On Coron's problem for the p-Laplacian

We prove that the critical problem for the $p$-Laplacian operator admits a nontrivial solution in annular shaped domains with sufficiently small inner hole. This extends Coron's problem to a class of quasilinear problems.Comment: 6 page

Cognitive fluctuations in connection to disgraphia a comparison of Alzheimer's disease with dementia Lewy bodies

Background: The purpose of the present study was to examine the relationship between cognitive impairment and the performance of handwritten scripts presented as “letter-writing” to a close relative by patients with dementia Lewy bodies (DLB), as fluctuations of the symptoms phase, and in a matched group of patients with Alzheimer’s disease (AD). The degree of writing disability and personal, spatial, and temporal orientation was compared in these two groups. Design and methods: Fourteen simple questions, designed in a form that could be utilized by any general practitioner in order to document the level of cognitive functioning of each patient, were presented to 30 AD patients and 26 DLB patients. The initial cognition test was designated PQ1. The patients were examined on tests of letter-writing ability. Directly after the letter-writing, the list of 14 questions presented in PQ1 was presented again in a repeated procedure that was designated PQ2. The difference between these two measures (PQ1 – PQ2) was designated D∆. This test of letter-writing ability and cognitive performance was administered over 19 days. Results: Several markedly strong relationships between dysgraphia and several measures of cognitive performance in AD patients and DLB patients were observed, but the deterioration of performance from PQ1 to PQ2 over all test days were markedly significant in AD patients and not significant in DLB patients. It is possible that in graphic expression even by patients diagnosed with moderate to relatively severe AD and DLB there remains some residual capacity for understanding and intention that may be expressed. Furthermore, the deterioration in performance and the differences noted in AD and DLB patients may be due to the different speed at which the process of the protein degradation occurs for functional modification of synapses. Conclusion: Our method can be used as part of neuropsychological tests to differentiate the diagnosis between AD and DL

Arithmetic of metaplectic modular forms

Modular forms came to the attention of number theorists through the wealth of their arithmetic behaviour, the development and applications of which continue to surprise. Arithmetic data of associated $L$-functions have conjectured links to fundamental questions, for example the generalised Riemann hypothesis and the BSD conjecture; special values of $L$-functions and their $p$-adic analogues have had a key role in progress towards BSD. Modular forms of half-integral weight have a number-theoretic history spanning as far back as that of their integral-weight counterparts, but their arithmetic theory has long been latent. Being fundamental variants of integral-weight modular forms, a fully fledged theory of half-integral weight modular forms has high potential for impact in areas of number theory. In this thesis, we develop four key areas in the arithmeticity of Siegel modular forms of half-integral weight, focusing on the behaviour of their Fourier coefficients and associated $L$-functions as follows: an analogue of Garrett's conjecture on the precise algebraicity of Klingen Eisenstein series and of the decomposition $\mathcal{M}_k = \mathcal{S}_k\oplus\mathcal{E}_k$; the precise algebraicity of special $L$-values; the existence of $p$-adic $L$-functions; and, for vector-valued modular forms, an explicit Rankin-Selberg integral expression. Some of the results, such as special values of $L$-functions, are further refinements of existing theorems; others, such as the construction of $p$-adic $L$-functions, are entirely new. The multifaceted nature of modular forms is a considerable characteristic of theirs. Classically developed as analytic objects, integral-weight modular forms have been reinterpreted algebraically in terms of automorphic representations and associations to motives. Since the algebraic viewpoint remains insufficient for our purposes we focus on the analytic theory and methods of proof for half-integral weight modular forms, using Shimura's theory of Hecke operators and his Rankin-Selberg expression as a basis, and modifying the established methods of Harris, Sturm, and Panchishkin to prove our results

Differences between eccentric and rotary tablet machines in the evaluation of powder densification behaviour

Differences in the dynamics of powder densification between eccentric and rotary machine were pointed out by compressing at different compression pressures microcrystal line cellulose, lactose monohydrate and dicalcium phosphate dihydrate and recovering the corresponding stress/strain data in both machines equipped to monitor punches displacement and compression forces. Heckel plots were then obtained from these stress/strain data. Curves obtained in the rotary machine possess a narrower zone of linearity for the calculation of P-Y and D-A. The effect of the different compression mechanism of the rotary machine on the shape of the Heckel plot is more noticeable in a non-deforming material such as dicalcium phosphate. The effect of the longer dwell time of the rotary machine on the porosity reduction occurring after the maximum pressure has been reached, is more noticeable in a ductile material such as microcrystalline cellulose. Heckel parameters obtained in the rotary press are in some cases different from those recovered in the eccentric machine because of the longer dwell time, machine deflection and punch tilting occurring in the rotary machine, although theoretically they could better describe the material densification in a high speed production rotary machine

Evolutionary Quantum Dynamics of a Generic Universe

The implications of an Evolutionary Quantum Gravity are addressed in view of formulating a new dark matter candidate. We consider a Schr\"odinger dynamics for the gravitational field associated to a generic cosmological model and then we solve the corresponding eigenvalues problem, inferring its phenomenological issue for the actual Universe. The spectrum of the super-Hamiltonian is determined including a free inflaton field, the ultrarelativistic thermal bath and a perfect gas into the dynamics. We show that, when a Planckian cut-off is imposed in the theory and the classical limit of the ground state is taken, then a dark matter contribution can not arise because its critical parameter $\Omega_{dm}$ is negligible today when the appropriate cosmological implementation of the model is provided. Thus, we show that, from a phenomenological point of view, an Evolutionary Quantum Cosmology overlaps the Wheeler-DeWitt approach and therefore it can be inferred as appropriate to describe early stages of the Universe without significant traces on the later evolution. Finally, we provide indications that the horizon paradox can be solved in the Planck era by the morphology of the Universe wave function.Comment: 7 pages, to appear on Phys. Lett.

