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This paper introduces a method based on a non-linear iterative map to evaluate node relevance in bipartite networks. By tuning a single parameter gamma, the method captures different concepts of node importance, including established measures like degree centrality, eigenvector centrality and the fitness-complexity ranking used in economics. The algorithm's flexibility allows for efficient ranking optimization tailored to specific tasks. As an illustrative example, we apply this method to ecological mutualistic networks, where ranking quality can be assessed by the extinction area - the rate at which the system collapses when species are removed in a certain order. The map with the optimal gamma value, which is dataset-specific, surpasses existing ranking methods on this task. Additionally, our method excels in evaluating nestedness, another crucial structural property of ecological systems, requiring specific node rankings. The final part of the paper explores the theoretical aspects of the map, revealing a phase transition at a critical $\gamma$ value dependent on the data structure that can be characterized analytically for random networks. Near the critical point, the map exhibits unique features and a distinctive triangular packing pattern of the adjacency matrix.

Its piezo- and potentially ferroelectric properties make the metastable kappa polymorph of Ga$_2$O$_3$ an interesting material for multiple applications, while In-incorporation into any polymorphs of Ga$_2$O$_3$ allows to lower their bandgap. In this work, we provide a guideline to achieve single phase $\kappa$-, $\beta$-Ga$_2$O$_3$ as well as their (In$_x$Ga$_{1-x}$)$_2$O$_3$ alloys up to x = 0.14 and x = 0.17 respectively, using In-mediated metal exchange catalysis in plasma assisted molecular beam epitaxy (MEXCAT-MBE). The polymorph transition from $\kappa$ to $\beta$ is also addressed, highlighting the fundamental role played by the thermal stability of the $\kappa$-Ga$_2$O$_3$. Additionally, we also demonstrate the possibility to grow ($\bar{2}$01) $\beta$-Ga$_2$O$_3$ on top of $\alpha$-Al$_2$O$_3$ (0001) at temperatures at least 100 {\deg}C above those achievable with conventional non-catalyzed MBE, opening the road for increased crystal quality in heteroepitaxy. The role of the substrate, as well as strain and structural defects in the growth of $\kappa$-Ga$_2$O$_3$ is also investigated by growing simultaneously on three different materials: (i) $\alpha$-Al$_2$O$_3$ (0001), (ii) 20 nm of ($\bar{2}$01) $\beta$-Ga$_2$O$_3$ on $\alpha$-Al$_2$O$_3$ (0001) and (iii) ($\bar{2}$01) $\beta$-Ga$_2$O$_3$ single crystal., Comment: Main text: 7 pages, 4 figures; Supplementary: 6 pages, 9 figures

Antigenic variation is the main immune escape mechanism for RNA viruses like influenza or SARS-CoV-2. While high mutation rates promote antigenic escape, they also induce large mutational loads and reduced fitness. It remains unclear how this cost-benefit trade-off selects the mutation rate of viruses. Using a traveling wave model for the co-evolution of viruses and host immune systems in a finite population, we investigate how immunity affects the evolution of the mutation rate and other non-antigenic traits, such as virulence. We first show that the nature of the wave depends on how cross-reactive immune systems are, reconciling previous approaches. The immune-virus system behaves like a Fisher wave at low cross-reactivities, and like a fitness wave at high cross-reactivities. These regimes predict different outcomes for the evolution of non-antigenic traits. At low cross-reactivities, the evolutionarily stable strategy is to maximize the speed of the wave, implying a higher mutation rate and increased virulence. At large cross-reactivities, where our estimates place H3N2 influenza, the stable strategy is to increase the basic reproductive number, keeping the mutation rate to a minimum and virulence low.

Chronic infections of the human immunodeficiency virus (HIV) create a very complex co-evolutionary process, where the virus tries to escape the continuously adapting host immune system. Quantitative details of this process are largely unknown and could help in disease treatment and vaccine development. Here we study a longitudinal dataset of ten HIV-infected people, where both the B-cell receptors and the virus are deeply sequenced. We focus on simple measures of turnover, which quantify how much the composition of the viral strains and the immune repertoire change between time points. At the single-patient level, the viral-host turnover rates do not show any statistically significant correlation, however they correlate if the information is aggregated across patients. In particular, we identify an anti-correlation: large changes in the viral pool composition come with small changes in the B-cell receptor repertoire. This result seems to contradict the naive expectation that when the virus mutates quickly, the immune repertoire needs to change to keep up. However, we show that the observed anti-correlation naturally emerges and can be understood in terms of simple population-genetics models.

