QCD Thermodynamics with Improved Actions

The thermodynamics of the SU(3) gauge theory has been analyzed with tree level and tadpole improved Symanzik actions. A comparison with the continuum extrapolated results for the standard Wilson action shows that improved actions lead to a drastic reduction of finite cut-off effects already on lattices with temporal extent $N_\tau=4$. Results for the pressure, the critical temperature, surface tension and latent heat are presented. First results for the thermodynamics of four-flavour QCD with an improved staggered action are also presented. They indicate similarly large improvement factors for bulk thermodynamics.Comment: Talk presented at LATTICE96(finite temperature) 4 pages, LaTeX2e file, 6 eps-file

Tropical polyhedra are equivalent to mean payoff games

We show that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum two player game problems. In particular, we set up an equivalence between the external representation of tropical convex sets and zero-sum stochastic games, in which tropical polyhedra correspond to deterministic games with finite action spaces. Then, we show that the winning initial positions can be determined from the associated tropical polyhedron. We obtain as a corollary a game theoretical proof of the fact that the tropical rank of a matrix, defined as the maximal size of a submatrix for which the optimal assignment problem has a unique solution, coincides with the maximal number of rows (or columns) of the matrix which are linearly independent in the tropical sense. Our proofs rely on techniques from non-linear Perron-Frobenius theory.Comment: 28 pages, 5 figures; v2: updated references, added background materials and illustrations; v3: minor improvements, references update

On hydrogen bond correlations at high pressures

In situ high pressure neutron diffraction measured lengths of O H and H O pairs in hydrogen bonds in substances are shown to follow the correlation between them established from 0.1 MPa data on different chemical compounds. In particular, the conclusion by Nelmes et al that their high pressure data on ice VIII differ from it is not supported. For compounds in which the O H stretching frequencies red shift under pressure, it is shown that wherever structural data is available, they follow the stretching frequency versus H O (or O O) distance correlation. For compounds displaying blue shifts with pressure an analogy appears to exist with improper hydrogen bonds.Comment: 12 pages,4 figure

Optimal topological simplification of discrete functions on surfaces

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse theory and persistent homology. Our method completely removes homological noise with persistence less than 2{\delta}, constructively proving the tightness of a lower bound on the number of critical points given by the stability theorem of persistent homology in dimension two for any input function. We also show that an optimal solution can be computed in linear time after persistence pairs have been computed.Comment: 27 pages, 8 figure

Towards Minimal Barcodes

In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs of birth and death times of homology classes are encoded in the form of intervals. Starting from a polyhedral complex K (an object subdivided into cells which are polytopes) and an initial order of the set of vertices, we are concerned with the general problem of searching for filters (an order of the rest of the cells) that provide a minimal barcode representation in the sense of having minimal number of “k-significant” intervals, which correspond to homology classes with life-times longer than a fixed number k. As a first step, in this paper we provide an algorithm for computing such a filter for k = 1 on the Hasse diagram of the poset of faces of K

Totally Splittable Polytopes

A split of a polytope is a (necessarily regular) subdivision with exactly two maximal cells. A polytope is totally splittable if each triangulation (without additional vertices) is a common refinement of splits. This paper establishes a complete classification of the totally splittable polytopes.Comment: 15 pages, 7 figures; v2: major revision: corrections of some minor errors and some addition

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

MSLICE Science Activity Planner for the Mars Science Laboratory Mission

MSLICE (Mars Science Laboratory InterfaCE) is the tool used by scientists and engineers on the Mars Science Laboratory rover mission to visualize the data returned by the rover and collaboratively plan its activities. It enables users to efficiently and effectively search all mission data to find applicable products (e.g., images, targets, activity plans, sequences, etc.), view and plan the traverse of the rover in HiRISE (High Resolution Imaging Science Experiment) images, visualize data acquired by the rover, and develop, model, and validate the activities the rover will perform. MSLICE enables users to securely contribute to the mission s activity planning process from their home institutions using off-the-shelf laptop computers. This software has made use of several plug-ins (software components) developed for previous missions [e.g., Mars Exploration Rover (MER), Phoenix Mars Lander (PHX)] and other technology tasks. It has a simple, intuitive, and powerful search capability. For any given mission, there is a huge amount of data and associated metadata that is generated. To help users sort through this information, MSLICE s search interface is provided in a similar fashion as major Internet search engines. With regard to the HiRISE visualization of the rover s traverse, this view is a map of the mission that allows scientists to easily gauge where the rover has been and where it is likely to go. The map also provides the ability to correct or adjust the known position of the rover through the overlaying of images acquired from the rover on top of the HiRISE image. A user can then correct the rover s position by collocating the visible features in the overlays with the same features in the underlying HiRISE image. MSLICE users can also rapidly search all mission data for images that contain a point specified by the user in another image or panoramic mosaic. MSLICE allows the creation of targets, which provides a way for scientists to collaboratively name features on the surface of Mars. These targets can also be used to convey instrument-pointing information to the activity plan. The software allows users to develop a plan of what they would like the rover to accomplish for a given time period. When developing the plan, the user can input constraints between activities or groups of activities. MSLICE will enforce said constraints and ensure that all mission flight rules are satisfied