Alternating Minimization for Regression with Tropical Rational Functions

We propose an alternating minimization heuristic for regression over the space of tropical rational functions with fixed exponents. The method alternates between fitting the numerator and denominator terms via tropical polynomial regression, which is known to admit a closed form solution. We demonstrate the behavior of the alternating minimization method experimentally. Experiments demonstrate that the heuristic provides a reasonable approximation of the input data. Our work is motivated by applications to ReLU neural networks, a popular class of network architectures in the machine learning community which are closely related to tropical rational functions

Relaxations and Duality for Multiobjective Integer Programming

Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a weighted-sum scalarization of the MOIP. At unsupported solutions, the convex hull relaxation is not tight and a Lagrangian relaxation may provide a tighter bound. Using the Lagrangian relaxation, we define a Lagrangian dual of an MOIP that satisfies weak duality and is strong at supported solutions under certain conditions on the primal feasible region. We include a numerical experiment to illustrate that bound sets obtained via Lagrangian duality may yield tighter bounds than those from a convex hull relaxation. Subsequently, we generalize the integer programming value function to MOIPs and use its properties to motivate a set-valued superadditive dual that is strong at supported solutions. We also define a simpler vector-valued superadditive dual that exhibits weak duality but is strongly dual if and only if the primal has a unique nondominated point

Aphid Thermal Tolerance Is Governed by a Point Mutation in Bacterial Symbionts

Symbiosis is a ubiquitous phenomenon generating biological complexity, affecting adaptation, and expanding ecological capabilities. However, symbionts, which can be subject to genetic limitations such as clonality and genomic degradation, also impose constraints on hosts. A model of obligate symbiosis is that between aphids and the bacterium Buchnera aphidicola, which supplies essential nutrients. We report a mutation in Buchnera of the aphid Acyrthosiphon pisum that recurs in laboratory lines and occurs in field populations. This single nucleotide deletion affects a homopolymeric run within the heat-shock transcriptional promoter for ibpA, encoding a small heat-shock protein. This Buchnera mutation virtually eliminates the transcriptional response of ibpA to heat stress and lowers its expression even at cool or moderate temperatures. Furthermore, this symbiont mutation dramatically affects host fitness in a manner dependent on thermal environment. Following a short heat exposure as juveniles, aphids bearing short-allele symbionts produced few or no progeny and contained almost no Buchnera, in contrast to aphids bearing symbionts without the deletion. Conversely, under constant cool conditions, aphids containing symbionts with the short allele reproduced earlier and maintained higher reproductive rates. The short allele has appreciable frequencies in field populations (up to 20%), further supporting the view that lowering of ibpA expression improves host fitness under some conditions. This recurring Buchnera mutation governs thermal tolerance of aphid hosts. Other cases in which symbiont microevolution has a major effect on host ecological tolerance are likely to be widespread because of the high mutation rates of symbiotic bacteria and their crucial roles in host metabolism and development

Landscapes for Neolithic People in Mainland, Orkney

Neolithic occupation of the Orkney Islands, in the north of Scotland, probably began in the mid fourth millennium cal BC, culminating in a range of settlements, including stone-built houses, varied stone-built tombs and two noteworthy stone circles. The environmental and landscape context of the spectacular archaeology, however, remains poorly understood. We applied the Multiple Scenario Approach (MSA) to Neolithic pollen records from Mainland, Orkney, in order to understand land cover and landscape openness across the timespan 4200–2200cal BC. Interpreted within a framework provided by Bayesian chronological modelling, 406 radiocarbon dates from archaeological contexts and a further 103 from palaeoenvironmental samples provide the basis for the first detailed reconstruction of the spatio-temporal patterns of Neolithic people and their environment. Major alterations to the land cover of Mainland took place from 3400cal BC (reduction in woodland from 20% to 10%) and from 3200cal BC (increase in disturbed land from 3% to 30%). The dramatic increase in disturbed land coincided with the Grooved Ware phenomenon and the establishment of settlements at Skara Brae and Ness of Brodgar. The upturn in the signal for disturbance communities in the pollen record may indicate an increase in the amount of land used as pasture. This accords with the archaeological record, since the Neolithic Orcadian economy probably relied heavily on cattle for subsistence. By 2800cal BC in the core of the Orkney Mainland, most settlements appear to have been ending, with people dispersing into the wider landscape, as the MSA modelling indicates a maintenance of disturbed land, and indeed a subsequent slight increase, implying persistence of human activity elsewhere in Mainland. People exhausted themselves rather than their land; that and its varied resources endured, while the intensive social relationships and practices of the peak of late Neolithic Orkney could not be maintained

