It is well known that the dynamical behavior of a rational map $f:\widehat {\mathbb C}\to \widehat {\mathbb C}$ is governed by the forward orbits of the critical points of f. The map f is said to be postcritically finite if every critical point has finite forward orbit, or equivalently, if every critical point eventually maps into a periodic cycle of f. We encode the orbits of the critical points of f with a finite directed graph called a ramification portrait. In this article, we study which graphs arise as ramification portraits. We prove that every abstract polynomial ramification portrait is realized as the ramification portrait of a postcritically finite polynomial and classify which abstract polynomial ramification portraits can only be realized by unobstructed maps.

The blue gum chalcid (Leptocybe invasa) is a serious invasive, galling insect pest of eucalypts grown outside Australia. Variability in resistance of species and genotypes of Eucalyptus to the pest is widely reported but without consideration of the influence of silviculture on the severity of galling. We assessed the variability of gall expression by 29 genotypes of E. camaldulensis by L. invasa in common nursery experiments and in 5 common garden arboreta planted in diverse climatic zones and soil types around Kenya. We quantified variation in growth and the concentrations of defensive chemical compounds (namely polyphenolic compounds) to assess possible genotype × environment interactions which we also relate to the climate of the parent seed trees in Australia. Generally, genotypes endemic to low latitude regions of Australia were more resistant to the pest while the concentration of quinic acid derivatives (QUIN) exhibited an interaction with arboretum location in Kenya. The concentration of QUIN in potted plants did not vary significantly with nitrogen supplementation. However, growth rates and total polyphenolic concentrations varied with arboretum location. Since QUIN, which have been previously shown to confer resistance against L. invasa, did not vary in different arboreta, resistant subspecies and genotypes of E. camaldulensis can be deployed in novel habitats and will not be galled. Our findings support the critical need to plant stock of known genotype(s) rather than planting stock grown from locally collected seed. This will require the establishment of eucalypt seed orchards if clonal production of planting stock is not possible.

Recently, social philosophers have argued for a practice-based social ontology that can furnish a robustly social account of oppression and, in turn, illuminate the obstacles to and possibilities for social change. This paper argues for an intersubjective approach to oppressive social practices. Oppressive meanings constitute relationships between agents in ways they neither choose nor decide on; agents uphold those meanings through their relationships to others. This approach, I argue, can illuminate a critical case of an oppressive social practice that revolves around struggles for recognition and the dynamics of social change.

Applying the New Entrepreneurial History framework, this paper examines how ArcBest Corporation, an integrated logistics firm based in Fort Smith, Arkansas, became the last legacy less-than-load (LTL) carrier operating in the United States. It argues that the firm’s enduring viability is partially the product of an internal distributed agency among executives over a century that involved continual entrepreneurial processes: Envisioning and valuing opportunities informed by the multiplicative form of values, strategically reallocating and reconfiguring resources, and legitimizing novelty to stakeholders in response to profound market and regulatory shifts. These entrepreneurial processes, paired with the company’s commitments to a unionized labor force, informed executives’ strategic decisions that transformed the carrier from a regional hauler into a national, technologically sophisticated, integrated logistics provider. In applying the new entrepreneurial history to ArcBest, it considers how entrepreneurial opportunities are enacted within the context of a single firm over time.

For $\lambda $ inaccessible, we show that “there is a nowhere trivial automorphism of $\mathcal P(\lambda )/[\lambda ]^{<\lambda }$” follows (in ZFC) from $2^\lambda =\lambda ^+$, and is consistent (via forcing) with $2^\lambda>\lambda ^+$.

This study seeks to elucidate the historical development and transmission of the traditions associated with the ‘Seven Sets’ through a cross-textual analysis of Pali, Sanskrit, Chinese, Tibetan, and Gāndhārī sources. The Seven Sets comprise the four establishings of mindfulness, the four right endeavors/abandonings, the four bases of success, the five faculties, the five powers, the seven factors of awakening, and the noble eightfold path. The Eight-Set tradition emerged alongside the Seven-Set tradition by the second century, followed by the forty-one and forty-three dharmas contributing to awakening (bodhipakkhiya/bodhipakṣya) by the fifth century. However, the Seven Sets became the most dominant. Both the Vaibhāṣika and Mahāvihāra schools upheld the Seven Sets as the definitive framework for the dharmas contributing to awakening, rejecting any additional items. The Vaibhāṣika dismissed the forty-one dharmas as heretical, whereas the Mahāvihāra excluded the four meditations incorporated into the Eight Sets. After the sixth century, the Eight-Set tradition was subsumed by the Seven-Set tradition. No evidence supports the long-term survival of the other two traditions. The dominance of the Seven Sets reflects the transition in South Asian Buddhism from pluralism to doctrinal unity.

This article was presented as the Presidential Address at the North American Conference on British Studies in Montreal in November 2025.

Let p and q be two primes with $(p,q)\equiv (1,5)$ or $(7,3) \pmod 8$. Lagrange [‘Nombres congruents et courbes elliptiques’, Séminaire Delange-Pisot-Poitou. Théorie des Nombres 16(1) (1974–1975), Article no. 16] and Qin [‘Congruent numbers, quadratic forms and $K_2$’, Math. Ann. 383(3–4) (2022), 1647–1686] showed that if $(\frac {q}{p})=-1$, then $2pq$ is not a congruent number. By using Qin’s method, we prove that if $(p,q)\equiv (1,5) \pmod 8$ and $(\frac {q}{p})=1$ with $h(-pq)\not \equiv p-1 \pmod {16}$, then $2pq$ is not a congruent number; if $(p,q)\equiv (7,3) \pmod 8$ and $(\frac {q}{p})=1$ with $h(-2pq)\not \equiv p+1 \pmod {16}$, then $2pq$ is not a congruent number. Here, $h(-d)$ denotes the class number of the imaginary quadratic field $\mathbb {Q}(\sqrt {-d})$.

Nies and Scholz formalized the notion of an infinite qubitstring and referred to it as a ‘state’. They defined ‘quantum Martin-Löf randomness’ for states. We give a notion of measurement of a state in a computable basis and introduce ‘quantum measurement randomness’, a randomness notion for states. A state is quantum measurement random if measuring it in any computable basis yields a Martin-Löf random bitstring with probability one. Our main result is that quantum Martin-Löf randomness strictly implies quantum measurement randomness. This uses the construction of a quantum measurement random state which is not quantum Martin-Löf random. We prove two general results on which this construction relies: The first concerns Martin-Löf randomness relative to computable measures and extends a result of V. Vovk. The second is a combinatorial result about Kronecker products.