Electrostatic Partners and Zeros of Orthogonal and Multiple Orthogonal Polynomials

For a given polynomial P with simple zeros, and a given semiclassical weight w, we present a construction that yields a linear second-order differential equation (ODE), and in consequence, an electrostatic model for zeros of P. The coefficients of this ODE are written in terms of a dual polynomial that we call the electrostatic partner of P. This construction is absolutely general and can be carried out for any polynomial with simple zeros and any semiclassical weight on the complex plane. An additional assumption of quasi-orthogonality of P with respect towallows us to give more precise bounds on the degree of the electrostatic partner. In the case of orthogonal and quasiorthogonal polynomials, we recover some of the known results and generalize others. Additionally, for the Hermite–Padé or multiple orthogonal polynomials of type II, this approach yields a system of linear second-order differential equations, from which we derive an electrostatic interpretation of their zeros in terms of a vector equilibrium. More detailed results are obtained in the special cases of Angelesco, Nikishin, and generalized Nikishin systems.We also discuss the discrete-to-continuous transition of thesemodels in the asymptotic regime, as the number of zeros tends to infinity, into the known vector equilibrium problems. Finally, we discuss how the system of obtained second-order ODEs yields a third-order differential equation for these polynomials, well described in the literature. We finish the paper by presenting several illustrative examples.The first author was partially supported by Simons Foundation Collaboration Grants for Mathematicians (grant 710499). He also acknowledges the support of the Spanish Government and the European RegionalDevelopment Fund (ERDF) through grant PID2021-124472NB-I00, Junta deAndalucía (research group FQM-229 and Instituto Interuniversitario Carlos I de Física Teórica y Computacional), and by the University of Almería (Campus de Excelencia Internacional del Mar CEIMAR) in the early stages of this project. The second and third authors were partially supported by Spanish Ministerio de Ciencia, Innovación y Universidades, under grant MTM2015-71352-P. The third author was additionally supported by Junta de Andalucía (research group FQM-384), the University of Granada (Research Project ERDF-UGR A-FQM-246-UGR20), and by the IMAG-Maria de Maeztu grant CEX2020-001105- M/AEI/10.13039/501100011033. Funding for open access publishing: Universidad de Granada/CBU

Semantic segmentation of major macroalgae in coastal environments using high-resolution ground imagery and deep learning

Macroalgae are a fundamental component of coastal ecosystems and play a key role in shaping community structure and functioning. Macroalgae are currently threatened by diverse stressors, particularly climate change and invasive species, but they do not all respond in the same way to the stressors. Effective methods of collecting qualitative and quantitative information are essential to enable better, more efficient management of macroalgae. Acquisition of high-resolution images, in which macroalgae can be distinguished on the basis of their texture and colour, and the automated processing of these images are thus essential. Although ground images are useful, labelling is tedious. This study focuses on the semantic segmentation of five macroalgal species in high-resolution ground images taken in 0.5 x 0.5 m quadrats placed along an intertidal rocky shore at low tide. The target species, Bifurcaria bifurcata, Cystoseira tamariscifolia, Sargassum muticum, Sacchoriza polyschides and Codium spp., which predominate on intertidal shores, belong to different morpho-functional groups. The study explains how to convert vector-labelled data to raster-labelled data for adaptation to convolutional neural network (CNN) input. Three CNNs (MobileNetV2, Resnet18, Xception) were compared, and ResNet18 yielded the highest accuracy (91.9%). The macroalgae were correctly segmented, and the main confusion occurred at the borders between different macroalgal species, a problem derived from labelling errors. In addition, the interior and exterior of the quadrats were correctly delimited by the CNNs. The results were obtained from only one hundred labelled images and can be performed on personal computers, without the need to resort to external servers. The proposed method helps automation of the labelling process.SIFundación Biodiversidad, the Ministerio para la Transición Ecológica y 383 el Reto Demográfico through the Pleamar program, co-funded by the European Maritime and Fisheries Fund (EMFF), call 2018; and Xunta de Galicia for human resources and competitive reference groupsFundación Biodiversidad, the Ministerio para la Transición Ecológica y 383 el Reto Demográfico through the Pleamar program, co-funded by the European Maritime and Fisheries Fund (EMFF), call 2018; and Xunta de Galicia for human resources and competitive reference groupsMinisterio de Ciencia, Innovación y Universidades -Gobierno de Españ

HDDP: Hybrid Domain Discovery Protocol for heterogeneous devices in SDN

Computer networks are adopting the new Software-Defined Networking (SDN) architecture, however not all devices can support it, mainly due to power and computational constraints. This paper proposes the Hybrid Domain Discovery Protocol (HDDP), a new discovery protocol that enhances theexisting OpenFlow Discovery Protocol (OFDP). HDDP allows thediscovery of hybrid network topologies composed of both SDNand non-SDN devices, which no other state-of-the-art protocolcan achieve. HDDP has been implemented in a software switchand emulated in diverse networks, where it discovers hybrid topologies by using a number of messages similar to competitors,as they only discover SDN devices.Comunidad de MadridUniversidad de Alcal

Analysis of P4 and XDP for IoT programmability in 6G and beyond

Recently, two technologies have emerged to provide advanced programmability in Software-Defined Networking (SDN) environments, namely P4 and XDP. At the same time, the Internet of Things (IoT) represents a pillar of future 6G networks, which will be also sustained by SDN. In this regard, there is a need to analyze the suitability of P4 and XDP for IoT. In this article, we aim to compare both technologies to help future research efforts in the field. To this purpose, we evaluate both technologies by implementing diverse use cases, assessing their performance and providing a quick qualitative overview. All tests and designed scenarios are publicly available in GitHub to guarantee replication and serve as initial steps for researchers that want to initiate in the field. Results illustrate that currently XDP is the best option for constrained IoT devices, showing lower latency times, half of CPU usage, and reduced memory in comparison with P4. However, development of P4 programs is more straightforward and the amount of code lines is more similar regardless of the scenario. Additionally, P4 has a lot of potential in IoT if a special effort is made to improve the most common software target, BMv2.Comunidad de MadridJunta de Comunidades de Castilla-La ManchaUniversidad de Alcal

