@misc{5438, abstract = {The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1, L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k. }, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Ibsen-Jensen, Rasmus and Otop, Jan}, issn = {2664-1690}, pages = {15}, publisher = {IST Austria}, title = {{Edit distance for pushdown automata}}, doi = {10.15479/AT:IST-2015-334-v1-1}, year = {2015}, } @misc{5440, abstract = {Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom for payoff in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. The fitness (or the reproductive rate) is a non-negative number, and depends on the payoff. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are as follows: First, we consider a special case of the general problem, where the residents do not reproduce. We show that the qualitative question is NP-complete, and the quantitative approximation question is #P-complete, and the hardness results hold even in the special case where the interaction and the replacement graphs coincide. Second, we show that in general both the qualitative and the quantitative approximation questions are PSPACE-complete. The PSPACE-hardness result for quantitative approximation holds even when the fitness is always positive.}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin}, issn = {2664-1690}, pages = {18}, publisher = {IST Austria}, title = {{The complexity of evolutionary games on graphs}}, doi = {10.15479/AT:IST-2015-323-v2-2}, year = {2015}, } @misc{5432, abstract = {Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution.The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are: (1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure). (2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time. }, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin}, issn = {2664-1690}, pages = {29}, publisher = {IST Austria}, title = {{The complexity of evolutionary games on graphs}}, doi = {10.15479/AT:IST-2015-323-v1-1}, year = {2015}, } @misc{5444, abstract = {A comprehensive understanding of the clonal evolution of cancer is critical for understanding neoplasia. Genome-wide sequencing data enables evolutionary studies at unprecedented depth. However, classical phylogenetic methods often struggle with noisy sequencing data of impure DNA samples and fail to detect subclones that have different evolutionary trajectories. We have developed a tool, called Treeomics, that allows us to reconstruct the phylogeny of a cancer with commonly available sequencing technologies. Using Bayesian inference and Integer Linear Programming, robust phylogenies consistent with the biological processes underlying cancer evolution were obtained for pancreatic, ovarian, and prostate cancers. Furthermore, Treeomics correctly identified sequencing artifacts such as those resulting from low statistical power; nearly 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumor heterogeneity among distinct samples. Importantly, we show that the evolutionary trees generated with Treeomics are mathematically optimal.}, author = {Reiter, Johannes and Makohon-Moore, Alvin and Gerold, Jeffrey and Bozic, Ivana and Chatterjee, Krishnendu and Iacobuzio-Donahue, Christine and Vogelstein, Bert and Nowak, Martin}, issn = {2664-1690}, pages = {25}, publisher = {IST Austria}, title = {{Reconstructing robust phylogenies of metastatic cancers}}, doi = {10.15479/AT:IST-2015-399-v1-1}, year = {2015}, } @misc{5443, abstract = {POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach.}, author = {Chatterjee, Krishnendu and Chmelik, Martin and Davies, Jessica}, issn = {2664-1690}, pages = {23}, publisher = {IST Austria}, title = {{A symbolic SAT-based algorithm for almost-sure reachability with small strategies in POMDPs}}, doi = {10.15479/AT:IST-2015-325-v2-1}, year = {2015}, } @article{5804, abstract = {We present here the first integer-based algorithm for constructing a well-defined lattice sphere specified by integer radius and integer center. The algorithm evolves from a unique correspondence between the lattice points comprising the sphere and the distribution of sum of three square numbers in integer intervals. We characterize these intervals to derive a useful set of recurrences, which, in turn, aids in efficient computation. Each point of the lattice sphere is determined by resorting to only a few primitive operations in the integer domain. The symmetry of its quadraginta octants provides an added advantage by confining the computation to its prima quadraginta octant. Detailed theoretical analysis and experimental results have been furnished to demonstrate its simplicity and elegance.}, author = {Biswas, Ranita and Bhowmick, Partha}, issn = {0304-3975}, journal = {Theoretical Computer Science}, number = {4}, pages = {56--72}, publisher = {Elsevier}, title = {{From prima quadraginta octant to lattice sphere through primitive integer operations}}, doi = {10.1016/j.tcs.2015.11.018}, volume = {624}, year = {2015}, } @article{5807, author = {Biswas, Ranita and Bhowmick, Partha}, issn = {0304-3975}, journal = {Theoretical Computer Science}, number = {11}, pages = {146--163}, publisher = {Elsevier}, title = {{On different topological classes of spherical geodesic paths and circles inZ3}}, doi = {10.1016/j.tcs.2015.09.003}, volume = {605}, year = {2015}, } @article{5808, author = {Biswas, Ranita and Bhowmick, Partha}, issn = {0178-2789}, journal = {The Visual Computer}, number = {6-8}, pages = {787--797}, publisher = {Springer Nature}, title = {{Layer the sphere}}, doi = {10.1007/s00371-015-1101-3}, volume = {31}, year = {2015}, } @article{594, abstract = {Transcription of eukaryotic protein-coding genes commences with the assembly of a conserved initiation complex, which consists of RNA polymerase II (Pol II) and the general transcription factors, at promoter DNA. After two decades of research, the structural basis of transcription initiation is emerging. Crystal structures of many components of the initiation complex have been resolved, and structural information on Pol II complexes with general transcription factors has recently been obtained. Although mechanistic details await elucidation, available data outline how Pol II cooperates with the general transcription factors to bind to and open promoter DNA, and how Pol II directs RNA synthesis and escapes from the promoter.}, author = {Sainsbury, Sarah and Bernecky, Carrie A and Cramer, Patrick}, journal = {Nature Reviews Molecular Cell Biology}, number = {3}, pages = {129 -- 143}, publisher = {Nature Publishing Group}, title = {{Structural basis of transcription initiation by RNA polymerase II}}, doi = {10.1038/nrm3952}, volume = {16}, year = {2015}, } @inproceedings{1511, abstract = {The fact that the complete graph K_5 does not embed in the plane has been generalized in two independent directions. On the one hand, the solution of the classical Heawood problem for graphs on surfaces established that the complete graph K_n embeds in a closed surface M if and only if (n-3)(n-4) is at most 6b_1(M), where b_1(M) is the first Z_2-Betti number of M. On the other hand, Van Kampen and Flores proved that the k-skeleton of the n-dimensional simplex (the higher-dimensional analogue of K_{n+1}) embeds in R^{2k} if and only if n is less or equal to 2k+2. Two decades ago, Kuhnel conjectured that the k-skeleton of the n-simplex embeds in a compact, (k-1)-connected 2k-manifold with kth Z_2-Betti number b_k only if the following generalized Heawood inequality holds: binom{n-k-1}{k+1} is at most binom{2k+1}{k+1} b_k. This is a common generalization of the case of graphs on surfaces as well as the Van Kampen--Flores theorem. In the spirit of Kuhnel's conjecture, we prove that if the k-skeleton of the n-simplex embeds in a 2k-manifold with kth Z_2-Betti number b_k, then n is at most 2b_k binom{2k+2}{k} + 2k + 5. This bound is weaker than the generalized Heawood inequality, but does not require the assumption that M is (k-1)-connected. Our proof uses a result of Volovikov about maps that satisfy a certain homological triviality condition.}, author = {Goaoc, Xavier and Mabillard, Isaac and Paták, Pavel and Patakova, Zuzana and Tancer, Martin and Wagner, Uli}, location = {Eindhoven, Netherlands}, pages = {476 -- 490}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{On generalized Heawood inequalities for manifolds: A Van Kampen–Flores-type nonembeddability result}}, doi = {10.4230/LIPIcs.SOCG.2015.476}, volume = {34 }, year = {2015}, }