The paper aims to discuss the results of testing a neural network which classifies the vowels of the vocalic system with the [ATR] (Advanced Tongue Root) contrast based on the data of Akebu (Kwa family). The acoustic nature of the [ATR] feature is yet understudied. The only reliable acoustic correlate of [ATR] is the magnitude of the first formant (F1) which can be also modulated by tongue height, resulting in significant overlap between high [-ATR] vowels and mid [+ATR] vowels. Other (...) acoustic metrics which had been associated with the [ATR], such as F1 bandwidth (B1), relative intensity of F1 to F2 (A1-A2), etc., are typically inconsistent across vowel types and speakers. The values of four metrics – F1, F2, A1-A2, B1 – were used for training and testing the neural network. We tested four versions of the model differing in the presence of the fifth variable encoding the speaker and the number of hidden layers. The models which included the variable encoding the speaker achieved slightly higher accuracy, whereas the precision and recall metrics of the three-layer model were generally higher than those with two hidden layers. (shrink)

A comparative study on Christian and Hindu conceptions of God.

The paper aims to discuss the results of testing a neural network which classifies the vowels of the vocalic system with the [ATR] (Advanced Tongue Root) contrast based on the data of Akebu (Kwa family). The acoustic nature of the [ATR] feature is yet understudied. The only reliable acoustic correlate of [ATR] is the magnitude of the first formant (F1) which can be also modulated by tongue height, resulting in significant overlap between high [-ATR] vowels and mid [+ATR] vowels. Other (...) acoustic metrics which had been associated with the [ATR], such as F1 bandwidth (B1), relative intensity of F1 to F2 (A1-A2), etc., are typically inconsistent across vowel types and speakers. The values of four metrics – F1, F2, A1-A2, B1 – were used for training and testing the neural network. We tested four versions of the model differing in the presence of the fifth variable encoding the speaker and the number of hidden layers. The models which included the variable encoding the speaker achieved slightly higher accuracy, whereas the precision and recall metrics of the three-layer model were generally higher than those with two hidden layers. (shrink)

We show that the theory $ATR_0$ is equivalent to a second-order generalization of the theory $\widehat{ID}_{<\omega}$. As a result, $ATR_0$ is conservative over $\widehat{ID}_{<\omega}$ for arithmetic sentences, though proofs in $ATR_0$ can be much shorter than their $\widehat{ID}_{<\omega}$ counterparts.

The paper aims to discuss the results of testing a neural network which classifies the vowels of the vocalic system with the [ATR] (Advanced Tongue Root) contrast based on the data of Akebu (Kwa family). The acoustic nature of the [ATR] feature is yet understudied. The only reliable acoustic correlate of [ATR] is the magnitude of the first formant (F1) which can be also modulated by tongue height, resulting in significant overlap between high [-ATR] vowels and mid [+ATR] vowels. Other (...) acoustic metrics which had been associated with the [ATR], such as F1 bandwidth (B1), relative intensity of F1 to F2 (A1-A2), etc., are typically inconsistent across vowel types and speakers. The values of four metrics – F1, F2, A1-A2, B1 – were used for training and testing the neural network. We tested four versions of the model differing in the presence of the fifth variable encoding the speaker and the number of hidden layers. The models which included the variable encoding the speaker achieved slightly higher accuracy, whereas the precision and recall metrics of the three-layer model were generally higher than those with two hidden layers. (shrink)

The correct execution of the DNA replication process is crucially import for the maintenance of genome integrity of the cell. Several types of sources, both endogenous and exogenous, can give rise to DNA damage leading to the DNA replication fork arrest. The processes by which replication blockage is sensed by checkpoint sensors and how the pathway leading to resolution of stalled forks is activated are still not completely understood. However, recent emerging evidence suggests that one candidate for a sensor of (...) replication stress is ATR and that, together with a member of RecQ family helicases, Werner syndrome protein (WRN) and MRE11 complex, can collaborate to promote the restarting of DNA synthesis through the resolution of stalled replication forks. Here, we discuss how WRN, the MRE11 complex and the ATR kinase could work together in response to replication blockage to avoid DNA replication fork collapse and genome instability. BioEssays 26:306–313, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

DNA replication stress threatens ordinary DNA synthesis. The evolutionarily conserved DNA replication stress response pathway involves sensor kinase Mec1/ATR, adaptor protein Mrc1/Claspin, and effector kinase Rad53/Chk1, which spurs a host of changes to stabilize replication forks and maintain genome integrity. DNA replication forks consist of largely distinct sets of proteins at leading and lagging strands that function autonomously in DNA synthesis in vitro. In this article, we discuss eSPAN and BrdU‐IP‐ssSeq, strand‐specific sequencing technologies that permit analysis of protein localization and (...) DNA synthesis at individual strands in budding yeast. Using these approaches, we show that under replication stress Rad53 stalls DNA synthesis on both leading and lagging strands. On lagging strands, it stimulates PCNA unloading, and on leading strands, it attenuates the replication function of Mrc1‐Tof1. We propose that in doing so, Rad53 couples leading and lagging strand DNA synthesis during replication stress, thereby preventing the emergence of harmful ssDNA. (shrink)

