We present a novel approach to synthesizing recursive functional programs from input–output examples. Synthesizing a recursive function is challenging because recursive subexpressions should be constructed while the target function has not been fully defined yet. We address this challenge by using a new technique we call block-based pruning. A block refers to a recursion- and conditional-free expression (i.e., straight-line code) that yields an output from a particular input. We first synthesize as many blocks as possible for each input–output example, and then we explore the space of recursive programs, pruning candidates that are inconsistent with the blocks. Our method is based on an efficient version space learning, thereby effectively dealing with a possibly enormous number of blocks. In addition, we present a method that uses sampled input–output behaviors of library functions to enable a goal-directed search for a recursive program using the library. We have implemented our approach in a system called Trio and evaluated it on synthesis tasks from prior work and on new tasks. Our experiments show that Trio significantly outperforms prior work.

The semiotic construction of corporate persons in law is key to the contemporary organization of global capitalism. The economic capacities enjoyed by corporations stem significantly from how the semiotics of corporate personhood work within domestic and international legal orders fundamentally designed for human persons. Signs (especially in documents—laws, incorporation papers, tax filings, etc.) construct corporations as legal persons—entities modeled on human persons yet differently bound to human embodiment. Corporations multiply themselves through the creation of legally independent corporate persons (“subsidiaries”), while unifying themselves through their control over these persons. Unlike human offspring, corporations’ corporate offspring are easily created, may take up residence in almost any jurisdiction, and always obey their parents. The paper will discuss the implications of these features of corporations with respect to tort liability, international trade, property, taxation, and private militaries.

While research shows that public preferences across policy domains tend to move in parallel, the mechanisms behind this dynamic remain unclear. We examine four explanations: (1) alignment in preferred policy levels; (2) parallel policy movement combined with domain-specific thermostatic feedback; (3) feedback to global policy across domains; and (4) responsiveness to presidential partisanship. These mechanisms matter for how we interpret public opinion change and policy responsiveness. We develop and test a theoretical model using data on four social spending domains in the USA. Our findings suggest that spending mood reflects both parallelism in preferred policy levels and responsiveness to overall social spending and presidential party affiliation.

In the UK, parents receiving working-age social security benefits have been the target of intensifying labour market activation policies, particularly following the introduction of Universal Credit (UC). Concurrently, state support for parents has reduced, and help with childcare is complex and limited. Under UC, parents, and increasingly mothers, are meeting more often with street-level agents, Work Coaches, who are responsible for ‘activating’ parents into work. Work Coaches operate at the interface between the state and citizens, but we know little about street-level implementation of UC. Through analysing interviews with ten Work Coaches and sixty-seven parents, this article draws on a gendered street-level approach to explore how policy limits choices for Work Coaches (by restricting spaces for personalisation) and parents (by rules determining how to manage work and care responsibilities). Within this rigid context, moral assumptions of low-income parents emerge, with increased expectations placed on mothers and outdated assumptions about fathers.

We introduce a set of axioms for locally topologically ordered quantum spin systems in terms of nets of local ground state projections, and we show they are satisfied by Kitaev’s Toric Code and Levin-Wen type models. For a locally topologically ordered spin system on $\mathbb {Z}^{k}$, we define a local net of boundary algebras on $\mathbb {Z}^{k-1}$, which provides a mathematically precise algebraic description of the holographic dual of the bulk topological order. We construct a canonical quantum channel so that states on the boundary quasi-local algebra parameterize bulk-boundary states without reference to a boundary Hamiltonian. As a corollary, we obtain a new proof of a recent result of Ogata [Oga24] that the bulk cone von Neumann algebra in the Toric Code is of type $\mathrm {II}$, and we show that Levin-Wen models can have cone algebras of type $\mathrm {III}$. Finally, we argue that the braided tensor category of DHR bimodules for the net of boundary algebras characterizes the bulk topological order in (2+1)D, and can also be used to characterize the topological order of boundary states.

This article re-examines archaic and classical treatment of beer drinking to argue, contra Nelson, that beer in archaic and classical Greek texts is not primarily feminine nor does it necessarily feminize its drinkers. Rather, a review of sympotic lyric, historiography, ethnography and Athenian drama demonstrates that beer is primarily an ethnic marker with no inherent gendered connotations. At the same time, in contexts where definitions of Greek masculinity are being constructed, beer can gain gendered connotations which enhance the ethnic otherness of the beverage and contribute to the definition of the Greek man. Any gendered implications of beer, furthermore, come not from the beverage itself but from the method of consumption, of sucking through a tube of sorts rather than sipping from a cup. This article thus argues that beer in the Archaic and Classical periods marks non-Greek status first and foremost and only secondarily effeminizes drinkers through associations with oral sex in contexts where ideas of masculinity are in play.

