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Networks specifying who interacts with whom are crucial for mathematical models of epidemic spreading. In the context of emerging diseases, these networks have the potential to encode multiple interaction contexts where non-pharmaceutical interventions can be introduced, allowing for proper comparisons among different intervention strategies in a plethora of contexts. Consequently, a multilayer network describing interactions in a population and detailing their contexts in different layers constitutes an appropriate tool for such descriptions. These approaches however become challenging in large-scale systems such as cities, particularly in a framework where data protection policies are enhanced. In this work, we present a methodology to build such multilayer networks and make those corresponding to five Spanish cities available. Our work uses approaches informed by multiple available datasets to create realistic digital twins of the citizens and their interactions and provides a playground to explore different pandemic scenario in realistic settings for better preparedness.

Professional sports enhance interaction among athletes through training groups, sponsored events and competitions. Among these, the Olympic Games represent the largest competition with a global impact, providing the participants with a unique opportunity for interaction. We studied the following patterns among highly successful athletes to understand the structure of their interactions. We used the list of Olympic medallists in the Tokyo 2020 Games to extract their follower-followee network in Twitter, finding 7,326 connections among 964 athletes. The network displayed frequent connections to similar peers in terms of their features including sex, country and sport. We quantified the influence of these features in the followees choice through a gravity approach capturing the number of connections between homogeneous groups. Our research remarks the importance of datasets built from public exposure of professional athletes, serving as a proxy to investigate interesting aspects of many complex socio-cultural systems at different scales.

The reduction in sea ice cover with Arctic warming facilitates the transit of ships through routes that are remarkably shorter than the traditional shipping routes. Automatic Identification System (AIS), ideally designed to avoid vessel collisions, transmits on vessel navigation information (currently 27 types of messages) such as name, position or speed, is a powerful data source to monitor the progress of Arctic shipping as the ice cover decreases. Based on the analysis of an online platform collecting shipping AIS data, we quantified the spatial distribution of shipping through the Arctic Ocean, its intensity and the temporal evolution, in relation to the area released by the sea ice area. Shipping through the Arctic Ocean is distributed spatially following a heavy-tailed distribution, implying heavy traffic through a limited Arctic area, with an exponent that depends on the vessel category. Fishing is the category with the largest spatial spread, with the width of shipping routes correlated with the proximal sea ice area. The time evolution of these routes is characterized by increasing extended periods of shipping activity through the year. AIS data offers valuable information on the activity of the international fleet worldwide. In the context of the new international agreements, it is a valuable source to monitor shipping, fishing and the potential impact in marine life among other aspects. Here we have focused on the Arctic shipping in recent years, which is rapidly growing, particularly around the Northeastern and Northwest Passage coastal routes, providing an opportunity for the design of shorter shipping routes and reduced greenhouse gas emissions from transport of goods, but at a risk of impacts on the Arctic ecosystem.

In railway applications, it is common to use an LC filter connected between the catenary and the input port of the main converter of the auxiliary and traction systems. In addition, in the auxiliary systems, there is a converter operating as a battery charger, which requires a very low ripple in the output current and output voltage, so a postfilter may be placed at the output port of the converter. This article proposes a step-by-step methodology to extend the injected-absorbed-current (IAC) method in order to obtain transfer functions that consider the effects of the input filter, output postfilter, and some feedforward compensations. The proposed methodology allows reusing the characteristic coefficients of the DC-DC converter model derived from the existing IAC method. One of the advantages of the proposed methodology is that the transfer functions obtained in this article are valid for cases where both, one or none of the filters, are implemented. Finally, for the experimental validation of the proposed methodology, the phase-shifted full-bridge converter was selected as a convenient example. Furthermore, the experimental measurements have been performed on two prototypes., Comment: This work was supported in part by the European Regional Development Fund (FEDER), in part by the Ministry of Science, Innovation and Universities, and in part by the State Research Agency through the Research Project: Modeling and Control Strategies for the Stabilization of the Interconnection of Power Electronic Converters CONEXPOT-2 under Grant DPI2017-84572-C2-2-R (AEI/FEDER, UE)

