Integrating the geodesic equations in the Schwarzschild and Kerr space-times using Beltrami's "geometrical" method

We revisit a little known theorem due to Beltrami, through which the integration of the geodesic equations of a curved manifold is accomplished by a method which, even if inspired by the Hamilton-Jacobi method, is purely geometric. The application of this theorem to the Schwarzschild and Kerr metrics leads straightforwardly to the general solution of their geodesic equations. This way of dealing with the problem is, in our opinion, very much in keeping with the geometric spirit of general relativity. In fact, thanks to this theorem we can integrate the geodesic equations by a geometrical method and then verify that the classical conservation laws follow from these equations.Comment: 12 pages; corrected typos, journal-ref adde

Pulmonary tumor embolism: A retrospective study over a 30-year period

BACKGROUND: Pulmonary tumor embolism (PTE) is difficult to detect before death, and it is unclear whether the discrepancy between antemortem clinical and postmortem diagnosis improves with the advance of the diagnostic technologies. In this study we determined the incidence of PTE and analyzed the discrepancy between antemortem clinical and postmortem diagnosis. METHODS: We performed a retrospective autopsy study on patients with the history of malignant solid tumors from 1990 to 2020 and reviewed all the slides of the patients with PTE. We also analyzed the discrepancies between antemortem clinical and postmortem diagnosis in 1999, 2009 and 2019 by using the Goldman criteria. Goldman category major 1 refers to cases in which an autopsy diagnosis was the direct cause of death and was not recognized clinically, but if it had been recognized, it may have changed treatment or prolonged survival. RESULTS: We found 20 (3%) cases with PTE out of the 658 autopsy cases with solid malignancies. Out of these 20 cases, urothelial carcinoma (30%, 6/20) and invasive ductal carcinoma of the breast (4/20, 20%) were the most common primary malignancies. Seven patients with shortness of breath died within 3-17 days (average 8.4+/-2.2 days) after onset of the symptoms. Pulmonary embolism was clinically suspected in seven out of twenty (35%, 7/20) patients before death, but only two patients (10, 2/20) were diagnosed by imaging studies before death. The rate of Goldman category major 1 was 13.2% (10/76) in 1999, 7.3% (4/55) in 2009 and 6.9% (8/116) in 2019. Although the rate of Goldman category major 1 appeared decreasing, the difference was not statistically significant. The autopsy rate was significantly higher in 2019 (8.4%, 116/1386) than in 2009 (4.4%, 55/1240). CONCLUSIONS: The incidence of PTE is uncommon. Despite the advances of the radiological techniques, radiological imaging studies did not detect the majority of PTEs. The discrepancy between the antemortem clinical and the postmortem diagnosis has not improved significantly over the past 30 years, emphasizing the value of autopsy

A new algorithm for the identification of dives reveals the foraging ecology of a shallow-diving seabird using accelerometer data

The identification of feeding events is crucial to our understanding of the foraging ecology of seabirds. Technology has made small devices, such as time-depth recorders (TDRs) and accelerometers available. However, TDRs might not be sensitive enough to identify shallow dives, whereas accelerometers might reveal more subtle behaviours at a smaller temporal scale. Due to the limitations of TDRs, the foraging ecology of many shallow-diving seabirds has been poorly investigated to date. We thus developed an algorithm to identify dive events in a shallowdiving seabird species, the Scopoli’s shearwater, using only accelerometer data. The accuracy in the identification of dives using either accelerometers or TDRs was compared. Furthermore, we tested if the foraging behaviour of shearwaters changed during different phases of reproduction and with foraging trip type. Data were collected in Linosa Island (35°51′33″N; 12°51′34″E) from 12 June to 8 September 2015 by deploying accelerometer data loggers on 60 Scopoli’s shearwaters. Four birds were also equipped with TDRs. TDRs recorded only 17.7% of the dives detected by the accelerometers using the algorithm. A total of 82.3% of dives identified by algorithm were too short or shallow to be detected by TDRs. Therefore, TDRs were not accurate enough to detect most of the dives in Scopoli’s shearwaters, which foraged mostly close to the sea surface. Our data showed that birds performed shorter foraging trips and dived more frequently in the early chick-rearing period compared with the late chick-rearing and incubation phases. Furthermore, parents dived more frequently during short foraging trips. Our results suggest that Scopoli’s shearwaters maximised their foraging effort (e.g. number of dives, short trips) during shorter foraging trips and during early chick-rearing

Landscape statistics of the low autocorrelated binary string problem

The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape structure which have been introduced in the Simulated Annealing literature, namely, depth and difficulty, we find that the landscape of LABSP, except perhaps for a very large degeneracy of the local minima energies, is qualitatively similar to some well-known landscapes such as that of the mean-field 2-spin glass model. Furthermore, we consider a mean-field approximation to the pure model proposed by Bouchaud and Mezard (1994, J. Physique I France 4 1109) and show both analytically and numerically that it describes extremely well the statistical properties of LABSP

Inter-individual differences in foraging tactics of a colonial raptor : consistency, weather effects, and fitness correlates

