Practical Efficient Global Optimization is No-regret
Jingyi Wang, Haowei Wang, Nai-Yuan Chiang
et al.
Efficient global optimization (EGO) is one of the most widely used noise-free Bayesian optimization algorithms.It comprises the Gaussian process (GP) surrogate model and expected improvement (EI) acquisition function. In practice, when EGO is applied, a scalar matrix of a small positive value (also called a nugget or jitter) is usually added to the covariance matrix of the deterministic GP to improve numerical stability. We refer to this EGO with a positive nugget as the practical EGO. Despite its wide adoption and empirical success, to date, cumulative regret bounds for practical EGO have yet to be established. In this paper, we present for the first time the cumulative regret upper bound of practical EGO. In particular, we show that practical EGO has sublinear cumulative regret bounds and thus is a no-regret algorithm for commonly used kernels including the squared exponential (SE) and Matérn kernels ($ν>\frac{1}{2}$). Moreover, we analyze the effect of the nugget on the regret bound and discuss the theoretical implication on its choice. Numerical experiments are conducted to support and validate our findings.
Practical Attribution Guidance for Rashomon Sets
Sichao Li, Amanda S. Barnard, Quanling Deng
Different prediction models might perform equally well (Rashomon set) in the same task, but offer conflicting interpretations and conclusions about the data. The Rashomon effect in the context of Explainable AI (XAI) has been recognized as a critical factor. Although the Rashomon set has been introduced and studied in various contexts, its practical application is at its infancy stage and lacks adequate guidance and evaluation. We study the problem of the Rashomon set sampling from a practical viewpoint and identify two fundamental axioms - generalizability and implementation sparsity that exploring methods ought to satisfy in practical usage. These two axioms are not satisfied by most known attribution methods, which we consider to be a fundamental weakness. We use the norms to guide the design of an $ε$-subgradient-based sampling method. We apply this method to a fundamental mathematical problem as a proof of concept and to a set of practical datasets to demonstrate its ability compared with existing sampling methods.
On Sums of Practical Numbers and Polygonal Numbers
Sai Teja Somu, Duc Van Khanh Tran
Practical numbers are positive integers $n$ such that every positive integer less than or equal to $n$ can be written as a sum of distinct positive divisors of $n$. In this paper, we show that all positive integers can be written as a sum of a practical number and a triangular number, resolving a conjecture by Sun. We also show that all sufficiently large natural numbers can be written as a sum of a practical number and two $s$-gonal numbers.
Comparative Analysis of Practical Identifiability Methods for an SEIR Model
Omar Saucedo, Amanda Laubmeier, Tingting Tang
et al.
Identifiability of a mathematical model plays a crucial role in parameterization of the model. In this study, we establish the structural identifiability of a Susceptible-Exposed-Infected-Recovered (SEIR) model given different combinations of input data and investigate practical identifiability with respect to different observable data, data frequency, and noise distributions. The practical identifiability is explored by both Monte Carlo simulations and a Correlation Matrix approach. Our results show that practical identifiability benefits from higher data frequency and data from the peak of an outbreak. The incidence data gives the best practical identifiability results compared to prevalence and cumulative data. In addition, we compare and distinguish the practical identifiability by Monte Carlo simulations and a Correlation Matrix approach, providing insights for when to use which method for other applications.
Franciszek Jabłoński, Terytoria misyjne w świetle Kongregacji Ewangelizowania Narodów w 390. rocznicę jej powstania (1622-2012), Wydawnictwo Missio Polonia, Warszawa 2012, ss. 390.
Wojciech Kluj
Ethnology. Social and cultural anthropology, Practical Theology
Practical Scheme for Realization of a Quantum Battery
Maryam Hadipour, Soroush Haseli, Dong Wang
et al.
We propose a practical scheme for a quantum battery consisting of an atom-cavity interacting system under a structured reservoir in the non-Markovian regime. We investigate a multi-parameter regime for the cavity-reservoir coupling and reveal how these parameters affect the performance of the quantum battery. Our proposed scheme is simple and may be achievable for practical realization and implementation.