In the unconventional superconductor Sr$_2$RuO$_4$, uniaxial stress along the $[100]$ direction tunes the Fermi level through a Van Hove singularity (VHS) in the density of states, causing a strong enhancement of the superconducting critical temperature $T_\textrm{c}$. Here, we report measurements of the London penetration depth $\lambda$ as this tuning is performed. We find that the zero-temperature superfluid density, here defined as $\lambda(0)^{-2}$, increases by $\sim$15%, with a peak that coincides with the peak in $T_\textrm{c}$. We also find that the low temperature form of $\lambda(T)$ is quadratic over the entire strain range. Using scanning tunneling microscopy, we find that the gap increases from $\Delta_0 \approx 350~\mu$eV in unstressed Sr$_2$RuO$_4$ to $\Delta_0 \approx 600~\mu$eV in a sample strained to near the peak in $T_c$. With a nodal order parameter, an increase in the superconducting gap could bring about an increase in the superfluid density through reduced sensitivity to defects and through reduced non-local effects in the Meissner screening. Our data indicate that tuning to the VHS increases the gap throughout the Brillouin zone, and that non-local effects are likely more important than reduced scattering.

We show that on the real $2$-dimensional Banach space $\ell_1^2$ there is an analytic function $f:B_{\ell_1^2}\rightarrow \mathbb{R}$ such that its power series at origin has radius of uniform convergence one, but for some $a\in B_{\ell_1^2}$ the power series centred at that point has radius of uniform convergence strictly less than $1-\|a\|$. This result highlights a fundamental distinction in real analytic functions (compared to complex analytic functions), where the radius of analyticity can differ from the radius of uniform convergence. Moreover, this example provides the first non-trivial upper bound for the constant of analyticity.

Mathematical modeling has been fundamental to achieving near real-time accurate forecasts of the spread of COVID-19. Similarly, the design of non-pharmaceutical interventions has played a key role in the application of policies to contain the spread. However, there is less work done regarding quantitative approaches to characterize the impact of each intervention, which can greatly vary depending on the culture, region, and specific circumstances of the population under consideration. In this work, we develop a high-resolution, data-driven agent-based model of the spread of COVID-19 among the population in five Spanish cities. These populations synthesize multiple data sources that summarize the main interaction environments leading to potential contacts. We simulate the spreading of COVID-19 in these cities and study the effect of several non-pharmaceutical interventions. We illustrate the potential of our approach through a case study and derive the impact of the most relevant interventions through scenarios where they are suppressed. Our framework constitutes a first tool to simulate different intervention scenarios for decision-making., Comment: Main text with 5 figures and 1 table, and Supplementary Material

Automated positioning devices can generate large datasets with information on the movement of humans, animals and objects, revealing patterns of movement, hot spots and overlaps among others. This information is obtained after cleaning the data from errors of different natures. However, in the case of Automated Information Systems (AIS), attached to vessels, these errors can come from intentional manipulation of the electronic device. Thus, the analysis of anomalies can provide valuable information on suspicious behaviour. Here, we analyse anomalies of fishing vessel trajectories obtained with the Automatic Identification System. The map of silence anomalies, those occurring when positioning data is absent for more than 24 h, shows that they occur more likely closer to land, observing 94.9% of the anomalies at less than 100 km from the shore. This behaviour suggests the potential of identifying silence anomalies as a proxy for illegal activities. With the increasing availability of high-resolution positioning of vessels and the development of powerful statistical analytical tools, we provide hints on the automatic detection of illegal activities that may help optimise monitoring, control and surveillance measures.

The Fe-based superconductor Fe (Se,Te) combines non-trivial topology with unconventional superconductivity and may be an ideal platform to realize exotic states such as high-order topological corner modes and Majorana modes. Thin films of Fe (Se,Te) are important for device fabrication, phase sensitive transport measurements and for realizing proposals to engineer higher-order modes. However, while bulk Fe (Se,Te) has been extensively studied with a variety of techniques, the nature of the superconducting order parameter in the monolayer limit has not yet been explored. In this work, we study monolayer films of Fe (Se,Te) on Bi2Te3 with scanning tunneling spectroscopy and Bogoliubov quasiparticle interference (BQPI). We discover that the monolayer Fe (Se,Te)/Bi2Te3 heterostructures host a robust, multigap superconducting state that strongly resembles the bulk. BQPI maps at the gap energies show a strong spatial modulation, oriented 45 degrees to the Fe-Se bond direction. Analysis of the phase-referenced quasiparticle interference signal reveals a sign-changing s-wave order parameter similar to the bulk. Moreover, we observe a unique pattern of sign changes in the BQPI signal which have not been observed in the bulk. Our work establishes monolayer Fe (Se,Te)/Bi2Te3 as a robust multi-band unconventional superconductor and sets the stage for explorations of non-trivial topology in this highly-tunable system., Comment: 23 pages, 4 figures

In this paper, we study the (uniform) strong subdifferentiability of the norms of the Banach spaces $\mathcal{P}(^N X, Y^*)$, $X \hat{\otimes}_\pi \cdots \hat{\otimes}_\pi X$ and $\hat{\otimes}_{\pi_s,N} X$. Among other results, we characterize when the norms of the spaces $\mathcal{P}(^N \ell_p, \ell_{q}), \mathcal{P}(^N l_{M_1}, l_{M_2})$, and $\mathcal{P}(^N d(w,p), l_{M_2})$ are strongly subdifferentiable. Analogous results for multilinear mappings are also obtained. Since strong subdifferentiability of a dual space implies reflexivity, we improve some known results on the reflexivity of spaces of $N$-homogeneous polynomials and $N$-linear mappings. Concerning the projective (symmetric) tensor norms, we provide positive results on the subsets $U$ and $U_s$ of elementary tensors on the unit spheres of $X \hat{\otimes}_\pi \cdots \hat{\otimes}_\pi X$ and $\hat{\otimes}_{\pi_s,N} X$, respectively. Specifically, we prove that $\hat{\otimes}_{\pi_s,N} \ell_2$ and $\ell_2 \hat{\otimes}_\pi \cdots \hat{\otimes}_\pi \ell_2$ are uniformly strongly subdifferentiable on $U_s$ and $U$, respectively, and that $c_0 \hat{\otimes}_{\pi_s} c_0$ and $c_0 \hat{\otimes}_\pi c_0$ are strongly subdifferentiable on $U_s$ and $U$, respectively, in the complex case., Comment: 38 pages

We study homomorphisms on the algebra of analytic functions of bounded type on a Banach space. When the domain space lacks symmetric regularity, we show that in every fiber of the spectrum there are evaluations (in higher duals) which do not coincide with evaluations in the second dual. We also consider the commutativity of convolutions between evaluations. We show that in some Banach spaces $X$ (for example, $X=\ell_1$) the only evaluations that commute with every other evaluation in $X''$ are those in $X$. Finally, we establish conditions ensuring the symmetry of the canonical extension of a symmetric multilinear operator (on a non-symmetrically regular space) and present some applications., Comment: 20 pages

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in graph space, following a latent graph dynamical system. Under this paradigm, we propose a way to measure how the network pulsates and collectively fluctuates over time and space. To this aim, we extend the notion of linear correlations function to the case of sequences of network snapshots, i.e. a network trajectory. We construct stochastic and deterministic graph dynamical systems and show that the emergent collective correlations are well captured by simple measures, and illustrate how these patterns are revealed in empirical networks arising in different domains.

