The Absolute Line Quadric and Camera Autocalibration

We introduce a geometrical object providing the same information as the absolute conic: the absolute line quadric (ALQ). After the introduction of the necessary exterior algebra and Grassmannian geometry tools, we analyze the Grassmannian of lines of P^3 from both the projective and Euclidean points of view. The exterior algebra setting allows then to introduce the ALQ as a quadric arising very naturally from the dual absolute quadric. We fully characterize the ALQ and provide clean relationships to solve the inverse problem, i.e., recovering the Euclidean structure of space from the ALQ. Finally we show how the ALQ turns out to be particularly suitable to address the Euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters, providing new linear and non-linear algorithms for this problem. We also provide experimental results showing the good performance of the techniques

Novel approach to the study of quantum effects in the early universe

We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function $\sigma(\eta)$ of the conformal time $\eta$, called the auxiliary field equation. At the classical level, $\sigma(\eta)$ can be expressed by means of two independent solutions of the ''master equation'' to which the perturbed Einstein equations for the gravitational waves can be reduced. At the quantum level, all the significant physical quantities can be formulated using Bogolubov transformations and the operator quadratic Hamiltonian corresponding to the classical version of a damped parametrically excited oscillator where the varying mass is replaced by the square cosmological scale factor $a^{2}(\eta)$. A quantum approach to the generation of gravitational waves is proposed on the grounds of the previous $\eta-$dependent Hamiltonian. An estimate in terms of $\sigma(\eta)$ and $a(\eta)$ of the destruction of quantum coherence due to the gravitational evolution and an exact expression for the phase of a gravitational wave corresponding to any value of $\eta$ are also obtained. We conclude by discussing a few applications to quasi-de Sitter and standard de Sitter scenarios.Comment: 20 pages, to appear on PRD. Already published background material has been either settled up in a more compact form or eliminate

Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential

The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.Comment: Phys. Rev. A (Brief Report), in pres

Line geometry and camera autocalibration

We provide a completely new rigorous matrix formulation of the absolute quadratic complex (AQC), given by the set of lines intersecting the absolute conic. The new results include closed-form expressions for the camera intrinsic parameters in terms of the AQC, an algorithm to obtain the dual absolute quadric from the AQC using straightforward matrix operations, and an equally direct computation of a Euclidean-upgrading homography from the AQC. We also completely characterize the 6×6 matrices acting on lines which are induced by a spatial homography. Several algorithmic possibilities arising from the AQC are systematically explored and analyzed in terms of efficiency and computational cost. Experiments include 3D reconstruction from real images

Pre-M Phase-promoting Factor Associates with Annulate Lamellae in Xenopus Oocytes and Egg Extracts

We have used complementary biochemical and in vivo approaches to study the compartmentalization of M phase-promoting factor (MPF) in prophase Xenopus eggs and oocytes. We first examined the distribution of MPF (Cdc2/CyclinB2) and membranous organelles in high-speed extracts of Xenopus eggs made during mitotic prophase. These extracts were found to lack mitochondria, Golgi membranes, and most endoplasmic reticulum (ER) but to contain the bulk of the pre-MPF pool. This pre-MPF could be pelleted by further centrifugation along with components necessary to activate it. On activation, Cdc2/CyclinB2 moved into the soluble fraction. Electron microscopy and Western blot analysis showed that the pre-MPF pellet contained a specific ER subdomain comprising "annulate lamellae" (AL): stacked ER membranes highly enriched in nuclear pores. Colocalization of pre-MPF with AL was demonstrated by anti-CyclinB2 immunofluorescence in prophase oocytes, in which AL are positioned close to the vegetal surface. Green fluorescent protein-CyclinB2 expressed in oocytes also localized at AL. These data suggest that inactive MPF associates with nuclear envelope components just before activation. This association may explain why nuclei and centrosomes stimulate MPF activation and provide a mechanism for targeting of MPF to some of its key substrates

Stuart Warren (24 Dec 1938–22 Mar 2020)

Celebrating the life of Stuart Warren

Temperature synchronizes temporal variation in laying dates across European hole-nesting passerines

Publisher Copyright: © 2022 The Authors. Ecology published by Wiley Periodicals LLC on behalf of The Ecological Society of America.Identifying the environmental drivers of variation in fitness-related traits is a central objective in ecology and evolutionary biology. Temporal fluctuations of these environmental drivers are often synchronized at large spatial scales. Yet, whether synchronous environmental conditions can generate spatial synchrony in fitness-related trait values (i.e., correlated temporal trait fluctuations across populations) is poorly understood. Using data from long-term monitored populations of blue tits (Cyanistes caeruleus, n = 31), great tits (Parus major, n = 35), and pied flycatchers (Ficedula hypoleuca, n = 20) across Europe, we assessed the influence of two local climatic variables (mean temperature and mean precipitation in February–May) on spatial synchrony in three fitness-related traits: laying date, clutch size, and fledgling number. We found a high degree of spatial synchrony in laying date but a lower degree in clutch size and fledgling number for each species. Temperature strongly influenced spatial synchrony in laying date for resident blue tits and great tits but not for migratory pied flycatchers. This is a relevant finding in the context of environmental impacts on populations because spatial synchrony in fitness-related trait values among populations may influence fluctuations in vital rates or population abundances. If environmentally induced spatial synchrony in fitness-related traits increases the spatial synchrony in vital rates or population abundances, this will ultimately increase the risk of extinction for populations and species. Assessing how environmental conditions influence spatiotemporal variation in trait values improves our mechanistic understanding of environmental impacts on populations.Peer reviewe

Fine roots stimulate nutrient release during early stages of leaf litter decomposition in a Central Amazon rainforest

Purpose Large parts of the Amazon rainforest grow on weathered soils depleted in phosphorus and rock-derived cations. We tested the hypothesis that in this ecosystem, fine roots stimulate decomposition and nutrient release from leaf litter biochemically by releasing enzymes, and by exuding labile carbon stimulating microbial decomposers. Methods We monitored leaf litter decomposition in a Central Amazon tropical rainforest, where fine roots were either present or excluded, over 188 days and added labile carbon substrates (glucose and citric acid) in a fully factorial design. We tracked litter mass loss, remaining carbon, nitrogen, phosphorus and cation concentrations, extracellular enzyme activity and microbial carbon and nutrient concentrations. Results Fine root presence did not affect litter mass loss but significantly increased the loss of phosphorus and cations from leaf litter. In the presence of fine roots, acid phosphatase activity was 43.2% higher, while neither microbial stoichiometry, nor extracellular enzyme activities targeting carbon- and nitrogen-containing compounds changed. Glucose additions increased phosphorus loss from litter when fine roots were present, and enhanced phosphatase activity in root exclusions. Citric acid additions reduced litter mass loss, microbial biomass nitrogen and phosphorus, regardless of fine root presence or exclusion. Conclusions We conclude that plant roots release significant amounts of acid phosphatases into the litter layer and mobilize phosphorus without affecting litter mass loss. Our results further indicate that added labile carbon inputs (i.e. glucose) can stimulate acid phosphatase production by microbial decomposers, highlighting the potential importance of plant-microbial feedbacks in tropical forest ecosystems