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Mellin-Barnes integral representation of one-loop off-shell box massless diagram is five-fold by construction. On the other hand, it is known from the year 1992 that it may be reduced to certain two-fold Mellin-Barnes integral. We propose a way to reduce the number of the Mellin-Barnes integration contours from five to two by using the Mellin-Barnes integral representation only in combination with basic methods of mathematical analysis such as analytical regularization. We do not use any Barnes lemma to prove the reduction but we use the integral Cauchy formula instead. We recover first the well-known two-fold Mellin-Barnes representation for the one-loop triangle massless diagram and then show how the five-fold Mellin-Barnes integral representation of one-loop box diagram with all the indices 1 in four spacetime dimensions may be reduced to the two-fold Mellin-Barnes representation for one-loop triangle diagram. Singular integrals over Feynman parameters appear in the integrand of the five-fold Mellin-Barnes integral representation at the intermediate step. Such integrals should be treated as distributions with respect to certain linear combinations of the initial Mellin-Barnes integration variables in the Mellin-Barnes integrands. These distributions may be integrated out with a finite number of residues in the limit of removing the analytical regularization. We explain how to apply this strategy to an arbitrary Feynman diagram in order to reduce the number of Mellin-Barnes integration contours. On the practical side, we analyze connections between the obtained results and the knot theory, Trotter integrals, quantum computing., Comment: revised version, 30 pages

We propose an imaging method to enhance and reveal structures within samples by using a polarization-based filter. This filter removes the isotropic content while amplifying the anisotropic component of depolarization. Whereas isotropic depolarization leads to a complete loss of polarimetric information, the anisotropic one is connected with intrinsic characteristics of samples. The filter has the capability to diminish the isotropic depolarization of samples, revealing their inherent information. As representative cases, we analyze the effect of the filter in heart and brain sections of animal origin. Results highlight the outstanding performance of the filter. In heart, myocardial and subendocardial structures are better visualized, whereas in the brain, fiber tracts are identified. These proves the significance of this filter in the medical field, paving the way to the early detection of pathologies. The methodologies here presented could be applied in a wide range of applications, providing a significant advance in polarization imaging where high isotropic depolarization response is present, this being a common scenario in nature.

This study investigates the prevalence and implications of nestedness within primate social networks, examining its relationship with cognitive and structural factors. We analysed data from 51 primate groups across 21 species, employing network analysis to evaluate nestedness and its correlation with modularity, neocortex ratio, and group size. We used Bayesian mixed effects modelling to investigate nestedness in primate social networks, controlling for phylogenetic dependencies and exploring various factors like neocortex ratio and group size. Our findings reveal a significant occurrence of nestedness in 66% of the species studied, exceeding chance expectations. This nestedness was more pronounced in groups with less steep dominance hierarchies, contrary to traditional assumptions linking it to hierarchical social structures. A notable inverse relationship between nestedness and modularity was observed, suggesting a structural trade-off in network formation. This pattern persisted even after controlling for species-specific social behaviours, indicating a general structural feature of primate networks. Surprisingly, our analysis showed no significant correlation between nestedness and neocortex ratio or group size, challenging the social brain hypothesis and suggesting a greater role for ecological factors in cognitive evolution. This study emphasises the importance of weak links in maintaining network resilience. Overall, our research provides new insights into primate social network structures, highlighting complex interplays between network characteristics and challenging existing paradigms in cognitive and evolutionary biology.

The method of brackets is an procedure to evaluate definite integrals. It is based on a small number of operational rules. The flexibility of this method is illustrated with the evaluation of an integral involving the Bessel K0 function and the exponential integral. Several proofs are presented.

The second virial coefficient for the Mie potential is evaluated using the method of brackets. This method converts a definite integral into a series in the parameters of the problem, in this case this is the temperature $T$. The results obtained here are consistent with some known special cases, such as the Lenard-Jones potential. The asymptotic properties of the second virial coefficient in molecular thermodynamic systems and complex fluid modeling are described in the limiting cases of $T \rightarrow 0$ and $T \rightarrow \infty$., Comment: 11 pages

We consider the finite alphabet phase retrieval problem: recovering a signal whose entries lie in a small alphabet of possible values from its Fourier magnitudes. This problem arises in the celebrated technology of X-ray crystallography to determine the atomic structure of biological molecules. Our main result states that for generic values of the alphabet, two signals have the same Fourier magnitudes if and only if several partitions have the same difference sets. Thus, the finite alphabet phase retrieval problem reduces to the combinatorial problem of determining a signal from those difference sets. Notably, this result holds true when one of the letters of the alphabet is zero, namely, for sparse signals with finite alphabet, which is the situation in X-ray crystallography.

Single quantum emitters play a fundamental role in the development of quantum technologies such as quantum repeaters, and quantum information processing. Isolating individual molecules with stable optical emission is an essential step for these applications, specially for those molecules that present large coherence times at room temperature. Among them, vanadium-oxide phthalocyanine (VOPc) molecules stand out as promising candidates due to their large coherence times measured in ensemble. However, the optical properties of individual molecules have not yet been reported. Here we show that single VOPc molecules with stable optical properties at room temperature can be isolated. We find that the optical response of the molecule under laser illumination of different polarization agrees well with a system having pyramidal C$_{4v}$ symmetry. Furthermore, the molecule reveals a non-radiative transition rate that depends on the excitation wavelength when its lifetime is interrogated. We provide theoretical calculations that support our experimental findings and provide insight to the role of phonons and internal electronic structure of the molecule. These results demonstrate that this single paramagnetic molecule can function as a single quantum emitter while displaying optical stability under ambient conditions to have their intrinsic properties investigated.