Este artículo explora las implicaciones para la bioética de los temas comunes entre el transhumanismo y la gobernanza global de la edición del genoma humano (HGE por sus siglas en inglés). En primer lugar, se aplicó el método de análisis temático reflexivo (ATR) a un conjunto de textos sobre el transhumanismo y sobre la gobernanza mundial de la edición del genoma humano. Como resultado de esta aplicación, surgieron tres temas comunes y sus elementos. Posteriormente se desarrolló un ejemplo de implicación (...) para la bioética de cada uno de dichos temas en donde cada implicación consideró la situación actual y una tarea para la bioética. Finalmente se concluye la importancia de reconocer la situación derivada de los temas comunes y la necesidad trabajar en las tres tareas identificadas es crucial para la bioética contemporánea. (shrink)

The socio-religious panorama of the African religion deserves a close observation of its foundation and function. The perception of the spirit world is dominant in Africa. Similarly, spiritual warfare in the African context is prevalent in the mind and worldview of an African. Spiritual warfare derives its framework from African Traditional Religion (ATR). Hence, understanding ATR’s complexity helps us with the understanding of spiritual warfare. Some essential questions to understand would be what is spiritual warfare from an ATR perspective? How (...) do Africans perceive spiritual warfare? And how do Africans engage in spiritual warfare? What is the place of ATR in spiritual warfare? African Traditional Religion acknowledges the reality and functionality of witchcraft. The perception of the reality of evil forces in Africa attracts all forms of spiritual rites, seeking more extraordinary spiritual powers for defensive and offensive spiritual warfare. This article argues that the effectual Christian response to spiritual warfare with witchcraft practices in Africa is ‘the classical model’ of spiritual warfare. The article provides a synopsis of the models of spiritual warfare, that is, the classical model (CW), world systems model (WSM), ground-level deliverance model (GLDM), and strategic-level deliverance model (SLSW). Subsequently, the article provides the framework for African spiritual warfare and witchcraft practices from traditional and contemporary perspectives. Lastly, the article argues that the Evangelical Christian Response to witchcraft practices is rooted in ‘the classical model’ of spiritual warfare. Contribution: The article contributes to African religiosity within the African context. It reveals the ongoing argument about the continuity and discontinuity of the ATR beliefs and practices in Christianity. The article adds to the evangelical or classical arguments in support of the discontinuity of ATR beliefs and practices in Christianity. (shrink)

Two countable well orderings are weakly comparable if there is an order preserving injection of one into the other. We say the well orderings are strongly comparable if the injection is an isomorphism between one ordering and an initial segment of the other. In [5], Friedman announced that the statement “any two countable well orderings are strongly comparable” is equivalent to ATR 0 . Simpson provides a detailed proof of this result in Chapter 5 of [13]. More recently, Friedman has (...) proved that the statement “any two countable well orderings are weakly comparable” is equivalent to ATR 0 . The main goal of this paper is to give a detailed exposition of this result. (shrink)

In [10], we have shown that the statement that all ∑ 1 1 partitions are Ramsey is deducible over ATR 0 from the axiom of ∑ 1 1 monotone inductive definition,but the reversal needs П 1 1 - CA 0 rather than ATR 0 . By contrast, we show in this paper that the statement that all ∑ 0 2 games are determinate is also deducible over ATR 0 from the axiom of ∑ 1 1 monotone inductive definition, but the (...) reversal is provable even in ACA 0 . These results illuminate the substantial differences among lightface theorems which can not be observed in boldface. (shrink)

Why do humans reason? Many animals draw inferences, but reasoning—the tendency to produce and respond to reason-giving performances—is biologically unusual, and demands evolutionary explanation. Mercier and Sperber advance our understanding of reason’s adaptive function with their argumentative theory of reason. On this account, the “function of reason is argumentative… to devise and evaluate arguments intended to persuade.” ATR, they argue, helps to explain several well-known cognitive biases. In this paper, I develop a neighboring hypothesis called the intention alignment model and (...) contrast it with ATR. I conjecture that reasoning evolved primarily because it helped social hominins more readily and fully align their intentions. We use reasons to advance various proximal ends, but in the main, we do it to overwrite the beliefs and desires of others: to get others to think like us. Reason afforded our ancestors a powerful way to build and maintain the shared outlooks necessary for a highly collaborative existence. Yes, we sometimes argue so as to gain argumentative advantage over others, or otherwise advantage ourselves at the expense of those we argue with, but more often, we reason in ways that are mutually advantageous. In fact, there are excellent reasons for thinking this must be so. IAM, I suggest, neatly explains the available evidence, while also providing a more coherent account of reason’s origins. (shrink)

In this article we study several reduction principles in the context of Simpson’s set theory ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} and Kripke-Platek set theory KP (with infinity). Since ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} is the set-theoretic version of ATR0 there is a direct link to second order arithmetic and the results for reductions over ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} are as expected and more or less (...) straightforward. However, over KP we obtain several interesting new results and are lead to some open questions. (shrink)

We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion (ATR_0) from the point of view of computability-theoretic reducibilities, in particular Weihrauch reducibility. Our main result states that it is equally hard to construct an embedding between two given well-orderings, as it is to construct a Turing jump hierarchy on a given well-ordering. This answers a question of Marcone. We obtain a similar result for Fraïssé's conjecture restricted to well-orderings.

