Statistics of shared components in complex component systems

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 figure

Zipf and Heaps laws from dependency structures in component systems

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

Heaps' law, statistics of shared components and temporal patterns from a sample-space-reducing process

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 figure

Evolutionary stability of antigenically escaping viruses

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

Enhancing Light Harvesting by Hierarchical Functionally Graded Transparent Conducting Al-doped ZnO Nano- and Mesoarchitectures

A functionally graded Al-doped ZnO structure is presented which combines conductivity, visible transparency and light scattering with mechanical flexibility. The nano and meso-architecture, constituted by a hierarchical, large surface area, mesoporous tree-like structure evolving in a compact layer, is synthesized at room temperature and is fully compatible with plastic substrates. Light trapping capability is demonstrated by showing up to 100% improvement of light absorption of a low bandgap polymer employed as the active layer.Comment: 21 pages, 6 figures, submitted to Solar Energy Materials and Solar Cell

Snail1 transcription factor controls telomere transcription and integrity

Besides controlling epithelial-to-mesenchymal transition (EMT) and cell invasion, the Snail1 transcriptional factor also provides cells with cancer stem cell features. Since telomere maintenance is essential for stemness, we have examined the control of telomere integrity by Snail1. Fluorescence in situ hybridization (FISH) analysis indicates that Snail1-depleted mouse mesenchymal stem cells (MSC) have both a dramatic increase of telomere alterations and shorter telomeres. Remarkably, Snail1-deficient MSC present higher levels of both telomerase activity and the long non-coding RNA called telomeric repeat-containing RNA (TERRA), an RNA that controls telomere integrity. Accordingly, Snail1 expression downregulates expression of the telomerase gene (TERT) as well as of TERRA 2q, 11q and 18q. TERRA and TERT are transiently downregulated during TGF-induced EMT in NMuMG cells, correlating with Snail1 expression. Global transcriptome analysis indicates that ectopic expression of TERRA affects the transcription of some genes induced during EMT, such as fibronectin, whereas that of TERT does not modify those genes. We propose that Snail1 repression of TERRA is required not only for telomere maintenance but also for the expression of a subset of mesenchymal genes

Tuning electrical properties of hierarchically assembled Al-doped ZnO nanoforests by room temperature Pulsed Laser Deposition

Large surface area, 3D structured transparent electrodes with effective light management capability may represent a key component in the development of new generation optoelectronic and energy harvesting devices. We present an approach to obtain forest-like nanoporous/hierarchical Al-doped ZnO conducting layers with tunable transparency and light scattering properties, by means of room temperature Pulsed Laser Deposition in a mixed Ar:O2 atmosphere. The composition of the background atmosphere during deposition can be varied to modify stoichiometry-related defects, and therefore achieve control of electrical and optical properties, while the total background pressure controls the material morphology at the nano- and mesoscale and thus the light scattering properties. This approach allows to tune electrical resistivity over a very wide range (10^-1 - 10^6 Ohm*cm), both in the in-plane and cross-plane directions. Optical transparency and haze can also be tuned by varying the stoichiometry and thickness of the nano-forests