@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},
}
@misc{5382,
abstract = {We consider two-player stochastic games played on a finite state space for an infinite num- ber 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 a probability distribution over the successor states. We also consider the important special case of turn-based stochastic games where players make moves in turns, rather than concurrently. We study concurrent games with ω-regular winning conditions specified as parity objectives. The value for player 1 for a parity objective is the maximal probability with which the player can guarantee the satisfaction of the objective against all strategies of the opponent. We study the problem of continuity and robustness of the value function in concurrent and turn-based stochastic parity games with respect to imprecision in the transition probabilities. We present quantitative bounds on the difference of the value function (in terms of the imprecision of the transition probabilities) and show the value continuity for structurally equivalent concurrent games (two games are structurally equivalent if the support of the transition func- tion is same and the probabilities differ). We also show robustness of optimal strategies for structurally equivalent turn-based stochastic parity games. Finally we show that the value continuity property breaks without the structurally equivalent assumption (even for Markov chains) and show that our quantitative bound is asymptotically optimal. Hence our results are tight (the assumption is both necessary and sufficient) and optimal (our quantitative bound is asymptotically optimal).},
author = {Chatterjee, Krishnendu},
issn = {2664-1690},
pages = {18},
publisher = {IST Austria},
title = {{Robustness of structurally equivalent concurrent parity games}},
doi = {10.15479/AT:IST-2011-0006},
year = {2011},
}
@misc{5383,
abstract = {We present a new decidable logic called TREX for expressing constraints about imperative tree data structures. In particular, TREX supports a transitive closure operator that can express reachability constraints, which often appear in data structure invariants. We show that our logic is closed under weakest precondition computation, which enables its use for automated software verification. We further show that satisfiability of formulas in TREX is decidable in NP. The low complexity makes it an attractive alternative to more expensive logics such as monadic second-order logic (MSOL) over trees, which have been traditionally used for reasoning about tree data structures.},
author = {Wies, Thomas and Muñiz, Marco and Kuncak, Viktor},
issn = {2664-1690},
pages = {25},
publisher = {IST Austria},
title = {{On an efficient decision procedure for imperative tree data structures}},
doi = {10.15479/AT:IST-2011-0005},
year = {2011},
}
@misc{5384,
abstract = {We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with positive probability; (ii) the almost decision problem asks whether there is a word that is accepted with probability 1; and (iii) the limit decision problem asks whether for every ε > 0 there is a word that is accepted with probability at least 1 − ε. We unify and generalize several decidability results for probabilistic automata over infinite words, and identify a robust (closed under union and intersection) subclass of probabilistic automata for which all the qualitative decision problems are decidable for parity conditions. We also show that if the input words are restricted to lasso shape words, then the positive and almost problems are decidable for all probabilistic automata with parity conditions.},
author = {Chatterjee, Krishnendu and Tracol, Mathieu},
issn = {2664-1690},
pages = {30},
publisher = {IST Austria},
title = {{Decidable problems for probabilistic automata on infinite words}},
doi = {10.15479/AT:IST-2011-0004},
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{5386,
abstract = {We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random field image segmentation model. Instead of including TPs as additional constraints during minimization of the energy function, we devise an efficient algorithm for modifying the unary potentials such that the resulting segmentation is guaranteed with the desired properties. Our method is more flexible in the sense that it handles more topology constraints than previous methods, which were only able to enforce pairwise or global connectivity. In particular, our method is very fast, making it for the first time possible to enforce global topological properties in practical image segmentation tasks.},
author = {Chen, Chao and Freedman, Daniel and Lampert, Christoph},
issn = {2664-1690},
pages = {69},
publisher = {IST Austria},
title = {{Enforcing topological constraints in random field image segmentation}},
doi = {10.15479/AT:IST-2011-0002},
year = {2011},
}
@misc{5387,
abstract = {We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean- payoff parity MDPs, the problem is solvable in polynomial time, improving a recent PSPACE bound.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{Energy and mean-payoff parity Markov decision processes}},