Background: Consistent inter-individual differences in behavioural phenotypes may entail differences in energy efficiency and expenditure, with different fitness payoffs. In colonial-breeding species, inter-individual differences in foraging behaviour may evolve to reduce resource use overlap among conspecifics exploiting shared foraging areas. Furthermore, individual differences in foraging behaviour may covary with individual characteristics, such as sex or physiological conditions. Methods: We investigated individual differences in foraging tactics of a colonial raptor, the lesser kestrel (Falco naumanni). We tracked foraging trips of breeding individuals using miniaturized biologgers. We classified behaviours from GPS data and identified tactics at the foraging trip level by cluster analysis. We then estimated energy expenditure associated to each tactic from tri-axial accelerometer data. Results: We obtained 489 foraging trips by 36 individuals. Two clusters of trips were identified, one (SF) characterized by more static foraging behaviour and the other (DF) by more dynamic foraging behaviour, with a higher proportion of flying activity and a higher energy expenditure compared to SF. Lesser kestrels showed consistent inter-individual differences in foraging tactics across weather condition gradients, favouring DF trips as solar radiation and crosswind intensity increased. DF trips were more frequent during the nestling-rearing than during the egg incubation stage. Nestlings whose tracked parent was more prone to perform DF trips experienced higher daily mass increase, irrespective of nestling feeding rates. Conclusions: Our study provided evidence that breeding lesser kestrels flexibly adopted different foraging tactics according to contingent weather landscapes, with birds showing consistent inter-individual differences in the tendency to adopt a given tactic. The positive correlation between the tendency to perform more energy-demanding DF trips and nestling growth suggests that individual differences in foraging behaviour may play a role in maintaining key life-history trade-offs between reproduction and self-maintenance

Grafting vigour is associated with DNA de-methylation in eggplant.

In horticulture, grafting is a popular technique used to combine positive traits from two different plants. This is achieved by joining the plant top part (scion) onto a rootstock which contains the stem and roots. Rootstocks can provide resistance to stress and increase plant production, but despite their wide use, the biological mechanisms driving rootstock-induced alterations of the scion phenotype remain largely unknown. Given that epigenetics plays a relevant role during distance signalling in plants, we studied the genome-wide DNA methylation changes induced in eggplant (Solanum melongena) scion using two interspecific rootstocks to increase vigour. We found that vigour was associated with a change in scion gene expression and a genome-wide hypomethylation in the CHH context. Interestingly, this hypomethylation correlated with the downregulation of younger and potentially more active long terminal repeat retrotransposable elements (LTR-TEs), suggesting that graft-induced epigenetic modifications are associated with both physiological and molecular phenotypes in grafted plants. Our results indicate that the enhanced vigour induced by heterografting in eggplant is associated with epigenetic modifications, as also observed in some heterotic hybrids

Last passage percolation and traveling fronts

We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida. The particles can be interpreted as last passage times in directed percolation on {1,...,N} of mean-field type. The particles remain grouped and move like a traveling wave, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. The Gumbel distribution plays a central role for the particle jumps, and we show that the scaling limit is a L\'evy process in this case. The case of bounded jumps yields a completely different behavior

A split-GFP tool reveals differences in the sub-mitochondrial distribution of wt and mutant alpha-synuclein

Parkinson's disease (PD), the second most common neurodegenerative disorder, is characterized by dopaminergic neuronal loss that initiates in the substantia nigra pars compacta and by the formation of intracellular inclusions mainly constituted by aberrant \u3b1-synuclein (\u3b1-syn) deposits known as Lewy bodies. Most cases of PD are sporadic, but about 10% are familial, among them those caused by mutations in SNCA gene have an autosomal dominant transmission. SNCA encodes \u3b1-syn, a small 140-amino acids protein that, under physiological conditions, is mainly localized at the presynaptic terminals. It is prevalently cytosolic, but its presence has been reported in the nucleus, in the mitochondria and, more recently, in the mitochondria-associated ER membranes (MAMs). Whether different cellular localizations may reflect specific \u3b1-syn activities is presently unclear and its action at mitochondrial level is still a matter of debate. Mounting evidence supports a role for \u3b1-syn in several mitochondria-derived activities, among which maintenance of mitochondrial morphology and modulation of complex I and ATP synthase activity. \u3b1-syn has been proposed to localize at the outer membrane (OMM), in the intermembrane space (IMS), at the inner membrane (IMM) and in the mitochondrial matrix, but a clear and comparative analysis of the sub-mitochondrial localization of WT and mutant \u3b1-syn is missing. Furthermore, the reasons for this spread sub-mitochondrial localization under physiological and pathological circumstances remain elusive. In this context, we decided to selectively monitor the sub-mitochondrial distribution of the WT and PD-related \u3b1-syn mutants A53T and A30P by taking advantage from a bimolecular fluorescence complementation (BiFC) approach. We also investigated whether cell stress could trigger \u3b1-syn translocation within the different mitochondrial sub-compartments and whether PD-related mutations could impinge on it. Interestingly, the artificial targeting of \u3b1-syn WT (but not of the mutants) to the mitochondrial matrix impacts on ATP production, suggesting a potential role within this compartment

Phase transition and landscape statistics of the number partitioning problem

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution, is investigated by examining the energy landscape of this classic optimization problem. This is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure, termed a barrier tree, the leaves and internal nodes of which represent, respectively, the minima and the lowest energy saddles connecting those minima. Here we apply several measures of shape (balance and symmetry) as well as of branch lengths (barrier heights) to the barrier trees that result from the landscape of the NPP, aiming at identifying traces of the easy/hard transition. We find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights. Only the {\it difficulty} measure, given by the maximum value of the ratio between the barrier height and the energy surplus of local minima, succeeded in detecting traces of the phase transition in the tree. In adddition, we show that the barrier trees associated with the NPP are very similar to random trees, contrasting dramatically with trees associated with the $p$ spin-glass and random energy models. We also examine critically a recent conjecture on the equivalence between the NPP and a truncated random energy model

Higher spin quaternion waves in the Klein-Gordon theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories