We introduce a mathematical model of bread leavening in a warm chamber by coupling heat transfer, yeast growth, and carbon dioxide production and diffusion with the deformation of baking paste. We analyze the corresponding system of partial differential equations. The system is discretized by using a semi-implicit Euler method and the finite-element method in the time and space domain, respectively. Numerical simulations are employed to identify the energy consumption necessary to achieve a target volume under different settings of the leavening chamber and different concentrations of yeast in the baking paste, thereby providing a tool for the identification of cost-effective protocols.
This paper presents research conducted at the University of Trento addressing an industrial challenge from Fater S.p.A. regarding the thermal bonding of non-woven fabrics for diaper production. The problem consists in a possible analysis of the behavior of the bonding process of a non-woven fabric. In particular, the bonding process is not given by the use of some kind of glue, but just by the pressure of two fiber webs through two high-velocity steel-made rollers. The research comprised the formulation and theoretical as well as numerical analysis of analytical, mechanical and thermal models for the stress-strain behavior of the non-woven fabric's fibers and for the bonding process with heating effects.
The present study focuses on particular properties of transonic flows through a planar channel featuring a circular bump on the lower wall. The selected geometry is reminiscent of the region surrounding the trailing edge of an airfoil at zero angle of attack and the resulting flow pattern is indeed similar to the fishtail shock-pattern that characterizes airfoils flying at nearly sonic speed. Numerical simulations have been conducted by solving the inviscid Euler equations using both a commercial and an in-house CFD code; discontinuities are modeled using shock-capturing in the former and shock-fitting in the latter. Numerical experiments reveal different shock-patterns obtained by independently varying the inlet Mach number and the outlet-to-inlet static pressure ratio. When shock-interactions occur, shock-polar analysis reveals that the branching point can be modeled using either von Neumann’s three-shock-theory or Guderley’s four-wave-theory, depending on the inlet Mach number. Furthermore, for certain pairs of boundary conditions, multiple solutions have been observed.
This paper is concerned with structure-preserving numerical approximations for a class of nonlinear nonlocal Fokker-Planck equations, which admit a gradient flow structure and find application in diverse contexts. The solutions, representing density distributions, must be non-negative and satisfy a specific energy dissipation law. We design an arbitrary high-order discontinuous Galerkin (DG) method tailored for these model problems. Both semi-discrete and fully discrete schemes are shown to admit the energy dissipation law for non-negative numerical solutions. To ensure the preservation of positivity in cell averages at all time steps, we introduce a local flux correction applied to the DDG diffusive flux. Subsequently, a hybrid algorithm is presented, utilizing a positivity-preserving limiter, to generate positive and energy-dissipating solutions. Numerical examples are provided to showcase the high resolution of the numerical solutions and the verified properties of the DG schemes.
In artificial intelligence applications, the model training phase is critical and computationally demanding. In the graph neural networks (GNNs) research field, it is interesting to investigate how varying the graph topological and spectral structure impacts the learning process and overall GNN performance. In this work, we aim to theoretically investigate how the topology and the spectrum of a graph changes when nodes and edges are added or removed. Numerical results highlight stability issues in the learning process on graphs. In this work, we aim to theoretically investigate how the topology and the spectrum of a graph changes when nodes and edges are added or removed. We propose the topological relevance function as a novel method to quantify the stability of graph-based neural networks when graph structures are perturbed. We also explore the relationship between this topological relevance function, Graph Edit Distance, and spectral similarity. Numerical results highlight stability issues in the learning process on graphs.