Most spreading processes require spatial proximity between agents. The stationary state of spreading dynamics in a population of mobile agents thus depends on the interplay between the time and length scales involved in the epidemic process and their motion in space. We analyze the steady properties resulting from such interplay in a simple model describing epidemic spreading (modeled as a Susceptible-Infected-Susceptible process) on self-propelled particles (performing Run-and-Tumble motion). Focusing our attention on the diffusive long-time regime, we find that the agents' motion changes qualitatively the nature of the epidemic transition characterized by the emergence of a macroscopic fraction of infected agents. Indeed, the transition becomes of the mean-field type for agents diffusing in one, two and three dimensions, while, in the absence of motion, the epidemic outbreak depends on the dimension of the underlying static network determined by the agents' fixed locations. The insights obtained from a continuum description of the system are validated by numerical simulations of an agent-based model. Our work aims at bridging soft active matter physics and theoretical epidemiology, and may be of interest for researchers in both communities.

In this work we study different notions of ranks and approximation of tensors. We consider the tensor rank, the nuclear rank and we introduce the notion of symmetric decomposable rank, a notion of rank defined only on symmetric tensors. We show that when approximating symmetric tensors, using the symmetric decomposable rank has some significant advantages over the tensor rank and the nuclear rank.

Measuring close proximity interactions between individuals can provide key information on social contacts in human communities. With the present study, we report the quantitative assessment of contact patterns in a village in rural Malawi, based on proximity sensors technology that allows for high-resolution measurements of social contacts. The system provided information on community structure of the village, on social relationships and social assortment between individuals, and on daily contacts activity within the village. Our findings revealed that the social network presented communities that were highly correlated with household membership, thus confirming the importance of family ties within the village. Contacts within households occur mainly between adults and children, and adults and adolescents. This result suggests that the principal role of adults within the family is the care for the youngest. Most of the inter-household interactions occurred among caregivers and among adolescents. We studied the tendency of participants to interact with individuals with whom they shared similar attributes (i.e., assortativity). Age and gender assortativity were observed in inter-household network, showing that individuals not belonging to the same family group prefer to interact with people with whom they share similar age and gender. Age disassortativity is observed in intra-household networks. Family members congregate in the early morning, during lunch time and dinner time. In contrast, individuals not belonging to the same household displayed a growing contact activity from the morning, reaching a maximum in the afternoon. The data collection infrastructure used in this study seems to be very effective to capture the dynamics of contacts by collecting high resolution temporal data and to give access to the level of information needed to understand the social context of the village.

Interactions between COVID-19 and other pathogens may change their dynamics. Specifically, this may hinder the modelling of empirical data when the symptoms of both infections are hard to distinguish. We introduce a model coupling the dynamics of COVID-19 and seasonal influenza, simulating cooperation, competition and asymmetric interactions. We find that the coupling synchronizes both infections, with a strong influence on the dynamics of influenza, reducing its time extent to a half.

$^{57}$Fe M\"ossbauer spectroscopy can probe several \emph{local} structural, electronic and magnetic properties of Fe-containing systems. However, to establish a direct relationship between these properties and a system's geometric structure, the experimental M\"ossbauer parameters need to be analyzed \emph{via} electronic structure calculations. Herein, structural, electronic and magnetic effects of iron substituents in the topological insulator $Bi_2Se_3$, as uniquely probed by $^{57}$Fe M\"ossbauer spectroscopy, have been determined \emph{via} spin-polarized electronic structure calculations. The iron ion substituents, of \emph{nominal} Fe$^{3+}(S = 5/2)$ oxidation and spin state, are unequivocally shown to substitute Bi$^{3+}$ sites in epitaxial $Bi_2Se_3$ thin-films used for M\"ossbauer measurements. Concomitant with iron substitution, \emph{localized} structural rearrangements take place whereby the longer Bi-Se bonds of the native system are replaced by significantly shorter Fe-Se counterparts in the Fe-containing system. The resulting distorted-octahedral environment about substituent iron ions gives rise to characteristic M\"ossbauer parameters ($\delta_{Fe} \approx$ 0.51 mm/s, $\Delta E_{Q} \approx$ 0.20 mm/s) which have been calculated in excellent agreement with measured values for Fe-doped $Bi_2Se_3$ thin films. Consistent with a substituent Fe$^{3+}$ ion's \emph{nominal} high-spin electronic configuration ($t_{2g}^{\uparrow \uparrow \uparrow} e_g^{\uparrow \uparrow}$), an Fe-centered spin density has been established which, nevertheless, extends towards neighboring Se atoms \emph{via} direct Fe-Se bonding and concomitant Fe(d)-Se(p) hybridization.

