Weighted Envy-freeness in Indivisible Item Allocation

We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. We propose two variants of weighted envy-freeness up to one item (WEF1): strong , where envy can be eliminated by removing an item from the envied agent’s bundle, and weak , where envy can be eliminated either by removing an item (as in the strong version) or by replicating an item from the envied agent’s bundle in the envying agent’s bundle. We show that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists and can be computed in pseudo-polynomial time; moreover, an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1, but it always satisfies the weak version of the property. Moreover, we establish that a generalization of the round-robin picking sequence algorithm produces in polynomial time a strongly WEF1 allocation for an arbitrary number of agents; for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the adjusted winner procedure. Our work highlights several aspects in which weighted fair division is richer and more challenging than its unweighted counterpart.

A geometric approach to Quillen’s conjecture

We introduce admissible collections for a finite group 𝐺 and use them to prove that most of the finite classical groups in non-defining characteristic satisfy the Quillen dimension at 𝑝 property, a strong version of Quillen’s conjecture, at a given odd prime divisor 𝑝 of | G | \lvert G\rvert . Compared to the methods in [M. Aschbacher and S. D. Smith, On Quillen’s conjecture for the 𝑝-groups complex, Ann. of Math. (2) 137 (1993), 3, 473–529], our techniques are simpler.

“The New State That We Are Building”: Authoritarianism and System-Justification in an Illiberal Democracy

The authoritarian personality is characterized by unquestionining obedience and respect to authority. System justification theory (SJT) argues that people are motivated to defend, bolster, and justify aspects of existing social, economic, and political systems. Commitment to the status quo is also a key characteristic of the authoritarian personality. It can be argued that the social context matters for how an underlying latent authoritarian character is expressed. This means that authoritarian regimes could be expected to lead to increased authoritarianism and stronger system-justification. We investigated this hypothesis in two representative samples of Hungarians, collected before (2010) and after (2018) 8 years of Fidesz’ rule (N = 1,000 in both samples). Moreover, the strong version of SJT argues that members of disadvantaged groups are likely to experience the most cognitive dissonance and that the need to reduce this dissonance makes them the most supportive of the status quo. This argument dovetails nicely with claims made by the political opposition to Fidesz, according to which Fidesz is especially popular among low-status members of society. We found that measures assessing authoritarian tendencies did not change between 2010 and 2018. However, more specific beliefs and attitudes did change, and these effects were especially pronounced among Fidesz supporters. Their belief in a just world and a just system has grown stronger, while their attitudes toward migrants had hardened. Low status was associated with lower levels of system-justifying ideologies. However, low status Fidesz voters justified the system more than high status opposition voters in 2018, lending some support for the strong version of SJT. Our results suggest that beliefs and attitudes of Hungarians have changed between 2010 and 2018, and that political leadership played a crucial role in this.

The Use of the Progressive in Light of the AH in Monolingual EFL-Instructed Spanish Learners at University Level: A Longitudinal Learner Corpus-Based SLA Study

Despite recent interest in the analysis of the progressive in light of the Aspect Hypothesis (AH), little information is available on the use of the progressive by EFL Spanish learners. To gain a better understanding of the use of the progressive in EFL-instructed Spanish learner writing at advanced levels, this longitudinal learner corpus-based SLA study examines the frequency of use of the progressive, as well as two of the associations of the AH: (i) the progressive with dynamic verbs; (ii) and, no overextension of the progressive to stative verbs. The effects derived from factors or variables such as the tense employed, target- and non-target-like uses, students’ academic year and expected higher proficiency level, task type and individual preferences are also discussed as a way to fine-tuning the strong version of the AH to the use of the progressive by this learner group

Urban Environmental Legislation and Green Innovation

With the panel data of 218 prefecture-level cities from 2003 to 2017, this paper empirically tested whether urban environmental legislation realized Porter Hypothesis(PH) in China. After a series of model estimation and robustness tests, the results show that urban environmental legislation increased the number of local green patents, which means that the weak Porter Hypothesis was established. However, the urban environmental legislation did not lead to an increase in green total factor productivity(GTFP). In other words, the strong version of PH did not hold. Further analysis shows that urban environmental legislation led to the decline of GTFP and the increase of green patents in the west of China, but not in the east and central cities. Besides, the legislation did not promote GTFP improvement through green innovation in the short term, which means it did not realize process compensation.

Rowan Williams’s Christ the Heart of Creation

This article engages Rowan Williams’s Christ the Heart of Creation. Its first section is interpretative. It reads Williams’s book as commending a noncompetitive account of divine and creaturely activity, a strong version of divine aseity, and an expansive ecclesiological-ethical vision. A second section lauds the breadth of Williams’s perspective and his commitment to public intellectual witness. A third section focuses on critique. It draws on Barth in order to advocate a more capacious approach to theological ontology than Williams allows; and it draws on liberationist insights to lend Williams’s christological program a sharper political edge.

Strict/Tolerant Logics Built Using Generalized Weak Kleene Logics

This paper continues my work of [9], which showed there was a broad family of many valued logics that have a strict/tolerant counterpart. Here we consider a generalization of weak Kleene three valued logic, instead of the strong version that was background for that earlier work. We explain the intuition behind that generalization, then determine a subclass of strict/tolerant structures in which a generalization of weak Kleene logic produces the same results that the strong Kleene generalization did. This paper provides much background, but is not self-contained. Some results from [9] are called on, and are not reproved here. [9] Melvin C. Fitting. “A Family of Strict/Tolerant Logics”. In: Journal of Philosophical Logic (2020). Online. Print publication forthcoming.

Considerations for Goldbach's Strong Conjecture

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.

Considerations for Goldbach's Strong Conjecture

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.

Projections of Poisson cut-outs in the Heisenberg group and the visual 3-sphere

We study projectional properties of Poisson cut-out sets E in non-Euclidean spaces. In the first Heisenbeg group \[\mathbb{H} = \mathbb{C} \times \mathbb{R}\] , endowed with the Korányi metric, we show that the Hausdorff dimension of the vertical projection \[\pi (E)\] (projection along the center of \[\mathbb{H}\] ) almost surely equals \[\min \{ 2,{\dim _\operatorname{H} }(E)\} \] and that \[\pi (E)\] has non-empty interior if \[{\dim _{\text{H}}}(E) > 2\] . As a corollary, this allows us to determine the Hausdorff dimension of E with respect to the Euclidean metric in terms of its Heisenberg Hausdorff dimension \[{\dim _{\text{H}}}(E)\] . We also study projections in the one-point compactification of the Heisenberg group, that is, the 3-sphere \[{{\text{S}}^3}\] endowed with the visual metric d obtained by identifying \[{{\text{S}}^3}\] with the boundary of the complex hyperbolic plane. In \[{{\text{S}}^3}\] , we prove a projection result that holds simultaneously for all radial projections (projections along so called “chains”). This shows that the Poisson cut-outs in \[{{\text{S}}^3}\] satisfy a strong version of the Marstrand’s projection theorem, without any exceptional directions.