Ga$_2$O$_3$ and its polymorphs are attracting increasing attention. The rich structural space of polymorphic oxide systems such as Ga$_2$O$_3$ offers potential for electronic structure engineering, which is of particular interest for a range of applications, such as power electronics. $\gamma$-Ga$_2$O$_3$ presents a particular challenge across synthesis, characterisation, and theory due to its inherent disorder and resulting complex structure -- electronic structure relationship. Here, density functional theory is used in combination with a machine learning approach to screen nearly one million potential structures, thereby developing a robust atomistic model of the $\gamma$-phase. Theoretical results are compared with surface and bulk sensitive soft and hard X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, spectroscopic ellipsometry, and photoluminescence excitation spectroscopy experiments representative of the occupied and unoccupied states of $\gamma$-Ga$_2$O$_3$. The first onset of strong absorption at room temperature is found at 5.1 eV from spectroscopic ellipsometry, which agrees well with the excitation maximum at 5.17 eV obtained by PLE spectroscopy, where the latter shifts to 5.33 eV at 5 K. This work presents a leap forward in the treatment of complex, disordered oxides and is a crucial step towards exploring how their electronic structure can be understood in terms of local coordination and overall structure.

Airborne Wind Energy is a lightweight technology that allows power extraction from the wind using airborne devices such as kites and gliders, where the airfoil orientation can be dynamically controlled in order to maximize performance. The dynamical complexity of turbulent aerodynamics makes this optimization problem unapproachable by conventional methods such as classical control theory, which rely on accurate and tractable analytical models of the dynamical system at hand. Here we propose to attack this problem through Reinforcement Learning, a technique that -- by repeated trial-and-error interactions with the environment -- learns to associate observations with profitable actions without requiring prior knowledge of the system. We show that in a simulated environment Reinforcement Learning finds an efficient way to control a kite so that it can tow a vehicle for long distances. The algorithm we use is based on a small set of intuitive observations and its physically transparent interpretation allows to describe the approximately optimal strategy as a simple list of manoeuvring instructions.

The oxidation-related issues in controlling Si doping from the Si source material in oxide molecular beam epitaxy (MBE) is addressed by using solid SiO as an alternative source material in a conventional effusion cell. Line-of-sight quadrupole mass spectrometry of the direct SiO-flux ($\Phi_{SiO}$) from the source at different temperatures ($T_{SiO}$) confirmed SiO molecules to sublime with an activation energy of 3.3eV. The $T_{SiO}$-dependent $\Phi_{SiO}$ was measured in vacuum before and after subjecting the source material to an O$_{2}$-background of $10^{-5}$ mbar (typical oxide MBE regime). The absence of a significant $\Phi_{SiO}$ difference indicates negligible source oxidation in molecular O$_{2}$. Mounted in an oxygen plasma-assisted MBE, Si-doped $\beta$-Ga2O3 layers were grown using this source. The $\Phi_{SiO}$ at the substrate was evaluated [from 2.9x10$^{9}$ cm$^{-2}$s$^{-1}$ ($T_{SiO}$=700{\deg}C) to 5.5x10$^{13}$ cm$^{-2}$s$^{-1}$ (T$_{SiO}$=1000{\deg}C)] and Si-concentration in the $\beta$-Ga2O3 layers measured by secondary ion mass spectrometry highlighting unprecedented control of continuous Si-doping for oxide MBE, i.e., $N_{Si}$ from 4x10$^{17}$ cm$^{-3}$ ($T_{SiO}$=700{\deg}C) up to 1.7x10$^{20}$ cm$^{-3}$ ($T_{SiO}$=900{\deg}C). For a homoepitaxial $\beta$-Ga2O3 layer an Hall charge carrier concentration of 3x10$^{19}$ cm$^{-3}$ in line with the provided $\Phi_{SiO}$ ($T_{SiO}$=800{\deg}C) is demonstrated. No SiO-incorporation difference was found between $\beta$-Ga2O3(010) layers homoepitaxially grown at 750{\deg}C and $\beta$-Ga2O3(-201) layers heteroepitaxially grown at 550{\deg}C. The presence of activated oxygen (plasma) resulted in partial source oxidation and related decrease of doping concentration (particularly at $T_{SiO}$<800{\deg}C) which has been tentatively explained with a simple model. Degassing the source at 1100{\deg}C reverted the oxidation.