We have parameterized Einstein’s thought experiment with atomic clocks, supposing that we knew neither if the space and time are relative or absolute, nor if the speed of light was ultimate speed or not. We have obtained a Parameterized Special Theory of Relativity (PSTR) (1982). Our PSTR generalized not only Einstein’s Special Theory of Relativity, but also our Absolute Theory of Relativity, and introduced three more possible Relativities to be studied in the future. After the 2011 CERN’s superluminal neutrino experiments, (...) we recall our ideas and invite researchers to deepen the study of PSTR, ATR, and check the three new mathematically emerged Relativities 4.3, 4.4, and 4.5. (shrink)

In this paper we establish the proof-theoretic equivalence of (i) $\hbox {\sf ATR}$ and $\widehat{\hbox{\sf ID}}_{\omega}$ , (ii) $\hbox{\sf ATR}_0+ (\Sigma^1_1-\hbox{\sf DC})$ and $\widehat{\hbox {\sf ID}}_{<\omega^\omega} , and (iii) $\hbox {\sf ATR}+(\Sigma^1_1-\hbox{\sf DC})$ and $\widehat{\hbox {\sf ID}}_{<\varepsilon_0} $.

There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far $\mathrm {ATR}_0$ has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.

John Mbiti, in his attempt to disprove the charge of paganism by EuroAmerican ethnographic and anthropological scholars against African Traditional Religions argues that traditional African religions are monotheistic. He insists that these traditional religious cultures have the same conception of God as found in the Abrahamic religions. The shared characteristics, according to him are foundational to the spread of the “gospel” in Africa. Mbiti’s effort, though motivated by the desire to refute the imperial charge of inferiority against African religions ran, (...) I argue, into a conceptual and descriptive conflation of ATRs with monotheistic faiths. In this paper, I challenge the superimposition of Judeo-Christian categories upon African religions. I argue that monotheism is just a strand, out of many, that expresses belief in God, and that it differs substantially from the polytheistic pre-colonial African understanding of religion. I provide a panentheistic paradigm using traditional Igbo ontology and religion to refute Mbiti’s generalization. Keywords: Monotheism, African Traditional Religion, Igbo, Paganism, Theology. (shrink)

Theorems of hyperarithmetic analysis occupy an unusual neighborhood in the realms of reverse mathematics and recursion-theoretic complexity. They lie above all the fixed iterations of the Turing jump but below ATR $_{0}$. There is a long history of proof-theoretic principles which are THAs. Until the papers reported on in this communication, there was only one mathematical example. Barnes, Goh, and Shore [1] analyze an array of ubiquity theorems in graph theory descended from Halin’s [9] work on rays in graphs. They (...) seem to be typical applications of ACA $_{0}$ but are actually THAs. These results answer Question 30 of Montalbán’s Open Questions in Reverse Mathematics [19] and supply several other natural principles of different and unusual levels of complexity.This work led in [25] to a new neighborhood of the reverse mathematical zoo: almost theorems of hyperarithmetic analysis. When combined with ACA $_{0}$ they are THAs but on their own are very weak. Denizens both mathematical and logical are provided. Generalizations of several conservativity classes are defined and these ATHAs as well as many other principles are shown to be conservative over RCA $_{0}$ in all these senses and weak in other recursion-theoretic ways as well. These results answer a question raised by Hirschfeldt and reported in [19] by providing a long list of pairs of principles one of which is very weak over RCA $_{0}$ but over ACA $_{0}$ is equivalent to the other which may be strong or very strong going up a standard hierarchy and at the end being stronger than full second-order arithmetic. (shrink)

Excerpt from L'Art de Sentir Et de Juger en Matière de Goût Nous 'zivons' employé trois especes de papier _à la réimpres'sion de ce livre; ce qui forme trois éditions. La premiere, de luxe et tirée àtrès petit nombre sur du papier Velin.' About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, (...) preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Alcoholism is endemic in Nigeria’s traditional religion and society. This abuse is especially common at New Yam festivals, Ekpe, Ekpo and Nmanwu masquerades festivals, burial rituals, birth, marriage and naming ceremonies. Some claim that this is driven by specific beliefs and activities in African culture, such as beliefs in ancestors, libation, hospitality and entertaining guests and strangers and the desire to maintain the cultural traditions of the ancestors. Alcohol abuse has generated major health and social issues for abusers, their families (...) and society, plunging families, towns and tribes into crises and conflicts that bring economic and political retrogression. This research studied how the African traditional religion encourages alcohol misuse and how to decrease it for national development. This study was on Nigeria’s South-South region. The study uses qualitative and ethnographic research methodologies, including key informants, in-depth and focus group interviews and the reward deficiency syndrome as a theoretical framework. Although African Traditional Religion (ATR) supports alcohol usage, greed, a lack of self-control, peer pressure, indiscipline and lack of moral upbringing led to alcohol misuse, which harms the person, family, community and country as a whole. Education and enlightenment are a remedy to free alcoholics and utilise them for national integration and development.Contribution: Some say Africans drink a lot because their religious heritage promotes drinking, leading to abuse. However, peer pressure, selfishness, a lack of self-control, bad parenting and not religion push persons with reward deficiency syndrome into alcoholism, according to this research. (shrink)

Peut-on vivre sans musique? Ce livre donne toutes les raisons pour lesquelles c'est impossible. De láa son titre. Il montre que la musique est une partie intâegrante et indispensable de notre vie quotidienne. Le timbre, la durâee, la hauteur, l'intensitâe du son musical dâeroulent, au long du temps humain, des ondes áa la vibration desquelles nos oreilles ne peuvent et ne veulent pas se soustraire. Les hommes sont si fortement attachâes áa la puissance de la musique, qu'ils ont inventâe, pour (...) la produire, une admirable diversitâe d'instruments, dont l'ingâeniositâe, le raffinement et les effets sonores dâefient l'imagination. C'est áa travers cet univers, extraordinaire autant que quotidien, que voyage le prâesent livre, en citant et expliquant d'innombrables oeuvres musicales, symphonies, concertos, sonates, quatuors, opâeras, plus fascinantes les unes que les autres, qui jalonnent l'histoire de l'effort opiniãatre des communautâes humaines pour s'enchanter elles-mãemes par cet âetincelant miracle : la musique"--Page 4 of cover. (shrink)