Formação Docente e Ensino Religioso: Exercícios Decoloniais em Territórios Latino-Americanos
Lilian Blanck de Oliveira, Simone Riske-Koch
O território latino-americano é marcado por colonialidades decorrentes dos processos de colonização. Espanhóis, portugueses e europeus chegando à região de Abya Yala — agora América Latina — trouxeram em sua bagagem intentos de invadir para expropriar, buscando colonizar política, cultural e economicamente as populações originárias. Neste processo, a colonialidade impetrada impingiu na educação formal práticas reprodutoras de visões de mundo dos colonizadores, historicamente hegemônicas. Todavia, a multiplicidade de povos da Abya Yala, com suas culturas e práticas peculiares, historicamente aprendeu a sobreviver, resistir e mover-se entre lógicas e códigos coloniais. Partimos de pressupostos de que, nos processos formativos coletivos e individuais, algumas possibilidades de uma decolonialidade na educação passam pela formação docente e se efetivam a partir de uma episte(me)todologia comprometida com a diferença — as diversidades. Neste artigo objetivamos problematizar efeitos da colonização na educação brasileira, especificamente no Ensino Religioso, analisando algumas práticas e exercícios decoloniais na formação docente inicial e continuada. A investigação é de perspectiva bibliográfica e documental, utilizando, especialmente, registros do curso de licenciatura em Ciências da Religião da Universidade Regional de Blumenau, referentes ao período entre 1996 e 2020. Os resultados sinalizam a existência de possibilidades de uma formação que acolhe e reconhece outras histórias, saberes e culturas. Indicam, ainda, a viabilidade de criar espaços de abertura e lugares de diálogo, de romper com hierarquizações de saberes e poderes e do reconhecimento de diversidades epistêmicas e metodológicas — ações que interpelam e afetam o ensino da/para/com a diversidade religiosa no cotidiano da educação básica.
JESUS E ZAQUEU
Max Silva da Rocha
Este trabalho objetiva realizar uma análise retórica acerca dos lugares da argumentação que fundamentaram o discurso teológico encontrado no Evangelho Segundo Lucas 19, 1-10. Esse texto bíblico apresenta o encontro entre o orador Jesus Cristo e o publicano Zaqueu. Assim, por Retórica, compreende-se o uso de técnicas argumentativas que visam persuadir; por discurso teológico, entende-se o uso de textos extraídos de livros considerados sagrados que falem sobre Deus. O discurso teológico toma como suporte textual a Bíblia, considerada um livro de expressiva importância para o Cristianismo. Metodologicamente, o trabalho filia-se a uma perspectiva qualitativa de análise retórica e embasa-se em Abreu (2009), Aristóteles (2011), Ferreira (2015), Meyer (2007), Perelman e Olbrechts-Tyteca (2014), Reboul (2004), Rocha (2020a, 2020b), entre outros. A partir da análise retórica, verificou-se que os lugares da argumentação foram decisivos para o ato de persuadir, no texto teológico destacado. Percebeu-se que o orador Jesus Cristo se serviu desses recursos retóricos (lugares argumentativos) para ganhar a confiança e persuadir o publicano Zaqueu.
Religion (General), Practical Theology
Practical Provenance in Astronomy
Mathieu Servillat, François Bonnarel, Mireille Louys
et al.
Recently the International Virtual Observatory Alliance (IVOA) released a standard to structure provenance metadata, and several implementations are in development in order to capture, store, access and visualize the provenance of astronomy data products. This BoF will be focused on practical needs for provenance in astronomy. A growing number of projects express the requirement to propose FAIR data (Findable, Accessible, Interoperable and Reusable) and thus manage provenance information to ensure the quality, reliability and trustworthiness of this data. The concepts are in place, but now, applied specifications and practical tools are needed to answer concrete use cases. During this session we discussed which strategies are considered by projects (observatories or data providers) to capture provenance in their context and how a end-user might query the provenance information to enhance her/his data selection and retrieval. The objective was to identify the development of tools and formats now needed to make provenance more practical needed to increase provenance take-up in the astronomical domain.