Methane (CH4) emissions estimates from top-down studies over oil and gas basins have revealed systematic under-estimation of CH4 emissions in current national inventories. Sparse but extremely large amounts of CH4 from oil and gas production activities have been detected across the globe, resulting in a significant increase of the overall O&G contribution. However, attribution to specific facilities remains a major challenge unless high-resolution images provide the sufficient granularity within O&G basin. In this paper, we monitor known oil-and-gas infrastructures across the globe using recurrent Sentinel-2 imagery to detect and quantify more than 800 CH4 emissions. In combination with emissions estimates from airborne and Sentinel-5P measurements, we demonstrate the robustness of the fit to a power law from 0.1 tCH4/hr to 600 tCH4/hr. We conclude here that the prevalence of ultra-emitters (> 25tCH4/hr) detected globally by Sentinel-5P directly relates to emission occurrences below its detection threshold. Similar power law coefficients arise from several major oil and gas producers but noticeable differences in emissions magnitudes suggest large differences in maintenance practices and infrastructures across countries., Comment: Preprint version of https://pubs.acs.org/doi/abs/10.1021/acs.est.1c08575

Methane emissions from oil and gas (O&G) production and transmission represent a significant contribution to climate change. These emissions comprise sporadic releases of large amounts of methane during maintenance operations or equipment failures not accounted for in current inventory estimates. We collected and analyzed hundreds of very large releases from atmospheric methane images sampled by the TROPOspheric Monitoring Instrument (TROPOMI) over 2019 and 2020 to quantify emissions from O&G ultra-emitters. Ultra-emitters are primarily detected over the largest O&G basins of the world, following a power-law relationship with noticeable variations across countries but similar regression slopes. With a total contribution equivalent to 8-12% of the global O&G production methane emissions, mitigation of ultra-emitters is largely achievable at low costs and would lead to robust net benefits in billions of US dollars for the six major producing countries when incorporating recent estimates of societal costs of methane.

High-throughput sequencing of T- and B-cell receptors makes it possible to track immune repertoires across time, in different tissues, in acute and chronic diseases and in healthy individuals. However quantitative comparison between repertoires is confounded by variability in the read count of each receptor clonotype due to sampling, library preparation, and expression noise. We review methods for accounting for both biological and experimental noise and present an easy-to-use python package NoisET that implements and generalizes a previously developed Bayesian method. It can be used to learn experimental noise models for repertoire sequencing from replicates, and to detect responding clones following a stimulus. We test the package on different repertoire sequencing technologies and datasets. We review how such approaches have been used to identify responding clonotypes in vaccination and disease data. Availability: NoisET is freely available to use with source code at github.com/statbiophys/NoisET.

Hyperspectral satellite images report greenhouse gas concentrations worldwide on a daily basis. While taking simple averages of these images over time produces a rough estimate of relative emission rates, atmospheric transport means that simple averages fail to pinpoint the source of these emissions. We propose using Wasserstein barycenters coupled with weather data to average gas concentration data sets and better concentrate the mass around significant sources.

Vertical $pn$ heterojunction diodes were prepared by plasma-assisted molecular beam epitaxy of unintentionally-doped $p$-type SnO layers with hole concentrations ranging from $p=10^{18}$ to $10^{19}$cm$^{-3}$ on unintentionally-doped $n$-type $\beta$-Ga$_{2}$O$_{3}$(-201) substrates with an electron concentration of $n=2.0\times10^{17}$cm$^{-3}$. The SnO layers consist of (001)-oriented grains without in-plane expitaxial relation to the substrate. After subsequent contact processing and mesa etching (which drastically reduced the reverse current spreading in the SnO layer and associated high leakage) electrical characterization by current-voltage and capacitance-voltage measurement was performed. The results reveal a type-I band alignment and junction transport by thermionic emission in forward bias. A rectification of $2\times10^{8}$ at $\pm1$V, an ideality factor of 1.16, differential specific on-resistance of 3.9m$\Omega\thinspace$cm$^{2}$, and built-in voltage of 0.96V were determined. The $pn$-junction isolation prevented parallel conduction in the highly-conductive Ga$_{2}$O$_{3}$ substrate (sheet resistance $R_{S}\approx3\thinspace\Omega$) during van-der-Pauw Hall measurements of the SnO layer on top ($R_{S}\approx150$k$\Omega$, $p\approx2.5\times10^{18}$cm$^{-3}$, Hall mobility $\approx1$cm$^{2}$/Vs). The measured maximum reverse breakdown voltage of the diodes was 66V, corresponding to a peak breakdown field 2.2MV/cm in the Ga$_{2}$O$_{3}$-depletion region. Higher breakdown voltages that are required in high-voltage devices could be achieved by reducing the donor concentration in the $\beta$-Ga$_{2}$O$_{3}$ to increase the depletion width as well as improving the contact geometry to reduce field crowding.

