TY - JOUR
AB - We consider scientific data sets that describe density functions over three-dimensional geometric domains. Such data sets are often large and coarsened representations are needed for visualization and analysis. Assuming a tetrahedral mesh representation, we construct such representations with a simplification algorithm that combines three goals: the approximation of the function, the preservation of the mesh topology, and the improvement of the mesh quality. The third goal is achieved with a novel extension of the well-known quadric error metric. We perform a number of computational experiments to understand the effect of mesh quality improvement on the density map approximation. In addition, we study the effect of geometric simplification on the topological features of the function by monitoring its critical points.
AU - Natarajan, Vijay
AU - Herbert Edelsbrunner
ID - 3987
IS - 5
JF - IEEE Transactions on Visualization and Computer Graphics
TI - Simplification of three-dimensional density maps
VL - 10
ER -
TY - CONF
AB - We give an algorithm that locally improves the fit between two proteins modeled as space-filling diagrams. The algorithm defines the fit in purely geometric terms and improves by applying a rigid motion to one of the two proteins. Our implementation of the algorithm takes between three and ten seconds and converges with high likelihood to the correct docked configuration, provided it starts at a position away from the correct one by at most 18 degrees of rotation and at most 3.0Angstrom of translation. The speed and convergence radius make this an attractive algorithm to use in combination with a coarse sampling of the six-dimensional space of rigid motions.
AU - Choi, Vicky
AU - Agarwal, Pankaj K
AU - Herbert Edelsbrunner
AU - Rudolph, Johannes
ID - 3988
TI - Local search heuristic for rigid protein docking
VL - 3240
ER -
TY - CONF
AB - We introduce local and global comparison measures for a collection of k less than or equal to d real-valued smooth functions on a common d-dimensional Riemannian manifold. For k = d = 2 we relate the measures to the set of critical points of one function restricted to the level sets of the other. The definition of the measures extends to piecewise linear functions for which they ace easy to compute. The computation of the measures forms the centerpiece of a software tool which we use to study scientific datasets.
AU - Herbert Edelsbrunner
AU - Harer, John
AU - Natarajan, Vijay
AU - Pascucci, Valerio
ID - 3989
TI - Local and global comparison of continuous functions
ER -
TY - JOUR
AB - The writhing number measures the global geometry of a closed space curve or knot. We show that this measure is related to the average winding number of its Gauss map. Using this relationship, we give an algorithm for computing the writhing number for a polygonal knot with n edges in time roughly proportional to n(1.6). We also implement a different, simple algorithm and provide experimental evidence for its practical efficiency.
AU - Agarwal, Pankaj K
AU - Herbert Edelsbrunner
AU - Wang, Yusu
ID - 3990
IS - 1
JF - Discrete & Computational Geometry
TI - Computing the writhing number of a polygonal knot
VL - 32
ER -
TY - CHAP
AU - Harold Vladar
AU - Cipriani, Roberto
AU - Scharifker, Benjamin
AU - Bubis, Jose
ED - Hanslmeier,A.
ED - Kempe,S.
ED - Seckbach,J.
ID - 4230
T2 - Life in the Universe From the Miller Experiment to the Search for Life on Other Worlds
TI - A mechanism for the prebiotic emergence of proteins
ER -
TY - CHAP
AU - Harold Vladar
AU - Cipriani, Roberto
AU - Scharifker, Benjamin
AU - Bubis, Jose
ED - Seckbach,J.
ED - Chela-Flores,J.
ED - Owen,T.
ED - Raulin,F.
ID - 4239
T2 - Life in the Universe From the Miller Experiment to the Search for Life on Other Worlds
TI - A Mechanism for the Prebiotic Emergence of Proteins
VL - 7
ER -
TY - JOUR
AB - We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r. If r = 0, this reduces to the study of a single selected locus. Assuming a Moran model for the population dynamics, we pass to a diffusion approximation and, assuming that the allele frequencies at the selected locus have reached stationarity, establish the joint generating function for the genealogy of a sample from the population and the frequency of the P allele. In essence this is the joint generating function for a coalescent and the random background in which it evolves. We use this to characterize, for the diffusion approximation, the probability of identity in state at the neutral locus of a sample of two individuals (whose type at the selected locus is known) as solutions to a system of ordinary differential equations. The only subtlety is to find the boundary conditions for this system. Finally, numerical examples are presented that illustrate the accuracy and predictions of the diffusion approximation. In particular, a comparison is made between this approach and one in which the frequencies at the selected locus are estimated by their value in the absence of fluctuations and a classical structured coalescent model is used.
AU - Nicholas Barton
AU - Etheridge, Alison M
AU - Sturm, Anja K
ID - 4253
IS - 2
JF - Annals of Applied Probability
TI - Coalescence in a Random Background
VL - 14
ER -
TY - CONF
AU - Maler, Oded
AU - Dejan Nickovic
ID - 4372
TI - Monitoring Temporal Properties of Continuous Signals
ER -
TY - CONF
AB - We present a type system for E code, which is an assembly language that manages the release, interaction, and termination of real-time tasks. E code specifies a deadline for each task, and the type system ensures that the deadlines are path-insensitive. We show that typed E programs allow, for given worst-case execution times of tasks, a simple schedulability analysis. Moreover, the real-time programming language Giotto can be compiled into typed E~code. This shows that typed E~code identifies an easily schedulable yet expressive class of real-time programs. We have extended the Giotto compiler to generate typed E code, and enabled the run-time system for E code to perform a type and schedulability check before executing the code.
AU - Thomas Henzinger
AU - Kirsch, Christoph M
ID - 4445
TI - A typed assembly language for real-time programs
ER -
TY - CONF
AB - The success of model checking for large programs depends crucially on the ability to efficiently construct parsimonious abstractions. A predicate abstraction is parsimonious if at each control location, it specifies only relationships between current values of variables, and only those which are required for proving correctness. Previous methods for automatically refining predicate abstractions until sufficient precision is obtained do not systematically construct parsimonious abstractions: predicates usually contain symbolic variables, and are added heuristically and often uniformly to many or all control locations at once. We use Craig interpolation to efficiently construct, from a given abstract error trace which cannot be concretized, a parsominous abstraction that removes the trace. At each location of the trace, we infer the relevant predicates as an interpolant between the two formulas that define the past and the future segment of the trace. Each interpolant is a relationship between current values of program variables, and is relevant only at that particular program location. It can be found by a linear scan of the proof of infeasibility of the trace.We develop our method for programs with arithmetic and pointer expressions, and call-by-value function calls. For function calls, Craig interpolation offers a systematic way of generating relevant predicates that contain only the local variables of the function and the values of the formal parameters when the function was called. We have extended our model checker Blast with predicate discovery by Craig interpolation, and applied it successfully to C programs with more than 130,000 lines of code, which was not possible with approaches that build less parsimonious abstractions.
AU - Thomas Henzinger
AU - Jhala, Ranjit
AU - Majumdar, Ritankar S
AU - McMillan, Kenneth L
ID - 4458
TI - Abstractions from proofs
ER -