New Results on EP Elements in Rings with Involution

In this paper, we mainly give characterizations of EP elements in terms of equations. In addition, a related notion named a central EP element is defined and investigated. Finally, we focus on characterizations of a generalized EP element, i.e., [Formula: see text]-DMP element.

Sequential metric dimension for random graphs

In the localization game on a graph, the goal is to find a fixed but unknown target node $v^\star$ with the least number of distance queries possible. In the jth step of the game, the player queries a single node $v_j$ and receives, as an answer to their query, the distance between the nodes $v_j$ and $v^\star$ . The sequential metric dimension (SMD) is the minimal number of queries that the player needs to guess the target with absolute certainty, no matter where the target is.The term SMD originates from the related notion of metric dimension (MD), which can be defined the same way as the SMD except that the player’s queries are non-adaptive. In this work we extend the results of Bollobás, Mitsche, and Prałat [4] on the MD of Erdős–Rényi graphs to the SMD. We find that, in connected Erdős–Rényi graphs, the MD and the SMD are a constant factor apart. For the lower bound we present a clean analysis by combining tools developed for the MD and a novel coupling argument. For the upper bound we show that a strategy that greedily minimizes the number of candidate targets in each step uses asymptotically optimal queries in Erdős–Rényi graphs. Connections with source localization, binary search on graphs, and the birthday problem are discussed.

Species and Salvation: Theology of History in the Anthropocene?

In this article I will discuss various thoughts of a few recent representatives of the tradition of the philosophy of history—Heinz Dieter Kittsteiner, Ulrich Beck, and finally Karl Rahner—and bring them into a conversation with Dipesh Chakrabarty's work on the problems of human species history and the Anthropocene. The aim of this undertaking is to gain greater clarity on the question of the work that theology continues to do for historical thought. I argue that Rahner's notions about “inclusivism”—according to which the possibility of salvation is vested in the species history of humanity rather than in the history of Christian revelation—and his related notion of an irresolvable tension between “anonymous” and what one might then call “onomastic” histories signal the continuing significance of a theology of the baptismal sacrament for historical thought. Rereading Rahner's thought sheds light on certain quandaries of the Anthropocene discussion, regarding the way in which species history can be related to other kinds of history writing, and the novel opening for theodicy generated by the breakdown of the culture–nature divide.

Structure and Colour in Triangle-Free Graphs

Motivated by a recent conjecture of the first author, we prove that every properly coloured triangle-free graph of chromatic number $\chi$ contains a rainbow independent set of size $\lceil\frac12\chi\rceil$. This is sharp up to a factor $2$. This result and its short proof have implications for the related notion of chromatic discrepancy. Drawing inspiration from both structural and extremal graph theory, we conjecture that every triangle-free graph of chromatic number $\chi$ contains an induced cycle of length $\Omega(\chi\log\chi)$ as $\chi\to\infty$. Even if one only demands an induced path of length $\Omega(\chi\log\chi)$, the conclusion would be sharp up to a constant multiple. We prove it for regular girth $5$ graphs and for girth $21$ graphs. As a common strengthening of the induced paths form of this conjecture and of Johansson's theorem (1996), we posit the existence of some $c >0$ such that for every forest $H$ on $D$ vertices, every triangle-free and induced $H$-free graph has chromatic number at most $c D/\log D$. We prove this assertion with 'triangle-free' replaced by 'regular girth 5'.

Language Complexity in Historical Perspective: The Enduring Tropes of Natural Growth and Abnormal Contact

Focusing on the work of John McWhorter and, to a lesser extent, Peter Trudgill, this paper critically examines some common themes in language complexity research from the perspective of intellectual history. The present-day conception that increase in language complexity is somehow a “natural” process which is disturbed under the “abnormal” circumstances of language contact is shown to be a recapitulation of essentially Romantic ideas that go back to the beginnings of disciplinary linguistics. A similar genealogy is demonstrated for the related notion that grammatical complexity is a kind of “ornament” on language, surplus to the needs of “basic communication.” The paper closes by examining the implications of these ideas for linguistic scholarship.

Dispensing Antiretrovirals During Covid-19 Lockdown: Pathways to Health System Resilience in Uganda

