229,880 research outputs found
AlSub: Fully Parallel and Modular Subdivision
In recent years, mesh subdivision---the process of forging smooth free-form
surfaces from coarse polygonal meshes---has become an indispensable production
instrument. Although subdivision performance is crucial during simulation,
animation and rendering, state-of-the-art approaches still rely on serial
implementations for complex parts of the subdivision process. Therefore, they
often fail to harness the power of modern parallel devices, like the graphics
processing unit (GPU), for large parts of the algorithm and must resort to
time-consuming serial preprocessing. In this paper, we show that a complete
parallelization of the subdivision process for modern architectures is
possible. Building on sparse matrix linear algebra, we show how to structure
the complete subdivision process into a sequence of algebra operations. By
restructuring and grouping these operations, we adapt the process for different
use cases, such as regular subdivision of dynamic meshes, uniform subdivision
for immutable topology, and feature-adaptive subdivision for efficient
rendering of animated models. As the same machinery is used for all use cases,
identical subdivision results are achieved in all parts of the production
pipeline. As a second contribution, we show how these linear algebra
formulations can effectively be translated into efficient GPU kernels. Applying
our strategies to , Loop and Catmull-Clark subdivision shows
significant speedups of our approach compared to state-of-the-art solutions,
while we completely avoid serial preprocessing.Comment: Changed structure Added content Improved description
Efficient simulation of quantum evolution using dynamical coarse-graining
A novel scheme to simulate the evolution of a restricted set of observables
of a quantum system is proposed. The set comprises the spectrum-generating
algebra of the Hamiltonian. The idea is to consider a certain open-system
evolution, which can be interpreted as a process of weak measurement of the
distinguished observables performed on the evolving system of interest. Given
that the observables are "classical" and the Hamiltonian is moderately
nonlinear, the open system dynamics displays a large time-scales separation
between the dephasing of the observables and the decoherence of the evolving
state in the basis of the generalized coherent states (GCS), associated with
the spectrum-generating algebra. The time scale separation allows the unitary
dynamics of the observables to be efficiently simulated by the open-system
dynamics on the intermediate time-scale.The simulation employs unraveling of
the corresponding master equations into pure state evolutions, governed by the
stochastic nonlinear Schroedinger equantion (sNLSE). It is proved that GCS are
globally stable solutions of the sNLSE, if the Hamilonian is linear in the
algebra elements.Comment: The version submitted to Phys. Rev. A, 28 pages, 3 figures, comments
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Extending the Functionality of a Compiler for Linear Algebra Optimization
Large scale scientific applications take a significant amount of time to run. Optimizing these applications is vital for reducing the time and the cost of running these applications. At the core of computations, these applications often use linear algebra operations on large matrices and vectors. Optimizing linear algebra kernels by hand is a tedious and lengthy process, so often times highly tuned libraries are used to simplify the process. Rapid hardware development consistently makes such libraries outdated though. Auto-tuning, which is when a compiler or some similar tool optimizes code for the user, is able to incorporate a range of optimizations for any particular given hardware. We have created a compiler that automates optimizing such linear algebra kernels for large scale scientific applications. Our compiler uses a mix of partitioning, cache tiling, and loop fusion to auto-tune code. In this paper I discuss the issues that the compiler aims to fix, my updates to the compiler, and why these updates are useful
Delayed choice for process algebra with abstraction
The delayed choice is an operator which serves to combine linear time and branching time within one process algebra. We study this operator in a theory with abstraction, more precisely, in a setting considering branching bisimulation. We show its use in scenario specifications and in verification to reduce irrelevant branching structure of a process
Quantum communication complexity of linear regression
Dequantized algorithms show that quantum computers do not have exponential
speedups for many linear algebra problems in terms of time and query
complexity. In this work, we show that quantum computers can have exponential
speedups in terms of communication complexity for some fundamental linear
algebra problems. We mainly focus on solving linear regression and Hamiltonian
simulation. In the quantum case, the task is to prepare the quantum state of
the result. To allow for a fair comparison, in the classical case the task is
to sample from the result. We investigate these two problems in two-party and
multiparty models, propose near-optimal quantum protocols and prove
quantum/classical lower bounds. In this process, we propose an efficient
quantum protocol for quantum singular value transformation, which is a powerful
technique for designing quantum algorithms. As a result, for many linear
algebra problems where quantum computers lose exponential speedups in terms of
time and query complexity, it is possible to have exponential speedups in terms
of communication complexity.Comment: 28 page
Eigen Problem Over Max-Plus Algebra on Determination of the T3 Brand Shuttlecock Production Schedule
The production process is included in the Discrete Event System (DES). The DES independent variable generally depends on the event, so an event is influenced by the previous event. Max-plus algebra can be applied in the DES problem to change the system of nonlinear equations obtained into linear equations. Max-plus algebra is a set of real numbers combined with equipped with operations max and plus ⊗ or can be denoted with . An effective and efficient production process needs to pay attention scheduling steps well. The purpose of this research is to determine the Shuttlecock T3 production schedule using eigenvalue and eigenvector in max-plus algebra. The research method in this research is study of literature and observation. Literature study is carried out by studying references about max-plus algebra, especially material related to scheduling problems, while observation are carried out in the process of taking data of the Shuttlecock T3 production process in Surakarta. The linear equation system that is formed based on the results of the observation is then presented in the form and . The periodic time and initial system production time are determined from the eigenvalue and eigenvector matrix where . The results of the research showed that the production system run periodically every 249 minutes, then the best time for each processing unit to start working can be determined, as well as the Shuttlecock T3 production schedule according to the working hours more effective and efficient can be determined too
Applications of a finite-dimensional duality principle to some prediction problems
Some of the most important results in prediction theory and time series
analysis when finitely many values are removed from or added to its infinite
past have been obtained using difficult and diverse techniques ranging from
duality in Hilbert spaces of analytic functions (Nakazi, 1984) to linear
regression in statistics (Box and Tiao, 1975). We unify these results via a
finite-dimensional duality lemma and elementary ideas from the linear algebra.
The approach reveals the inherent finite-dimensional character of many
difficult prediction problems, the role of duality and biorthogonality for a
finite set of random variables. The lemma is particularly useful when the
number of missing values is small, like one or two, as in the case of
Kolmogorov and Nakazi prediction problems. The stationarity of the underlying
process is not a requirement. It opens up the possibility of extending such
results to nonstationary processes.Comment: 15 page
SIZING, CYCLE TIME AND PLANT CONTROL USING DIOID ALGEBRA
Using an industrial process from the car sector, we show how dioid algebra may be used for the performance evaluation, sizing, and control of this discrete-event dynamic system. Based on a Petri net model as an event graph, max-plus algebra and min-plus algebra permit to write linear equations of the behavior. From this formalism, the cycle time is determined and an optimal sizing is characterized for a required cyclic behavior. Finally, a strict temporal constraint the system is subject to is reformulated in terms of inequalities that the (min, +) system should satisfy, and a control law is designed so that the controlled system satisfies the constraint
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