In and among the many models developed for engaging in inter-religious dialogue was a model that became known as scriptural reasoning (SR). SR basically serves the purpose of being hospitable towards the Abrahamic religions. The current approach of SR, by virtue of its focus only on scripture as the basis of engagement, obviously excludes other faith traditions that possess no sacred scripture. One such religion is African traditional religion (ATR). As a result of this exclusion, this article intends to engage (...) SR to consider reinterpreting imaginatively, or to use a synonym, to reconceptualise, its basis of only scripture as the primary source of engagement and as such to expand its basis to include religions with an oral-orientated tradition. This article explores such a possibility for the inclusion of ATR, as an oral tradition, to be considered as an equal partner in a reimagined SR or as a parallel model with similar guidelines and outcomes as found in SR. (shrink)

New targets for brain tumor therapies may be identified by mutations that cause hereditary microcephaly. Brain growth depends on the repeated proliferation of stem and progenitor cells. Microcephaly syndromes result from mutations that specifically impair the ability of brain progenitor or stem cells to proliferate, by inducing either premature differentiation or apoptosis. Brain tumors that derive from brain progenitor or stem cells may share many of the specific requirements of their cells of origin. These tumors may therefore be susceptible to (...) disruptions of the protein products of genes that are mutated in microcephaly. The potential for the products of microcephaly genes to be therapeutic targets in brain tumors are highlighted hereby reviewing research on EG5, KIF14, ASPM, CDK6, and ATR. Treatments that disrupt these proteins may open new avenues for brain tumor therapy that have increased efficacy and decreased toxicity. -/- . (shrink)

We study the computability-theoretic complexity and proof-theoretic strength of the following statements: (1) "If X is a well-ordering, then so is ε X ", and (2) "If X is a well-ordering, then so is φ(α, X)", where α is a fixed computable ordinal and φ represents the two-placed Veblen function. For the former statement, we show that ω iterations of the Turing jump are necessary in the proof and that the statement is equivalent to ${\mathrm{A}\mathrm{C}\mathrm{A}}_{0}^{+}$ over RCA₀. To prove the (...) latter statement we need to use ω α iterations of the Turing jump, and we show that the statement is equivalent to ${\mathrm{\Pi }}_{{\mathrm{\omega }}^{\mathrm{\alpha }}}^{0}{-\mathrm{C}\mathrm{A}}_{0}$ . Our proofs are purely computability-theoretic. We also give a new proof of a result of Friedman: the statement "if x is a well-ordering, then so is φ(x, 0)" is equivalent to ATR₀ over RCA₀. (shrink)

This article revisits the hope of the First and Fourth Missiological Institute (MI) consultations in 1965 and 1967 regarding the survival of African Spirituality as relevant to the daily life of South African churches. African Spirituality has played a significant role in the cultural context of Africans. In the African context, African Spirituality is intertwined with life, death, and health, which co-exist with material aspects and the economy as gracious gifts from God. The churches in South Africa and elsewhere in (...) Africa have been challenged by the African worldview of healing and culture. Thus, Africans mostly prefer the African-centred church with more African Christianity, instead of Western Christianity. This has been a serious challenge in African church circles for centuries, even in the current 21st century. The question therefore arises whether this is a matter for the Africanisation, indigenisation, and decolonisation of the church in Africa. CONTRIBUTION: The article analyses the two MI consultations and whether the church in the 21st century has Africanised and decolonised itself in service of its African members. The study is a historical approach given the history of the MI's contribution in South Africa. The concept of African Spirituality is unpacked and contextualised within the African Independent Churches' (AIC) Zionist type churches such as the Zion Christian Church (ZCC), the St John's Apostolic Faith Mission (AFM), and other Ethiopian type churches such as Lutheran Bapedi Church and others in South Africa and African Traditional Religions (ATR). The article engages the importance of how African Spirituality differs from other spiritualities within the context of Christian spirituality. (shrink)

Beginning with the role of the Sex Pistols’s “God Save the Queen” in Lee Edelman and J. Jack Halberstam’s debates about queer death and failure, I follow a musical motive from the Pistols track to its reappearance in Atari Teenage Riot’s 1995 “Delete Yourself .” In this song, as in much of ATR’s work from the 1990s, overlapping queer and Afro-diasporic aesthetics condense around the idea of death or “bare life.” ATR’s musical strategies treat this death as a form of (...) de-intensification and divestment— not, as in Edelman or the Pistols, as a form of negation . I will show that ATR’s musical recontextualization of the Pistols’s riff mirrors the political recontextualization of queerness and queer death from negation to disinvestment. Pushing this misprision or sticky interface between cyberpunk, queer, and Afro-diasporic musical aesthetics, I use ATR’s music to consider how queer death might work as a political response to neoliberal demands to invest in “normal” life. I first discuss the traditional concept of death as negation in both the Sex Pistols song "God Save the Queen," and in Lee Edelman and Jack Halberstam’s formulations. I then argue that Atari Teenage Riot's song “Delete Yourself” describes a neoliberal, biopolitical concept of death, death as carefully administered divestment. Finally, I use Deleuze and Guattari’s discussion of drugs, and Ronald Bogue’s Deleuzian reading of death metal to identify and explain how “MIDIjunkies” and “Into the Death” complicate the biopolitical/neoliberal management of death by reworking traditional black/queer critical aesthet- ics. In these songs, ATR undermine biopolitical neoliberalism’s demand to invest in and intensify regular “normal” life: rather than treating death as a nadir of intensity, they intensify it–that is, they go into the death. This strategy of going “into the death” is one possible queer necropolitical response to neoliberalism. (shrink)

