Search results for "probabilistic method"
showing 8 items of 8 documents
Improving Lossless Image Compression with Contextual Memory
2019
With the increased use of image acquisition devices, including cameras and medical imaging instruments, the amount of information ready for long term storage is also growing. In this paper we give a detailed description of the state-of-the-art lossless compression software PAQ8PX applied to grayscale image compression. We propose a new online learning algorithm for predicting the probability of bits from a stream. We then proceed to integrate the algorithm into PAQ8PX&rsquo
Numerical decomposition of geometric constraints
2005
Geometric constraint solving is a key issue in CAD/CAM. Since Owen's seminal paper, solvers typically use graph based decomposition methods. However, these methods become difficult to implement in 3D and are misled by geometric theorems. We extend the Numerical Probabilistic Method (NPM), well known in rigidity theory, to more general kinds of constraints and show that NPM can also decompose a system into rigid subsystems. Classical NPM studies the structure of the Jacobian at a random (or generic) configuration. The variant we are proposing does not consider a random configuration, but a configuration similar to the unknown one. Similar means the configuration fulfills the same set of inci…
Amount of Nonconstructivity in Finite Automata
2009
When D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P.Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L. E. J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was "nonconstructive arguments have no value for mathematics". However, P. Erdos got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. R.Freivalds [7] showed that nonconstructive methods in coding theory are related to the notion of…
CAD-Based Training of an Expert System and a Hidden Markov Model for Obstacle Detection in an Industrial Robot Environment
2012
Abstract Deploying industrial robots in harsh outdoor environments require additional functionalities not currently provided. For instance, movement of standard industrial robots are pre-programmed to avoid collision. In dynamic and less structured environments, however, the need for online detection and avoidance of unmodelled objects arises. This paper focus on online obstacle detection using a laser sensor by proposing three different approaches, namely a CAD-based Expert System (ES) and two probabilistic methods based on a Hidden Markov Model (HMM) which requires observation based training. In addition, this paper contributes by providing a comparison between the CAD-based ES and the tw…
Amount of nonconstructivity in deterministic finite automata
2010
AbstractWhen D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P. Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L.E.J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was “nonconstructive arguments have no value for mathematics”. However, P. Erdös got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. The author (Freivalds, 2008) [10] showed that nonconstructive methods in coding theory are…
A new method in investigations of bubble cluster shapes in two-phase flow
1991
Abstract In this paper a new probabilistic method is used to analyse the distribution of air bubbles in two-phase flow. So far, the method has been applied in astronomy and cosmology to investigate the distribution of galaxies. The basic idea is presented and the method applied to the photographed population of air bubbles in a liquid. The method allows the homogeneity of the flow to be evaluated qualitatively and quantitatively.
Discontinuous, although “highly” differentiable, real functions and algebraic genericity
2021
Abstract We exhibit a class of functions f : R → R which are bounded, continuous on R ∖ Q , left discontinuous on Q , right differentiable on Q , and upper left Dini differentiable on R ∖ Q . Other properties of these functions, such as jump sizes and local extrema, are also discussed. These functions are constructed using probabilistic methods. We also show that the families of functions satisfying similar properties contain large algebraic structures (obtaining lineability, algebrability and coneability).
Robustness and Randomness
2008
The study of robustness problems for computational geometry algorithms is a topic that has been subject to intensive research efforts from both computer science and mathematics communities. Robustness problems are caused by the lack of precision in computations involving floating-point instead of real numbers. This paper reviews methods dealing with robustness and inaccuracy problems. It discusses approaches based on exact arithmetic, interval arithmetic and probabilistic methods. The paper investigates the possibility to use randomness at certain levels of reasoning to make geometric constructions more robust.