The boundary of a smooth set has full Hausdorff dimension

AbstractWe prove that if the restriction of the Lebesgue measure to a set A⊂[0,1] with 0<|A|<1 is a smooth measure, then the boundary of A must have full Hausdorff dimension

Lagrangian studies, circulation and mixing in the Southern Ocean

Oceans play a vital role as one of the major components of Earth's climate system. The study of oceanic processes and the complexity inherent in dynamic ows is essential for understanding their regulatory character on the climate's variability. A key region for the study of such intrinsic oceanic variability is the Southern Ocean. In the form of a wind-driven, zonally unbounded, strong eastward ow, the Antarctic Circumpolar Current (ACC) circumnavigates the Antarctic continent connecting each of the ocean basins. The dynamics of the ACC, which is characterised by the absence of land barriers, apart from when crossing Drake Passage, have long been a topic of debate [Rintoul et al., 2001]. The main interests of this study focus on inferring and mapping the dynamic variability the ACC exhibits by means of transient disturbances [Hughes, 2005] (such as mesoscale eddies) and subsequent mixing from Lagrangian trajectories. The distribution of eddy transport and intensity, the mixing of conservative quantities and ow dynamics through to the interaction of eddy kinetic energy, mean ow and topography are examined. The sparseness of observations in the Southern Ocean and the necessity to understand the role of the oceanic circulation in the climate by a holistic approach highlights computational ocean circulation models as indispensable. In the context of this study, output from the run401 of the Ocean Circulation and Climate Advance Model (OCCAM) 1/12� ocean model, developed at the U.K. National Oceanography Centre, is utilised. In order to deduce the temporal and spatial variability of the ow dynamics, as well as its vertical distribution, simulation of monthly releases of passive particles using di�erent schemes (i.e. cluster or linear alignment) on isobaric and isoneutral surfaces was conducted. An analysis of the Lagrangian trajectories reveals the characteristics of the dynamics that control the ow and depict regions of enhanced eddy activity and mixing. The model's ability to simulate real oceanic ows is established through comparison with a purposeful release of the tracer CF3SF5, which is conducted as part of the DIMES experiment (http://dimes.ucsd.edu/). We �nd that topography plays a fundamental role in the context of Southern Ocean mixing through the association of high EKE regions, where the interaction of vortical elements and multi �lamented jets in non-parallel ows supports an e�ective mechanism for eddy stirring, resulting in the enhanced dispersion of particles. Suppression of mixingin regions where the ow is delineated by intensi�ed and coherent, both in space and time, jets (strong PV gradients) signifying the separation of the ow in di�erentiated kinematic environments, is illustrated. The importance of a local approximation to mixing instead of the construction of zonal averages is presented. We present the caveats of classical di�usion theory in the presence of persistent structures and �nd that values of 1000-2000 m2

A multi-measure approach for assessing the performance of fMRI preprocessing strategies in resting-state functional connectivity

It is well established that head motion and physiological processes (e.g. cardiac and breathing activity) should be taken into consideration when analyzing and interpreting results in fMRI studies. However, even though recent studies aimed to evaluate the performance of different preprocessing pipelines there is still no consensus on the optimal strategy. This is partly due to the fact that the quality control (QC) metrics used to evaluate differences in performance across pipelines have often yielded contradictory results. Furthermore, preprocessing techniques based on physiological recordings or data decomposition techniques (e.g. aCompCor) have not been comprehensively examined. Here, to address the aforementioned issues, we propose a framework that summarizes the scores from eight previously proposed and novel QC metrics to a reduced set of two QC metrics that reflect the signal-to-noise ratio and the reduction in motion artifacts and biases in the preprocessed fMRI data. Using this framework, we evaluate the performance of three commonly used practices on the quality of data: 1) Removal of nuisance regressors from fMRI data, 2) discarding motion-contaminated volumes (i.e., scrubbing) before regression, and 3) low-pass filtering the data and the nuisance regressors before their removal. Using resting-state fMRI data from the Human Connectome Project, we show that the scores of the examined QC metrics improve the most when the global signal (GS) and about 17% of principal components from white matter (WM) are removed from the data. Finally, we observe a small further improvement with low-pass filtering at 0.20 Hz and milder variants of WM denoising, but not with scrubbing

The distinction between laiko and logio as a particular characteristic of the Modern Greek language: historical interpretation, contemporary function and didactic usage

It is well known that the Greek language, despite its long history and the various adventures it has experienced over the centuries and in contrast with other ancient European languages (e.g. Latin), has not undergone any radical changes with the passage of time. Instead, it has maintained a noteworthy diachronic homogeneity and a unified character that have made it intriguing for scholars and, at the same time, give it a unique nature. The functional presence of a large number of diachronic elements within contemporary Modern Greek undoubtedly make it a unique case. They have not, however, been sufficiently researched, and this paper aims to make a contribution in this direction

EFFECT OF SUBSIDIES ON HEDONIC PRICE MODEL – CASE OF HOTEL ROOM RATES IN CYPRUS DURING COVID-19

Hedonički cjenovni model koristi se za analizu cijena hotelskih soba od početka 1990-ih godina i danas se smatra standardnim načinom određivanja faktora koji najviše utječu na cijene hotelskih soba. Međutim, neki oblici državnih intervencija, poput putnih subvencija, mogu smanjiti razmjer u kojem cijene soba odražavaju implicitne cijene značajki hotela, što predstavlja izazov za primjenjivost hedoničkog cjenovnog modela ako postoje subvencije. U ovome se radu istražuju ti izazovi procjenjivanjem hedoničkih cjenovnih modela na primjeru cijene hotelskih soba na Cipru – državi čije je gospodarstvo vrlo ovisno o sektoru putovanja i turizma – odmah nakon uvođenja programa izdašnog subvencioniranja odmora. Glavni rezultati sugeriraju da subvencije iskrivljuju implicitne cijene karakteristika hotela, što ukazuje na potreban oprez u primjeni hedoničkog modela određivanja cijena u slučajevima državnih intervencija. Rezultati također traže poboljšanja teoretskog okvira hedoničke analize čijim bi se uključivanjem objasnio učinak cjenovnih subvencija na implicitne cijene značajki hotela.The hedonic price model has been used to analyse the price of hotel rooms since the beginning of the 1990s and it has subsequently become the standard manner of determining which factors affect room rates the most. However, some forms of government interventions, such as the implementation of travel subsidies, may diminish the degree in which the room rates reflect the implicit prices of hotel characteristics, something that generates concerns regarding applicability of the hedonic pricing model in the presence of subsidies. This article investigates these concerns by estimating hedonic price models using room rates from Cyprus – a nation whose economy is heavily reliant on the sector of travel and tourism – on the implementation of a substantial holiday subsidy scheme. The main findings suggest that the implicit prices of hotel attributes are distorted in the presence of subsidies, thus calling for precaution when the hedonic pricing model is applied as governmental intervention. The findings also require amendments of the theoretical framework hedonic analysis to incorporate and explain the effect of price subsidies in the implicit prices of the characteristics of the hotels