Kruskal proved that finite trees are well-quasi-ordered by hom(e)omorphic embeddability. Friedman observed that this statement is not provable in predicative analysis. Friedman also proposed (see in [Simpson]) some stronger variants of the Kruskal theorem dealing with finite labeled trees under home(e)omorphic embeddability with a certain gap-condition, where labels are arbitrary finite ordinals from a fixed initial segment of ω. The corresponding limit statement, expressing that for all initial segments of ω these labeled trees are well-quasi-ordered, is provable in Π 1 (...) 1 -CA, but not in the analogous theory Π 1 1 -CA 0 with induction restricted to sets. Schutte and Simpson proved that the one-dimensional case of Friedman's limit statement dealing with finite labeled intervals is not provable in Peano arithmetic. However, Friedman's gap-condition fails for finite trees labeled with transfinite ordinals. In [Gordeev 1] I proposed another gap-condition and proved the resulting one-dimensional modified statements for all (countable) transfinite ordinal-labels. The corresponding universal modified one-dimensional statement UM 1 is provable in (in fact, is equivalent to) the familiar theory ATR 0 whose proof-theoretic ordinal is Γ 0 . In [Gordeev 1] I also announced that, in the general case of arbitrarily-branching finite trees labeled with transfinite ordinals, in the proof-theoretic sense the hierarchy of the limit modified statements $\mathbf{M}_{ (which are denoted by LM λ in the present note) is as strong as the hierarchy of the familiar theories of iterated inductive definitions (more precisely, see [Gordeev 1, Concluding Remark 3]). In this note I present a "positive" proof of the full universal modified statement UM, together with a short proof of the crucial "reverse" results which is based on Okada's interpretation of the well-established ordinal notations of Buchholz corresponding to the theories of iterated inductive definitions. Formally the results are summarized in $\S5$ below. (shrink)

A rank function for a directed graph G assigns elements of a well ordering to the vertices of G in a fashion that preserves the order induced by the edges. While topological sortings require a one-to-one matching of vertices and elements of the ordering, rank functions frequently must assign several vertices the same value. Theorems stating basic properties of rank functions vary significantly in logical strength. Using the techniques of reverse mathematics, we present results that require the subsystems ${\ensuremath{\vec{RCA}_0}}$ , (...) ${{\vec{ACA}_0}}$ , ${{\vec{ATR}_0}}$ , and ${{\vec{\Pi^1_1 - CA}_0}}$. (shrink)

We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to $\mathrm {ATR_0}$ from the point of view of reverse mathematics, there is not a canonical way to phrase them as multivalued functions. We identify eight different multivalued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility. In particular one of our functions turns out to be strictly (...) stronger than any previously studied multivalued functions arising from statements around $\mathrm {ATR}_0$. (shrink)

Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use $[\lambda |X]_T^{\rm{\Lambda }}\varphi$ as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.For a set of formulas Γ, define predicative oracle reflection for T over Γ ) to be the schema that asserts that, if X ⊆ ℕ, Λ is a well-order and φ ∈ Γ, then$$\forall \,\lambda (...) < {\rm{\Lambda }}\,.$$In particular, define predicative oracle consistency ) as Pred–O–RFN{0=1}.Our main result is as follows. Let ATR0 be the second-order theory of Arithmetical Transfinite Recursion, ${\rm{RCA}}_0^{\rm{*}}$ be Weakened Recursive Comprehension and ACA be Arithmetical Comprehension with Full Induction. Then,$${\rm{ATR}}_0 \equiv {\rm{RCA}}_0^{\rm{*}} + {\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - RFN}}\,_{{\bf{\Pi }}_2^1 } \left.$$We may even replace ${\rm{RCA}}_0^{\rm{*}}$ by the weaker ECA0, the second-order analogue of Elementary Arithmetic.Thus we characterize ATR0, a theory often considered to embody Predicative Reductionism, in terms of strong reflection and consistency principles. (shrink)

Nigeria is a multi-ethnic and multicultural society, and therefore, Nigeria’s religious inclinations differ broadly. There are currently three religions dominant in Nigeria, namely Christianity, Islam and African Traditional Religion (ATR). These three religions, especially the first two, have demonstrated varying levels of fanaticism in the past leading to many recounted crises and jungle justice incidents in Nigeria. Because of Nigerian politics, we have witnessed the use of armed thugs by politicians to harass and even kill party opponents and displace their (...) families. These two factors have caused many young, highly skilled persons to flee Nigeria for a safer haven. This study therefore tries to review current religious fanaticism and electioneering thuggery leading to loss of lives and property, which consequently sees to the fall of the Nigerian economy and the subsequent enthronement of insecurity in the country. It suggests that these factors are foundational problems consequent to the amalgamation of 1914 and are leading causes for the rapid rate of migration of Nigerian experts out of the country. Contribution: At a time when Nigeria is in dire need of great brains to help in its developmental struggle, politicians and religious bigots have constituted a serious blockade to this ambition. This article is a review of recent political and religious turmoil in Nigeria with a view to call the attention of all warring religious and political stakeholders to the damage their extremism has already caused and to also bring the attention of Nigerians to the foundation of these problems, namely the amalgamation and the need to address it. (shrink)