The disjoint multipath challenge: multiple disjoint paths guaranteeing scalability

The multipath challenge is a research line in continuous development because of its multiple benefits, however, these benefits are overshadowed by scalability, which goes down considerably when the paths are multiple and disjoint. The disjointness aggregates an extra value to the multiple paths, but it also implies more complex mathematical operations that increase the computational cost. In fact, diverse proposals exist that try to increase scalability by limiting the number of paths obtained to the minimum possible (two-disjoint paths), which is enough for backup applications but not for other purposes. This paper presents an algorithm that solves these drawbacks by discovering multiple disjoint paths among multiple nodes in an efficient way, while keeping bounded the computational cost and ensuring scalability. The proposed algorithm has been validated thoroughly by performing a theoretical analysis, bolstered afterwards by an exhaustive experimental evaluation. The collected results are promising, our algorithm reduces the time spent to obtain the disjoint paths regarding its competitors between one and three orders of magnitude, at the cost of a slight decrease in the number of paths discovered.Comunidad de MadridJunta de Comunidades de Castilla-La Manch

One-Shot Multiple Disjoint Path Discovery Protocol (1S-MDP)

Multipath routing over disjoint paths is a classic solution to allow better resource allocation, resilience, and security. Current proposals rely on centralised computation or iterative distributed algorithms and exhibit large convergence times. We propose 1S-MDP, a distributed mechanism based on a single network exploration with concurrent path selection to discover multiple available paths among the target node and the remaining nodes in the network. The paper evaluates 1S-MDP in two different scenarios against previous solutions. We show how it reduces the convergence time by several orders of magnitude with a small decrease in the number of disjoint paths discovered.Comunidad de Madri

ARP-P4: deep analysis of a hybrid SDN ARP-Path/P4-Runtime switch

The Software-Defined Networking (SDN) architecture decouples the control plane from the data plane, but it does not explicitly state where the control should be located. This article analyses the benefits of maintaining the control as close as possible to the data plane, instead of the more traditional centralised control plane approach. To this purpose, it delves into the study of ARP-P4, a hybrid software switch defined by using the P4 language to facilitate its future use and deployment in P4 targets. Its hybrid properties come from supporting two complementary different ways of establishing paths: a centralised SDN approach based on P4-Runtime and a traditional distributed approach based on the ARP-Path protocol that obtains a similar performance to centralised solutions based on Equal Cost Multi-Path (ECMP) and Dijkstra. The results show the feasibility of hybrid devices that combine different forwarding paradigms without losing performance with respect to well-known solutions such as ECMP, and how their combined use can lead to enhance and scale communication networks.Comunidad de MadridUniversidad de Alcal

Influence of the Water Vapour Permeability of Airtight Sheets on the Behaviour of Facade

The air-tightness of the thermal envelope of buildings is one of the measures to reduce their energy demands in order to achieve global warming reduction targets. To this end, airtight sheets with different water vapour permeability characteristics are used. The different products studied are highly dispersed in terms of equivalent air thickness values, leading to confusion. After the analysis carried out, it is concluded that all airtight sheets are vapour barriers. To clarify whether or not these sheets are necessary as vapour barriers, a condensation analysis was carried out on 13 different facades for 3 climate zones with severe winters as defined in Spanish regulations. The results reveal that interstitial condensation occurs in only 7 of the 39 case studies, with the traditional facades of brickwork with render causing the greatest problems if the appropriate products are not used. In these cases, airtight sheets with water vapour barrier characteristics must be applied on the interior face of the insulating material. In all other cases (32), the airtight sheets must be permeable to water vapour if it is looked for a more breathable wall to water vapour and a better control of the interior humidity conditions

Amaru: plug&play resilient in-band control for SDN

Software-Defined Networking (SDN) is a pillar of next-generation networks. ImplementingSDN requires the establishment of a decoupled control communication, which might be installed either as anout-of-band or in-band network. While the benefits of in-band control networks seem apparent, no standardprotocol exists and most of setups are based on ad-hoc solutions. This article defines Amaru, a protocolthat provides plug&play resilient in-band control for SDN with low-complexity and high scalability. Amarufollows an exploration mechanism to find all possible paths between the controller and any node of thenetwork, which drastically reduces convergence time and exchanged messages, while increasing robustness.Routing is based on masked MAC addresses, which also simplifies routing tables, minimizing the numberof entries to one per path, independently of the network size. We evaluated Amaru with three differentimplementations and diverse types of networks and failures, and obtained excellent results, providing almoston-the-fly rerouting and low recovery time.Comunidad de MadridUniversidad de Alcal

TEDP: an enhanced topology discovery service for Software-Defined Networking

Currently, software-defined networking (SDN) platforms leverage the link-layer discovery protocol (LLDP) to discover the underlying topology. However, the LLDP is suboptimal in terms of message load. In this letter, we present the tree exploration discovery protocol (TEDP), proving that shortest paths can be built at the same time that the topology information is gathered, without extra messages compared with LLDP. We also analyze two alternative implementations for the TEDP and give insights into some features that SDN platforms should ideally provide for an efficient topology discovery service.Comunidad de Madri