Accurate Reconstruction of the Radiation of Sparse Sources from a Small Set of Near-Field Measurements by Means of a Smooth-Weighted Norm for Cluster-Sparsity Problems

The aim of this contribution is to present an approach that allows to improve the quality of the reconstruction of the far-field from a small number of measured samples by means of sparse recovery using a relatively coarse grid for source positions (with sample spacing of the order of λ/8) compared to the grid usually required. In particular, the iterative method proposed employs a smooth-weighted constrained minimization, that guarantees a better probability of correct estimate of the sparse sources and an improved quality in the reconstruction, with a similar computational effort respect to the standard ℓ1 re-weighted minimization approach.

Grounding Electrodes with Internal Resistance: Application to Feasibility Study of the Driven-Rod Method for Modeling the Soil Electrical Resistivity Profile

The paper presents a model to include the internal resistance of the grounding electrodes in the calculation of its electrical features. The semi-analytical expressions for the calculation of the grounding resistance arising from the model are used to study the feasibility of the driven-rod method for the estimation of the soil resistivity profile since, unlike other methods, the internal resistance of the conductors can be of great influence for a correct estimate. From the grounding resistance profile an inverse problem based on the minimization of the quadratic differences between the resistance measured and that calculated from the model is posed. Several synthetic examples are used to assess the limitations of the method in conditions close to real situations. Finally, some real cases involving data measured in the field are analyzed. Whether in synthetic examples or in real soils it is found that the spatial frequency of the driven-rod resistance sampling is a determinant factor in order to study the feasibility of the driven–rod method.

Differences of clinical and imaging findings in multiple generations of secondary COVID-19 infection in Xi’an, China

PURPOSEIn the global presence of secondary infections with the coronavirus disease 2019 (COVID-19), little is known about the transmission characteristics of COVID-19 outside Wuhan, China. We evaluated differences in clinic and radiologic findings of multiple generations of COVID-19 infection in Xi’an (Shaanxi, China) to provide more clues for the correct estimate of the disease.METHODSAll COVID-19 infected patients reported in Xi’an up to 10 February 2020 were included for this analysis. Among these cases, clinical and chest CT data of 62 cases were obtained from three hospital in Xi’an. With this information, patients were grouped on basis of exposure history and transmission chains as first-generation, second-generation and third-generation patients. We described clinical characteristics and evaluated CT score/patterns in these COVID-19 cases.RESULTSThere was a clear age differences in multiple generations with COVID-19 infection. Above two thirds of the second-generation (75.0%) and third-generation patients (77.8%) were aged ≥45 years while 40.0% of first-generation cases at this age (p=0.001). More than half of second-generation patients (52.8%) and third-generation patients (55.6%) have comorbidities and is predominantly hypertensive (22.8% of second-generation vs. 27.8% of third-generation infections). The main exposure of second- and third-generation patients in Xi’an is family exposure (35.2%). For evaluation of CT findings of pulmonary involvement, the total CT score were 4.22±3.00 in first-generation group, 4.35±3.03 in second-generation group and 7.62±3.56 in third-generation group (p<0.001). In all of three generations, the predominant pattern of abnormality observed was organizing pneumonia (65.5% in first-generation group, 61.5% in second-generation group and 71.4% in third-generation group). The average courses of the disease in third-generation infections has obviously extension (22.93±7.22 days of first-generation, 21.53±8.31 days of second-generation vs. 31.00±8.12 days of third-generation group, p=0.004). There were no significant differences of the pulmonary sequelae among three generation patients.CONCLUSIONThere is more serious pulmonary infection of COVID-19 pneumonia in second- and third-generation patients, which might be attribute to the elder age and comorbidity of these patients.

Near-Real-Time Loss Estimates for Future Italian Earthquakes Based on the M6.9 Irpinia Example

The number of fatalities and injured was calculated, using the computer code QLARM and its data set and assuming information about the Irpinia 1980 earthquake became available in near-real-time. The casualties calculated for a point source, an approximate line source and a well-defined line source would have become available about 30 min, 60 min and years after the main shock, respectively. The first estimate would have been satisfactory, indicating the seriousness of the disaster. The subsequent loss estimate after 60 min would have defined the human losses accurately, and the ultimate estimate was most accurate. In 2009, QLARM issued a correct estimate of the number of fatalities within 22 min of the M6.3 L’Aquila main shock. These two results show that the number of casualties and injuries in large and major earthquakes in Italy can be estimated correctly within less than an hour by using QLARM.

Fatigue monitoring of climbing ropes

Safety improvements in mountaineering gear have enabled the increasing popularity of rock climbing as a sport. Both amateurs and experts want to know the condition of their equipment with a high degree of reliability. For climbing ropes, diagnostics are only carried out qualitatively by visual inspection. The assessment is left to the personal judgment of the user, thus leaving considerable margins of uncertainty on the rope’s condition. To address this shortcoming, this article explores the possibility of estimating fatigue damage from the impact force on the rope. This value is estimated from the measurements of the climber’s acceleration using a wearable device. Then, force data are correlated to the fatigue characteristic of the rope. In this study, three ropes were used by professional climbers through different routes. After this field conditioning, the ropes were tested following the UIAA standard and compared to a control rope. The results show that the proposed method can estimate the rope cumulative damage, but it relies on the accuracy of the damage model. In particular, the parameter describing the contact between the rope and the runner is important for a correct estimate.