In a quest for greater coherence between parochial identities, culture and Christianity, there exists an African consciousness which seeks to indigenise and decolonise Christianity. Africans are profoundly religious people who view their faith as part of their way of life, as strengthening their cultures and providing a moral compass for daily living. In efforts to transform society, the Christian religion has played a significant role in the path to African development. Christianity in Africa dates to the very inception of the (...) church. Africans consequently played a crucial role in establishing the doctrines and theology of the early church. While African Traditional religion (ATR) is paramount, it is the purpose of this article to suggest that the Christian faith has and continuous to play a significant role on the African continent in its development. While there are many indigenous African beliefs, these have been to a large extent supported by Christianity in a quest to systematize novel knowledge and promote peace and tolerance across the continent. Many Africans have sought facets of Christianity that are similar to their religious and personal practices and continue to do so. Thus, while there exist numerous similarities and also differences between Christianity and ATR, it is imperative to preserve old-style regional distinctiveness and Christianity as the unifying rudiments in nation building endeavours and in efforts to spread the gospel of Jesus Christ. Africans can and should come to comprehend the Triune Godhead as being consistent with their own spiritual consciousness and existential veracities. Indigenization of Christianity requires enculturation and essentially an understanding that it is indeed ecumenical and also embraces diversity and fundamentally requires viewing Holy Scriptures and the truths they propound as being applicable to any context and cultural milieu across the ages. Christians after all espouse a faith in the Ekklesia or body of Christ for all its people who are the Laos of God. (shrink)

Theorems of hyperarithmetic analysis (THAs) occupy an unusual neighborhood in the realms of reverse mathematics and recursion theoretic complexity. They lie above all the fixed (recursive) iterations of the Turing Jump but below ATR $_{0}$ (and so $\Pi _{1}^{1}$ -CA $_{0}$ or the hyperjump). There is a long history of proof theoretic principles which are THAs. Until Barnes, Goh, and Shore [ta] revealed an array of theorems in graph theory living in this neighborhood, there was only one mathematical denizen. In (...) this paper we introduce a new neighborhood of theorems which are almost theorems of hyperarithmetic analysis (ATHAs). When combined with ACA $_{0}$ they are THAs but on their own they are very weak. We generalize several conservativity classes ( $\Pi _{1}^{1}$, r- $\Pi _{2}^{1}$, and Tanaka) and show that all our examples (and many others) are conservative over RCA $_{0}$ in all these senses and weak in other recursion theoretic ways as well. We provide denizens, both mathematical and logical. These results answer a question raised by Hirschfeldt and reported in Montalbán [2011] by providing a long list of pairs of principles one of which is very weak over RCA $_{0}$ but over ACA $_{0}$ is equivalent to the other which may be strong (THA) or very strong going up a standard hierarchy and at the end being stronger than full second order arithmetic. (shrink)

This article brings into perspective the need to decolonise the concept of the Trinity (as the specific doctrine and Christian name of God) as a crucial step in decolonising the religious education curriculum. It discusses the concept of decolonisation and its applicability to religious education, specifically Christianity, within higher education (e.g. in Teacher Education Programmes) in the South African context. God as the Trinity has throughout the history of Atlantic slavery and colonialism been employed to legitimise colonial rule and it, (...) therefore, needs to be decolonised. To decolonise the concept of the Trinity is, however, highly problematic, as the historic relation between Christianity and African traditional religions (ATRs) indicates. Decolonising the concept of the Trinity can quickly develop into a tension between a position of either continuity or discontinuity (of ATR with Christianity). Contribution: This article argues for an alternative approach for the decolonisation of the concept of the Trinity, namely to allow for the deconstruction of the concept of the Trinity, and by implication of other concepts – like decolonisation and religion – as well. This approach is proposed to develop more openness and playfulness with regard to religious beliefs in general. I argue that this may provide a hopeful, open and just vision of life which should be part of the decolonised religious education curriculum. (shrink)

We show that the theory ATR 0 is equivalent to a second-order generalization of the theory $\widehat{ID}_{ . As a result, ATR 0 is conservative over $\widehat{ID}_{ for arithmetic sentences, though proofs in ATR 0 can be much shorter than their $\widehat{ID}_{ counterparts.