doi = {10.15479/AT:IST-2011-0001},
year = {2011},
}
@article{6496,
abstract = {We report the switching behavior of the full bacterial flagellum system that includes the filament and the motor in wild-type Escherichia coli cells. In sorting the motor behavior by the clockwise bias, we find that the distributions of the clockwise (CW) and counterclockwise (CCW) intervals are either exponential or nonexponential with long tails. At low bias, CW intervals are exponentially distributed and CCW intervals exhibit long tails. At intermediate CW bias (0.5) both CW and CCW intervals are mainly exponentially distributed. A simple model suggests that these two distinct switching behaviors are governed by the presence of signaling noise within the chemotaxis network. Low noise yields exponentially distributed intervals, whereas large noise yields nonexponential behavior with long tails. These drastically different motor statistics may play a role in optimizing bacterial behavior for a wide range of environmental conditions.},
author = {Park, Heungwon and Oikonomou, Panos and Guet, Calin C and Cluzel, Philippe},
issn = {0006-3495},
journal = {Biophysical Journal},
number = {10},
pages = {2336--2340},
publisher = {Elsevier BV},
title = {{Noise underlies switching behavior of the bacterial flagellum}},
doi = {10.1016/j.bpj.2011.09.040},
volume = {101},
year = {2011},
}
@inproceedings{3163,
abstract = {We study multi-label prediction for structured output sets, a problem that occurs, for example, in object detection in images, secondary structure prediction in computational biology, and graph matching with symmetries. Conventional multilabel classification techniques are typically not applicable in this situation, because they require explicit enumeration of the label set, which is infeasible in case of structured outputs. Relying on techniques originally designed for single-label structured prediction, in particular structured support vector machines, results in reduced prediction accuracy, or leads to infeasible optimization problems. In this work we derive a maximum-margin training formulation for multi-label structured prediction that remains computationally tractable while achieving high prediction accuracy. It also shares most beneficial properties with single-label maximum-margin approaches, in particular formulation as a convex optimization problem, efficient working set training, and PAC-Bayesian generalization bounds.},
author = {Lampert, Christoph},
location = {Granada, Spain},
publisher = {Neural Information Processing Systems},
title = {{Maximum margin multi-label structured prediction}},
year = {2011},
}
@inproceedings{3264,
abstract = {Verification of programs with procedures, multi-threaded programs, and higher-order functional programs can be effectively au- tomated using abstraction and refinement schemes that rely on spurious counterexamples for abstraction discovery. The analysis of counterexam- ples can be automated by a series of interpolation queries, or, alterna- tively, as a constraint solving query expressed by a set of recursion free Horn clauses. (A set of interpolation queries can be formulated as a single constraint over Horn clauses with linear dependency structure between the unknown relations.) In this paper we present an algorithm for solving recursion free Horn clauses over a combined theory of linear real/rational arithmetic and uninterpreted functions. Our algorithm performs resolu- tion to deal with the clausal structure and relies on partial solutions to deal with (non-local) instances of functionality axioms.},
author = {Gupta, Ashutosh and Popeea, Corneliu and Rybalchenko, Andrey},
editor = {Yang, Hongseok},
location = {Kenting, Taiwan},
pages = {188 -- 203},
publisher = {Springer},
title = {{Solving recursion-free Horn clauses over LI+UIF}},
doi = {10.1007/978-3-642-25318-8_16},
volume = {7078},
year = {2011},
}
@inproceedings{3266,
abstract = {We present a joint image segmentation and labeling model (JSL) which, given a bag of figure-ground segment hypotheses extracted at multiple image locations and scales, constructs a joint probability distribution over both the compatible image interpretations (tilings or image segmentations) composed from those segments, and over their labeling into categories. The process of drawing samples from the joint distribution can be interpreted as first sampling tilings, modeled as maximal cliques, from a graph connecting spatially non-overlapping segments in the bag [1], followed by sampling labels for those segments, conditioned on the choice of a particular tiling. We learn the segmentation and labeling parameters jointly, based on Maximum Likelihood with a novel Incremental Saddle Point estimation procedure. The partition function over tilings and labelings is increasingly more accurately approximated by including incorrect configurations that a not-yet-competent model rates probable during learning. We show that the proposed methodologymatches the current state of the art in the Stanford dataset [2], as well as in VOC2010, where 41.7% accuracy on the test set is achieved.},
