We show that all large enough positive integral surgeries on algebraic knots bound a 4-manifold with a negative definite plumbing tree, which we describe explicitly. Then we apply the lattice embedding obstruction coming from Donaldson’s Theorem to classify the ones of the form $S^3_n(T(p_1,k_1p_1+1; p_2, k_2p_2\pm 1))$ that also bound rational homology 4-balls.

We find that male participants in Harvard Business School’s New Venture Competition who were randomly exposed to more venture capital (VC) investors on their panel were substantially more likely to start a VC-backed startup post-graduation, indicating that access to investors impacts fundraising independent of the quality of ideas. However, female participants experience no benefit from exposure to male or female venture capitalists (VCs), which appears related to a reduced propensity to reach out to VCs to whom they were exposed. Our results therefore also demonstrate gender-based differences in the degree to which increased exposure to investors can address networking frictions in venture capital.

With only a few exceptions, the historical study of individual-level correlates of child mortality in the United States has been limited to the period surrounding the turn of the twentieth century, when children ever born and children surviving data collected by the 1900 and 1910 censuses allow indirect estimation of child mortality. The recent release of linked census data, such as the IPUMS MLP datasets, allows a different type of indirect estimation over a longer period. By following couples across subsequent decennial censuses, it is possible to infer child mortality by measuring whether couples’ own children in the first census were still present in the second census. We focus our analysis on children aged 1–3 in the first of two linked censuses, who were less likely to be undercounted by the census than infants, and unlikely to be living apart from their parents in the second census. We estimate child mortality over the intervening decade and use OLS regression to correlate that mortality to the residence location and socioeconomic characteristics of their parents’ households. We limit our analysis to three panel datasets for married couples linked between the 1850–60, 1860–70, and 1870–80 censuses, when real estate and personal estate wealth data were collected. Our results indicate a significant negative relationship between wealth and child mortality across all regions of the United States and over the entire period examined.

We describe a new sea spider species, Pantopipetta hosodai sp. nov., based on one juvenile female collected from a submarine cave (‘Akumanoyakata’ Cave) in Shimojijima Island, Miyako Island Group, Ryukyu Islands, southwestern Japan. It was collected from the second slope zone of the cave, 80–100 m from the entrance, no light, low salinity and with rocky substrate. This is the first record globally of a Pantopipetta species from a submarine cave and anchialine environment. Pantopipetta hosodai sp. nov. resembles Pantopipetta auxiliata, Pantopipetta lenis and Pantopipetta oculata in having auxiliary claws, but differs from them in having a palp with three short distal articles, lateral processes without dorsodistal tubercles, coxae 1 and 3 of legs 1–3 each with one long dorsal tubercle and one dorsodistal tubercle bearing a seta on each femur. Features of the palp appear to delineate two species groups in Pantopipetta, i.e. (1) those having four small distal articles, and a small, basal palp article between the lateral cephalon process and longest palp article (eight-articulate palp) and (2) those having three small distal articles, and lacking the small basal article (six-articulate palp), but further detail examination of the described species is needed. We discuss the diagnostic characters separating Pantopipetta and Austrodecus and the generic affiliation of Austrodecus aconae. Few pycnogonids from marine or anchialine caves have been identified to species, and it is generally unknown whether cave-dwelling pycnogonids tend to be troglobites.

We show that categories of modules over a ring in homotopy type theory (HoTT) satisfy the internal versions of the AB axioms from homological algebra. The main subtlety lies in proving AB4, which is that coproducts indexed by arbitrary sets are left-exact. To prove this, we replace a set X with the strict category of lists of elements in X. From showing that the latter is filtered, we deduce left-exactness of the coproduct. More generally, we show that exactness of filtered colimits (AB5) implies AB4 for any abelian category in HoTT. Our approach is heavily inspired by Roswitha Harting’s construction of the internal coproduct of abelian groups in an elementary topos with a natural numbers object. To state the AB axioms, we define and study filtered (and sifted) precategories in HoTT. A key result needed is that filtered colimits commute with finite limits of sets. This is a familiar classical result but has not previously been checked in our setting. Finally, we interpret our most central results into an $\infty$-topos $ {\mathscr{X}} $. Given a ring R in $ {\tau_{\leq 0}({{\mathscr{X}}})} $ – for example, an ordinary sheaf of rings – we show that the internal category of R-modules in $ {\mathscr{X}} $ represents the presheaf which sends an object $ X \in {\mathscr{X}} $ to the category of $ (X{\times}R) $-modules in ${\mathscr{X}} / X$. In general, our results yield a product-preserving left adjoint to base change of modules over X. When X is 0-truncated, this left adjoint is the internal coproduct. By an internalisation procedure, we deduce left-exactness of the internal coproduct as an ordinary functor from its internal left-exactness coming from HoTT.

