Understanding how time averaging changes during burial is essential for using Holocene and Anthropocene cores to analyze ecosystem change, given the many ways in which time averaging affects biodiversity measures. Here, we use transition-rate matrices to explore how the extent of time averaging changes downcore as shells transit through a taphonomically complex mixed layer into permanently buried historical layers: this is a null model, without any temporal changes in rates of sedimentation or bioturbation, to contrast with downcore patterns that might be produced by human activity. Assuming stochastic burial and exhumation movements of shells between increments within the mixed layer and stochastic disintegration within increments, we find that almost all combinations of net sedimentation, mixing, and disintegration produce a downcore increase in time averaging (interquartile range [IQR] of shell ages), this trend is typically associated with a decrease in kurtosis and skewness and by a shift from right-skewed to symmetrical age distributions. A downcore increase in time averaging is thus the null expectation wherever bioturbation generates an internally structured mixed layer (i.e., a surface, well-mixed layer is underlain by an incompletely mixed layer): under these conditions, shells are mixed throughout the entire mixed layer at a slower rate than they are buried below it by sedimentation. This downcore trend created by mixing is further amplified by the downcore decline in disintegration rate. We find that transition-rate matrices accurately reproduce the downcore changes in IQR, skewness, and kurtosis observed in bivalve assemblages from the southern California shelf. The right-skewed shell age-frequency distributions typical of surface death assemblages—the focus of most actualistic research—might be fossilized under exceptional conditions of episodic anoxia or sudden burial. However, such right-skewed assemblages will typically not survive transit through the surface mixed layer into subsurface historical layers: they are geologically transient. The deep-time fossil record will be dominated instead by the more time-averaged assemblages with weakly skewed age distributions that form in the lower parts of the mixed layer.

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper.

We answer some questions about graphs that are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership $x\in y\in x$ . We show that there are continuum-many such graphs, and study their connected components. We describe their complete theories and prove that each has continuum-many countable models, some of which are not reducts of models of Anti-Foundation.

The Variables and Slow Transients Survey (VAST) on the Australian Square Kilometre Array Pathfinder (ASKAP) is designed to detect highly variable and transient radio sources on timescales from 5 s to $\sim\!5$ yr. In this paper, we present the survey description, observation strategy and initial results from the VAST Phase I Pilot Survey. This pilot survey consists of $\sim\!162$ h of observations conducted at a central frequency of 888 MHz between 2019 August and 2020 August, with a typical rms sensitivity of $0.24\ \mathrm{mJy\ beam}^{-1}$ and angular resolution of $12-20$ arcseconds. There are 113 fields, each of which was observed for 12 min integration time, with between 5 and 13 repeats, with cadences between 1 day and 8 months. The total area of the pilot survey footprint is 5 131 square degrees, covering six distinct regions of the sky. An initial search of two of these regions, totalling 1 646 square degrees, revealed 28 highly variable and/or transient sources. Seven of these are known pulsars, including the millisecond pulsar J2039–5617. Another seven are stars, four of which have no previously reported radio detection (SCR J0533–4257, LEHPM 2-783, UCAC3 89–412162 and 2MASS J22414436–6119311). Of the remaining 14 sources, two are active galactic nuclei, six are associated with galaxies and the other six have no multi-wavelength counterparts and are yet to be identified.