In this work we investigate the growth of $\beta$-Ga2O3 homoepitaxial layers on top of (100) oriented substrates via indium-assisted metal exchange catalyzed molecular beam epitaxy (MEXCAT-MBE) which have exhibited prohibitively low growth rates by non-catalyzed MBE in the past. We demonstrate that the proper tuning of the MEXCAT growth parameters and the choice of a proper substrate offcut allow for the deposition of thin films with high structural quality via step-flow growth mechanism at relatively high growth rates for $\beta$-Ga2O3 homoepitaxy (i.e., around 1.5 nm/min, $\approx$45% incorporation of the incoming Ga flux), making MBE growth on this orientation feasible. Moreover, through the employment of the investigated four different (100) substrate offcuts along the [00-1] direction (i.e., 0$^\circ$, 2$^\circ$, 4$^\circ$, 6$^\circ$) we give experimental evidence on the fundamental role of the (-201) step edges as nucleation sites for growth of (100)-oriented Ga2O3 films by MBE.

Holding promising applications in power electronics, the wide band gap material gallium oxide has emerged as a vital alternative to materials like GaN and SiC. The detailed study of phonon modes in $\beta$-Ga$_{2}$O$_{3}$ provides insights into fundamental material properties such as crystal structure and orientation and can contribute to the identification of dopants and point defects. We investigate the Raman active phonon modes of $\beta$-Ga$_{2}$O$_{3}$ in two different oxygen isotope compositions ($^{16}$O,$^{18}$O) by experiment and theory: By carrying out polarized micro-Raman spectroscopy measurements on the (010) and ($\bar{2}$01) planes, we determine the frequencies of all 15 Raman active phonons for both isotopologues. The measured frequencies are compared with the results of density functional perturbation theory (DFPT) calculations. In both cases, we observe a shift of Raman frequencies towards lower energies upon substitution of $^{16}$O with $^{18}$O. By quantifying the relative frequency shifts of the individual Raman modes, we identify the atomistic origin of all modes (Ga-Ga, Ga-O or O-O) and present the first experimental confirmation of the theoretically calculated energy contributions of O lattice sites to Raman modes. We find that oxygen substitution on the O$_{\mathrm{II}}$ site leads to an elevated relative frequency shift compared to O$_{\mathrm{I}}$ and O$_{\mathrm{III}}$ sites. This study presents a blueprint for the future identification of different point defects in Ga$_{2}$O$_{3}$ by Raman spectroscopy.

Transparent conducting or semiconducting oxides are important materials for (transparent) optoelectronics and power electronics applications. While most of these oxides can be doped n-type only with room-temperature electron mobilities on the order of 100cm^2/Vs p-type oxides are needed for the realization of pn-junction devices but typically suffer from exessively low (<<1cm^2/Vs) hole mobilities. Tin monoxide (SnO) is one of the few p-type oxides with a higher hole mobility, lacking a well-established understanding of its hole transport properties. Moreover, growth of SnO is complicated by its metastability with respect to SnO2 and Sn, requiring epitaxy for the realization of single crystalline material typically required for high-end applications. Here, we give a comprehensive account on the epitaxial growth of SnO, its (meta)stability, and its thermoelectric transport properties in the context of the present literature. Textured and single-crystalline, unintentionally-doped p-type SnO(001) films are grown by plasma-assisted molecular beam epitaxy. The metastability of this semiconducting oxide is addressed theoretically through an equilibrium phase diagram. Experimentally, the related SnO growth window is rapidly determined by an in-situ growth kinetics study as function of Sn-to-O-plasma flux ratio and growth temperature. The presence of secondary Sn and SnOx (1 < x <= 2) phases is comprehensively studied by different methods, indicating the presence of Sn3O4 or Sn as major secondary phases, as well as a fully oxidized SnO2 film surface. The hole transport properties, Seebeck coefficient, and density-of-states effective mass are determined and critically discussed in the context of the present literature on SnO, considering its anisotropic hole-effective mass.