Towards Practical Mean Bounds for Small Samples
My Phan, Philip S. Thomas, Erik Learned-Miller
Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffding's inequality that use weaker assumptions but produce much looser (wider) intervals. In 1969, Anderson (1969) proposed a mean confidence interval strictly better than or equal to Hoeffding's whose only assumption is that the distribution's support is contained in an interval $[a,b]$. For the first time since then, we present a new family of bounds that compares favorably to Anderson's. We prove that each bound in the family has {\em guaranteed coverage}, i.e., it holds with probability at least $1-α$ for all distributions on an interval $[a,b]$. Furthermore, one of the bounds is tighter than or equal to Anderson's for all samples. In simulations, we show that for many distributions, the gain over Anderson's bound is substantial.
La cuestión disputada De simplicitate divine esse de Tomás de Aquino
Juan José Herrera
Entre los textos de Tomás consagrados a la simplicidad divina, la cuestión disputada De simplicitate divine esse sobresale por su original enfoque. Esta obra no se limita a probar la ausencia de toda clase de composición en Dios, sino que también muestra el impacto de ese atributo en el campo del lenguaje teológico. En efecto, la simplicidad cumple un papel fundamental a la hora de precisar el verdadero alcance de los nombres absolutos y relativos atribuidos a Dios. La temática está lejos de ser irrelevante puesto que la imagen que el teólogo se forme de Dios y enseñe a los demás depende de la correcta comprensión de esos predicados. Nuestro trabajo ofrece una introducción a este texto medieval con el doble propósito de despertar o acrecentar el interés por su estudio y de descubrir que Tomás de Aquino tiene todavía mucho que decir sobre el Dios absolutamente simple.
Doctrinal Theology, Practical Theology
O princípio pluralista diante das dimensões do lúdico e da festividade
Claudio de Oliveira Ribeiro
A pesquisa tem como foco destacar aspectos de novas linguagens teológicas, forjadas nas expressões dos desejos humanos e associadas às dimensões lúdicas e místicas de formas de vida marcadas pela festividade, pela alteridade, pela afirmação da diferença, pela poesia e pelo empoderamento de grupos subalternizados que, nos entrelugares de suas culturas, revelam visões plurais e criativas de vida. Entre os resultados alcançados na pesquisa, destacamos o valor das teologias narrativas e da teopoética, que representam visões de recriação da linguagem teológica, com elementos simbólicos e de forte apelo existencial que traduzem concepções teológicas fundamentais da fé. Metodologicamente, procuramos seguir na trilha de pensar a vida e as experiências religiosas a partir do lugar criativo e propositivo dos entrelugares e fronteiras das culturas, assim como estar atentos à perspectiva dos estudos culturais decoloniais que destaca a tríplice demanda de decoloniadade do poder, do saber e do ser. Para isso, nos esforçamos em articular o princípio pluralista com visões antropológicas que valorizam o lúdico e a festividade, uma vez que tais dimensões nem sempre são realçadas nas análises teológicas e constituem intensa força mobilizadora da vida.
Interactional leadership: Jesus’ model of leadership – A case of Mark 7:25–29
John K. Addo Jnr, Zorodzai Dube
Inspired by Goffman and Mead Social Interactionism theory and Ghanaian traditional leadership model, this article interprets Mark 7:24–30 as text that re-imagines alternative leadership practice. The study suggest that social interactionism theory tenants of ritual making, people processing, characterisation, frame making and dramaturgy provide a alternative heuristic tools to understand Jesus’ view of leadership. Seemingly and for Jesus, leadership is a product of social interaction derived from the manner one interacts with various people. This study proposes that the Ghanaian Akan traditional notion of leadership based on social interaction provides analogical model that complements social interactionism theory in interpreting Jesus’ leadership practices. Therefore, the study explains social interactionism theory and then illustrated it through Akan leadership model analogue. The story of the Syrophoenician woman in Mark 7:24–30 gives the social interaction, people processing, characterisation, frame making and dramaturgy that informs Jesus’ leadership model to be modelled by the Church.
The Bible, Practical Theology
Entropy for practical stabilization
Fritz Colonius, Boumediene Hamzi
For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for the diverse entropies are proved, with special attention to exponential KL-functions. The relation to feedbacks is discussed, the linear case and several nonlinear examples are analyzed in detail.