The polarization constant of a Banach space $X$ is defined as $$\mathbf c(X):= \limsup\limits_{k\rightarrow \infty} \mathbf c(k, X)^\frac{1}{k},$$ where $\mathbf c(k, X)$ stands for the best constant $C>0$ such that $ \Vert \overset{\vee}{P} \Vert \leq C \Vert P \Vert$ for every $k$-homogeneous polynomial $P \in \mathcal P(^kX)$. We show that if $X$ is a finite dimensional complex space then $\mathbf c(X)=1$. We derive some consequences of this fact regarding the convergence of analytic functions on such spaces.The result is no longer true in the real setting. Here we relate this constant with the so-called Bochnak's complexification procedure. We also study some other properties connected with polarization. Namely, we provide necessary conditions related with the geometry of $X$ for $\mathbf c(2,X)=1$ to hold. Additionally we link polarization's constants with certain estimates of the nuclear norm of the product of polynomials., Comment: Math. Proc. Cambridge Philos. Soc., accepted

Spin-triplet superconductivity is a condensate of electron pairs with spin-1 and an odd-parity wavefunction. A particularly interesting manifestation of triplet pairing is a chiral p-wave state which is topologically non-trivial and a natural platform for realizing Majorana edge modes. Triplet pairing is however rare in solid state systems and so far, no unambiguous identification has been made in any bulk compound. Since pairing is most naturally mediated by ferromagnetic spin fluctuations, uranium based heavy fermion systems containing f electron elements that can harbor both strong correlations and magnetism are considered ideal candidate spin-triplet superconductors. In this work we present scanning tunneling microscopy (STM) studies of the newly discovered heavy fermion superconductor, UTe2 with a T$_{SC}$ of 1.6 K. We find signatures of coexisting Kondo effect and superconductivity which show competing spatial modulations within one unit-cell. STM spectroscopy at step edges show signatures of chiral in-gap states, predicted to exist at the boundaries of a topological superconductor. Combined with existing data indicating triplet pairing, the presence of chiral edge states suggests that UTe2 is a strong candidate material for chiral-triplet topological superconductivity., Comment: 24 pages, 4+8 figures, with Supplementary Material

We consider ride-sharing networks served byhuman-driven vehicles and autonomous vehicles. First, wepropose a novel model for ride-sharing in this mixed autonomysetting for a multi-location network in which the platformsets prices for riders, compensation for drivers, and operatesautonomous vehicles for a fixed price. Then we study thepossible benefits, in the form of increased profits, to the ride-sharing platform that are possible by introducing autonomousvehicles. We first establish a nonconvex optimization problemcharacterizing the optimal profits for a network operatingat a steady-state equilibrium and then propose a convexproblem with the same optimal profits that allows for efficientcomputation. Next, we study the relative mix of autonomous andhuman-driven vehicles that results at equilibrium for variouscosts of operation for autonomous vehicles. In particular, weshow that there is a regime for which the platform will chooseto mix autonomous and human-driven vehicles in order tooptimize profits. Our results provide insights into how suchride-sharing platforms might choose to integrate autonomousvehicles into their fleet., Comment: 8 pages with full proof details. To be presented at American Control Conference 2019