author = {Ion, Adrian and Carreira, Joao and Sminchisescu, Cristian},
booktitle = {NIPS Proceedings},
location = {Granada, Spain},
pages = {1827 -- 1835},
publisher = {Neural Information Processing Systems Foundation},
title = {{Probabilistic joint image segmentation and labeling}},
volume = {24},
year = {2011},
}
@article{3267,
abstract = {We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We study the problem with different measures: volume, diameter and radius. For volume, that is, the 1-norm of a cycle, two main results are presented. First, we prove that the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O(1). The latter result leads to the inapproximability of the problem of computing the nonbounding cycle with the smallest volume and computing cycles representing a homology basis with the minimal total volume. As for the other two measures defined by pairwise geodesic distance, diameter and radius, we show that the localization problem is NP-hard for diameter but is polynomial for radius. Our work is restricted to homology over the ℤ2 field.},
author = {Chen, Chao and Freedman, Daniel},
journal = {Discrete & Computational Geometry},
number = {3},
pages = {425 -- 448},
publisher = {Springer},
title = {{Hardness results for homology localization}},
doi = {10.1007/s00454-010-9322-8},
volume = {45},
year = {2011},
}
@article{3269,
abstract = {The unintentional scattering of light between neighboring surfaces in complex projection environments increases the brightness and decreases the contrast, disrupting the appearance of the desired imagery. To achieve satisfactory projection results, the inverse problem of global illumination must be solved to cancel this secondary scattering. In this paper, we propose a global illumination cancellation method that minimizes the perceptual difference between the desired imagery and the actual total illumination in the resulting physical environment. Using Gauss-Newton and active set methods, we design a fast solver for the bound constrained nonlinear least squares problem raised by the perceptual error metrics. Our solver is further accelerated with a CUDA implementation and multi-resolution method to achieve 1–2 fps for problems with approximately 3000 variables. We demonstrate the global illumination cancellation algorithm with our multi-projector system. Results show that our method preserves the color fidelity of the desired imagery significantly better than previous methods.},
author = {Sheng, Yu and Cutler, Barbara and Chen, Chao and Nasman, Joshua},
journal = {Computer Graphics Forum},
number = {4},
pages = {1261 -- 1268},
publisher = {Wiley-Blackwell},
title = {{Perceptual global illumination cancellation in complex projection environments}},
doi = {10.1111/j.1467-8659.2011.01985.x},
volume = {30},
year = {2011},
}
@inproceedings{3270,
abstract = {The persistence diagram of a filtered simplicial com- plex is usually computed by reducing the boundary matrix of the complex. We introduce a simple op- timization technique: by processing the simplices of the complex in decreasing dimension, we can “kill” columns (i.e., set them to zero) without reducing them. This technique completely avoids reduction on roughly half of the columns. We demonstrate that this idea significantly improves the running time of the reduction algorithm in practice. We also give an output-sensitive complexity analysis for the new al- gorithm which yields to sub-cubic asymptotic bounds under certain assumptions.},
author = {Chen, Chao and Kerber, Michael},
location = {Morschach, Switzerland},
pages = {197 -- 200},
publisher = {TU Dortmund},
title = {{Persistent homology computation with a twist}},
year = {2011},
}
@inbook{3271,
abstract = {In this paper we present an efficient framework for computation of persis- tent homology of cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is adapted to the setting of cubical complexes. The proposed approach enables efficient application of persistent homology in domains where the data is naturally given in a cubical form. By avoiding triangulation of the data, we significantly reduce the size of the complex. We also present a data-structure de- signed to compactly store and quickly manipulate cubical complexes. By means of numerical experiments, we show high speed and memory efficiency of our ap- proach. We compare our framework to other available implementations, showing its superiority. Finally, we report performance on selected 3D and 4D data-sets.},
author = {Wagner, Hubert and Chen, Chao and Vuçini, Erald},
booktitle = {Topological Methods in Data Analysis and Visualization II},
editor = {Peikert, Ronald and Hauser, Helwig and Carr, Hamish and Fuchs, Raphael},
pages = {91 -- 106},
publisher = {Springer},
title = {{Efficient computation of persistent homology for cubical data}},
doi = {10.1007/978-3-642-23175-9_7},
year = {2011},
}
@phdthesis{3273,
author = {Maître, Jean-Léon},
publisher = {IST Austria},
title = {{Mechanics of adhesion and de‐adhesion in zebrafish germ layer progenitors}},