INTRODUCTIONAlthough there is an emerging evidence base on the impact of Covid-19 pandemic on access to health services in low-and middle-income countries, the related notion of health system resilience has received little empirical attention. The objective of this study was to explore health system resilience at the sub-national level in Uganda with regard to strategies for dispensing of antiretrovirals during Covid-19 lockdown restrictions.METHODSWe conducted a qualitative case-study of eight districts from Eastern Uganda (Mbale, Sironko, Manafwa, Bulambuli, Bududa) and Western Uganda (Kabarole, Kyegegwa, Kyenjonjo) purposively selected due to having a relatively high HIV burden. Between June and September 2020, we conducted key informant interviews with district health team leaders (n=9), with ART clinic managers (n=36), representatives of PEPFAR implementing organizations (n=6) and six focus group discussions with recipients of HIV/AIDS care (48 participants). Qualitative data were analyzed using thematic approach.RESULTSFive broad strategies for distributing antiretrovirals during ‘lockdown’ emerged in our analysis: accelerating home-based antiretroviral therapy (ART) deliveries,; extending multi-month dispensing from three to six months for stable patients; leveraging the Community Drug Distribution Points (CDDPs) model for ART refill pick-ups at outreach sites in the community; an increased reliance on health information systems, including geospatial technologies, to support ART refill distribution in unmapped rural settings. District health teams reported benefiting from the Covid-19 outbreak response funding to deliver ART refills to homesteads in rural communities.CONCLUSIONAlthough Covid-19 ‘lockdown’ undoubtedly impeded access to facility-based HIV services, it unraveled new possibilities and innovations in the distribution of antiretrovirals in the predominantly rural settings of our case-study districts. Further research is recommended to evaluate the potential of home-based deliveries as an alternative differentiated ART delivery model in Uganda and other countries with a high HIV burden.

Maximality and collapse in the hierarchy of α-c.a. degrees

In (A Hierarchy of Turing Degrees: A Transfinite Hierarchy of Lowness Notions in the Computably Enumerable Degrees, Unifying Classes, and Natural Definability (2020), Annals of Mathematics Studies, Princeton University Press), Downey and Greenberg define a transfinite hierarchy of low 2 c.e. degrees – the totally α-c.a. degrees, for appropriately small ordinals α. This new hierarchy is of particular interest because it has already given rise to several natural definability results, and provides a new definable antichain in the c.e. degrees. Several levels of this hierarchy contain maximal degrees. We discuss how maximality interacts with upper cones, and the related notion of hierarchy collapse in upper cones. For example, we show that there is a totally ω-c.a. degree above which there is no maximal totally ω-c.a. degree.

Perceived Corruption and Trust in Government

Chapter 4 examines the relationship between perceptions of corruption and trust in government. The analysis begins by reviewing variation in levels of trust over time, and proceeds to an estimation of the relationship between perceptions of corruption and trust, as posited by the Court. This chapter also tests the Court’s assumption that states with more substantial campaign finance regulations will evince greater trust in government. Finally, it examines the related notion—implicitly suggested by the Court’s teleology—that lower levels of campaign spending are likely to be associated with greater trust in government. The data are not consistently supportive of this line of reasoning. After accounting for endogeneity, the empirical model shows that perceived corruption does not have a significant impact on trust in government.

Tracking—A

This chapter explains how to estimate an unobserved random variable or vector from available observations. This problem arises in many examples, as illustrated in Sect. 9.1. The basic problem is defined in Sect. 9.2. One commonly used approach is the linear least squares estimate explained in Sect. 9.3. A related notion is the linear regression covered in Sect. 9.4. Section 9.5 comments on the problem of overfitting. Sections 9.6 and 9.7 explain the minimum means squares estimate that may be a nonlinear function of the observations and the remarkable fact that it is linear for jointly Gaussian random variables. Section 9.8 is devoted to the Kalman filter, which is a recursive algorithm for calculating the linear least squares estimate of the state of a system given previous observations.

The Welfare of Each and Everyone in Russian Legal Theory

The prerequisite for the study was the spread of views in the academic literature that the category of public welfare, without accounting for concretising factors, was a void abstraction, and that in Russia, public welfare was seen as the dominant principle over the individual. The main purpose of the study is to analyse the content of the term ‘the welfare of each and everyone’ in Russian legal theory. The author uses the methods of conceptual history and intellectual history to analyse the concept of ‘the welfare of each and everyone’ in the works of pre-revolutionary authors and the relationship between the concepts of ‘the welfare of each and everyone’ and ‘the common good’. The author determined that: ‘public welfare’ can be classified as fiction, purpose, method, interest and balance, depending on the context of use and semantic scope. The term ‘the welfare of each and every one’ became theoretically meaningful (as an objective, method, and interest), and was enshrined in law in Russian Empire in the XVIII -early XX centuries. The term was understood as achieving the common good, preserving the good of everyone and the reduction of public harm. Twentyfirst century Russian legal theory uses the related notion of ‘public welfare’, understood as a fiction, a goal, a method, an interest, a balance. The main findings of the study suggest that today the ‘public welfare’ is reduced to bringing benefits to anyone and everyone (D. I. Dedov), which is close to the historical understanding of ‘the welfare of each and every one’. The public welfare theory incorporates progressive elements such as the veil of ignorance, the win-win principle, and shapes institutions, resources, practices and formulates the issue of the emergence of a new generation of human rights.