Automatic spotting and classification of facial Micro-Expressions (MEs) in 'in-the-wild' videos is a topic of great interest in different fields involving sentiment analysis. Unfortunately, automatic spotting also represents a great challenge due to MEs quick temporal evolution and the lack of correctly annotated videos captured in the wild. In fact, the former makes ME difficult to grasp, while the latter results in the scarcity of real examples of spontaneous expressions in uncontrolled contexts. This paper proposes a novel but very simple spotting method that mainly exploits MEs perceptual characteristics. Specifically, the contribution is twofold: i) a distinguishing feature is defined for MEs in a domain that can capture and represent the peceptual stimuli of MEs, thus representing a suitable input for a standard binary classifier; ii) a proper numerical strategy is developed to augment the training set used to define the classification model. The rationale is that since MEs are visible by a human observer almost regardless of the specific context, it stands to reason that they have some sort of perceptual signature that activates pre-attentive vision. In this work this fingerprint is called Perceptual Emotional Signature (PES) and is modelled using the well-known Structural SIMilarity index (SSIM), which is a measure based on visual perception. A machine learning based classifier is then appropriately trained to recognize PESs. For this purpose, a suitable numerical strategy is applied to augment the training set; it mainly exploits error propagation rules in accordance with perceptual sensitivity to noise. The whole procedure is called PESMESS - Perceptual Emotional Signature of Micro- Expressions via SSIM and SVM. Preliminary studies show that SSIM can effectively guide the detection of MEs by identifying frames that contain PESs. Localization of PESs is accomplished using a properly trained Support Vector Machine (SVM) classifier that benefits from very short input feature vectors. Various tests on different benchmarking databases, containing both 'simulated' and 'in-the-wild' videos, confirm the potential and promising effectiveness of PESMESS when trained on appropriately perception-based augmented feature vectors.
This study investigates the use of exploratory data analysis and supervised learning techniques to analyze plant phenotyping traits, with a specific focus on: i) genetic diversity (wild type vs mutant tomato plants); ii) plant-plant interactions (primed vs non-primed plants using volatiles emitted by other stressed plants); and iii) plant stress response (using drought stress and comparing droughted plants with controls). The analyzed data consisted of high-throughput imaging at multiple wavelengths, which allowed for the examination of various morphological traits. The dataset contained the phenotypic characteristics of both wildtype and mutated tomato plants exposed to water stress. Machine learning algorithms were used to identify significant phenotypic indicators and predict plant stress responses. The use of techniques such as K-means clustering and Bayesian classifiers provided valuable insights into the temporal dynamics of plant traits under a variety of experimental conditions. This research emphasizes the importance of employing advanced statistical and machine learning methods to improve the precision and efficacy of phenotypic analysis in plant sciences.
In the framework of the theory of Landscape Ecology, a review of Lotka-Volterrra type models is proposed. Such models can be considered useful tools in order to represent and evaluate the dynamical behavior and the ecological stability of an environmental system which, as known, is subjected during time to several transformations. At this purpose, after such a review and presentation of different models, an application to an important wine region in France is performed using a model recently introduced in literature.
The application of the Partition of Unity Method (PUM) to signal approximation on graphs represents a recent advancement of this versatile and efficient interpolation technique. Given the novelty of this approach, little is yet known regarding the role of kernel parameters employed in constructing the associated Graph Basis Functions (GBFs). In order to shed light on this aspect, this study proposes several numerical tests obtained using GBFs generated by heat kernels and variational spline kernels.
This article outlines an innovative procedure to improve the accessibility of Mathematics for secondary school students with visual impairments. Using LATEX, a widely used typesetting system, a transformative approach is developed that converts traditional mathematical content into three accessible formats: PDF, MathJax and LAMBDA. Central to this system is the integration of alternative text, which offers full descriptions of images and mathematical formulae and promotes a richer understanding of its content. The broader implications of this project include the introduction of novel teaching models for educators, enhanced accessibility of Mathematics programmes, and the potential to encourage the enrolment of visually impaired students in science degree courses. Ultimately, this work contributes to the creation of the conditions for the development of an inclusive and barrier-free learning environment in Mathematics education.
Abstract Neurophysiological signal analysis is crucial for understanding the complex dynamics of brain function and its deviations in various pathological conditions. Traditional linear methods, while insightful, often fail to capture the full spectrum of inherently non-linear brain dynamics. This review explores the efficacy and applicability of the Higuchi fractal dimension (HFD) in interpreting neurophysiological signals such as scalp electroencephalography (EEG) and stereotactic intracranial encephalography (sEEG). We focus on three case studies: i) distinguishing between Alzheimer’s disease (AD) and healthy controls; ii) classifying neurodynamics across diverse brain parcels looking for a signature of that cortical parcel; and iii) differentiating states of consciousness. Our study highlights the potential of non-linear analysis for deeper insights into brain dynamics and its potential for improving clinical diagnostics.