By an algebraic semantics we shall mean a class K of matrices M = for a propositional language L such that D is a singleton, D = fdg. A logic has an algebraic semantics i C =6 ; and there exists an algebraic semantics K strongly adequate for C, i.e., C = CnK. Proposition. If a logic has an algebraic semantics, then every factorial matrix M 2 M atr has the following properties: M is of the form, where 1A 2 (...) A each formula 2 C denes the constant 1A in A, that is, A[a1; : : : ; an] = 1A for any a1; : : : ; an 2 A. (shrink)

This article is about the juxtaposition of the notion of perichoresis in the work and theology of the Cappadocian Fathers and the notion of Ubuntu in the African Traditional Religion. Perichoresis was a result of an attempt to understand and to resolve the relationships within the Trinity. The issue at hand was how to make sense between the one and the many at the same time. The Cappadocian Fathers understood the oneness of God as unity in plurality, not a singularity. (...) One Ousia and three hypostases were based on the understanding of the relationships within the trinity. The question of three yet one God, the apostles according to the information we have never question nor try to resolve the position and status of Jesus within the oneness. It appears as though they celebrated the tension rather than resolving it. They heard from Jesus, who said to them ‘you believe in God believe also in me’ and ‘if you had known me, you would have known my Father also. From now on you do know him and have seen him … whoever has seen me has seen the Father’. They also heard him when he said ‘I am in the Father and the Father is in me’. The article is going to investigate and analyse the two notions, Perichoresis and Ubuntu, within the African Christian context. Yet there is a tension between Jesus and the ancestors. Can this tension be resolved? The notion of Ubuntu is based upon the understanding that a person becomes fully a person in the presence of other persons. It is a notion that deals with the relationships from an individual to the community and from physical to spiritual perspectives. The article shall also attempt to analyse any categories of thinking that are within the ATR that may better explain the relationship within the Trinity. (shrink)

Purpose: The purpose of this article is threefold: First, to present the African traditional ritual concept of salvation. Second, to demonstrate that this concept subconsciously forms the worldview through which African Christians interpret biblical narratives and salvation. Third, to access if certain ecclesiastical practices are influenced by the African salvific expressions. Methodology: The methodology used is exploratory, where aspects of African salvific rituals and selected ecclesiastical practices are explored. Part one of this article deals with African expressions of salvation. Three (...) aspects of salvation in the African Traditional Religion (ATR) are; one- traditional rituals that ward-off evil, two- continuity of life through genealogies and three- consciousness of ancestral spiritual world/living dead. Findings: The findings are that these three are the hallmarks of African worldview as expression of salvation. Part two of the article deals with ecclesiastical interventions, specifically on contextual biblical hermeneutic(s) expounded in worship praxis paved by African worldview. The typological and allegorical hermeneutical theories of biblical interpretation are enriched by traditional African concept of salvation in African Christianity. Contribution to Theory and Practice: In practice the African Church ought to spread the salvation of Jesus Christ through contextually interpreted biblical rituals. (shrink)

This paper addresses the challenging problem of automating the human's intelligent ability to evaluate output from machine translation systems, which are subsystems of Speech-to-Speech MT systems. Conventional automatic MT evaluation methods include BLEU, which MT researchers have frequently used. BLEU is unsuitable for SSMT evaluation for two reasons. First, BLEU assesses errors lightly at the beginning or ending of translations and heavily in the middle, although the assessments should be independent from the positions. Second, BLEU lacks tolerance in accepting colloquial (...) sentences with small errors, although such errors do not prevent us from continuing conversation. In this paper, the authors report a new evaluation method called RED that automatically grades each MT output by using a decision tree. The DT is learned from training examples that are encoded by using multiple edit distances and their grades. The multiple edit distances are normal edit dista nce defined by insertion, deletion, and replacement, as well as extensions of ED. The use of multiple edit distances allows more tolerance than either ED or BLEU. Each evaluated MT output is assigned a grade by using the DT. RED and BLEU were compared for the task of evaluating SSMT systems, which have various performances, on a spoken language corpus, ATR's Basic Travel Expression Corpus. Experimental results showed that RED significantly outperformed BLEU. (shrink)

The Old Testament connects environmental disasters with sin. The expulsion from the paradeiso (Gn 3:23–24), the plagues on Egypt (Ex 7–11) and droughts (Am 4.6; Jr 14:1–7) are all portrayed as linked with sin. Theologically, human sin, therefore, can lead to actions that have adverse effects upon humans and the environment. It is against this reality that this research explores the effects of necrophilia not only upon humans but also on the environment. The argument raised here is that while world (...) leaders are making concerted efforts to achieve gender equality, among other goals by 2030, necrophilia is likely to offset this vision as women continue being reduced to mere sex machines in life and beyond death. Spiritually, as a result of the evil nature of necrophilia, God and the ancestors also are forced to turn their faces from a land where such abomination is practiced, hence exposing the land to environmental catastrophes. Using largely the qualitative approach as well as comparative analysis, the research engages in an informed conversation with African traditional religion (ATR), Christianity and Islam (religions that have a large following in Zimbabwe), examining to what extent they can be used to curb necrophilia. Contribution: The research makes a unique contribution to Religion and/or Theology and Constructions of Earth and Gender through raising an awareness of the high chances of necrophilia offsetting efforts to achieve gender equality by 2030. It also proffers tangible ways of curbing the harmful effects of necrophilia upon human societies and Mother Earth. (shrink)

Recently discovered transcription‐independent features of p53 involve the choice of DNA damage repair pathway after PARylation, and p53's complex formation with phosphoinositide lipids, PI(4,5)P2. PARylation‐mediated rapid accumulation of p53 at DNA damage sites is linked to the recruitment of downstream repair factors and tumor suppression. This links p53's capability to sense damaged DNA in vitro and its relevant functions in cells. Further, PI(4,5)P2 rapidly accumulates at damage sites like p53 and complexes with p53, while it is required for ATR recruitment. (...) These findings help explain how p53 and PI(4,5)P2 maintain genome stability by directing DNA repair pathway choice. Additionally, there is a strong correlation between p53 sequence homology, genome mutation rates as well as lifespans across various mammalian species. Further investigation is required to better understand the connections between genome stability, tumor suppression, longevity and the transcriptional‐independent function of p53. (shrink)

Solovay has shown that if $\cal{O}$ is an open subset of $P(\omega)$ with code $S$ and no infinite set avoids $\cal{O}$ , then there is an infinite set hyperarithmetic in $S$ that lands in $\cal{O}$ . We provide a direct proof of this theorem that is easily formalizable in $ATR_0$.