When and Why? The Chronology and Context of Flint Mining at Grime’s Graves, Norfolk, England

New radiocarbon dating and chronological modelling have refined understanding of the character and circumstances of flint mining at Grime’s Graves through time. The deepest, most complex galleried shafts were worked probably from the third quarter of the 27th century cal BC and are amongst the earliest on the site. Their use ended in the decades around 2400 cal BC, although the use of simple, shallow pits in the west of the site continued for perhaps another three centuries. The final use of galleried shafts coincides with the first evidence of Beaker pottery and copper metallurgy in Britain. After a gap of around half a millennium, flint mining at Grime’s Graves briefly resumed, probably from the middle of the 16th century cal BC to the middle of the 15th. These ‘primitive’ pits, as they were termed in the inter-war period, were worked using bone tools that can be paralleled in Early Bronze Age copper mines. Finally, the scale and intensity of Middle Bronze Age middening on the site is revealed, as it occurred over a period of probably no more than a few decades in the 14th century cal BC. The possibility of connections between metalworking at Grime’s Graves at this time and contemporary deposition of bronzes in the nearby Fens is discussed

House time: Neolithic settlement development at Racot during the 5th millennium cal b.c. in the Polish lowlands

The settlement of Racot 18 in the western Polish lowlands is used as a case study in the investigation of continued development and expansion following initial Neolithic beginnings, and in the formal chronological modelling, in a Bayesian framework, of settlement development. The site belongs to the Late Lengyel culture of the later fifth millennium cal BC, and represents the intake of new land following earlier initial colonisation. The formally estimated chronology for the settlement suggests spans for individual house biographies from as little as a generation to over a century; distinctive substantial buildings, from late in the sequence, may have lasted longest. Racot 18 is compared to its formally modelled context of the later fifth millennium cal BC

Rows with the neighbours: the short lives of longhouses at the Neolithic site of Versend-Gilencsa

Longhouses are a key feature of Neolithic Linearbandkeramik (LBK) settlements in Central Europe, but debate persists concerning their usage, longevity and social significance. Excavations at Versend-Gilencsa in south-west Hungary (c. 5200 cal BC) revealed clear rows of longhouses. New radiocarbon dates suggest that these houses experienced short lifespans. This paper produces a model for the chronology of Versend, and it considers the implications of the new date estimates for a fuller understanding of the layout and duration of LBK longhouse settlements

Interwoven strands for refining the chronology of the Neolithic tell of Vinča-Belo Brdo, Serbia

A formally modeled radiocarbon chronology for a new profile through the great Neolithic tell of Vinča-Belo Brdo, Serbia, is the third interwoven strand in refining the chronology of the tell. This now joins models for the whole sequence based on the archive of early excavations, and for the last two known horizons at the top of the settlement mound, investigated in recent decades. In the new deep sounding, Vinča culture occupation from the 52nd century cal BC is slightly later than in the main sequence, probably reflecting the horizontal extension of the tell as it began to grow. The last dated occupation falls in the late 47th–early 46th century cal BC, slightly earlier than in the main sequence, but the top of the profile is affected by the slippage that caused the new excavations. Formal estimates are given for the succession and varying durations of burnt and unburnt houses, and indicate a period in the first part of the 5th millennium without house burning. Overall, the combined results from the three interwoven strands serve to produce a radically enhanced understanding of the temporality of the tell, which builds on, rather than supplants, previous research. We knew previously that Vinča-Belo Brdo was very long-lived, but now we can time that history with much greater precision. We can assert with much greater confidence that its vertical buildup was steady and largely uninterrupted. We have begun, from the work on the top of the tell and in the new deep sounding, to grasp better the fluctuations in house durations from generation to generation, and can now contrast the relative fortunes of unburnt and burnt houses. We can say much more about the timing and tempo of the ending of the tell, and about the possible circumstances in which that took place