year = {2011},
}
@phdthesis{3275,
abstract = {Chemokines organize immune cell trafficking by inducing either directed (tactic) or random (kinetic) migration and by activating integrins in order to support surface adhesion (haptic). Beyond that the same chemokines can establish clearly defined functional areas in secondary lymphoid organs. Until now it is unclear how chemokines can fulfill such diverse functions. One decisive prerequisite to explain these capacities is to know how chemokines are presented in tissue. In theory chemokines could occur either soluble or immobilized, and could be distributed either homogenously or as a concentration gradient. To dissect if and how the presenting mode of chemokines influences immune cells, I tested the response of dendritic cells (DCs) to differentially displayed chemokines. DCs are antigen presenting cells that reside in the periphery and migrate into draining lymph nodes (LNs) once exposed to inflammatory stimuli to activate naïve T cells. DCs are guided to and within the LN by the chemokine receptor CCR7, which has two ligands, the chemokines CCL19 and CCL21. Both CCR7 ligands are expressed by fibroblastic reticular cells in the LN, but differ in their ability to bind to heparan sulfate residues. CCL21 has a highly charged C-terminal extension, which mediates binding to anionic surfaces, whereas CCL19 is lacking such residues and likely distributes as a soluble molecule. This study shows that surface-bound CCL21 causes random, haptokinetic DC motility, which is confined to the chemokine coated area by insideout activation of β2 integrins that mediate cell binding to the surface. CCL19 on the other hand forms concentration gradients which trigger directional, chemotactic movement, but no surface adhesion. In addition DCs can actively manipulate this system by recruiting and activating serine proteases on their surfaces, which create - by proteolytically removing the adhesive C-terminus - a solubilized variant of CCL21 that functionally resembles CCL19. By generating a CCL21 concentration gradient DCs establish a positive feedback loop to recruit further DCs from the periphery to the CCL21 coated region. In addition DCs can sense chemotactic gradients as well as immobilized haptokinetic fields at the same time and integrate these signals. The result is chemotactically biased haptokinesis - directional migration confined to a chemokine coated track or area - which could explain the dynamic but spatially tightly controlled swarming leukocyte locomotion patterns that have been observed in lymphatic organs by intravital microscopists. The finding that DCs can approach soluble cues in a non-adhesive manner while they attach to surfaces coated with immobilized cues raises the question how these cells transmit intracellular forces to the environment, especially in the non-adherent migration mode. In order to migrate, cells have to generate and transmit force to the extracellular substrate. Force transmission is the prerequisite to procure an expansion of the leading edge and a forward motion of the whole cell body. In the current conceptions actin polymerization at the leading edge is coupled to extracellular ligands via the integrin family of transmembrane receptors, which allows the transmission of intracellular force. Against the paradigm of force transmission during migration, leukocytes, like DCs, are able to migrate in threedimensional environments without using integrin transmembrane receptors (Lämmermann et al., 2008). This reflects the biological function of leukocytes, as they can invade almost all tissues, whereby their migration has to be independent from the extracellular environment. How the cells can achieve this is unclear. For this study I examined DC migration in a defined threedimensional environment and highlighted actin-dynamics with the probe Lifeact-GFP. The result was that chemotactic DCs can switch between integrin-dependent and integrin- independent locomotion and can thereby adapt to the adhesive properties of their environment. If the cells are able to couple their actin cytoskeleton to the substrate, actin polymerization is entirely converted into protrusion. Without coupling the actin cortex undergoes slippage and retrograde actin flow can be observed. But retrograde actin flow can be completely compensated by higher actin polymerization rate keeping the migration velocity and the shape of the cells unaltered. Mesenchymal cells like fibroblast cannot balance the loss of adhesive interaction, cannot protrude into open space and, therefore, strictly depend on integrinmediated force coupling. This leukocyte specific phenomenon of “adaptive force transmission” endows these cells with the unique ability to transit and invade almost every type of tissue. },
author = {Schumann, Kathrin},
pages = {141},
publisher = {IST Austria},
title = {{The role of chemotactic gradients in dendritic cell migration}},
year = {2011},
}
@article{3287,
