@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}, }