Dixon Resultant method can eliminate many variables simultaneously. It is often used to solve a system of polynomial equations. However, the Dixon matrix is often singular, and the Dixon Resultant vanishes identically...
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Transformation-Interaction-Rational is a representation for symbolic Regression created withthe intent to constrain the search space of mathematical expressions with only simple models. In short, this representation ...
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ISBN:
(纸本)9781665465458
Transformation-Interaction-Rational is a representation for symbolic Regression created withthe intent to constrain the search space of mathematical expressions with only simple models. In short, this representation is a rational of two linear models with transformed variables. Even though the representation makes the model nonlinear w.r.t. its numerical parameters, it is possible to rewrite the expression such that the parameters become linear and, thus, can be adjusted using the Ordinary Least Squares method, that guarantees the global optima solution. But, when we are working with a noisy data set, the reparametrization procedure may skew the noise distribution leading to an incorrect value for the numerical parameters. In this work, we test and compare the use of Ordinary Least Square and a non-linear optimization in simulated benchmarks withthe presence of noise. the results show evidence that OLS is robust to noise and always returns a similar solution to the non-linear optimization algorithm.
the computation of self-intersection loci of parametrized surfaces is needed for constructing trimmed parametrizations and describing the topology of the considered surfaces in real settings. this paper presents two g...
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ISBN:
(纸本)9780769539645
the computation of self-intersection loci of parametrized surfaces is needed for constructing trimmed parametrizations and describing the topology of the considered surfaces in real settings. this paper presents two general and efficient methods for determining self-intersection loci of rationally parametrized surfaces. One of the methods, based on regular systems, is capable of computingthe exact parametric locus of self-intersection of a given surface and the other, based on Grobner bases, can compute the minimal variety passing through the exact parametric locus. the relation between the results computed by the two methods is established and two algorithms for computing parametric loci of self-intersection are described. Experimental results and comparisons with some existing methods show that our algorithms have a good performance for parametrized surfaces.
Weighted round robin load balancing is a common routing policy offered in cloud load balancers. However, there is a lack of effective mechanisms to decide the weights assigned to each server to achieve an overall opti...
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ISBN:
(纸本)9781479984480
Weighted round robin load balancing is a common routing policy offered in cloud load balancers. However, there is a lack of effective mechanisms to decide the weights assigned to each server to achieve an overall optimal revenue of the system. In this paper, we first experimentally explore the relation between probabilistic routing and weighted round robin load balancing policies. From the experiment a similar behavior is found between these two policies, which makes it possible to assign the weights according to the routing probability estimated from queueing theoretic heuristic and optimization algorithms studied in the literature. We focus in particular on algorithms based on closed queueing networks for multi-class workloads, which can be used to describe application with service level agreements differentiated across users. We also compare the efficiency of queueing theoretic methods with simple heuristics that do not require to specify a stochastic model of the application. Results indicate that queueing theoretical algorithms yield significantly better results than than routings proportional to the VM capacity with respect to throughput maximization.
the identification of non-linearities or undesirable dynamic behavior of electrical components is a common problem. Previous modeling forms are largely based on extensive physical knowledge at the semiconductor level,...
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ISBN:
(纸本)9781665465458
the identification of non-linearities or undesirable dynamic behavior of electrical components is a common problem. Previous modeling forms are largely based on extensive physical knowledge at the semiconductor level, which has produced reliable solutions over the past decades. this however implies the measurement of physical prototypes in laboratories, which can be costly. It is therefore desirable to have reliable software models of the prototypes available to outsource this procedure to simulators. this paper presents a number of solutions from the field of empirical modeling including symbolic regression, which allow to parameterize such models from measured values. As an example we are utilizing time-domain data from a real radio-frequency power amplifier circuit. We compare a Hammerstein-Wiener model with two methods for symbolic regression, and find that the Hammerstein-Wiener model produces the best predictions but has many non-zero coefficients. Bothsymbolic regression methods produce short linear models with slightly higher prediction error than the HW model.
We continue the Coxeter spectral study of finite connected loop-free edge-bipartite graphs Delta, with n >= 2 vertices (a class of signed graphs), started in [ SIAM J. Discrete Math., 27(2013), 827-854] by means of...