abstract = {Diffusing membrane constituents are constantly exposed to a variety of forces that influence their stochastic path. Single molecule experiments allow for resolving trajectories at extremely high spatial and temporal accuracy, thereby offering insights into en route interactions of the tracer. In this review we discuss approaches to derive information about the underlying processes, based on single molecule tracking experiments. In particular, we focus on a new versatile way to analyze single molecule diffusion in the absence of a full analytical treatment. The method is based on comprehensive comparison of an experimental data set against the hypothetical outcome of multiple experiments performed on the computer. Since Monte Carlo simulations can be easily and rapidly performed even on state-of-the-art PCs, our method provides a simple way for testing various - even complicated - diffusion models. We describe the new method in detail, and show the applicability on two specific examples: firstly, kinetic rate constants can be derived for the transient interaction of mobile membrane proteins; secondly, residence time and corral size can be extracted for confined diffusion.},
author = {Ruprecht, Verena and Axmann, Markus and Wieser, Stefan and Schuetz, Gerhard},
journal = {Current Protein & Peptide Science},
number = {8},
pages = {714 -- 724},
publisher = {Bentham Science Publishers},
title = {{What can we learn from single molecule trajectories?}},
doi = {10.2174/138920311798841753},
volume = {12},
year = {2011},
}
@article{3288,
abstract = {The zonula adherens (ZA) of epithelial cells is a site of cell-cell adhesion where cellular forces are exerted and resisted. Increasing evidence indicates that E-cadherin adhesion molecules at the ZA serve to sense force applied on the junctions and coordinate cytoskeletal responses to those forces. Efforts to understand the role that cadherins play in mechanotransduction have been limited by the lack of assays to measure the impact of forces on the ZA. In this study we used 4D imaging of GFP-tagged E-cadherin to analyse the movement of the ZA. Junctions in confluent epithelial monolayers displayed prominent movements oriented orthogonal (perpendicular) to the ZA itself. Two components were identified in these movements: a relatively slow unidirectional (translational) component that could be readily fitted by least-squares regression analysis, upon which were superimposed more rapid oscillatory movements. Myosin IIB was a dominant factor responsible for driving the unilateral translational movements. In contrast, frequency spectrum analysis revealed that depletion of Myosin IIA increased the power of the oscillatory movements. This implies that Myosin IIA may serve to dampen oscillatory movements of the ZA. This extends our recent analysis of Myosin II at the ZA to demonstrate that Myosin IIA and Myosin IIB make distinct contributions to junctional movement at the ZA.},
author = {Smutny, Michael and Wu, Selwin and Gomez, Guillermo and Mangold, Sabine and Yap, Alpha and Hamilton, Nicholas},
journal = {PLoS One},
number = {7},
publisher = {Public Library of Science},
title = {{Multicomponent analysis of junctional movements regulated by Myosin II isoforms at the epithelial zonula adherens}},
doi = {10.1371/journal.pone.0022458},
volume = {6},
year = {2011},
}
@article{3290,
abstract = {Analysis of genomic data requires an efficient way to calculate likelihoods across very large numbers of loci. We describe a general method for finding the distribution of genealogies: we allow migration between demes, splitting of demes [as in the isolation-with-migration (IM) model], and recombination between linked loci. These processes are described by a set of linear recursions for the generating function of branch lengths. Under the infinite-sites model, the probability of any configuration of mutations can be found by differentiating this generating function. Such calculations are feasible for small numbers of sampled genomes: as an example, we show how the generating function can be derived explicitly for three genes under the two-deme IM model. This derivation is done automatically, using Mathematica. Given data from a large number of unlinked and nonrecombining blocks of sequence, these results can be used to find maximum-likelihood estimates of model parameters by tabulating the probabilities of all relevant mutational configurations and then multiplying across loci. The feasibility of the method is demonstrated by applying it to simulated data and to a data set previously analyzed by Wang and Hey (2010) consisting of 26,141 loci sampled from Drosophila simulans and D. melanogaster. Our results suggest that such likelihood calculations are scalable to genomic data as long as the numbers of sampled individuals and mutations per sequence block are small.},
author = {Lohse, Konrad and Harrison, Richard and Barton, Nicholas H},
journal = {Genetics},
number = {3},
pages = {977 -- 987},
publisher = {Genetics Society of America},
title = {{A general method for calculating likelihoods under the coalescent process}},
doi = {10.1534/genetics.111.129569},
volume = {189},
year = {2011},
}