Complex geometry and kinematics of subsidiary faults within a carbonate-hosted relay ramp

Minor fault geometry and kinematics within relay ramps is strongly related to the stress field perturbations that can be produced when two major fault segments overlap and interact. Here we integrate classical fieldwork and interpretation of a virtual outcrop to investigate the geometry and kinematics of subsidiary faults within a relay ramp along the Tre Monti normal fault in the Central Apennines. Although the Tre Monti fault strikes parallel to the regional extension (NE-SW) it shows predominant dip-slip kinematics, suggesting a NW-SE oriented extension acting at sub-regional scale (1–10 km). Conversely, the slickenlines collected on the front segment of the relay ramp highlight right-lateral kinematics. The subsidiary faults in the relay ramp show a complex geometry (variable attitudes) and slickenlines describe multiple kinematics (left-lateral, dip-slip, right-lateral), independently of their orientation. Our fault slip analysis indicates that a local stress field retrieved from the kinematic inversion of the slickenlines collected on the front segment, and likely promoted by the interaction between the overlapping fault segments that bound the relay zone, can explain most of the geometry and kinematics of the subsidiary faults. Further complexity is added by the temporal interaction with both the regional and sub-regional stress fields

Modified FMCW scheme for improved ultrasonic positioning and ranging of unmanned ground vehicles at distances < 50 mm

Unmanned ground vehicles (UGVs) find extensive use in various applications, including that within industrial environments. Efforts have been made to develop cheap, portable, and light-ranging/positioning systems to accurately locate their absolute/relative position and to automatically avoid potential obstacles and/or collisions with other drones. To this aim, a promising solution is the use of ultrasonic systems, which can be set up on UGVs and can potentially output a precise reconstruction of the drone’s surroundings. In this framework, a so-called frequency-modulated continuous wave (FMCW) scheme is widely employed as a distance estimator. However, this technique suffers from low repeatability and accuracy at ranges of less than 50 mm when used in combination with low-resource hardware and commercial narrowband transducers, which is a distance range of the utmost importance to avoid potential collisions and/or imaging UGV surroundings. We hereby propose a modified FMCW-based scheme using an ad hoc time-shift of the reference signal. This was shown to improve performance at ranges below 50 mm while leaving the signal unaltered at greater distances. The capabilities of the modified FMCW were evaluated numerically and experimentally. A dramatic enhancement in performance was found for the proposed FMCW with respect to its standard counterpart, which is very close to that of the correlation approach. This work paves the way for the future use of FMCWs in applications requiring high precision

Cerebellar white matter disruption in Alzheimer’s Disease patients: a Diffusion Tensor Imaging study

The cognitive role of the cerebellum has recently gained much attention, and its pivotal role in Alzheimer’s disease (AD) has now been widely recognized. Diffusion tensor imaging (DTI) has been used to evaluate the disruption of the microstructural milieu in AD, and though several white matter (WM) tracts such as corpus callosum, inferior and superior longitudinal fasciculus, cingulum, fornix, and uncinate fasciculus have been evaluated in AD, data on cerebellar WM tracts are currently lacking. We performed a tractography-based DTI reconstruction of the middle cerebellar peduncle (MCP), and the left and right superior cerebellar peduncles separately (SCPL and SCPR) and addressed the differences in fractional anisotropy (FA), axial diffusivity (Dax), radial diffusivity (RD), and mean diffusivity (MD) in the three tracts between 50 patients with AD and 25 healthy subjects. We found that AD patients showed a lower FA and a higher RD compared to healthy subjects in MCP, SCPL, and SCPR. Moreover, a higher MD was found in SCPR and SCPL and a higher Dax in SCPL. This result is important as it challenges the traditional view that WM bundles in the cerebellum are unaffected in AD and might identify new targets for therapeutic interventions

Photogrammetric 3D model via smartphone GNSS sensor. Workflow, error estimate, and best practices

Geotagged smartphone photos can be employed to build digital terrain models using structure from motion-multiview stereo (SfM-MVS) photogrammetry. Accelerometer, magnetometer, and gyroscope sensors integrated within consumer-grade smartphones can be used to record the orientation of images, which can be combined with location information provided by inbuilt global navigation satellite system (GNSS) sensors to geo-register the SfM-MVS model. The accuracy of these sensors is, however, highly variable. In this work, we use a 200 m-wide natural rocky cliff as a test case to evaluate the impact of consumer-grade smartphone GNSS sensor accuracy on the registration of SfM-MVS models. We built a high-resolution 3D model of the cliff, using an unmanned aerial vehicle (UAV) for image acquisition and ground control points (GCPs) located using a differential GNSS survey for georeferencing. This 3D model provides the benchmark against which terrestrial SfM-MVS photogrammetry models, built using smartphone images and registered using built-in accelerometer/gyroscope and GNSS sensors, are compared. Results show that satisfactory post-processing registrations of the smartphone models can be attained, requiring: (1) wide acquisition areas (scaling with GNSS error) and (2) the progressive removal of misaligned images, via an iterative process of model building and error estimation

The visual function assessment: from birth to the follow up

Preterm infants have a high risk to develop visual deficits due to retinopathy of prematurity (ROP), brain lesionsand prematurity per se [1]. The possibility to assess different aspects of visual function can allow early and specific intervention in an attempt to reduce the risk of difficulties in motor coordination, attention and learning at school age. The aim is to identify early signs of visual and motorperceptual deficit in the first years in order to program a specific intervention before school age