopy to determine the role of NC cohesion in FBMN migration. We show that reducing NC cohesion by interfering with Cadherin 2 (Cdh2) activity results in FBMNs positioned at the basal side of the neuroepithelium moving apically towards the neural tube midline instead of tangentially towards r6/7. In embryos with strongly reduced NC cohesion, ectopic apical FBMN movement frequently results in fusion of the bilateral FBMN clusters over the apical midline of the neural tube. By contrast, reducing cohesion among FBMNs by interfering with Contactin 2 (Cntn2) expression in these cells has little effect on apical FBMN movement, but reduces the fusion of the bilateral FBMN clusters in embryos with strongly diminished NC cohesion. These data provide direct experimental evidence that NC cohesion functions in tangential FBMN migration by restricting their apical movement.}, author = {Stockinger, Petra and Heisenberg, Carl-Philipp J and Maître, Jean-Léon}, journal = {Development}, keywords = {Epithelial cohesion, Hindbrain, Neuronal migration, Zebrafish}, number = {21}, pages = {4673 -- 4683}, publisher = {Company of Biologists}, title = {{Defective neuroepithelial cell cohesion affects tangential branchiomotor neuron migration in the zebrafish neural tube}}, doi = {10.1242/dev.071233}, volume = {138}, year = {2011}, } @article{3379, abstract = {The process of gastrulation is highly conserved across vertebrates on both the genetic and morphological levels, despite great variety in embryonic shape and speed of development. This mechanism spatially separates the germ layers and establishes the organizational foundation for future development. Mesodermal identity is specified in a superficial layer of cells, the epiblast, where cells maintain an epithelioid morphology. These cells involute to join the deeper hypoblast layer where they adopt a migratory, mesenchymal morphology. Expression of a cascade of related transcription factors orchestrates the parallel genetic transition from primitive to mature mesoderm. Although the early and late stages of this process are increasingly well understood, the transition between them has remained largely mysterious. We present here the first high resolution in vivo observations of the blebby transitional morphology of involuting mesodermal cells in a vertebrate embryo. We further demonstrate that the zebrafish spadetail mutation creates a reversible block in the maturation program, stalling cells in the transition state. This mutation creates an ideal system for dissecting the specific properties of cells undergoing the morphological transition of maturing mesoderm, as we demonstrate with a direct measurement of cell–cell adhesion.}, author = {Row, Richard and Maître, Jean-Léon and Martin, Benjamin and Stockinger, Petra and Heisenberg, Carl-Philipp J and Kimelman, David}, journal = {Developmental Biology}, number = {1}, pages = {102 -- 110}, publisher = {Elsevier}, title = {{Completion of the epithelial to mesenchymal transition in zebrafish mesoderm requires Spadetail}}, doi = {10.1016/j.ydbio.2011.03.025}, volume = {354}, year = {2011}, } @article{3781, abstract = {We bound the difference in length of two curves in terms of their total curvatures and the Fréchet distance. The bound is independent of the dimension of the ambient Euclidean space, it improves upon a bound by Cohen-Steiner and Edelsbrunner, and it generalizes a result by Fáry and Chakerian.}, author = {Fasy, Brittany Terese}, issn = {2064-8316}, journal = {Acta Scientiarum Mathematicarum}, number = {1-2}, pages = {359 -- 367}, publisher = {Springer Nature}, title = {{The difference in length of curves in R^n}}, doi = {10.1007/BF03651375}, volume = {77}, year = {2011}, } @inproceedings{3383, author = {Heisenberg, Carl-Philipp J}, booktitle = {The FEBS Journal}, location = {Torino, Italy}, number = {S1}, pages = {24 -- 24}, publisher = {Wiley}, title = {{Invited Lectures ‐ Symposia Area}}, doi = {10.1111/j.1742-4658.2011.08136.x}, volume = {278}, year = {2011}, } @article{3368, abstract = {Tissue surface tension (TST) is an important mechanical property influencing cell sorting and tissue envelopment. The study by Manning et al. (1) reported on a mathematical model describing TST on the basis of the balance between adhesive and tensile properties of the constituent cells. The model predicts that, in high-adhesion cell aggregates, surface cells will be stretched to maintain the same area of cell–cell contact as interior bulk cells, resulting in an elongated and flattened cell shape. The authors (1) observed flat and elongated cells at the surface of high-adhesion zebrafish germ-layer explants, which they argue are undifferentiated stretched germ-layer progenitor cells, and they use this observation as a validation of their model.}, author = {Krens, Gabriel and Möllmert, Stephanie and Heisenberg, Carl-Philipp J}, journal = {PNAS}, number = {3}, pages = {E9 -- E10}, publisher = {National Academy of Sciences}, title = {{Enveloping cell layer differentiation at the surface of zebrafish germ layer tissue explants}}, doi = {10.1073/pnas.1010767108}, volume = {108}, year = {2011}, } @article{3373, abstract = {The use of optical traps to measure or apply forces on the molecular level requires a precise knowledge of the trapping force field. Close to the trap center, this field is typically approximated as linear in the displacement of the trapped microsphere. However, applications demanding high forces at low laser intensities can probe the light-microsphere interaction beyond the linear regime. Here, we measured the full nonlinear force and displacement response of an optical trap in two dimensions using a dual-beam optical trap setup with back-focal-plane photodetection. We observed a substantial stiffening of the trap beyond the linear regime that depends on microsphere size, in agreement with Mie theory calculations. Surprisingly, we found that the linear detection range for forces exceeds the one for displacement by far. Our approach allows for a complete calibration of an optical trap.