166 research outputs found
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 . 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
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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
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