The musha mukadzi (Shona) or umuzi ngumama (Ndebele) is an African gendered philosophy that means women make up the home. This philosophy has been researched in African traditional religions (ATRs) and is interrogated from interdisciplinary angles in academia. African feminist research has highlighted how this philosophy can be derogatory, stereotyped and oppressive to women if it is naïvely used in domestic contexts. As a result, contemporary African feminists and gender scholars attempt to expose both the liberative and oppressive nature of (...) this philosophy. This study seeks to interrogate how women from the grassroots understand this philosophy. It draws from in-depth interviews with women from Zimunya, Mutare, in Zimbabwe who describe this philosophy as a resource for sustainable livelihoods. Methods used to collect data involved in-depth interviews from a sample of 10 women whose ages ranged from 35 to 50 years. The findings highlight that for both single and married women in Zimunya, the musha mukadzi or umuzi ngumama philosophy has empowering traits that enhance women’s agency and sustainable livelihoods in the domestic household. They describe how this philosophy has empowered them to initiate income-generating projects that include rearing of poultry (road runners), membership to a sewing club, selling dried traditional foods and money savings (mikando).Contributions: This article explores an African gendered philosophy, musha mukadzi or umuzi ngumama [women make the home], and how this has been used as a resource by women in sustaining livelihoods. (shrink)

The musha mukadzi (Shona) or umuzi ngumama (Ndebele) is an African gendered philosophy that means women make up the home. This philosophy has been researched in African traditional religions (ATRs) and is interrogated from interdisciplinary angles in academia. African feminist research has highlighted how this philosophy can be derogatory, stereotyped and oppressive to women if it is naïvely used in domestic contexts. As a result, contemporary African feminists and gender scholars attempt to expose both the liberative and oppressive nature of (...) this philosophy. This study seeks to interrogate how women from the grassroots understand this philosophy. It draws from in-depth interviews with women from Zimunya, Mutare, in Zimbabwe who describe this philosophy as a resource for sustainable livelihoods. Methods used to collect data involved in-depth interviews from a sample of 10 women whose ages ranged from 35 to 50 years. The findings highlight that for both single and married women in Zimunya, the musha mukadzi or umuzi ngumama philosophy has empowering traits that enhance women’s agency and sustainable livelihoods in the domestic household. They describe how this philosophy has empowered them to initiate income-generating projects that include rearing of poultry (road runners), membership to a sewing club, selling dried traditional foods and money savings ( mikando ). Contributions: This article explores an African gendered philosophy, musha mukadzi or umuzi ngumama [women make the home], and how this has been used as a resource by women in sustaining livelihoods. (shrink)

A partial ordering $\mathbb{P}$ is $n$-Ramsey if, for every coloring of $n$-element chains from $\mathbb{P}$ in finitely many colors, $\mathbb{P}$ has a homogeneous subordering isomorphic to $\mathbb{P}$. In their paper on Ramsey properties of the complete binary tree, Chubb, Hirst, and McNicholl ask about Ramsey properties of other partial orderings. They also ask whether there is some Ramsey property for pairs equivalent to $\mathit{ACA}_{0}$ over $\mathit{RCA}_{0}$. A characterization theorem for finite-level partial orderings with Ramsey properties has been proven by the (...) second author. We show, over $\mathit{RCA}_{0}$, that one direction of the equivalence given by this theorem is equivalent to $\mathit{ACA}_{0}$, and the other is provable in $\mathit{ATR}_{0}$. We answer Chubb, Hirst, and McNicholl’s second question by showing that there is a primitive recursive partial ordering $\mathbb{P}$ such that, over $\mathit{RCA}_{0}$, “$\mathbb{P}$ is 2-Ramsey” is equivalent to $\mathit{ACA}_{0}$. (shrink)

E l auto r de f iend e un a democraci a a r mónica , qu e n o e s u n model o nu ev o d e democracia sin o l a relació n equilibrad a d e la s do s modalidade s clásica s d e democracia , l a representat iv a y l a directa , a la s qu e s e añadirí a l a democraci a pa r ticipat iv (...) a prom o vid a po r lo s ciudadanos, ind i vidualment e o e n gr upo , a l ma r ge n d e lo s pa r tido s políticos . L a resultant e serí a un nu evo marc o polític o co n meno s democraci a representat iva (l a d e lo s pa r tido s político s y lo s representante s electos) , q u e actualment e e s l a democraci a e xclus iva y e xclu y ent e en la s sociedade s política s a v anzadas , má s democraci a direct a (l a d e lo s ciudadano s qu e sin inte r mediario s v otaría n política s y n o sól o a su s representantes ) y u n nu evo espaci o polític o ocupad o po r lo s ciudadanos-actore s político s si n militanci a pa r tidista . E n cad a uno d e esto s tre s modelo s democrático s s e analiz a l a de f inició n de l modelo , e l escenari o que actualment e atr a vies a y la s propuesta s concreta s d e cambio. (shrink)