A C 0 conforming dg finite element method for biharmonic equations on triangle/tetrahedron

A C 0 conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the biharmonic equation. The first strong gradient of C 0 finite element functions is a vector of discontinuous piecewise polynomials. The second gradient is the weak gradient of discontinuous piecewise polynomials. This method, by its name, uses nonconforming (non C 1) approximations and keeps simple formulation of conforming finite element methods without any stabilizers. Optimal order error estimates in both a discrete H 2 norm and the L 2 norm are established for the corresponding finite element solutions. Numerical results are presented to confirm the theory of convergence.

Mutation-related apparent myelin, not axon density, drives white matter differences in premanifest Huntington's disease: Evidence from in vivo ultra-strong gradient MRI

White matter (WM) alterations have been observed early in Huntington's disease (HD) progression but their role in the disease-pathophysiology remains unknown. We exploited ultra-strong-gradient MRI to tease apart contributions of myelin (with the magnetization transfer ratio), and axon density (with the restricted volume fraction from the Composite Hindered and Restricted Model of Diffusion) to WM differences between premanifest HD patients and age- and sex-matched controls. Diffusion tensor MRI (DT-MRI) measures were also assessed. We used tractometry to investigate region-specific changes across callosal segments with well-characterized early- and late-myelinating axonal populations, while brain-wise alterations were explored with tract-based cluster analysis (TBCA). Behavioural measures were included to explore disease-associated brain-function relationships. We detected lower myelin in the rostrum of patients (tractometry: p = 0.0343; TBCA: p = 0.030), but higher myelin in their splenium (p = 0.016). Importantly, patients' myelin and mutation size were positively associated (all p-values < 0.01), indicating that increased myelination might be a direct result of the mutation. Finally, myelin was higher than controls in younger patients but lower in older patients (p = 0.003), suggesting detrimental effects of increased myelination later in the course of the disease. Higher FR in patients' left cortico-spinal tract (CST) (p = 0.03) was detected, and was found to be positively associated with MTR in the posterior callosum (p = 0.033), possibly suggesting compensation to myelin alterations. This comprehensive, ultra-strong gradient MRI investigation provides novel evidence of CAG-driven myelin alterations in premanifest HD which may reflect neurodevelopmental, rather than neurodegenerative disease-associated changes.

Fate of turbid glacial inflows in a hydroelectric reservoir

Turbidity from glacial meltwater limits light penetration with potential ecological consequences. Using profiles of temperature, conductivity, and turbidity, we examine the physical processes driving changes in the epilimnetic turbidity of Carpenter Reservoir, a long and narrow, glacier-fed reservoir in southwest British Columbia, Canada. Following the onset of permanent summer stratification, the relatively dense inflows plunged into the hypolimnion, and despite the high glacial load entering the reservoir, the epilimnion cleared due to particle settling. Using a one-dimensional (longitudinal) diffusion equation for a decaying substance to describe the variation in epilimnetic turbidity, we obtain two nondimensional parameters: the epilimnetic inflow parameter, $$\mathcal {I}$$ I , a measure of the turbidity flux into the epilimnion; and the dispersion parameter, $${\mathcal {D}}$$ D , a measure of longitudinal dispersion. In the case of Carpenter Reservoir: $$\mathcal {I}\ll 1$$ I ≪ 1 , indicating that turbidity declines over the summer; and $${\mathcal {D}}\ll 1$$ D ≪ 1 , indicating a strong gradient in turbidity along the epilimnion. Using our theoretical formulation of epilimnetic turbidity variations in conjunction with monthly field surveys, we compute the particle settling velocity ($${\sim}{0.25}\,{\hbox {m}\,\hbox {d}^{-1}}$$ ∼ 0.25 m d - 1 ), the longitudinal dispersion coefficient (50–70 $${\hbox {m}^{2}\,\hbox {s}^{-1}}$$ m 2 s - 1 ), and the flux of turbid water into the epilimnion ($${\sim }1{\%}$$ ∼ 1 % of the total inflow). Our approach is applicable to other reservoirs and can be used to investigate changes in turbidity in response to changes in $$\mathcal {I}$$ I and $${\mathcal {D}}$$ D .

Warming in Europe: Recent Trends in Annual and Seasonal temperatures

Contemporary climate warming is a key problem faced not only by scientists, but also all by humanity because, as is shown by the experience of recent years, it has multiple environmental, economic and biometeorological implications. In this paper, the authors identify the magnitude of annual and seasonal temperature changes in Europe and its immediate surroundings on the basis of data from 210 weather stations from 1951 to 2020. An analysis of temperatures in the 70-year period shows that air temperature has continued to grow linearly in Europe since 1985. The rate of temperature rise in three seasons of the year, namely winter, spring and summer, does not differ greatly. The highest growth over the 1985–2020 timespan was recorded in spring and the lowest in autumn—0.061 °C/year and 0.045 °C/year, respectively. In winter, the rise in temperature should be considered the least steady, as opposed to the summer when it displays the greatest stability. Overall, the warming intensifies towards the north-east of the continent. Such a strong gradient of change is especially perceivable in winter and spring, and is also marked in autumn. The opposite is true in summer, when it increases towards the south and south-west.

