Search results for "Computation"

Theoretical and methodological aspects of MCMC computations with noisy likelihoods

2018

Approximate Bayesian computation (ABC) [11, 42] is a popular method for Bayesian inference involving an intractable, or expensive to evaluate, likelihood function but where simulation from the model is easy. The method consists of defining an alternative likelihood function which is also in general intractable but naturally lends itself to pseudo-marginal computations [5], hence making the approach of practical interest. The aim of this chapter is to show the connections of ABC Markov chain Monte Carlo with pseudo-marginal algorithms, review their existing theoretical results, and discuss how these can inform practice and hopefully lead to fruitful methodological developments. peerReviewed

The link of a finitely determined map germ from R 2 to R 2

2010

Let f: (R2, 0) → (R2, 0) be a finitely determined map germ. The link of f is obtained by taking a small enough representative f: U ⊂ R2 → R2 and the intersection of its image with a small enough sphere Sε1 centered at the origin in R2. We will describe the topology of f in terms of the Gauss word associated to its link.

Some Remarks about Product Spaces

2018

Summary This article covers some technical aspects about the product topology which are usually not given much of a thought in mathematics and standard literature like [7] and [6], not even by Bourbaki in [4]. Let {Ti}i∈I be a family of topological spaces. The prebasis of the product space T = ∏ i∈I Ti is defined in [5] as the set of all π −1 i (V) with i ∈ I and V open in Ti . Here it is shown that the basis generated by this prebasis consists exactly of the sets ∏ i∈I Vi with Vi open in Ti and for all but finitely many i ∈ I holds Vi = Ti . Given I = {a} we have T ≅ Ta , given I = {a, b} with a≠ b we have T ≅ Ta ×Tb . Given another family of topological spaces {Si}i∈I such that Si ≅ Ti fo…

Tractional Motion Machines extend GPAC-generable functions

2012

In late 17th century there appeared the Tractional Motion instruments, mechanical devices which plot the curves solving differential equations by the management of the tangent. In early 20th century Vannevar Bush’s Differential Analyzer got the same aim: in this paper we’ll compare the Differential Analyzer mathematical model (the Shannon’s General Purpose Analog Computer, or GPAC) with the Tractional Motion Machine potentials. Even if we will not arrive in defining the class of the functions generated by Tractional Motion Machines, we’ll see how this class will strictly extend the GPAC-generable functions.

The impact of non-dipolar magnetic fields in core-collapse supernovae

2019

The magnetic field is believed to play an important role in at least some core-collapse supernovae if its magnitude reaches $10^{15}\,\rm{G}$, which is a typical value for a magnetar. In the presence of fast rotation, such a strong magnetic field can drive powerful jet-like explosions if it has the large-scale coherence of a dipole. The topology of the magnetic field is, however, probably much more complex with strong multipolar and small-scale components and the consequences for the explosion are so far unclear. We investigate the effects of the magnetic field topology on the dynamics of core-collapse supernovae and the properties of forming proto-neutron star (PNS) by comparing pre-collap…

Husserl's Transcendentalization of Mathematical Naturalism

2020

Abstract The paper aims to capture a form of naturalism that can be found “built-in” in phenomenology, namely the idea to take science or mathematics on its own, without postulating extraneous normative “molds” on it. The paper offers a detailed comparison of Penelope Maddy’s naturalism about mathematics and Husserl’s approach to mathematics in Formal and Transcendental Logic (1929). It argues that Maddy’s naturalized methodology is similar to the approach in the first part of the book. However, in the second part Husserl enters into a transcendental clarification of the evidences and presuppositions of the mathematicians’ work, thus “transcendentalizing” his otherwise naturalist approach t…

Parametric sensitivity of a CFD model concerning the hydrodynamics of trickle-bed reactor (TBR)

2016

Abstract The aim of the present study was to investigate the sensitivity of a multiphase Eulerian CFD model with respect to relations defining drag forces between phases. The mean relative error as well as standard deviation of experimental and computed values of pressure gradient and average liquid holdup were used as validation criteria of the model. Comparative basis for simulations was our own data-base obtained in experiments carried out in a TBR operating at a co-current downward gas and liquid flow. Estimated errors showed that the classical equations of Attou et al. (1999) defining the friction factors Fjk approximate experimental values of hydrodynamic parameters with the best agre…

Application of the Information Bottleneck method to discover user profiles in a Web store

2018

The paper deals with the problem of discovering groups of Web users with similar behavioral patterns on an e-commerce site. We introduce a novel approach to the unsupervised classification of user sessions, based on session attributes related to the user click-stream behavior, to gain insight into characteristics of various user profiles. The approach uses the agglomerative Information Bottleneck (IB) algorithm. Based on log data for a real online store, efficiency of the approach in terms of its ability to differentiate between buying and non-buying sessions was validated, indicating some possible practical applications of the our method. Experiments performed for a number of session sampl…

Pricavy-Preserving Aspects for Data Mining in ICT Services

The steady adoption of systems for profiling users behavior, collecting and critically interpreting as much information as possible about likes and dislikes, interests and habits of Internet residents and generic services consumers have rapidly become some of the hottest keywords within networking research community. Indeed, mining information about users behavior is an advantage for both service providers and service customers: on one side, providers can improve their revenues by focusing on the most successful features of their services, while on the other side, users can enjoy services which reflect closer their specific needs. There are many examples of user profiling applications. Inte…

Model organisms and their application in environmental epigenetics

2020

Abstract Epigenetic mechanisms operate at the interface between the environment and the genome of a given organism. More particularly, they convert environmental stimuli as diverse as chemical pollutants, nutritional components, temperature changes, and social conditions into changes in the chromatin landscape, which influence gene expression in the absence of alterations in the DNA sequence, ultimately leading to phenotype adaptation and diversification. The use of experimental model organisms in epigenetics research allows for the careful manipulation of environmental factors in order to understand how they mechanistically modulate the establishment, maintenance, and inheritance of epigen…