The possible realization of Majorana fermions as quasiparticle excitations in condensed matter physics has created much excitement. Most recent studies have focused on Majorana bound states which can serve as topological qubits. More generally, akin to elementary particles, Majorana fermions can propagate and display linear dispersion. These excitations have not yet been directly observed, and can also be used for quantum information processing. One route to realizing this is in a line junction between two phase-shifted superconductors coupled to topological surface states. Recent theory indicates that in iron-based superconductors, a particular type of crystalline defect, i.e., a domain wall (DW) between two regions with a half-unit cell shift between them, should create a $\pi$-phase shift in the superconducting order parameter. Combined with recent data showing topological surface states in FeSe$_x$Te$_{1-x}$ we find that this is the ideal system to realize helical 1D-dispersing Majorana modes. Here we report scanning tunneling spectroscopic (STS) measurements of crystalline DWs in FeSe$_{0.45}$Te$_{0.55}$. By analyzing large-area superconducting gap maps, we identify the gap in the topological surface state, demonstrating that our sample is an effective Fu-Kane proximitized topological system. We further locate DWs across which the atoms shift by half a unit cell. STS data on these DWs reveal a flat density of states inside the superconducting gap, a hallmark of linearly dispersing modes in 1D. This unique signature is absent in DWs in the related superconductor, FeSe which is not in the topological phase. Our combined data are consistent with the observation of dispersing Majorana states at a $\pi$-phase shift DW in a proximitized topological material., Comment: 14 pages, 4 figures; with supplementary information;added Acknowledgement

We characterize the sets of norm one vectors $\mathbf{x}_1,\ldots,\mathbf{x}_k$ in a Hilbert space $\mathcal H$ such that there exists a $k$-linear symmetric form attaining its norm at $(\textbf{x}_1,\ldots,\mathbf{x}_k)$. We prove that in the bilinear case, any two vectors satisfy this property. However, for $k\ge 3$ only collinear vectors satisfy this property in the complex case, while in the real case this is equivalent to $\mathbf{x}_1,\ldots,\mathbf{x}_k$ spanning a subspace of dimension at most 2. We use these results to obtain some applications to symmetric multilinear forms, symmetric tensor products and the exposed points of the unit ball of $\mathcal L_s(^k\mathcal{H})$., Comment: 17 pages

Interactions often require the proximity between particles. The movement of particles, thus, drives the change of the neighbors which are located in their proximity, leading to a sequence of interactions. In pathogenic contagion, infections occur through proximal interactions, but at the same time the movement facilitates the co-location of different strains. We analyze how the particle velocity impacts on the phase transitions on the contagion process of both a single infection and two cooperative infections. First, we identify an optimal velocity (close to half of the interaction range normalized by the recovery time) associated with the largest epidemic threshold, such that decreasing the velocity below the optimal value leads to larger outbreaks. Second, in the cooperative case, the system displays a continuous transition for low velocities, which becomes discontinuous for velocities of the order of three times the optimal velocity. Finally, we describe these characteristic regimes and explain the mechanisms driving the dynamics., Comment: 9 pages, 5 figures, 12 supplementary figures

The growing number of large databases of animal tracking provides an opportunity for analyses of movement patterns at the scales of populations and even species. We used analytical approaches, developed to cope with big data, that require no a priori assumptions about the behaviour of the target agents, to analyse a pooled tracking dataset of 272 elephant seals (Mirounga leonina) in the Southern Ocean, that was comprised of >500,000 location estimates collected over more than a decade. Our analyses showed that the displacements of these seals were described by a truncated power law distribution across several spatial and temporal scales, with a clear signature of directed movement. This pattern was evident when analysing the aggregated tracks despite a wide diversity of individual trajectories. We also identified marine provinces that described the migratory and foraging habitats of these seals. Our analysis provides evidence for the presence of intrinsic drivers of movement, such as memory, that cannot be detected using common models of movement behaviour. These results highlight the potential for big data techniques to provide new insights into movement behaviour when applied to large datasets of animal tracking., Comment: 18 pages, 5 figures, 6 supplementary figures

We study the spreading of cooperative infections in an empirical temporal network of contacts between people, including health care workers and patients, in a hospital. The system exhibits a phase transition leading to one or several endemic branches, depending on the connectivity pattern and the temporal correlations. There are two endemic branches in the original setting and the non-cooperative case. However, the cooperative interaction between infections reinforces the upper branch, leading to a smaller epidemic threshold and a higher probability for having a big outbreak. We show the microscopic mechanisms leading to these differences, characterize three different risks, and use the influenza features as an example for this dynamics.