Martin, Mossinghoff, and Trudgian [19] recently introduced a family of arithmetic functions called “fake $\mu $’s,” which are multiplicative functions for which there is a $\{-1,0,1\}$-valued sequence $(\varepsilon _j)_{j=1}^{\infty }$ such that $f(p^j) = \varepsilon _j$ for all primes p. They investigated comparative number-theoretic results for fake $\mu $’s and, in particular, proved oscillation results at scale $\sqrt {x}$ for the summatory functions of fake $\mu $’s with $\varepsilon _1=-1$ and $\varepsilon _2=1$. In this article, we establish new oscillation results for the summatory functions of all nontrivial fake $\mu $’s at scales $x^{1/2\ell }$ where $\ell $ is a positive integer (the “critical index”) depending on f; for $\ell =1$ this recovers the oscillation results in [19]. Our work also recovers results on the indicator functions of powerfree and powerfull numbers; we generalize techniques applied to each of these examples to extend to all fake $\mu $’s.

We prove the existence of small-amplitude periodic travelling waves in dimer Fermi–Pasta–Ulam–Tsingou (FPUT) lattices without assumptions of physical symmetry. Such lattices are infinite, one-dimensional chains of coupled particles in which the particle masses and/or the potentials of the coupling springs can alternate. Previously, periodic travelling waves were constructed in a variety of limiting regimes for the symmetric mass and spring dimers, in which only one kind of material data alternates. The new results discussed here remove the symmetry assumptions by exploiting the gradient structure and translation invariance of the travelling wave problem. Together, these features eliminate certain solvability conditions that symmetry would otherwise manage and facilitate a bifurcation argument involving a two-dimensional kernel and cokernel.

The Underworld is a ‘shared space’ for poets and their poems, but one that exists on different timelines to Upperworld spaces, such that it is built on cyclicality rather than linearity. In this article, I explore the cycles within and between the homoerotic Underworld poetry of Tibullus, Domitius Marsus, Ovid and Statius. Using a combination of traditional philology and queer temporal approaches, I show how characters ‘recycle’ through these texts, so that Tibullus’ Marathus cycles into Statius’ Philetus through metapoetic metempsychosis. I begin with the role of the Underworld in Latin poetry, before turning to Tibullus’ death, as commemorated by Ovid and Marsus. Next, I explore how Tibullus ‘kills’ Marathus, so that Ovid can hint at his being in the Underworld. Finally, I turn to Statius’ poem on Philetus to show how it continues the cycles of earlier poetry, before concluding with a discussion of the consequences of Elysium’s queerness.

Polymorphism, the occurrence of different morphs of a trait within the population of a single species, plays a crucial role in species diversification, genetic variation, and adaptation. Detecting polymorphism in a single character helps us to understand population dynamics, particularly in species that inhabit diverse environments. However, detecting polymorphisms in fossil taxa is challenging due to the fragmentary and incomplete records. Dimorphism, defined as the occurrence of different morphs of a trait within the population of a single species, represents the simplest and most common form of polymorphism. This study focuses on dimorphism instead of polymorphism, which allows for a more streamlined analysis. We use computational simulation experiments to estimate the minimum sample size required to detect bimodal distribution in univariate morphological variables. We describe the morphological diversity of a measured variable (e.g., body mass or skeletal length) as a probability density distribution with specific parameter sets. Subsequently, we simulate the diversity of the measured variable with varying sample sizes and conduct resampling procedures to ensure the robustness. Four key parameters that characterize the probability distribution are identified as having significant influence on the minimum sample size for dimorphism recognition. According to the simulation experiments, a model is built to estimate the minimum sample size for dimorphism recognition based on these parameters. A dataset from extant avian and reptilian species is used to test the model. Furthermore, we calculate a reference for the minimal sample size required for assessing phenotypic dimorphism in fossil avian taxa by applying parameters derived from extant avian species.

Molecular evidence (28S DNA) has suggested that Triplotaenia undosa from macropodid marsupials is a species complex. Additional data (cox 1) presented in this study confirmed the hypothesis and a morphological examination of all available specimens identified a new species, T. macropodis sp. nov., in the grey kangaroos Macropus fuliginosus and M. giganteus as well as the tammar wallaby, Notamacropus eugenii, and the red kangaroo, Osphranter rufus. The new species differs in the ratio of the number of testes to the number of female genital complexes. Specimens of T. undosa from the swamp wallaby, Wallabia bicolor, the type host, and the common wallaroo, Osphranter robustus, are each genetically distinct, but the fixed material from O. robustus is too fragmentary to permit a detailed morphological description. An amended description and new illustrations of T. undosa from W. bicolor are provided.