Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Uncertainty in context-aware systems: A case study for intelligent environments

Data used be context-aware systems is naturally incomplete and not always reflect real situations. The dynamic nature of intelligent environments leads to the need of analysing and handling uncertain information. Users can change their acting patterns within a short space of time. This paper presents a case study for a better understanding of concepts related to context awareness and the problem of dealing with inaccurate data. Through the analysis of identification of elements that results in the construction of unreliable contexts, it is aimed to identify patterns to minimize incompleteness. Thus, it will be possible to deal with flaws caused by undesired execution of applications.Programa Operacional Temático Factores de Competitividade (POCI-01-0145-

Аспекти ведення інформаційної та гібридної війни в контексті застосування комунікаційних технологій

Смола Л. Є. Аспекти ведення інформаційної та гібридної війни в контексті застосування комунікаційних технологій / Л. Є. Смола // S.P.A.C.E. Society, Politics, Administration in Central Europe : електронний науково-практичний журнал / редкол.: Д. В. Яковлев (голов. ред.), К. М. Вітман (заст. голов. ред.), Д. Ю. Дворніченко (відп. секр.) [та ін.] ; НУ «ОЮА». – Одеса, 2016. – Вип. 1. – С. 48-53.У статті розглядається поняття «інформаційна війна», «гібридна війна», цілі, способи та методи її ведення. Аналізуються новітні комунікаційні технології як інструменти інформаційної війни: соціальні мережі, блоги та форуми. Описується нове інформаційне явище – меми. Стверджується, що прийоми та методи інформаційного протиборства з воєнної сфери успішно перенесені у політичну площину. Робиться висновок, що інтерактивні формати із соціальни- ми медіа дозволять протидіяти інформаційній агресії. Зазначаються основні аспекти інформаційного домінування: проникнення в інформаційне середовище країни, формування внутрішніх конфліктів, паніки, хаосу в інформаційному просторі, руйнування елементів соціальної системи.В статье рассматривается термин «информационная война», «гибридная война», цели, способы и методы её ведения. Анализируются новейшие коммуникационные технологии как инструменты информационной войны: социальные сети, блоги и форумы. Описывается новое информационное явление – мемы. Утверждается, что приемы и методы информационного противоборства с военной сферы успешно перенесены в политическую плоскость. Делается вывод, что интерактивные форматы с социальными медиа позволят противодействовать информационной агрессии. Указываются основные аспекты информационного доминирования: проникновение в информационную среду страны, формирование внутренних конфликтов, паники, хаоса в информационном пространстве, разрушение элементов социальной системы.In this article term «information warfare», «hybrid warfare», its targets, methods and practices are examined. Latest communication technologies as tools of information warfare is analyzed, all kinds of social networks, blogs and forums. Memes – new information phenomenon is described. It is alleged that the techniques and methods of information confrontation with the military sphere is successfully transferred to the political plane. It is concluded that interactive with social media information will resist aggression. Indicate the main aspects of information dominance, penetration into the information environment of the country, formation of internal conflicts, panic, chaos in cyberspace, destruction of elements of the social system and so on

Statistical Mechanical Development of a Sparse Bayesian Classifier

The demand for extracting rules from high dimensional real world data is increasing in various fields. However, the possible redundancy of such data sometimes makes it difficult to obtain a good generalization ability for novel samples. To resolve this problem, we provide a scheme that reduces the effective dimensions of data by pruning redundant components for bicategorical classification based on the Bayesian framework. First, the potential of the proposed method is confirmed in ideal situations using the replica method. Unfortunately, performing the scheme exactly is computationally difficult. So, we next develop a tractable approximation algorithm, which turns out to offer nearly optimal performance in ideal cases when the system size is large. Finally, the efficacy of the developed classifier is experimentally examined for a real world problem of colon cancer classification, which shows that the developed method can be practically useful.Comment: 13 pages, 6 figure

Knot selection in sparse Gaussian processes with a variational objective function

Sparse, knot‐based Gaussian processes have enjoyed considerable success as scalable approximations of full Gaussian processes. Certain sparse models can be derived through specific variational approximations to the true posterior, and knots can be selected to minimize the Kullback‐Leibler divergence between the approximate and true posterior. While this has been a successful approach, simultaneous optimization of knots can be slow due to the number of parameters being optimized. Furthermore, there have been few proposed methods for selecting the number of knots, and no experimental results exist in the literature. We propose using a one‐at‐a‐time knot selection algorithm based on Bayesian optimization to select the number and locations of knots. We showcase the competitive performance of this method relative to optimization of knots simultaneously on three benchmark datasets, but at a fraction of the computational cost

The need for open source software in machine learning

Open source tools have recently reached a level of maturity which makes them suitable for building large-scale real-world systems. At the same time, the field of machine learning has developed a large body of powerful learning algorithms for diverse applications. However, the true potential of these methods is not used, since existing implementations are not openly shared, resulting in software with low usability, and weak interoperability. We argue that this situation can be significantly improved by increasing incentives for researchers to publish their software under an open source model. Additionally, we outline the problems authors are faced with when trying to publish algorithmic implementations of machine learning methods. We believe that a resource of peer reviewed software accompanied by short articles would be highly valuable to both the machine learning and the general scientific community

Lamb meat quality assessment by support vector machines

The correct assessment of meat quality (i.e., to fulfill the consumer's needs) is crucial element within the meat industry. Although there are several factors that affect the perception of taste, tenderness is considered the most important characteristic. In this paper, a Feature Selection procedure, based on a Sensitivity Analysis, is combined with a Support Vector Machine, in order to predict lamb meat tenderness. This real-world problem is defined in terms of two difficult regression tasks, by modeling objective (e.g. Warner-Bratzler Shear force) and subjective (e.g. human taste panel) measurements. In both cases, the proposed solution is competitive when compared with other neural (e.g. Multilayer Perceptron) and Multiple Regression approaches