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ISBN:
(纸本)9781479930357
We continue the Coxeter spectral study of finite connected loop-free edge-bipartite graphs Delta, with n >= 2 vertices (a class of signed graphs), started in [ SIAM J. Discrete Math., 27(2013), 827-854] by means of the complex Coxeter spectrum specc(Delta) subset of C. Here, we discuss Coxeter spectral analysis problems of non-negative edge-bipartite graphs of corank s <= n - 1, which means that the symmetric Gram matrix G(Delta) is an element of M-n(Z) is positive semi-definite of rank n - s <= n. In particular, we study in details the loop-free edge-bipartite graphs of corank s = n - 1. We present algorithmsthat generate all such edge-bipartite graphs of a given size and, using symbolic and numerical computer calculations in Python, and we obtain their complete classification in relation with Diophantine geometry problems. We also construct algorithmsthat allow us to classify all connected loop-free non-negative edge-bipartite graphs Delta, with a fixed number n >= 2 of vertices, by means of their Coxeter spectra specc(Delta).
Vendor lock-in and cloud outages are two important challenges that make IT managers reluctant in widely adopting the cloud within the enterprise. Vendor lock-in happens when the adoption of cloud provider-specific tec...
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ISBN:
(纸本)9781479930357
Vendor lock-in and cloud outages are two important challenges that make IT managers reluctant in widely adopting the cloud within the enterprise. Vendor lock-in happens when the adoption of cloud provider-specific technologies and APIs forces consumers to stay withthe same provider even if they would like to change. Cloud outages can happen to any provider, as the events of the last years have largely demonstrated, and have a critical impact on the actual reliability of cloud applications. A solution to both problems could be to support application developers and operators in the adoption of a multi-cloud approach: applications are built to run and replicate on different clouds, and mechanisms for fast switching from a cloud installation to the other are offered. In the MODA Clouds project we pursue this approach and rely on model-driven development combined with risk analysis and quality prediction. In this paper we provide an overview of our approach and present the architecture of the corresponding platform.
Mathematics is characterized by its method of gaining knowledge, namely reasoning. the automation of reasoning has seen significant advances over the past decades and, thus, the expectation was that these advances wou...
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ISBN:
(纸本)9780769527406
Mathematics is characterized by its method of gaining knowledge, namely reasoning. the automation of reasoning has seen significant advances over the past decades and, thus, the expectation was that these advances would also have significant impact on the practice of doing mathematics. However, so far, this impact is small. We think that the reason for this is the fact that automated reasoning so far concentrated on the automated proof of individual theorems whereas, in the practice of mathematics, one proceeds by building up entire theories in a step-by-step process. this process of exploring mathematical theories consists of the invention of notions, the invention and proof of propositions (lemmas, theorems), the invention of problems, and the invention and verification of methods (algorithms) that solve problems.
Cloud computing is a promising technology for the realization of large, scalable, and on-demand provisioned computing infrastructures. Currently, many enterprises are adopting Clouds to achieve high performance and sc...
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ISBN:
(纸本)9781479930357
Cloud computing is a promising technology for the realization of large, scalable, and on-demand provisioned computing infrastructures. Currently, many enterprises are adopting Clouds to achieve high performance and scalability for their applications while maintaining low costs. Service provisioning in the Cloud is based on a set of predefined nonfunctional properties specified and negotiated by means of Service Level Agreements (SLAs). Cloud workloads are dynamic and change constantly. thus, in order to reduce steady human interactions, self-manageable Cloud techniques are required to comply withthe agreed customers' SLAs. Flexible and reliable management of SLAs is of paramount importance for both, Cloud providers and consumers. On one hand, the prevention of SLA violations avoids penalties that are costly to providers. On the other hand, based on flexible and timely reactions to possible SLA violation threats, user interaction withthe system can be minimized enabling Cloud computing to take roots as a flexible and reliable form of on-demand computing. Furthermore, a trade-off has to be found between proactive actions that prevent SLA violations and those that reduce energy consumption, i.e., increase energy efficiency. In this talk we discuss how the application of Cloud computing technologies can support the work of scientists working in the field of high-throughput sequencing, while at the same time optimizing utilization of resource and increasing energy efficiency.
Even if clouds are not fit for high-end HPC applications, they could be profitably used to bring the power of economic and scalable parallel computing to the masses. But this requires both simple development environme...
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ISBN:
(纸本)9781479984480
Even if clouds are not fit for high-end HPC applications, they could be profitably used to bring the power of economic and scalable parallel computing to the masses. But this requires both simple development environments, able to exploit cloud scalability, and the capability to easily predict the cost of HPC application runs. this paper presents a framework built on the top of a cloud-aware programming platform (mOSAIC) for the development of bag-of-tasks scientific applications. the framework integrates a cloud-based simulation environment able to predict the behavior of the developed applications. Simulations enable the developer to predict at an early development stage performance and cloud resource usage, and so the infrastructure lease cost on a public cloud. the paper sketches the framework organization and discusses the approach followed for application development. Moreover, some validation tests of prediction results are presented.
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