The fractal geometry of polymeric materials surfaces: surface area and fractal length scales.

Using three common polymeric materials (polypropylene (PP), polytetrafluoroethylene (PTFE) and polycaprolactone (PCL)), a standard oxygen-plasma treatment and atomic force microscopy (AFM), we performed a scaling analysis of the modified surfaces yielding effective Hurst exponents (H ≃ 0.77 ± 0.02 (PP), ≃0.75 ± 0.02 (PTFE), and ≃0.83 ± 0.02 (PCL)), for the one-dimensional profiles, corresponding to the transversal sections of the surface, by averaging over all possible profiles. The surface fractal dimensions are given by ds = 3 - H, corresponding to ds ≃ 2.23, 2.25, and 2.17, respectively. We present a simple method to obtain the surface area from the AFM images stored in a matrix of 512 × 512 pixels. We show that the considerable increase found in the surface areas of the treated samples w.r.t. to the non-treated ones (43% for PP, 85% for PTFE, and 25% for PCL, with errors of about 2.5% on samples of 2 µm × 2 µm) is consistent with the observed increase in the length scales of the fractal regime to determine H, typically by a factor of about 2, extending from a few to hundreds of nanometres. We stipulate that the intrinsic roughness already present in the original non-treated material surfaces may serve as 'fractal' seeds undergoing significant height fluctuations during plasma treatment, suggesting a pathway for the future development of advanced material interfaces with large surface areas at the nanoscale.

Toward the Definition of a Soundscape Ranking Index (SRI) in an Urban Park Using Machine Learning Techniques.

The goal of estimating a soundscape index, aimed at evaluating the contribution of the environmental sound components, is to provide an accurate "acoustic quality" assessment of a complex habitat. Such an index can prove to be a powerful ecological tool associated with both rapid on-site and remote surveys. The soundscape ranking index (SRI), introduced by us recently, can empirically account for the contribution of different sound sources by assigning a positive weight to natural sounds (biophony) and a negative weight to anthropogenic ones. The optimization of such weights was performed by training four machine learning algorithms (decision tree, DT; random forest, RF; adaptive boosting, AdaBoost; support vector machine, SVM) over a relatively small fraction of a labeled sound recording dataset. The sound recordings were taken at 16 sites distributed over an area of approximately 22 hectares at Parco Nord (Northern Park) of the city Milan (Italy). From the audio recordings, we extracted four different spectral features: two based on ecoacoustic indices and the other two based on mel-frequency cepstral coefficients (MFCCs). The labeling was focused on the identification of sounds belonging to biophonies and anthropophonies. This preliminary approach revealed that two classification models, DT and AdaBoost, trained by using 84 extracted features from each recording, are able to provide a set of weights characterized by a rather good classification performance (F1-score = 0.70, 0.71). The present results are in quantitative agreement with a self-consistent estimation of the mean SRI values at each site that was recently obtained by us using a different statistical approach.

Self-Consistent Soundscape Ranking Index: The Case of an Urban Park.

We have performed a detailed analysis of the soundscape inside an urban park (located in the city of Milan) based on simultaneous sound recordings at 16 locations within the park. The sound sensors were deployed over a regular grid covering an area of about 22 hectares, surrounded by a variety of anthropophonic sources. The recordings span 3.5 h each over a period of four consecutive days. We aimed at determining a soundscape ranking index (SRI) evaluated at each site in the grid by introducing 4 unknown parameters. To this end, a careful aural survey from a single day was performed in order to identify the presence of 19 predefined sound categories within a minute, every 3 minutes of recording. It is found that all SRI values fluctuate considerably within the 70 time intervals considered. The corresponding histograms were used to define a dissimilarity function for each pair of sites. Dissimilarity was found to increase significantly with the inter-site distance in space. Optimal values of the 4 parameters were obtained by minimizing the standard deviation of the data, consistent with a fifth parameter describing the variation of dissimilarity with distance. As a result, we classify the sites into three main categories: "poor", "medium" and "good" environmental sound quality. This study can be useful to assess the quality of a soundscape in general situations.

Spreading of infections on random graphs: A percolation-type model for COVID-19.

We introduce an epidemic spreading model on a network using concepts from percolation theory. The model is motivated by discussing the standard SIR model, with extensions to describe effects of lockdowns within a population. The underlying ideas and behaviour of the lattice model, implemented using the same lockdown scheme as for the SIR scheme, are discussed in detail and illustrated with extensive simulations. A comparison between both models is presented for the case of COVID-19 data from the USA. Both fits to the empirical data are very good, but some differences emerge between the two approaches which indicate the usefulness of having an alternative approach to the widespread SIR model.