The recent increase in well-localised fast radio bursts (FRBs) has facilitated in-depth studies of global FRB host properties, the source circumburst medium, and the potential impacts of these environments on the burst properties. The Australian Square Kilometre Array Pathfinder (ASKAP) has localised 11 FRBs with sub-arcsecond to arcsecond precision, leading to sub-galaxy localisation regions in some cases and those covering much of the host galaxy in others. The method used to astrometrically register the FRB image frame for ASKAP, in order to align it with images taken at other wavelengths, is currently limited by the brightness of continuum sources detected in the short-duration (‘snapshot’) voltage data captured by the Commensal Real-Time ASKAP Fast Transients (CRAFT) software correlator, which are used to correct for any frame offsets due to imperfect calibration solutions and estimate the accuracy of any required correction. In this paper, we use dedicated observations of bright, compact radio sources in the low- and mid-frequency bands observable by ASKAP to investigate the typical astrometric accuracy of the positions obtained using this so-called ‘snapshot’ technique. Having captured these data with both the CRAFT software and ASKAP hardware correlators, we also compare the offset distributions obtained from both data products to estimate a typical offset between the image frames resulting from the differing processing paths, laying the groundwork for future use of the longer duration, higher signal-to-noise ratio (S/N) data recorded by the hardware correlator. We find typical offsets between the two frames of ${\sim}0.6$ and ${\sim}0.3$ arcsec in the low- and mid-band data, respectively, for both RA and Dec. We also find reasonable agreement between our offset distributions and those of the published FRBs. We detect only a weak dependence in positional offset on the relative separation in time and elevation between target and calibrator scans, with the trends being more pronounced in the low-band data and in Dec. Conversely, the offsets show a clear dependence on frequency in the low band, which we compare to the frequency-dependent Dec. offsets found in FRB 200430. In addition, we present a refined methodology for estimating the overall astrometric accuracy of CRAFT FRBs.

Over the past seventy-five years, the UN has evolved significantly, often in response to geopolitical dynamics and new waves of thinking. In some respects, the UN has registered remarkable achievements, stimulating a wide range of multilateral treaties, promoting significant growth of human rights, and at times playing a central role in containing and preventing large-scale armed conflict. As part of the special issue on “The United Nations at Seventy-Five: Looking Back to Look Forward,” this essay argues that the organization has been the most impactful in three areas: producing, shaping, and driving key ideas, particularly on development and rights; generating such effective operational agencies as UNICEF and the World Food Program; and, especially in the immediate post–Cold War period, addressing major conflict risks through the Security Council. Since then, however, the UN has struggled to meet emerging challenges on many fronts and been increasingly hampered by internal ossification and institutional sprawl as well as internecine dysfunction. The twenty-first century has confronted the UN with further challenges relating most notably to climate change; to risks arising from new technologies; and to the increasingly fraught relationships between China, Russia, and the United States. If the past seventy-five years can offer one lesson, it is that new thinking and new ideas will need to drive the organization to evolve still further and faster, or else risk irrelevance.

We investigate the class of bipartite Borel graphs organized by the order of Borel homomorphism. We show that this class is unbounded by finding a jump operator for Borel graphs analogous to a jump operator of Louveau for Borel equivalence relations. The proof relies on a nonseparation result for iterated Fréchet ideals and filters due to Debs and Saint Raymond. We give a new proof of this fact using effective descriptive set theory. We also investigate an analogue of the Friedman-Stanley jump for Borel graphs. This analogue does not yield a jump operator for bipartite Borel graphs. However, we use it to answer a question of Kechris and Marks by showing that there is a Borel graph with no Borel homomorphism to a locally countable Borel graph, but each of whose connected components has a countable Borel coloring.

Many snow models have been developed for various applications such as hydrology, global atmospheric circulation models and avalanche forecasting. The degree of complexity of these models is highly variable, ranging from simple index methods to multi-layer models that simulate snow-cover stratigraphy and texture. In the framework of the Snow Model Intercomparison Project (SnowMIP), 23 models were compared using observed meteorological parameters from two mountainous alpine sites. The analysis here focuses on validation of snow energy-budget simulations. Albedo and snow surface temperature observations allow identification of the more realistic simulations and quantification of errors for two components of the energy budget: the net short- and longwave radiation. In particular, the different albedo parameterizations are evaluated for different snowpack states (in winter and spring). Analysis of results during the melting period allows an investigation of the different ways of partitioning the energy fluxes and reveals the complex feedbacks which occur when simulating the snow energy budget. Particular attention is paid to the impact of model complexity on the energy-budget components. The model complexity has a major role for the net longwave radiation calculation, whereas the albedo parameterization is the most significant factor explaining the accuracy of the net shortwave radiation simulation.