Investigation of space-borne trace gas products over St. Petersburg and Yekaterinburg, Russia by using COCCON observations

This work employs ground- and space-based observations, together with model data to study columnar abundances of atmospheric trace gases (XH2O, XCO2, XCH4, and XCO) in two high-latitude Russian cities, St. Petersburg and Yekaterinburg. Two portable COllaborative Column Carbon Observing Network (COCCON) spectrometers were used for continuous measurements at these locations during 2019 and 2020. Additionally, a subset of data of special interest (a strong gradient in XCH4 and XCO was detected) collected in the framework of a mobile city campaign performed in 2019 using both instruments is investigated. All studied satellite products (TROPOMI, OCO-2, GOSAT, MUSICA IASI) show generally good agreement with COCCON observations. Satellite and ground-based observations at high latitude are much sparser than at low or mid latitude, which makes direct coincident comparisons between remote-sensing observations more difficult. Therefore, a method of scaling continuous CAMS model data to the ground-based observations is developed and used for creating virtual COCCON observations. These adjusted CAMS data are then used for satellite validation, showing good agreement in both Peterhof and Yekaterinburg cities. The gradients between the two study sites (ΔXgas) are similar between CAMS and CAMS-COCCON data sets, indicating that the model gradients are in agreement with the gradients observed by COCCON. This is further supported by a few simultaneous COCCON and satellite ΔXgas measurements, which also agree with the model gradient. With respect to the city campaign observations recorded in St. Petersburg, the downwind COCCON station measured obvious enhancements for both XCH4 (10.6 ppb) and XCO (9.5 ppb), which is nicely reflected by TROPOMI observations, which detect city-scale gradients of the order 9.4 ppb for XCH4 and 12.5 ppb XCO, respectively.

Sodium Radiofrequency Coils for Magnetic Resonance: From Design to Applications

Sodium (23Na) is the most abundant cation present in the human body and is involved in a large number of vital body functions. In the last few years, the interest in Sodium Magnetic Resonance Imaging (23Na MRI) has considerably increased for its relevance in physiological and physiopathological aspects. Indeed, sodium MRI offers the possibility to extend the anatomical imaging information by providing additional and complementary information on physiology and cellular metabolism with the heteronuclear Magnetic Resonance Spectroscopy (MRS). Constraints are the rapidly decaying of sodium signal, the sensitivity lack due to the low sodium concentration versus 1H-MRI induce scan times not clinically acceptable and it also constitutes a challenge for sodium MRI. With the available magnetic fields for clinical MRI scanners (1.5 T, 3 T, 7 T), and the hardware capabilities such as strong gradient strengths with high slew rates and new dedicated radiofrequency (RF) sodium coils, it is possible to reach reasonable measurement times (~10–15 min) with a resolution of a few millimeters, where it has already been applied in vivo in many human organs such as the brain, cartilage, kidneys, heart, as well as in muscle and the breast. In this work, we review the different geometries and setup of sodium coils described in the available literature for different in vivo applications in human organs with clinical MR scanners, by providing details of the design, modeling and construction of the coils.

Security for eHealth system: data hiding in AMBTC compressed images via gradient-based coding

Various eHealth applications based on the Internet of Things (IoT) contain a considerable number of medical images and visual electronic health records, which are transmitted through the Internet everyday. Information forensics thus becomes a critical issue. This paper presents a data hiding algorithm for absolute moment block truncation coding (AMBTC) images, wherein secret data, or the authentication code, can be embedded in images to enhance security. Moreover, in view of the importance of transmission efficiency in IoT, image compression is widely used in Internet-based applications. To cope with this challenge, we present a novel compression method named gradient-based (GB) compression, which is compatible with AMBTC compression. Therefore, after applying the block classification scheme, GB compression and data hiding can be performed jointly for blocks with strong gradient effects, and AMBTC compression and data hiding can be performed jointly for the remaining blocks. From the experimental results, we demonstrate that the proposed method outperforms other state-of-the-art methods.

WISDOM project – VII. Molecular gas measurement of the supermassive black hole mass in the elliptical galaxy NGC 7052

ABSTRACT Supermassive black hole (SMBH) masses can be measured by resolving the dynamical influences of the SMBHs on tracers of the central potentials. Modern long-baseline interferometers have enabled the use of molecular gas as such a tracer. We present here Atacama Large Millimeter/submillimeter Array observations of the elliptical galaxy NGC 7052 at 0${^{\prime\prime}_{.}}$11 ($37\,$pc) resolution in the 12CO(2-1) line and $1.3\,$ mm continuum emission. This resolution is sufficient to resolve the region in which the potential is dominated by the SMBH. We forward model these observations, using a multi-Gaussian expansion of a Hubble Space Telescope F814W image and a spatially constant mass-to-light ratio to model the stellar mass distribution. We infer an SMBH mass of $2.5\pm 0.3\times 10^{9}\, \mathrm{M_\odot }$ and a stellar I-band mass-to-light ratio of $4.6\pm 0.2\, \mathrm{M_\odot /L_{\odot ,I}}$ (3σ confidence intervals). This SMBH mass is significantly larger than that derived using ionized gas kinematics, which however appears significantly more kinematically disturbed than the molecular gas. We also show that a central molecular gas deficit is likely to be the result of tidal disruption of molecular gas clouds due to the strong gradient in the central gravitational potential.