COVID 19:Seroprevalence and vaccine responses in UK dental care professionals

Dental care professionals (DCPs) are thought to be at enhanced risk of occupational exposure to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). However, robust data to support this from large-scale seroepidemiological studies are lacking. We report a longitudinal seroprevalence analysis of antibodies to SARS-CoV-2 spike glycoprotein, with baseline sampling prior to large-scale practice reopening in July 2020 and follow-up postimplementation of new public health guidance on infection prevention control (IPC) and enhanced personal protective equipment (PPE). In total, 1,507 West Midlands DCPs were recruited into this study in June 2020. Baseline seroprevalence was determined using a combined IgGAM enzyme-linked immunosorbent assay and the cohort followed longitudinally for 6 mo until January/February 2021 through the second wave of the coronavirus disease 2019 pandemic in the United Kingdom and vaccination commencement. Baseline seroprevalence was 16.3%, compared to estimates in the regional population of 6% to 7%. Seropositivity was retained in over 70% of participants at 3- and 6-mo follow-up and conferred a 75% reduced risk of infection. Nonwhite ethnicity and living in areas of greater deprivation were associated with increased baseline seroprevalence. During follow-up, no polymerase chain reaction–proven infections occurred in individuals with a baseline anti–SARS-CoV-2 IgG level greater than 147.6 IU/ml with respect to the World Health Organization international standard 20-136. After vaccination, antibody responses were more rapid and of higher magnitude in those individuals who were seropositive at baseline. Natural infection with SARS-CoV-2 prior to enhanced PPE was significantly higher in DCPs than the regional population. Natural infection leads to a serological response that remains detectable in over 70% of individuals 6 mo after initial sampling and 9 mo from the peak of the first wave of the pandemic. This response is associated with protection from future infection. Even if serological responses wane, a single dose of the Pfizer-BioNTech 162b vaccine is associated with an antibody response indicative of immunological memory

Island questions: the chronology of the Brochtorff Circle at Xagħra, Gozo, and its significance for the Neolithic sequence on Malta

Bayesian chronological modelling of radiocarbon dates from the Brochtorff Circle at Xagħra, Gozo, Malta (achieved through the ToTL and FRAGSUS projects), provides a more precise chronology for the sequence of development and use of a cave complex. Artefacts show that the site was in use from the Żebbuġ period of the late 5th/early 4th millennium cal BC to the Tarxien Cemetery phase of the later 3rd/early 2nd millennia cal BC. Absolutely dated funerary activity, however, starts with a small rock-cut tomb, probably in use in the mid to late fourth millennium cal BC, in the Ġgantija period. After an interval of centuries, burial resumed on a larger scale, probably in the 30th century cal BC, associated with Tarxien cultural material, with the use of the cave for collective burial and other depositions, with a series of structures, most notably altar-like settings built from massive stone slabs, which served to monumentalise the space. This process continued at intervals until the deposition of the last burials, probably in the 24th century cal BC; ceremonial activity may have ended at this time or a little later, to be followed by occupation in the Tarxien Cemetery period. The implications for the development of Neolithic society on Malta are discussed, as well as the changing character of Neolithic Malta in comparison to contemporary communities in Sicily, peninsular Italy and southern Iberia. It is argued that underground settings and temples on Malta may have served to reinforce locally important values of cooperation and consensus, against a wider tide of differentiation and accumulation, but that there could also have been increasing control of the treatment of the dead through time. The end of the Maltese Neolithic is also briefly discussed