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In this article, we report on four observations of loggerhead sea turtles (Caretta caretta) foraging on sea cucumbers (Holothuria spp.), on Zakynthos Island, Greece. Direct observations of this behaviour are underreported in the literature. Foraging on such prey was in general a challenging process as the turtles used their flippers and their beak to cut the sea cucumbers albeit without success. They ended up shallowing the sea cucumbers most likely in one intact piece. Even though this behaviour is rare in this site, two out of four observations involved the same male sea turtle, indicating potentially specific dietary preferences for this individual.

In this short report, we provide a direct evidence that loggerhead sea turtles Caretta caretta are capable of partially burying themselves in the sand by actively moving their front flippers and stirring the sea bottom sediment. In particular, we report the cases of three male loggerhead sea turtles from Zakynthos island, Greece, which, after obtaining a resting position on a sandy spot at the sea bottom, they actively performed digging and stirring movements with their front flippers, resulting to the sand getting raised at the sea column. When the sand settled back, the turtles ended up half-buried and camouflaged. To our current knowledge, this self-burying behaviour has not been described in the literature.

Documenting how human pressure on wildlife changes over time is important to minimise potential adverse effects through implementing appropriate management and policy actions; however, obtaining objective measures of these changes and their potential impacts is often logistically challenging, particularly in the natural environment. Here, we developed a modular stochastic model that infers the ratio of actual viewing pressure on wildlife in consecutive time periods (years) using social media, as this medium is widespread and easily accessible. Pressure was calculated from the number of times individual animals appeared in social media in pre-defined time windows, accounting for time-dependent variables that influence them (e.g. number of people with access to social media). Formulas for the confidence intervals of viewing pressure ratios were rigorously developed and validated, and corresponding uncertainty was quantified. We applied the developed framework to calculate changes to wildlife viewing pressure on loggerhead sea turtles (Caretta caretta) at Zakynthos island (Greece) before and during the COVID-19 pandemic (2019-2021) based on 2646 social media entries. Our model ensured temporal comparability across years of social media data grouped in time window sizes, by correcting for the interannual increase of social media use. Optimal sizes for these windows were delineated, reducing uncertainty while maintaining high time-scale resolution. The optimal time window was around 7-days during the peak tourist season when more data were available in all three years, and >15 days during the low season. In contrast, raw social media data exhibited clear bias when quantifying changes to viewing pressure, with unknown uncertainty. The framework developed here allows widely-available social media data to be used objectively when quantifying temporal changes to wildlife viewing pressure. Its modularity allowed viewing pressure to be quantified for all data combined, or subsets of data (different groups, situations or locations), and could be applied to any site supporting wildlife exposed to tourism.

Animal imagery uploaded on social media has been identified as an important tool in wildlife research and conservation and has been used in a variety of recent studies. Here a case study is presented, where a detailed analysis of social media content revealed a shift of a long-term foraging habitat for a juvenile loggerhead sea turtle (Caretta caretta) in Greece. In particular, this individual was a long term resident of Zakynthos island, Greece, from 2016 until 2020 (5 consecutive summer seasons), regularly foraging on a nearshore reef, with no observations of it being made during the 2021 season. However regular social media image mining combined with photo-identification, detected this individual foraging in the Gulf of Corinth in August 2021, more that 200km away from his previous foraging habitat. This case study (i) shows the possibility for juvenile loggerheads to shift their foraging site even after long term use, with implications in capture-mark-recapture studies and (ii) once more highlights the usefulness of social media mining and citizen science in diverse aspects of sea turtle studies.

