Search results for "Approx"
showing 10 items of 922 documents
Prediction of peak shape as a function of retention in reversed-phase liquid chromatography
2004
Optimisation of the resolution of multicomponent samples in HPLC is usually carried out by changing the elution conditions and considering the variation in retention of the analytes, to which a standard peak shape is assigned. However, the change in peak shape with the composition of the mobile phase can ruin the optimisation process, yielding unexpected overlaps in the experimental chromatograms for the predicted optimum, especially for complex mixtures. The possibility of modelling peak shape, in addition to peak position, is therefore attractive. A simple modified-Gaussian model with a parabolic variance, which is a function of conventional experimental parameters: retention time (tR), p…
Upper Bound for the Approximation Error for the Kirchhoff-Love Arch Problem
2013
In this paper, a guaranteed and computable upper bound of approximation errors for the Kirchhoff-Love arch problem is derived. In general, it belongs to the class of functional a posteriori error estimates. The derivation method uses purely functional arguments and, therefore, the estimates are valid for any conforming approximation within the energy space. The computational implementation of the upper bound is discussed and demonstrated by a numerical example.
Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information
2014
Published version of an article in the journal: Multidimensional Systems and Signal Processing. Also available from the publisher at: http://dx.doi.org/10.1007/s11045-013-0276-x This paper is concerned with the problem of {Mathematical expression} model approximation for a class of two-dimensional (2-D) discrete-time Markovian jump linear systems with state-delays and imperfect mode information. The 2-D system is described by the well-known Fornasini-Marchesini local state-space model, and the imperfect mode information in the Markov chain simultaneously involves the exactly known, partially unknown and uncertain transition probabilities. By using the characteristics of the transition proba…
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
Relaxation for a Class of Control Systems with Unilateral Constraints
2019
We consider a nonlinear control system involving a maximal monotone map and with a priori feedback. We assume that the control constraint multifunction $U(t,x)$ is nonconvex valued and only lsc in the $x \in \mathbb{R}^{N}$ variable. Using the Q-regularization (in the sense of Cesari) of $U(t,\cdot )$, we introduce a relaxed system. We show that this relaxation process is admissible.
Emergent Collective Behaviors in a Multi-agent Reinforcement Learning Pedestrian Simulation: A Case Study
2015
In this work, a Multi-agent Reinforcement Learning framework is used to generate simulations of virtual pedestrians groups. The aim is to study the influence of two different learning approaches in the quality of generated simulations. The case of study consists on the simulation of the crossing of two groups of embodied virtual agents inside a narrow corridor. This scenario is a classic experiment inside the pedestrian modeling area, because a collective behavior, specifically the lanes formation, emerges with real pedestrians. The paper studies the influence of different learning algorithms, function approximation approaches, and knowledge transfer mechanisms on performance of learned ped…
Collocation Method for Linear BVPs via B-spline Based Fuzzy Transform
2018
The paper is devoted to an application of a modified F-transform technique based on B-splines in solving linear boundary value problems via the collocation method. An approximate solution is sought as a composite F-transform of a discrete function (which allows the solution to be compactly stored as the values of this discrete function). We demonstrate the effectiveness of the described technique with numerical examples, compare it with other methods and propose theoretical results on the order of approximation when the fuzzy partition is based on cubic B-splines.
Languages with mismatches
2007
AbstractIn this paper we study some combinatorial properties of a class of languages that represent sets of words occurring in a text S up to some errors. More precisely, we consider sets of words that occur in a text S with k mismatches in any window of size r. The study of this class of languages mainly focuses both on a parameter, called repetition index, and on the set of the minimal forbidden words of the language of factors of S with errors. The repetition index of a string S is defined as the smallest integer such that all strings of this length occur at most in a unique position of the text S up to errors. We prove that there is a strong relation between the repetition index of S an…
A Characterization of Bispecial Sturmian Words
2012
A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian wo…
"Indexing structures for approximate string matching
2003
In this paper we give the first, to our knowledge, structures and corresponding algorithms for approximate indexing, by considering the Hamming distance, having the following properties. i) Their size is linear times a polylog of the size of the text on average. ii) For each pattern x, the time spent by our algorithms for finding the list occ(x) of all occurrences of a pattern x in the text, up to a certain distance, is proportional on average to |x| + |occ(x)|, under an additional but realistic hypothesis.