This paper describes a decentralized low-cost system designed to reinforce personal security in big events in case of emergency. The proposal consists of using smart contracts supported by blockchain in the management of events. An alternative communication channel that does not require any cloud service is also provided with the aim of improving the coordination of emergency services. Peers may use this emergency support tool to interact with each other through a chat when additional support is required. Since information security is mandatory in this scenario, Identity-Based Signcryption schemes are here used in order to guarantee communication confidentiality, authenticity and integrity. Depending on the communication mode (peer-to-peer or broadcast), different signcryption methods are used. A first implementation of the proposal has produced promising results.

This work describes an integrated solution to face a civil security problem in the area of Search And Rescue (SAR) of missing people. This proposal is based on the use of emerging technologies such as Unmanned Aerial Vehicles (UAV), also known as drones, and the use of simulated beacons on smartphones. In particular, in the presented tool, drones fly synchronously in a specific area so that each drone uses on-board sensors to scan and detect any signal emitted by Bluetooth Low Energy (BLE) beacons from smartphones of missing people. This technique allows getting the GPS position of any detected missing person. This work also includes some security issues related to possible attacks focused on the perimeter and physical security.

In this paper, a collision avoidance system is presented to detect red light running and warn nearby vehicles and pedestrians in real time in order to prevent possible accidents. No complex infrastructure-based solution such as those based on radars or cameras is here required. Instead, a new solution based on smartphones carried by drivers and pedestrians is proposed so that it is the device inside the vehicle violating a traffic light, the one that self-reports the offence in order to generate alerts and warn nearby vehicles and pedestrians to prevent accidents. The proposal could also be used by road authorities to collect data on traffic lights that are most frequently violated in order to define an action plan to investigate causes and look for solutions. It includes a classifier for learning and estimating driver behaviour based on collected data, which is used to predict whether he/she is about to run a red light or detect whether that has already happened. In the first case, the system broadcasts warnings directly to close vehicles and pedestrians through Wi-Fi, while in the second case, the proposal warns vehicles and pedestrians in the neighbourhood through a server. The solution also includes a prioritization system based on changing traffic lights at intersections according to the needs and characteristics of the traffic at all times, giving the top priority to emergency vehicles. Furthermore, the proposal involves the use of cryptographic schemes to protect authenticity and integrity of messages sent from traffic lights, smartphones and servers, and privacy and anonymity to promote the use of the system. A beta version with some parts of the proposal has been implemented and the obtained results are promising.

Nowadays, many technological advances applied to the Internet of Things (IoT) make the introduction of innovative sensors aimed to deploy efficient wireless sensor networks possible. In order to improve the environment and people's lives, real time analysis of certain environmental variables may favor the reduction of health risks related to the deterioration of air quality. To this respect, the proposed system implements a particular prototype of IoT device characterized by the assembly of ambient sensors capable of measuring pollutant gases, temperature and humidity. For this purpose, Raspberry Pi and Arduino platforms are used. Several security methods are introduced to ensure the integrity of air quality data by implementing Merkle Trees on each IoT node and on the Cloud server. Besides, the authenticity of IoT devices and the confidentiality of communications are guaranteed by implementing HTTPS requests. Finally, authentication tokens are used to identify system users, and different security rules are applied to manage database operations.

We offer a new perspective to the problem of characterizing mesoscopic fluctuations in the inter-plateau region of the integer quantum Hall transition. We found that longitudinal and transverse conductance fluctuations, generated by varying the external magnetic field within a microscopic model, are multifractal and lead to distributions of conductance increments (magnetoconductance) with heavy tails (intermittency) and signatures of a hierarchical structure (a cascade) in the corresponding stochastic process, akin to Kolmogorov's theory of fluid turbulence. We confirm this picture by interpreting the stochastic process of the conductance increments in the framework of H-theory, which is a continuous-time stochastic approach that incorporates the basic features of Kolmogorov's theory. The multifractal analysis of the conductance "time series," combined with the H-theory formalism provides, strong support for the overall characterization of mesoscopic fluctuations in the quantum Hall transition as a multifractal stochastic phenomenon with multiscale hierarchy, intermittency, and cascade effects.

This article addresses how diverse collective behaviors arise from simple and realistic decisions made entirely at the level of each agent's personal space in the sense of the Voronoi diagram. We present a discrete time model in 2D in which individual agents are aware of their local Voronoi environment and may seek static target locations. In particular, agents only communicate directly with their Voronoi neighbors and make decisions based on the geometry of their own Voronoi cells. With two effective control parameters, it is shown numerically to capture a wide range of collective behaviors in different scenarios. Further, we show that the Voronoi topology facilitates the computation of several novel observables for quantifying discrete collective behaviors. These observables are applicable to all agent-based models and to empirical data., Comment: 17 pages, 7 figures, Gonzalez and Tisdell contributed equally

The method of brackets is a method for the evaluation of definite integrals based on a small number of rules. This is employed here for the evaluation of Mellin-Barnes integral. The fundamental idea is to transform these integral representations into a bracket series to obtain their values. The expansion of the gamma function in such a series constitute the main part of this new application. The power and flexibility of this procedure is illustrated with a variety of examples.

Finding optimal (or low energy) centroidal Voronoi tessellations (CVTs) on a 2D domain is a challenging problem. One must navigate an energy landscape whose desirable critical points have sufficiently small basins of attractions that they are inaccessible with Monte-Carlo initialized gradient descent methods. We present a simple deterministic method for efficiently navigating the energy landscape in order to it access these low energy CVTs. The method has two parameters and is based upon each generator moving away from the closest neighbor by a certain distance. We give a statistical analysis of the performance of this hybrid method comparing with the results of a large number of runs for both Lloyd's method and state of the art quasi-Newton methods. Stochastic alternatives are also considered., Comment: 27 pages, 72 figures