Recent innovations in the technology and applications of low-dimensional CuO nanostructures for sensing, energy and catalysis.

Low-dimensional copper oxide nanostructures are very promising building blocks for various functional materials targeting high-demanded applications, including energy harvesting and transformation systems, sensing and catalysis. Featuring a very high surface-to-volume ratio and high chemical reactivity, these materials have attracted wide interest from researchers. Currently, extensive research on the fabrication and applications of copper oxide nanostructures ensures the fast progression of this technology. In this article we briefly outline some of the most recent, mostly within the past two years, innovations in well-established fabrication technologies, including oxygen plasma-based methods, self-assembly and electric-field assisted growth, electrospinning and thermal oxidation approaches. Recent progress in several key types of leading-edge applications of CuO nanostructures, mostly for energy, sensing and catalysis, is also reviewed. Besides, we briefly outline and stress novel insights into the effect of various process parameters on the growth of low-dimensional copper oxide nanostructures, such as the heating rate, oxygen flow, and roughness of the substrates. These insights play a key role in establishing links between the structure, properties and performance of the nanomaterials, as well as finding the cost-and-benefit balance for techniques that are capable of fabricating low-dimensional CuO with the desired properties and facilitating their integration into more intricate material architectures and devices without the loss of original properties and function.

Fractional derivatives of random walks: time series with long-time memory.

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly decaying autocorrelation functions. The relation between these correlated walks and the well-known fractionally integrated autoregressive models with conditional heteroskedasticity (FIGARCH), commonly used in econometric studies, is discussed. The application of correlated random walks to simulate empirical financial times series is considered and compared with the predictions from FIGARCH and the simpler FIARCH processes. A comparison with empirical data is performed.

Temperature-dependent structural behavior of self-avoiding walks on Sierpinski carpets.

We study the temperature-dependent structural behavior of self-avoiding walks (SAWs) on two-dimensional Sierpinski carpets as a simple model of polymers adsorbed on a disordered surface. Thereby, the Sierpinski carpet defines two types of sites with energy 0 and >0 , respectively, yielding a deterministic fractal energy landscape. In the limiting cases of temperature T-->0 and T-->infinity , the known behaviors of SAWs on Sierpinski carpets and on regular square lattices, respectively, are recovered. For finite temperatures, the structural behavior is found to be intermediate between the two limiting cases; the characteristic exponents, however, display a nontrivial dependence on temperature.

A protein evolution model with independent sites that reproduces site-specific amino acid distributions from the Protein Data Bank.

BACKGROUND: Since thermodynamic stability is a global property of proteins that has to be conserved during evolution, the selective pressure at a given site of a protein sequence depends on the amino acids present at other sites. However, models of molecular evolution that aim at reconstructing the evolutionary history of macromolecules become computationally intractable if such correlations between sites are explicitly taken into account. RESULTS: We introduce an evolutionary model with sites evolving independently under a global constraint on the conservation of structural stability. This model consists of a selection process, which depends on two hydrophobicity parameters that can be computed from protein sequences without any fit, and a mutation process for which we consider various models. It reproduces quantitatively the results of Structurally Constrained Neutral (SCN) simulations of protein evolution in which the stability of the native state is explicitly computed and conserved. We then compare the predicted site-specific amino acid distributions with those sampled from the Protein Data Bank (PDB). The parameters of the mutation model, whose number varies between zero and five, are fitted from the data. The mean correlation coefficient between predicted and observed site-specific amino acid distributions is larger than = 0.70 for a mutation model with no free parameters and no genetic code. In contrast, considering only the mutation process with no selection yields a mean correlation coefficient of = 0.56 with three fitted parameters. The mutation model that best fits the data takes into account increased mutation rate at CpG dinucleotides, yielding = 0.90 with five parameters. CONCLUSION: The effective selection process that we propose reproduces well amino acid distributions as observed in the protein sequences in the PDB. Its simplicity makes it very promising for likelihood calculations in phylogenetic studies. Interestingly, in this approach the mutation process influences the effective selection process, i.e. selection and mutation must be entangled in order to obtain effectively independent sites. This interdependence between mutation and selection reflects the deep influence that mutation has on the evolutionary process: The bias in the mutation influences the thermodynamic properties of the evolving proteins, in agreement with comparative studies of bacterial proteomes, and it also influences the rate of accepted mutations.

Violation of the des Cloizeaux relation for self-avoiding walks on Sierpinski square lattices.