The search for new wide band gap materials is intensifying to satisfy the need for more advanced and energy efficient power electronic devices. Ga$_2$O$_3$ has emerged as an alternative to SiC and GaN, sparking a renewed interest in its fundamental properties beyond the main $\beta$-phase. Here, three polymorphs of Ga$_2$O$_3$, $\alpha$, $\beta$ and $\varepsilon$, are investigated using X-ray diffraction, X-ray photoelectron and absorption spectroscopy, and ab initio theoretical approaches to gain insights into their structure - electronic structure relationships. Valence and conduction electronic structure as well as semi-core and core states are probed, providing a complete picture of the influence of local coordination environments on the electronic structure. State-of-the-art electronic structure theory, including all-electron density functional theory and many-body perturbation theory, provide detailed understanding of the spectroscopic results. The calculated spectra provide very accurate descriptions of all experimental spectra and additionally illuminate the origin of observed spectral features. This work provides a strong basis for the exploration of the Ga$_2$O$_3$ polymorphs as materials at the heart of future electronic device generations., Comment: Updated manuscript version after peer review

Smooth interfaces and surfaces are beneficial for most (opto)electronic devices based on thin films and their heterostructures. For example, smoother interfaces in (010) beta-Ga2O3/(AlxGa1-x)2O3 heterostructures, whose roughness is ruled by that of the Ga2O3 layer, can enable higher mobility 2DEGs by reducing interface roughness scattering. To this end we experimentally prove that a substrate offcut along the [001] direction allows to obtain smooth beta-Ga2O3 layers in (010)-homoepitaxy under metal-rich conditions. Applying In-mediated metal-exchange catalysis (MEXCAT) in molecular beam epitaxy at high substrate temperatures (Tg = 900 {\deg}C) we compare the morphology of layers grown on (010)-oriented substrates with different unintentional offcuts. The layer roughness is generally ruled by (i) (110) and (-110)-facets visible as elongated features along the [001] direction (rms < 0.5 nm), and (ii) trenches (5-10 nm deep) orthogonal to [001]. We show that an unintentional substrate offcut of only 0.1{\deg} almost oriented along the [001] direction suppresses these trenches resulting in a smooth morphology with a roughness exclusively determined by the facets, i.e., rms 0.2 nm. Since we found the facet-and-trench morphology in layers grown by MBE with and without MEXCAT, we propose that the general growth mechanism for (010)-homoepitaxy is ruled by island growth whose coalescence results in the formation of the trenches. The presence of a substrate offcut in the [001] direction can allow for step-flow growth or island nucleation at the step edges, which prevents the formation of trenches. Moreover, we give experimental evidence for a decreasing surface diffusion length or increasing nucleation density with decreasing metal-to-oxygen flux ratio. Based on our results we can rule-out step bunching as cause of the trench formation as well as a surfactant-effect of indium during MEXCAT.

The choice of the control frequency of a system has a relevant impact on the ability of reinforcement learning algorithms to learn a highly performing policy. In this paper, we introduce the notion of action persistence that consists in the repetition of an action for a fixed number of decision steps, having the effect of modifying the control frequency. We start analyzing how action persistence affects the performance of the optimal policy, and then we present a novel algorithm, Persistent Fitted Q-Iteration (PFQI), that extends FQI, with the goal of learning the optimal value function at a given persistence. After having provided a theoretical study of PFQI and a heuristic approach to identify the optimal persistence, we present an experimental campaign on benchmark domains to show the advantages of action persistence and proving the effectiveness of our persistence selection method.

Resource sharing outside the kinship bonds is rare. Besides humans, it occurs in chimpanzee, wild dogs and hyenas as well as in vampire bats. Resource sharing is an instance of animal cooperation, where an animal gives away part of the resources that it owns for the benefit of a recipient. Taking inspiration from blood-sharing in vampire bats, here show the emergence of generosity in a Markov game, which couples the resource sharing between two players with the gathering task of that resource. At variance with the classical evolutionary models for cooperation, the optimal strategies of this game can be potentially learned by animals during their life-time. The players act greedily, that is, they try to individually maximize only their personal income. Nonetheless, the analytical solution of the model shows that three non trivial optimal behaviours emerge depending on conditions. Besides the obvious case when players are selfish in their choice of resource division, there are conditions under which both players are generous. Moreover, we also found a range of situations in which one selfish player exploits another generous individual, for the satisfaction of both players. Our results show that resource sharing is favoured by three factors: a long time horizon over which the players try to optimize their own game, the similarity among players in their ability of performing the resource-gathering task, as well as by the availability of resources in the environment. These concurrent requirements lead to identify necessary conditions for the emergence of generosity., Comment: 19 pages, 7 figures

Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component frequencies. Stochastic processes based on a sample-space-reducing (SSR) mechanism, in which the number of accessible states reduces as the system evolves, have been recently proposed as a simple explanation for the ubiquitous emergence of this law. However, many complex component systems are characterized by other statistical patterns beyond Zipf's law, such as a sublinear growth of the component vocabulary with the system size, known as Heap's law, and a specific statistics of shared components. This work shows, with analytical calculations and simulations, that these statistical properties can emerge jointly from a SSR mechanism, thus making it an appropriate parameter-poor representation for component systems. Several alternative (and equally simple) models, for example based on the preferential attachment mechanism, can also reproduce Heaps' and Zipf's laws, suggesting that additional statistical properties should be taken into account to select the most-likely generative process for a specific system. Along this line, we will show that the temporal component distribution predicted by the SSR model is markedly different from the one emerging from the popular rich-gets-richer mechanism. A comparison with empirical data from natural language indicates that the SSR process can be chosen as a better candidate model for text generation based on this statistical property. Finally, a limitation of the SSR model in reproducing the empirical "burstiness" of word appearances in texts will be pointed out, thus indicating a possible direction for extensions of the basic SSR process., Comment: 14 pages, 4 figures

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here, we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless, and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the "Zipfian ensemble" in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sub-linear and saturating) that we characterize quantitatively.

Many complex systems are modular. Such systems can be represented as "component systems", i.e., sets of elementary components, such as LEGO bricks in LEGO sets. The bricks found in a LEGO set reflect a target architecture, which can be built following a set-specific list of instructions. In other component systems, instead, the underlying functional design and constraints are not obvious a priori, and their detection is often a challenge of both scientific and practical importance, requiring a clear understanding of component statistics. Importantly, some quantitative invariants appear to be common to many component systems, most notably a common broad distribution of component abundances, which often resembles the well-known Zipf's law. Such "laws" affect in a general and non-trivial way the component statistics, potentially hindering the identification of system-specific functional constraints or generative processes. Here, we specifically focus on the statistics of shared components, i.e., the distribution of the number of components shared by different system-realizations, such as the common bricks found in different LEGO sets. To account for the effects of component heterogeneity, we consider a simple null model, which builds system-realizations by random draws from a universe of possible components. Under general assumptions on abundance heterogeneity, we provide analytical estimates of component occurrence, which quantify exhaustively the statistics of shared components. Surprisingly, this simple null model can positively explain important features of empirical component-occurrence distributions obtained from data on bacterial genomes, LEGO sets, and book chapters. Specific architectural features and functional constraints can be detected from occurrence patterns as deviations from these null predictions, as we show for the illustrative case of the "core" genome in bacteria., Comment: 18 pages, 7 main figures, 7 supplementary figures

We present a study on the crystallization process of undoped and Ta doped TiO2 amorphous thin films. In particular, the effect of ultra-fast annealing treatments in environments characterized by different oxygen concentrations is investigated via in-situ resistance measurements. The accurate examination of the key parameters involved in this process allows us to reduce the time needed to obtain highly conducting and transparent polycrystalline thin films (resistivity about $6 \times 10^{-4}$ {\Omega}cm, mean transmittance in the visible range about $81\%$) to just 5 minutes (with respect to the 180 minutes required for a standard vacuum annealing treatment) in nitrogen atmosphere (20 ppm oxygen concentration) at ambient pressure. Experimental evidence of superficial oxygen incorporation in the thin films and its detrimental role for the conductivity are obtained by employing different concentrations of traceable 18O isotopes during ultra-fast annealing treatments. The results are discussed in view of the possible implementation of the ultra-fast annealing process for TiO2-based transparent conducting oxides as well as electron selective layers in solar cell devices; taking advantage of the high control of the ultra-fast crystallization processes which has been achieved, these two functional layers are shown to be obtainable from the crystallization of a single homogeneous thin film., Comment: 30 pages (including Supporting Information and graphical TOC), 4 figures