We derive conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results by Menshikov and Volkov [‘Urn-related random walk with drift $\rho x^\alpha /t^\beta $’, Electron. J. Probab. 13 (2008), 944–960] follow.

The symbiotic relationship between people and the genus Agave spans millennia and a vast geographical area encompassing Mexico, the southwestern United States, and the Texas borderlands. In the early 1950s, Richard MacNeish's investigations in Tamaulipas yielded evidence of past agave use in the mountains of northeastern Mexico. Excavations in the Ocampo Caves revealed 9,000 years of sporadic occupations by hunter-gatherers, mixed forager-farmers, and finally, periodic visits by residents of nearby agricultural villages. Although these discoveries are incompletely published—and existing publications largely underemphasize the range of utilized wild resources in favor of domesticated maize, beans, and squash—agave is among the wild plant taxa most often mentioned in use throughout the Holocene. Unpublished field notes, curated plant assemblages recovered during MacNeish's excavations, and data from recent archaeological survey complement the published literature to explore the role of this prominent plant in this important archaeological region.

In this paper, we investigate the thermal evolution in a one-dimensional bagasse stockpile. The mathematical model involves four unknowns: the temperature, oxygen content, liquid water content and water vapour content. We first nondimensionalize the model to identify dominant terms and so simplify the system. We then calculate solutions for the approximate and full system. It is shown that under certain conditions spontaneous combustion will occur. Most importantly, we show that spontaneous combustion can be avoided by sequential building. To be specific, in a situation where, say, a $4.7\,$m stockpile can spontaneously combust, we could construct a $3\,$m pile and then some days later add another $1.7\,$m to produce a stable $4.7\,$m pile.

As it is presently employed, grounding permits grounding many things from one ground. In this paper, I show why this is a mistake by pushing for a uniqueness principle on grounding. After arguing in favor of this principle, I say something about it and kinds of grounding, discuss a similar principle, and consider its import on a formal feature of grounding, ontology, and ontological simplicity.

Cardiac tumours are extremely rare. Most of the cases are diagnosed post-mortem.

In this case, a tumour was found in a neonate during routine ultrasound screening in the first trimester of pregnancy. After birth, resection of the formation was performed and histologically confirmed as a cavernous haemangioma. Additionally, propranolol was prescribed in order to prevent relapse.

Among the forms of anthropogenic disturbance, agricultural land use is one of the main threats to biodiversity. Understanding how interactions between parasites and hosts are affected by agricultural land use allows predictions of how these anthropogenic impacts affect parasites. Although parasitism patterns are affected by agricultural land use, it is noteworthy that different groups of parasites can respond differently to these environmental alterations. While heteroxenous species need more than one host to complete their life cycle and tend to be more harmed by anthropization, monoxenous species, which need only one host to complete their life cycle, tend to be less harmed. In this work, we evaluate how agricultural land use affects the abundance and prevalence of parasitism for monoxenous and heteroxenous helminths in the generalist lizard Tropidurus hispidus in Caatinga Domain, Brazil. We recorded differences in abundance and prevalence of heteroxeneous (higher in conserved areas) and monoxenous helminths (higher in agricultural areas). Heteroxenous helminths that have lizards as definitive hosts are mainly obtained through diet. Tropidurus hispidus predominantly consumes insects, so it is possible that the lower abundance and prevalence of heteroxenous parasites in agricultural areas, beyond habitat simplification, is related to the decrease in the insect population. As monoxenous species do not need an intermediate host, it is possible that this aspect has influenced their greater success in anthropogenic environments than heteroxenous species. This contrasting result reinforces the need for a separate assessment between these groups when evaluating effects of land use.

Let p be a prime and let r, s be positive integers. In this paper, we prove that the Goormaghtigh equation $(x^m-1)/(x-1)=(y^n-1)/(y-1)$, $x,y,m,n \in {\mathbb {N}}$, $\min \{x,y\}>1$, $\min \{m,n\}>2$ with $(x,y)=(p^r,p^s+1)$ has only one solution $(x,y,m,n)=(2,5,5,3)$. This result is related to the existence of some partial difference sets in combinatorics.

We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localization, analogous results to those obtained in the category of groups hold, and we provide existence theorems for certain localization functors in specific semi-abelian categories. We prove that a Birkhoff subcategory of an ideal determined category yields a conditionally flat localization, and explain how conditional flatness corresponds to the property of admissibility of an adjunction from the point of view of categorical Galois theory. Under the assumption of fiberwise localization, we give a simple criterion to determine when a (normal epi)-reflection is a torsion-free reflection. This is shown to apply, in particular, to nullification functors in any semi-abelian variety of universal algebras. We also relate semi-left-exactness for a localization functor L with what is called right properness for the L-local model structure.