This article reviews current knowledge about how the tendency to reflect on personal experience is related to the tendency to take another's perspective. While it is well established that self-reflection leads to a greater understanding of one's own emotions, cognitions, and behaviours, the extent to which it is associated with understanding others is less well understood, despite the implications of this for the development of more effective interventions to improve empathy. The types of self-reflection that are used in clinical and psychotherapeutic interventions are used to illustrate the possibilities here, and ways in which clinicians may increase their own self-reflection are also considered.

This paper uses the framework of reverse mathematics to investigate the strength of two recurrence theorems of topological dynamics. It establishes that one of these theorems, the existence of an almost periodic point, lies strictly between WKL and ACA (working over RCA0). This is the first example of a theorem with this property. It also shows the existence of an almost periodic point is conservative over RCA0 for ${\rm{\Pi }}_1^1$-sentences.

This study tested the hypothesis that it is easier to take the perspective of another person when one has similar past experience. Volunteer participants (N = 154) were asked to take the perspective of a protagonist in one of four problematic interpersonal situations and then to rate the ease with which they felt able to perspective take and the extent of their personal past experience of similar situations. Similar past experience predicted ease of perspective taking, with the relationship influenced by reflection on past experience. Ease of perspective taking mediated the relationship between similar past experience and participant perceptions of their accuracy in understanding the other person, but ease was not associated with emotional arousal. The findings have potential therapeutic applications for attempts to increase empathy and understanding in people for whom perspective taking may be difficult.

Every K-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.

This study aimed to investigate the influence of sex and gender role identity on anger experience at varying levels of provocation in a sample of 585 Australian students. Participants viewed videotaped vignettes of a potentially anger-triggering event where the intent of another person was either ambiguous or unambiguous. Measures of self-predicted anger, trait anger, and gender role identity were then completed. Results supported the hypothesis that it is gender role identity rather than sex that is more closely related to angry emotion. There was, however, no support for the hypothesis that anger arousal would be greater in circumstances in which the intention behind a provoking event is ambiguous when the respondent identifies with a masculine gender role. The implications of these findings for the development of anger management programs are discussed.

This paper investigates indifferent sets for comeager classes in Cantor space focusing of the class of all 1-generic sets and the class of all weakly 1-generic sets. Jockusch and Posner showed that there exist 1-generic sets that have indifferent sets [10]. Figueira, Miller and Nies have studied indifferent sets for randomness and other notions [7]. We show that any comeager class in Cantor space contains a comeager class with a universal indifferent set. A forcing construction is used to show that any 1-generic set, or weakly 1-generic set, has an indifferent set. Such an indifferent set can by computed by any set in which bounds the (weakly) 1-generic. We show by approximation arguments that some, but not all, 1-generic sets can compute an indifferent set for themselves. We show that all weakly 1-generic sets can compute an indifferent set for themselves. Additional results on indifferent sets, including one of Miller, and two of Fitzgerald, are presented.

The ability to take the perspectives of others is considered a prerequisite for effective interpersonal interaction. Despite extensive investigation into the correlates of perspective taking, there have been few previous attempts to understand the process by which people take another's psychological point of view. The purpose of this exploratory study was to identify the strategies used by individuals when attempting to take the perspective of another person. Twelve participants discussed a time they engaged in perspective taking. The analysis revealed that perspective taking was used in situations in which significant negative emotions could arise, and that participants shifted between the use of self-information (e.g., switching places, past experience) and other-information (e.g., target's personal characteristics) during the process of perspective taking. Different emotions and cognitions were associated with taking one's own perspective and taking that of the other person. The study provides a direct consideration of an under-investigated component of social and personal relationships.