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Disjointly strictly singular inclusions between variable Lebesgue spaces $L^{p(\cdot)}(\mu)$ on finite measure are characterized. Suitable criteria in terms of the (bounded or unbounded) exponents are given. It is proved the equivalence of $L$-weak compactness (also called almost compactness) and disjoint strict singularity for variable Lebesgue space inclusions. For infinite measure any inclusion $L^{p(\cdot)}(\mu) \hookrightarrow L^{q(\cdot)}(\mu)$ is not disjointly strictly singular. No restrictions on the exponent are imposed.

Vector beams display varying polarisation over planes transversal to their direction of propagation. The variation of polarisation implies that the electric field cannot be expressed as a product of a spatial mode and its polarisation. This non-separability has been analysed for particular vector beams in terms of non--quantum entanglement between the spatial and the polarisation-degrees of freedom, and equivalently, with respect to the degree of polarisation of light. Here we demonstrate theoretically and experimentally that Mathieu-Gauss vector modes violate a Bell-like inequality known as the Clauser-Horn-Shimony-Holt-Bell (CHSH-Bell) inequality. This demonstration provides new insights into that fact that a more general class of vector modes with elliptical symmetry also violate Bell inequalities., Comment: 8 pages, 6 figures

Complex vector modes of light, non-separable in their spatial and polarisation degrees of freedom, are revolutionising a wide variety of research fields. It is therefore not surprising that the generation techniques have evolved quite dramatically since their inception. At present it is common to use computer-controlled devices, among which digital micromirror devices have become popular. Some of the reason for this are their low-cost, their polarisation-insensitive and their high-refresh rates. As such, in this manuscript we put forward a novel technique characterised by its high stability, which is achieved through a common-path interferometer. We demonstrate the capabilities of this technique experimentally, first by generating arbitrary vector modes on a higher-order Poincar\'e sphere, secondly, by generating vector modes in different coordinates systems and finally, by generating various vector modes simultaneously. Our technique will find applications in fields such as optical manipulations, optical communications, optical metrology, among others., Comment: 7 pages, 6 figures

The detection of critical infrastructures in large territories represented by aerial and satellite images is of high importance in several fields such as in security, anomaly detection, land use planning and land use change detection. However, the detection of such infrastructures is complex as they have highly variable shapes and sizes, i.e., some infrastructures, such as electrical substations, are too small while others, such as airports, are too large. Besides, airports can have a surface area either small or too large with completely different shapes, which makes its correct detection challenging. As far as we know, these limitations have not been tackled yet in previous works. This paper presents (1) a smart Critical Infrastructure dataset, named CI-dataset, organised into two scales, small and large scales critical infrastructures and (2) a two-level resolution-independent critical infrastructure detection (DetDSCI) methodology that first determines the spatial resolution of the input image using a classification model, then analyses the image using the appropriate detector for that spatial resolution. The present study targets two representative classes, airports and electrical substations. Our experiments show that DetDSCI methodology achieves up to 37,53% F1 improvement with respect to Faster R-CNN, one of the most influential detection models.

Despite the constant advances in computer vision, integrating modern single-image detectors in real-time handgun alarm systems in video-surveillance is still debatable. Using such detectors still implies a high number of false alarms and false negatives. In this context, most existent studies select one of the latest single-image detectors and train it on a better dataset or use some pre-processing, post-processing or data-fusion approach to further reduce false alarms. However, none of these works tried to exploit the temporal information present in the videos to mitigate false detections. This paper presents a new system, called MULTI Confirmation-level Alarm SysTem based on Convolutional Neural Networks (CNN) and Long Short Term Memory networks (LSTM) (MULTICAST), that leverages not only the spacial information but also the temporal information existent in the videos for a more reliable handgun detection. MULTICAST consists of three stages, i) a handgun detection stage, ii) a CNN-based spacial confirmation stage and iii) LSTM-based temporal confirmation stage. The temporal confirmation stage uses the positions of the detected handgun in previous instants to predict its trajectory in the next frame. Our experiments show that MULTICAST reduces by 80% the number of false alarms with respect to Faster R-CNN based-single-image detector, which makes it more useful in providing more effective and rapid security responses.