}, author = {Jahnel, Marcus and Behrndt, Martin and Jannasch, Anita and Schaeffer, Erik and Grill, Stephan}, journal = {Optics Letters}, number = {7}, pages = {1260 -- 1262}, publisher = {Optica Publishing Group}, title = {{Measuring the complete force field of an optical trap}}, doi = {10.1364/OL.36.001260}, volume = {36}, year = {2011}, } @article{3393, abstract = {Unlike unconditionally advantageous “Fisherian” variants that tend to spread throughout a species range once introduced anywhere, “bistable” variants, such as chromosome translocations, have two alternative stable frequencies, absence and (near) fixation. Analogous to populations with Allee effects, bistable variants tend to increase locally only once they become sufficiently common, and their spread depends on their rate of increase averaged over all frequencies. Several proposed manipulations of insect populations, such as using Wolbachia or “engineered underdominance” to suppress vector-borne diseases, produce bistable rather than Fisherian dynamics. We synthesize and extend theoretical analyses concerning three features of their spatial behavior: rate of spread, conditions to initiate spread from a localized introduction, and wave stopping caused by variation in population densities or dispersal rates. Unlike Fisherian variants, bistable variants tend to spread spatially only for particular parameter combinations and initial conditions. Wave initiation requires introduction over an extended region, while subsequent spatial spread is slower than for Fisherian waves and can easily be halted by local spatial inhomogeneities. We present several new results, including robust sufficient conditions to initiate (and stop) spread, using a one-parameter cubic approximation applicable to several models. The results have both basic and applied implications.}, author = {Barton, Nicholas H and Turelli, Michael}, issn = {1537-5323}, journal = {American Naturalist}, number = {3}, pages = {E48 -- E75}, publisher = {University of Chicago Press}, title = {{Spatial waves of advance with bistable dynamics: Cytoplasmic and genetic analogues of Allee effects}}, doi = {10.1086/661246}, volume = {178}, year = {2011}, } @article{22556, abstract = {Numerous studies across multiple disciplines search for insights on the effects of climate change at local spatial scales and at fine time resolutions. This study presents an overall methodology of using a weather generator for downscaling an ensemble of climate model outputs. The downscaled predictions can explicitly include climate model uncertainty, which offers valuable information for making probabilistic inferences about climate impacts. The hourly weather generator that serves as the downscaling tool is briefly presented. The generator is designed to reproduce a set of meteorological variables that can serve as input to hydrological, ecological, geomorphological, and agricultural models. The generator is capable of reproducing a wide set of climate statistics over a range of temporal scales, from extremes, to low-frequency interannual variability; its performance for many climate variables and their statistics over different aggregation periods is highly satisfactory. The use of the weather generator in simulations of future climate scenarios, as inferred from climate models, is described in detail. Using a previously developed methodology based on a Bayesian approach, the stochastic downscaling procedure derives the frequency distribution functions of factors of change for several climate statistics from a multi-model ensemble of outputs of General Circulation Models. The factors of change are subsequently applied to the statistics derived from observations to re-evaluate the parameters of the weather generator. Using embedded causal and statistical relationships, the generator simulates future realizations of climate for a specific point location at the hourly scale. Uncertainties present in the climate model realizations and the multi-model ensemble predictions are discussed. An application of the weather generator in reproducing present (1961–2000) and forecasting future (2081–2100) climate conditions is illustrated for the location of Tucson (AZ). The stochastic downscaling is carried out using simulations of eight General Circulation Models adopted in the IPCC 4AR, A1B emission scenario.}, author = {Fatichi, Simone and Ivanov, Valeriy Y. and Caporali, Enrica}, issn = {0309-1708}, journal = {Advances in Water Resources}, keywords = {Weather generator, Stochastic downscaling, Climate change, Hydro-meteorology, Rainfall model}, number = {4}, pages = {448--467}, publisher = {Elsevier}, title = {{Simulation of future climate scenarios with a weather generator}}, doi = {10.1016/j.advwatres.2010.12.013}, volume = {34}, year = {2011}, } @article{3375, abstract = {By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as five loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.}, author = {de Vladar, Harold and Barton, Nicholas H}, journal = {Journal of the Royal Society Interface}, number = {58}, pages = {720 -- 739}, publisher = {Royal Society}, title = {{The statistical mechanics of a polygenic character under stabilizing selection mutation and drift}}, doi = {10.1098/rsif.2010.0438}, volume = {8}, year = {2011}, } @inproceedings{10908, abstract = {We present ABC, a software tool for automatically computing symbolic upper bounds on the number of iterations of nested program loops. The system combines static analysis of programs with symbolic summation techniques to derive loop invariant relations between program variables. Iteration bounds are obtained from the inferred invariants, by replacing variables with bounds on their greatest values. We have successfully applied ABC to a large number of examples. The derived symbolic bounds express non-trivial polynomial relations over loop variables. We also report on results to automatically infer symbolic expressions over harmonic numbers as upper bounds on loop iteration counts.}, author = {Blanc, Régis and Henzinger, Thomas A and Hottelier, Thibaud and Kovács, Laura}, booktitle = {Logic for Programming, Artificial Intelligence, and Reasoning}, editor = {Clarke, Edmund M and Voronkov, Andrei}, isbn = {9783642175107}, issn = {1611-3349}, location = {Dakar, Senegal}, pages = {103--118}, publisher = {Springer Nature}, title = {{ABC: Algebraic Bound Computation for loops}}, doi = {10.1007/978-3-642-17511-4_7}, volume = {6355}, year = {2010}, }