The statistics of self-avoiding walks (SAWs) on deterministic fractal structures with infinite ramification, modeled by Sierpinski square lattices, is revisited in two and three dimensions using the reptation algorithm. The probability distribution function of the end-to-end distance of SAWs, consisting of up to 400 steps, is obtained and its scaling behavior at small distances is studied. The resulting scaling exponents are confronted with previous calculations for much shorter linear chains (20 to 30 steps) based on the exact enumeration (EE) technique. The present results coincide with the EE values in two dimensions, but differ slightly in three dimensions. A possible explanation for this discrepancy is discussed. Despite this, the violation of the so-called des Cloizeaux relation, a renormalization result that holds on regular lattices and on deterministic fractal structures with finite ramification, is confirmed numerically.

Principal eigenvector of contact matrices and hydrophobicity profiles in proteins.

With the aim of studying the relationship between protein sequences and their native structures, we adopted vectorial representations for both sequence and structure. The structural representation was based on the principal eigenvector of the fold's contact matrix (PE). As has been recently shown, the latter encodes sufficient information for reconstructing the whole contact matrix. The sequence was represented through a hydrophobicity profile (HP), using a generalized hydrophobicity scale that we obtained from the principal eigenvector of a residue-residue interaction matrix, and denoted as interactivity scale. Using this novel scale, we defined the optimal HP of a protein fold, and, by means of stability arguments, predicted to be strongly correlated with the PE of the fold's contact matrix. This prediction was confirmed through an evolutionary analysis, which showed that the PE correlates with the HP of each individual sequence adopting the same fold and, even more strongly, with the average HP of this set of sequences. Thus, protein sequences evolve in such a way that their average HP is close to the optimal one, implying that neutral evolution can be viewed as a kind of motion in sequence space around the optimal HP. Our results indicate that the correlation coefficient between N-dimensional vectors constitutes a natural metric in the vectorial space in which we represent both protein sequences and protein structures, which we call vectorial protein space. In this way, we define a unified framework for sequence-to-sequence, sequence-to-structure and structure-to-structure alignments. We show that the interactivity scale is nearly optimal both for the comparison of sequences to sequences and sequences to structures.

Looking at structure, stability, and evolution of proteins through the principal eigenvector of contact matrices and hydrophobicity profiles.

We review and further develop an analytical model that describes how thermodynamic constraints on the stability of the native state influence protein evolution in a site-specific manner. To this end, we represent both protein sequences and protein structures as vectors: structures are represented by the principal eigenvector (PE) of the protein contact matrix, a quantity that resembles closely the effective connectivity of each site; sequences are represented through the "interactivity" of each amino acid type, using novel parameters that are correlated with hydropathy scales. These interactivity parameters are more strongly correlated than the other hydropathy scales that we examine with: (1) the change upon mutations of the unfolding free energy of proteins with two-states thermodynamics; (2) genomic properties as the genome-size and the genome-wide GC content; (3) the main eigenvectors of the substitution matrices. The evolutionary average of the interactivity vector correlates very strongly with the PE of a protein structure. Using this result, we derive an analytic expression for site-specific distributions of amino acids across protein families in the form of Boltzmann distributions whose "inverse temperature" is a function of the PE component. We show that our predictions are in agreement with site-specific amino acid distributions obtained from the Protein Data Bank, and we determine the mutational model that best fits the observed site-specific amino acid distributions. Interestingly, the optimal model almost minimizes the rate at which deleterious mutations are eliminated by natural selection.

Autoregressive processes with exponentially decaying probability distribution functions: applications to daily variations of a stock market index.

We consider autoregressive conditional heteroskedasticity (ARCH) processes in which the variance sigma(2)(y) depends linearly on the absolute value of the random variable y as sigma(2)(y) = a+b absolute value of y. While for the standard model, where sigma(2)(y) = a + b y(2), the corresponding probability distribution function (PDF) P(y) decays as a power law for absolute value of y-->infinity, in the linear case it decays exponentially as P(y) approximately exp(-alpha absolute value of y), with alpha = 2/b. We extend these results to the more general case sigma(2)(y) = a+b absolute value of y(q), with 0 < q < 2. We find stretched exponential decay for 1 < q < 2 and stretched Gaussian behavior for 0 < q < 1. As an application, we consider the case q=1 as our starting scheme for modeling the PDF of daily (logarithmic) variations in the Dow Jones stock market index. When the history of the ARCH process is taken into account, the resulting PDF becomes a stretched exponential even for q = 1, with a stretched exponent beta = 2/3, in a much better agreement with the empirical data.

Self-avoiding walks on Sierpinski lattices in two and three dimensions.