Practical central binomial coefficients
Carlo Sanna
A practical number is a positive integer $n$ such that all positive integers less than $n$ can be written as a sum of distinct divisors of $n$. Leonetti and Sanna proved that, as $x \to +\infty$, the central binomial coefficient $\binom{2n}{n}$ is a practical number for all positive integers $n \leq x$ but at most $O(x^{0.88097})$ exceptions. We improve this result by reducing the number of exceptions to $\exp\!\big(C (\log x)^{4/5} \log \log x\big)$, where $C > 0$ is a constant.
Dynamic Matching Algorithms in Practice
Monika Henzinger, Shahbaz Khan, Richard Paul
et al.
In recent years, significant advances have been made in the design and analysis of fully dynamic maximal matching algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. In this paper, we attempt to bridge the gap between theory and practice that is currently observed for the fully dynamic maximal matching problem. We engineer several algorithms and empirically study those algorithms on an extensive set of dynamic instances.
Practical numbers among the binomial coefficients
Paolo Leonetti, Carlo Sanna
A "practical number" is a positive integer $n$ such that every positive integer less than $n$ can be written as a sum of distinct divisors of $n$. We prove that most of the binomial coefficients are practical numbers. Precisely, letting $f(n)$ denote the number of binomial coefficients $\binom{n}{k}$, with $0 \leq k \leq n$, that are not practical numbers, we show that \begin{equation*} f(n) < n^{1 - (\log 2 - δ)/\log \log n} \end{equation*} for all integers $n \in [3, x]$, but at most $O_γ(x^{1 - (δ- γ) / \log \log x})$ exceptions, for all $x \geq 3$ and $0 < γ< δ< \log 2$. Furthermore, we prove that the central binomial coefficient $\binom{2n}{n}$ is a practical number for all positive integers $n \leq x$ but at most $O(x^{0.88097})$ exceptions. We also pose some questions on this topic.
Media Education as Theoretical and Practical Paradigm for Digital Literacy: An Interdisciplinary Analysis
Jose Gomez-Galan
In this article we offer an analysis of the practical and theoretical paradigm of media education as a fundamental pedagogical model for the adequate development of the current methods of digital literacy. In a society dominated by the flow of information and communicative processes - in which digitalization has led to techno-media convergence, the complete uniting of ICT novelties and traditional media - it is essential to use all the vast experience of basic principles, pedagogical theories and practice which this educational paradigm has offered during decades. The current techno-media society is not an altruistic system; the communicative processes continue to be dominated by economic, political and social elites whose main interest is to influence and control the population. In this context -conceiving education as the only way to achieve the full and democratic development of our society, for its growth in values and solidarity - an analysis of reality starting in school is essential by forming a citizenship conscious of the power and influence of the ICT and its true meaning in the world. An authentic digital literacy should include the correct understanding of the new techno-media languages, and cannot simply be reduced to a formation of a technical and instrumental kind.
A long walk to obedience: Missiology and mission under scrutiny (1910-2010)
Johannes J. Knoetze
This article describes the discipline of missiology and mission over the last century since Edinburgh 1910 followed by two world wars to Edinburgh 2010, as a long walk to obedience – a walk in discerning God’s will. Even in biblical times, mission as spreading the gospel to those who do not yet believe in the Trinitarian God, was under scrutiny from within and outside the church (cf. Ac 10-11, 15 and Galatians). Throughout history until today it was never different. This article looks at the development of mission over the last 100 years from a Western (mainline missionary churches – MMCs) perspective. The development of missiology as a subject and theological discipline will be described along the lines of some of the mission conferences. Attention will be given to the following questions: What does it mean to b eobedient to the mission calling in a broken and traumatised world? Is there a credible way of redeeming mission and missiology from its own past?
Practical Theology, Practical religion. The Christian life
Practical Statistics for Particle Physicists
Harrison B. Prosper
These lectures introduce the basic ideas and practices of statistical analysis for particle physicists, using a real-world example to illustrate how the abstractions on which statistics is based are translated into practical application.