In this article, we introduce a new class of polynomials, known as Apostol Hermite Bernoulli-type polynomials, and explore some of their algebraic properties, including summation formulas and their determinant form. The majority of our results are proven using generating function methods. Additionally, we investigate the monomiality principle related to these polynomials and identify the corresponding derivative and multiplicative operators.
This article explores some properties of degenerate hypergeometric Bernoulli polynomials, which are defined through the following generating function tme lambda x(t)e lambda x(t)-Sigma l=0m-1(1)l,lambda tll!=Sigma n=0 infinity Bn,lambda[m-1](x)tnn!, |t|<min{2 pi,1|lambda|},lambda is an element of R\{0}. We deduce their associated summation formulas and their corresponding determinant form. Also we focus our attention on the zero distribution of such polynomials and perform some numerical illustrative examples, which allow us to compare the behavior of the zeros of degenerate hypergeometric Bernoulli polynomials with the zeros of their hypergeometric counterpart. Finally, using a monomiality principle approach we present a differential equation satisfied by these polynomials.
The Weierstrass' theory of one-dimensional Lagrangian systems and a quasi-continuum approach are employed to study the propagation of solitary waves in tensegrity mass-spring chains, which exhibit softening-type elastic response in the large displacement regime and are subject to external pre-compression. The presented study analytically derives the shape of the traveling rarefaction pulses, and limiting values of the speeds of such pulses. Use is made of a tensegrity-like interaction potential that captures the main features of the real force-displacement response of the examined units. The Weierstrass approach is validated through numerical applications that establish comparisons between the theory developed in the present work and previous results available in literature.
In this paper we study linear fractional differential equations involving tempered Caputo-type derivatives in the hyperbolic space. We consider in detail the three-dimensional case for its simple and useful structure. We also discuss the probabilistic meaning of our results in relation to the distribution of an hyperbolic Brownian motion time-changed with the inverse of a tempered stable subordinator. The generalization to an arbitrary dimension n can be easily obtained. We also show that it is possible to construct a particular solution for the non-linear porous-medium type tempered equation by using elementary functions.
We investigate the numerical calculation of the general Heun equation using Wolfram Mathematica's functions, comparing the numerical solutions with hypergeometric and explicit solutions. This exploration sheds light on the efficacy and accuracy of the numerical algorithm implemented in Mathematica for computing Heun functions.
A review on the classical Plateau problem is presented. Then, the state of the art about the Kirchhoff-Plateau problem is illustrated as well as some possible future directions of research.
We review recent mathematical results concerning the analysis of hydrostatic equations in the context of stably stratified fluids. Beginning with the simpler and better understood setting of homogeneous fluids, we emphasize the additional mathematical challenges posed by non-homogeneous framework. We present both positive and negative results, including well-posedness and proof of the hydrostatic limit with a suitable regularization, alongside ill-posedness in the fully inviscid setting and the breakdown of the hydrostatic limit in specific scenarios.
Mathematics has been applied to physics and engineering in the last few centuries, substantially contributing to the various phases of the industrial revolution. Its application to biology is instead relatively more recent. In this paper we provide an overview of some problems in a few fields mainly related to ecology. The models discussed help in fighting pests in agriculture to improve crop harvesting and to combat the phenomenon of alien species invasions, that due to worldwide trading and climate changes is affecting the temperate regions, threatening the survival of the native species. A pair of examples related to primary oxygen production and fallacies of our linear way of thinking are also presented, to stress the fact that raising temperatures entail huge unforeseen problems. Finally we delve briefly in the vaste field of epidemiology, that would deserve a review on its own, to discuss models for diseases in the environment and one instance related epidemics affecting humans, prompted by the important role of asymptomatics played in them.
