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.

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.

We discuss USA stock market data from 1789 until 2020, focusing our attention on the S&P 500 index (1957–2020). We find that the data can be split into two periods, (1789–1948) and (1948–2020), displaying roughly 2% and 7% growth rates, respectively. The index variations from each trend appear similar, suggesting some degree of stationarity in market fluctuations. We then correlate market behavior to macroeconomic data, such as world (and USA) population growth and gross domestic product (GDP), on different time horizons. The analysis signals that the S&P 500 might be overvalued, possibly undergoing a series of bubbles, since the 1990s. To understand this behavior, we introduce a model for bubbles, showing that they can be caused by a lack of correlations between stock prices and a virtual market index, the latter calculated self-consistently from the stock prices. We argue that variations, $ \Delta\gamma $, in the "bubble parameter" (or decoupling factor $ \gamma $), are anticorrelated to variations of the Federal Funds Rate (FFR), which may trigger a bubble phenomenon ($ \gamma\to1 $) when persistent rate cuts become too pronounced. The FFR are confronted with the consumer price index (CPI) in the period (1955–2020) as an attempt to complete the picture. Our analyses suggest that the strong departure of the S&P 500 from historical fundamental trends within (1990–2020) may reflect the development of financial anomalies, in part related to monetary policies, which should be carefully addressed in the near future.

Predicting the sound quality of an environment represents an important task especially in urban parks where the coexistence of sources of anthropic and biophonic nature produces complex sound patterns. To this end, an index has been defined by us, denoted as soundscape ranking index (SRI), which assigns a positive weight to natural sounds (biophony) and a negative one to anthropogenic sounds. A numerical strategy to optimize the weight values has been implemented by training two machine learning algorithms, the random forest (RF) and the perceptron (PPN), over an augmented data-set. Due to the availability of a relatively small fraction of labelled recorded sounds, we employed Monte Carlo simulations to mimic the distribution of the original data-set while keeping the original balance among the classes. The results show an increase in the classification performance. We discuss the issues that special care needs to be addressed when the augmented data are based on a too small original data-set.

We study the dynamics of user-agent interactions in virtual environments through mathematical models derived in a Lagrangian formalism. The goal is to optimize the number of agents required to solve a generic predefined task while minimizing the computational cost to achieve it. Specifically, we derived Euler-Lagrange equations of motion to describe the different ways in which agents may interact with users. The main advantage of this approach lies in its peculiarity to derive a scaling law for any interaction rule one wishes to design, ensuring that the system scales while optimizing the global impact of the interactions. By specifying an action functional over interaction trajectories and enforcing its minimization, the optimal way to allocate agents emerges naturally as Euler–Lagrange equations, embedding the entire optimization strategy directly into the formalism. This intrinsic coupling of dynamics and cost yields a universal procedure to compute the scaling laws for arbitrary interaction rules, ensuring that agent populations and computational expense grow according with environmental complexity. We illustrate the methodology with two specific example. These results also offer a foundation for further research into multi-agent dynamics and their applications in virtual environments.

Generalized modeling provides a powerful framework for the local analysis of broad classes of nonlinear dynamical systems without fixing specific functional forms. A foundational step in this approach is the assumption that a steady state exists, followed by the normalization of the state variables and the construction of the Jacobian in terms of generalized parameters. In this paper, we provide a rigorous justification for this assumption across a broad class of finite-dimensional models. Under natural boundary sign conditions on a compact hyperrectangle, the Poincaré–Miranda theorem guarantees the existence of at least one steady state. We demonstrate how these conditions can be routinely verified in compartmental systems via donor-vanishing and upper-face dominance criteria and we derive a Brouwer-degree refinement that establishes topological robustness under admissible perturbations when the boundary inequalities are strict. The general theory is illustrated using representative examples from physics and biology, including a two-patch metapopulation model, an open SEIR system with immigration and a coupled-laser model. Together, these results provide a rigorous topological foundation for the steady-state hypothesis commonly used in generalized modeling, offering a highly practical criterion for verifying it in applications. Graphical Under natural boundary sign conditions on a compact hyper rectangle, the Poincaré–Miranda theorem guarantees the existence of at least one steady state $$x^*$$ x ∗ in generalized gain-loss dynamical systems without requiring specific functional forms. The inward-pointing components of the vector field along opposite boundary faces ( $$f_i \ge 0$$ f i ≥ 0 on lower faces $$F_i^-$$ F i - and $$f_i \le 0$$ f i ≤ 0 on upper faces $$F_i^+$$ F i + ) provide a rigorous, model-independent topological foundation and degree-theoretic robustness for the steady-state hypothesis across physical, ecological, and epidemiological networks