On Some Classical andWeighted Estimates for SL4

The purpose of this paper is two-sided. First, we obtain the correct estimate of the error term in the classical prime geodesic theorem for compact symmetric space SL4. As it turns out, the corrected error term depends on the degree of a certain polynomial appearing in the functional equation of the attached zeta function. This is in line with the known result in the case of compact Riemann surface, or more generally, with the corresponding result in the case of compact locally symmetric spaces of real rank one. Second, we derive a weighted form of the theorem. In particular, we prove that the aforementioned error term can be significantly improved when the classical approach is replaced by its higher level analogue.

Making bright giants invisible at the Galactic Centre

ABSTRACT Current observations of the Galactic Centre (GC) seem to display a core-like distribution of bright stars from ∼5 arcsec inwards. On the other hand, we observe young, massive stars at the GC, with roughly 20–50 per cent of them in a disc, mostly in the region where the bright giants appear to be lacking. In a previous publication we put the idea forward that the missing stars are deeply connected to the presence of this disc. The progenitor of the stellar disc is very likely to have been a gaseous disc that at some point fragmented and triggered star formation. This caused the appearance of overdensity regions in the disc that had high enough densities to ensure stripping large giants of their atmospheres and thus rendering them very faint. In this paper, we use a stellar evolution code to derive the properties that a red giant would display in a colour–magnitude diagram, as well as a non-linearity factor required for a correct estimate of the mass loss. We find that in a very short time-scale, the red giants leave their standard evolutionary track. The non-linearity factor has values that not only depend on the properties of the clumps, but also on the physical conditions of the giant stars, as we predicted analytically. According to our results, envelope stripping works, moving stars on a short time-scale from the giant branch to the white dwarf stage, thus rendering them invisible to observations.

On the Rank of a Random Binary Matrix

We study the rank of a random $n \times m$ matrix $\mathbf{A}_{n,m;k}$ with entries from $GF(2)$, and exactly $k$ unit entries in each column, the other entries being zero. The columns are chosen independently and uniformly at random from the set of all ${n \choose k}$ such columns. We obtain an asymptotically correct estimate for the rank as a function of the number of columns $m$ in terms of $c,n,k$, and where $m=cn/k$. The matrix $\mathbf{A}_{n,m;k}$ forms the vertex-edge incidence matrix of a $k$-uniform random hypergraph $H$. The rank of $\mathbf{A}_{n,m;k}$ can be expressed as follows. Let $|C_2|$ be the number of vertices of the 2-core of $H$, and $|E(C_2)|$ the number of edges. Let $m^*$ be the value of $m$ for which $|C_2|= |E(C_2)|$. Then w.h.p. for $m<m^*$ the rank of $\mathbf{A}_{n,m;k}$ is asymptotic to $m$, and for $m \ge m^*$ the rank is asymptotic to $m-|E(C_2)|+|C_2|$. In addition, assign i.i.d. $U[0,1]$ weights $X_i, i \in {1,2,...m}$ to the columns, and define the weight of a set of columns $S$ as $X(S)=\sum_{j \in S} X_j$. Define a basis as a set of $n-𝟙 (k\text{ even})$ linearly independent columns. We obtain an asymptotically correct estimate for the minimum weight basis. This generalises the well-known result of Frieze [On the value of a random minimum spanning tree problem, Discrete Applied Mathematics, (1985)] that, for $k=2$, the expected length of a minimum weight spanning tree tends to $\zeta(3)\sim 1.202$.

Robotic ecology: Tracking small dynamic animals with an autonomous aerial vehicle

Understanding animal movements that underpin ecosystem processes is fundamental to ecology. Recent advances in animal tags have increased the ability to remotely locate larger species; however, this technology is not suitable for up to 70% of the world’s bird and mammal species. The most widespread technique for tracking small animals is to manually locate low-power radio transmitters from the ground with handheld equipment. Despite this labor-intensive technique being used for decades, efforts to reduce or automate this process have had limited success. Here, we present an approach for tracking small radio-tagged animals by using an autonomous and lightweight aerial robot. We present experimental results where we used the robot to locate critically endangered swift parrots (Lathamus discolor) within their winter range. The system combines a miniaturized sensor with newly developed estimation algorithms to yield unambiguous bearing- and range-based measurements with associated measures of uncertainty. We incorporated these measurements into Bayesian data fusion and information-based planning algorithms to control the position of the robot as it collected data. We report estimated positions that lie within about 50 meters of the true positions of the birds on average, which are sufficiently accurate for recapture or observation. Further, in comparison with experienced human trackers from locations where the signal was detectable, the robot produced a correct estimate as fast or faster than the human. These results provide validation of robotic systems for wildlife radio telemetry and suggest a way for widespread use as human-assistive or autonomous devices.