Establishing how wildlife viewing pressure is distributed across individual animals within a population can inform the management of this activity, and ensure targeted individuals or groups are sufficiently protected. Here, we used social media data to quantify whether tourism pressure varies in a loggerhead sea turtle (Caretta caretta) population and elucidate potential implications. Laganas Bay (Zakynthos, Greece) supports both breeding (migratory, and hence transient) and foraging (resident) turtles, with turtle viewing representing a major component of the tourism industry. Social media entries spanning two seasons (April to November, 2018 and 2019) were evaluated, and turtles were identified via photo-identification. For both years, 1684 and 2105 entries of 139 and 122 unique turtles were obtained from viewings, respectively (boats and underwater combined). However, while residents represented less than one-third of uniquely identified turtles, they represented 81.9% and 87.9% of all entries. Even when the seasonal breeding population was present (May to July), residents represented more than 60% entries. Of note, the same small number of resident turtles (

We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of the operator in all basic Lebesgue, Sobolev and BV spaces as well as corresponding approximation results. The results are then applied to extend recently developed theory concerning the density of convex intersections., 28 pages

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided.

Sex-biased survival linked to anthropogenic threats places populations at risk. We show the utility of long-term multidecadal photo-identification (photo-id) combined with long-term high-resolution (Fastloc-GPS) satellite telemetry to investigate the links between mortality rates and patterns of movement for a wide-ranging, endangered marine vertebrate. Using a photo-identification database of 947 loggerhead turtles (Caretta caretta) compiled over 18 yr, we estimated greater annual survival rates of females (0.89; 95% confidence interval [CI] 0.87-0.90) compared to males (0.73; 95% CI 0.67-0.78). For males satellite-tracked across multiple breeding seasons, 100% (26 of 26) returned to the same breeding site, suggesting the calculated lower male survival rate was likely not due to emigration to breed elsewhere. 10,111 and 2,524 tracking days for males (n = 39 individuals) and females (n = 18 individuals), respectively, revealed different habitat-use patterns outside the breeding season: males tended to occupy foraging sites closer to shore and closer to breeding sites but, due to their generally annual breeding, compared to biennial breeding for females, males migrated further per year on average. These differences in movement patterns likely contribute to higher mortality in males through increased interaction with anthropogenic threats. Long-term identification coupled with tracking offers great promise for estimating the survival rates of other wide-ranging species.

Quantitative magnetic resonance imaging (qMRI) is concerned with estimating (in physical units) values of magnetic and tissue parameters e.g., relaxation times $T_1$, $T_2$, or proton density $\rho$. Recently in [Ma et al., Nature, 2013], Magnetic Resonance Fingerprinting (MRF) was introduced as a technique being capable of simultaneously recovering such quantitative parameters by using a two step procedure: (i) given a probe, a series of magnetization maps are computed and then (ii) matched to (quantitative) parameters with the help of a pre-computed dictionary which is related to the Bloch manifold. In this paper, we first put MRF and its variants into a perspective with optimization and inverse problems to gain mathematical insights concerning identifiability of parameters under noise and interpretation in terms of optimizers. Motivated by the fact that the Bloch manifold is non-convex and that the accuracy of the MRF-type algorithms is limited by the "discretization size" of the dictionary, a novel physics-based method for qMRI is proposed. In contrast to the conventional two step method, our model is dictionary-free and is rather governed by a single non-linear equation, which is studied analytically. This non-linear equation is efficiently solved via robustified Newton-type methods. The effectiveness of the new method for noisy and undersampled data is shown both analytically and via extensive numerical examples for which also improvement over MRF and its variants is documented.

The purpose of the present chapter is to bind together and extend some recent developments regarding data-driven nonsmooth regularization techniques in image processing through the means of a bilevel minimization scheme. The scheme, considered in function space, takes advantage of a dualization framework and it is designed to produce spatially varying regularization parameters adapted to the data for well-known regularizers, e.g., total variation and total generalized variation, leading to automated (monolithic), image reconstruction workflows. An inclusion of the theory of bilevel optimization and the theoretical background of the dualization framework, as well as a brief review of the aforementioned regularizers and their parameterization, makes this chapter a self-contained one. Aspects of the numerical implementation of the scheme are discussed and numerical examples are provided.

In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable total variation type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted total variation for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable., Comment: 34 pages, 89 figures