The scaling properties of linear polymers on deterministic fractal structures, modeled by self-avoiding random walks (SAW) on Sierpinski lattices in two and three dimensions, are studied. To this end, all possible SAW configurations of N steps are enumerated exactly and averages over suitable sets of starting lattice points for the walks are performed to extract the mean quantities of interest reliably. We determine the critical exponent describing the mean end-to-end chemical distance (-)l(N) after N steps and the corresponding distribution function, P(S)(l,N). A des Cloizeaux-type relation between the exponent characterizing the asymptotic shape of the distribution, for l-->0 and N--> infinity, and the one describing the total number of SAW of N steps is suggested and supported by numerical results. These results are confronted with those obtained recently on the backbone of the incipient percolation cluster, where the corresponding exponents are very well described by a generalized des Cloizeaux relation valid for statistically self-similar structures.

Autoregressive processes with anomalous scaling behavior: applications to high-frequency variations of a stock market index.

We employ autoregressive conditional heteroskedasticity processes to model the probability distribution function (PDF) of high-frequency relative variations of the Standard & Poors 500 market index data, obtained at the time horizon of 1 min. The model reproduces quantitatively the shape of the PDF, characterized by a Lévy-type power-law decay around its center, followed by a crossover to a faster decay at the tails. Furthermore, it is able to reproduce accurately the anomalous decay of the central part of the PDF at larger time horizons and, by the introduction of a short-range memory, also the crossover behavior of the corresponding standard deviations and the time scale of the exponentially decaying autocorrelation function of returns displayed by the empirical data.

Long-time correlations in company profit fluctuations: presence of extreme events.

The accuracy of earnings predictions is hampered by the several predominantly unpredictable effects due to the complex evolution of economy. Finding out which are the dominant market features embracing uncertainty is therefore the key to get beyond present state-of-art earnings forecasts. The analysis of annual revenues and earnings data (1954-2008) from the 500 largest-revenue U.S. companies suggests a linear relation between company expected mean profit and revenue. Annual profit fluctuations are then obtained as difference between actual annual profits and expected mean values. It is found that the temporal evolution of profit fluctuations for a single company displays a slowly decaying autocorrelation, yielding Hurst exponents in the range H=0.75+/-0.17 . The study of profits cross correlations between companies suggests a way to distinguish typical earnings years from anomalous ones by looking at minimal information structures contained within the space defined by the associated covariance metric.

Prediction of site-specific amino acid distributions and limits of divergent evolutionary changes in protein sequences.

We derive an analytic expression for site-specific stationary distributions of amino acids from the structurally constrained neutral (SCN) model of protein evolution with conservation of folding stability. The stationary distributions that we obtain have a Boltzmann-like shape, and their effective temperature parameter, measuring the limit of divergent evolutionary changes at a given site, can be predicted from a site-specific topological property, the principal eigenvector of the contact matrix of the native conformation of the protein. These analytic results, obtained without free parameters, are compared with simulations of the SCN model and with the site-specific amino acid distributions obtained from the Protein Data Bank. These results also provide new insights into how the topology of a protein fold influences its designability, i.e., the number of sequences compatible with that fold. The dependence of the effective temperature on the principal eigenvector decreases for longer proteins, as a possible consequence of the fact that selection for thermodynamic stability becomes weaker in this case.

Lack of self-averaging in neutral evolution of proteins.

We simulate neutral evolution of proteins imposing conservation of the thermodynamic stability of the native state in the framework of an effective model of folding thermodynamics. This procedure generates evolutionary trajectories in sequence space which share two universal features for all of the examined proteins. First, the number of neutral mutations fluctuates broadly from one sequence to another, leading to a non-Poissonian substitution process. Second, the number of neutral mutations displays strong correlations along the trajectory, thus causing the breakdown of self-averaging of the resulting evolutionary substitution process.

Statistical properties of neutral evolution.

Neutral evolution is the simplest model of molecular evolution and thus it is most amenable to a comprehensive theoretical investigation. In this paper, we characterize the statistical properties of neutral evolution of proteins under the requirement that the native state remains thermodynamically stable, and compare them to the ones of Kimura's model of neutral evolution. Our study is based on the Structurally Constrained Neutral (SCN) model which we recently proposed. We show that, in the SCN model, the substitution rate decreases as longer time intervals are considered. Fluctuations from one branch of the evolutionary tree to another are strong, leading to a non-Poissonian statistics for the substitution process. Such strong fluctuations are in part due to the fact that neutral substitution rates for individual residues are strongly correlated for most residue pairs. Interestingly, structurally conserved residues, characterized by a much below average substitution rate, are also much less correlated to other residues and evolve in a much more regular way. Our results can improve methods aimed at distinguishing between neutral and adaptive substitutions as well as methods for computing the expected number of substitutions occurred since the divergence of two protein sequences. In particular, we compute the minimal sequence similarity below which no information about the evolutionary divergence of the compared sequences can be obtained.