Two-dimensional non commutative Swanson model and its bicoherent states

We introduce an extended version of the Swanson model, defined on a two-dimensional non commutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the biorthogonal sets of eigenstates of the Hamiltonian and of its adjoint are explicitly constructed. We also show that it is possible to construct two displacement-like operators from which a family of bi-coherent states can be obtained. These states are shown to be eigenstates of the deformed lowering operators, and their projector allows to produce a suitable resolution of the identity in a dense subspace of \Lc^2(\Bbb R^2)

A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from an integral formulation of the radiation condition at infinity. In this Letter, we implement a Fourier-Chebyschev collocation method and show that this approach reduce the computational cost significantly. As a consequence, we give numerical evidence of some convergence estimates available in literature and we study the robustness of the algorithm at low and mid-high frequencies

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented

A Phenomenological Operator Description of Dynamics of Crowds: Escape Strategies

We adopt an operatorial method, based on creation, annihilation and number operators, to describe one or two populations mutually interacting and moving in a two--dimensional region. In particular, we discuss how the two populations, contained in a certain two-dimensional region with a non--trivial topology, react when some alarm occurs. We consider the cases of both low and high densities of the populations, and discuss what is changing as the strength of the interaction increases. We also analyze what happens when the region has either a single exit or two ways out

Support Vector Regression for Rainfall-Runoff Modeling in Urban Drainage: A Comparison with the EPA's Storm Water Management Model

Rainfall-runoff models can be classified into three types: physically based models, conceptual models, and empirical models. In this latter class of models, the catchment is considered as a black box, without any reference to the internal processes that control the transformation of rainfall to runoff. In recent years, some models derived from studies on artificial intelligence have found increasing use. Among these, particular attention should be paid to Support Vector Machines (SVMs). This paper shows a comparative study of rainfall-runoff modeling between a SVM-based approach and the EPA's Storm Water Management Model (SWMM). The SVM is applied in the variant called Support Vector regression (SVR). Two different experimental basins located in the north of Italy have been considered as case studies. Two criteria have been chosen to assess the consistency between the recorded and predicted flow rates: the root-mean square error (RMSE) and the coefficient of determination. The two models showed comparable performance. In particular, both models can properly model the hydrograph shape, the time to peak and the total runoff. The SVR algorithm tends to underestimate the peak discharge, while SWMM tends to overestimate it. SVR shows great potential for applications in the field of urban hydrology, but currently it also has significant limitations regarding the model calibration

Small interfering RNAs in tendon homeostasis.

Background: Tenogenesis and tendon homeostasis are guided by genes encoding for the structural molecules of tendon fibres. Small interfering RNAs (siRNAs), acting on gene regulation, can therefore participate in the process of tendon healing.Sources of data: A systematic search of different databases to October 2020 identified 17 suitable studies.Areas of agreement: SiRNAs can be useful to study reparative processes of tendons and identify possible therapeutic targets in tendon healing.Areas of controversy: Many genes and growth factors involved in the processes of tendinopathy and tendon healing can be regulated by siRNAs. It is however unclear which gene silencing determines the expected effect.Growing points: Gene dysregulation of growth factors and tendon structural proteins can be influenced by siRNA.Areas timely for developing research: It is not clear whether there is a direct action of the siRNAs that can be used to facilitate the repair processes of tendons

Melatonin and adolescent idiopathic scoliosis: The present evidence

Adolescent idiopathic scoliosis (AIS) is a multifactorial condition with genetic predisposing factors, and several causes have been put forward for its aetiopathogenesis, including possible hormonal dysfunction. Melatonin seems to play significant role in AIS

machine learning models for spring discharge forecasting

Nowadays, drought phenomena increasingly affect large areas of the globe; therefore, the need for a careful and rational management of water resources is becoming more pressing. Considering that most of the world's unfrozen freshwater reserves are stored in aquifers, the capability of prediction of spring discharges is a crucial issue. An approach based on water balance is often extremely complicated or ineffective. A promising alternative is represented by data-driven approaches. Recently, many hydraulic engineering problems have been addressed by means of advanced models derived from artificial intelligence studies. Three different machine learning algorithms were used for spring discharge forecasting in this comparative study: M5P regression tree, random forest, and support vector regression. The spring of Rasiglia Alzabove, Umbria, Central Italy, was selected as a case study. The machine learning models have proven to be able to provide very encouraging results. M5P provides good short-term predictions of monthly average flow rates (e.g., in predicting average discharge of the spring after 1 month, R2=0.991, RAE=14.97%, if a 4-month input is considered), while RF is able to provide accurate medium-term forecasts (e.g., in forecasting average discharge of the spring after 3 months, R2=0.964, RAE=43.12%, if a 4-month input is considered). As the time of forecasting advances, the models generally provide less accurate predictions. Moreover, the effectiveness of the models significantly depends on the duration of the period considered for input data. This duration should be close to the aquifer response time, approximately estimated by cross-correlation analysis