We study the rate of weak convergence of Markov chains to diffusion processes under quite general assumptions. We give an example in the financial framework, applying the convergence analysis to a multiple jumps tree approximation of the CIR process. Then, we combine the Markov chain approach with other numerical techniques in order to handle the different components in jump- diffusion coupled models. We study the analytical speed of convergence of this hybrid approach and provide an example in finance, applying our results to a tree-finite difference approximation in the Heston and Bates models. © 2021 Society for Industrial and Applied Mathematics.

The societal impact of traffic is a long-standing and complex problem. We focus on the estimation of ground-level ozone production due to vehicular traffic. We propose a comprehensive computational approach combining four consecutive modules: a traffic simulation module, an emission module, a module for the main chemical reactions leading to ozone production, and a module for the diffusion of gases in the atmosphere. The traffic module is based on a second-order traffic flow model, obtained by choosing a special velocity function for the Collapsed Generalized Aw-Rascle-Zhang model. A general emission module is taken from literature, and tuned on NGSIM data together with the traffic module. Last two modules are based on reaction-diffusion partial differential equations. The system of partial differential equations describing the main chemical reactions of nitrogen oxides presents a source term given by the general emission module applied to the output of the traffic module. We use the proposed approach to analyze the ozone impact of various traffic scenarios and describe the effect of traffic light timing. The numerical tests show the negative effect of vehicles restarts on emissions, and the consequent increase in pollutants in the air, suggesting to increase the length of the green phase of traffic lights.

In order to solve Prandtl--type equations we propose a collocation--quadrature method based on de la Vallée Poussin (briefly VP) filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in a couple of Holder--Zygmund spaces of locally continuous functions. With respect to classical methods based on Lagrange interpolation at the same collocation nodes, we succeed in reproducing the optimal convergence rates of the L2 case and cut off the typical log factor which seemed inevitable dealing with uniform norms. Such an improvement does not require a greater computational effort. In particular, we propose a fast algorithm based on the solution of a simple 2-bandwidth linear system and prove that, as its dimension tends to infinity, the sequence of the condition numbers (in any natural matrix norm) tends to a finite limit.

The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order s in (0, 1), and higher-order spaces are considered. Related Hardy type inequalities are proposed as well.

Some recent results on the theory of fractional Orlicz-Sobolev spaces are surveyed. They concernSobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, andcriteria for compact embeddings. The limits of these spaces when the smoothness parameter s in (0, 1) tendsto either of the endpoints of its range are also discussed. This note is based on the papers [1, 2, 3, 4], whereadditional material and proofs can be found.

Short-Term Load Forecasting (STLF) is a fundamental instrument in the efficient operational management and planning of electric utilities. Emerging smart grid technologies pose new challenges and opportunities. Although load forecasting at the aggregate level has been extensively studied, electrical load forecasting at fine-grained geographical scales of households is more challenging. Among existing approaches, semi-parametric generalized additive models (GAM) have been increasingly popular due to their accuracy, flexibility, and interpretability. Their applicability is justified when forecasting is addressed at higher levels of aggregation, since the aggregated load pattern contains relatively smooth additive components. High resolution data are highly volatile, forecasting the average load using GAM models with smooth components does not provide meaningful information about the future demand. Instead, we need to incorporate irregular and volatile effects to enhance the forecast accuracy. We focus on the analysis of such hybrid additive models applied on smart meters data and show that it leads to improvement of the forecasting performances of classical additive models at low aggregation levels. (C) 2020 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

We investigate the rheology of strain-hardening spherical capsules, from the dilute tothe concentrated regime under a confined shear flow using three-dimensional numericalsimulations. We consider the effect of capillary number, volume fraction and membrane inextensibility on the particle deformation and on the effective suspension viscosity andnormal stress differences of the suspension. The suspension displays a shear-thinningbehaviour that is a characteristic of soft particles such as emulsion droplets, vesicles,strain-softening capsules and red blood cells. We find that the membrane inextensibilityplays a significant role on the rheology and can almost suppress the shear-thinning. Forconcentrated suspensions a non-monotonic dependence of the normal stress differenceson the membrane inextensibility is observed, reflecting a similar behaviour in the particleshape. The effective suspension viscosity, instead, grows and eventually saturates, for verylarge inextensibilities, approaching the solid particle limit. In essence, our results revealthat strain-hardening capsules share rheological features with both soft and solid particlesdepending on the ratio of the area dilatation to shear elastic modulus. Furthermore, thesuspension viscosity exhibits a universal behaviour for the parameter space defined by the capillary number and the membrane inextensibility, when introducing the particlegeometrical changes at the steady state in the definition of the volume fraction.

ZFP57 is required to maintain the germline-marked differential methylation at imprinting control regions (ICRs) in mouse embryonic stem cells (ESCs). Although DNA methylation has a key role in genomic imprinting, several imprinted genes are controlled by different mechanisms, and a comprehensive study of the relationship between DMR methylation and imprinted gene expression is lacking. To address the latter issue, we differentiated wild-type and Zfp57-/- hybrid mouse ESCs into neural precursor cells (NPCs) and evaluated allelic expression of imprinted genes. In mutant NPCs, we observed a reduction of allelic bias of all the 32 genes that were imprinted in wild-type cells, demonstrating that ZFP57-dependent methylation is required for maintaining or acquiring imprinted gene expression during differentiation. Analysis of expression levels showed that imprinted genes expressed from the non-methylated chromosome were generally up-regulated, and those expressed from the methylated chromosome were down-regulated in mutant cells. However, expression levels of several imprinted genes acquiring biallelic expression were not affected, suggesting the existence of compensatory mechanisms that control their RNA level. Since neural differentiation was partially impaired in Zfp57-mutant cells, this study also indicates that imprinted genes and/or non-imprinted ZFP57-target genes are required for proper neurogenesis in cultured ESCs.

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that is, a limit value for the electron mean velocity as the electric field increases. For the steady state system, we prove the existence of smooth solutions in the subsonic case, with a suitable assumption on the mobility function. Furthermore, we prove uniqueness of subsonic solutions for sufficiently small currents.

Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as s->1^- of the Gagliardo-Slobodeckij fractional seminorm are established in the Orlicz space setting. The results hold for fractional Orlicz-Sobolev spaces built upon general Young functions, as well. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation. An extended version of the Maz'ya-Shaposhnikova theorem on the limit as s->0^+ of the Gagliardo-Slobodeckij fractional seminorm is established in the Orlicz space setting. The result holds in fractional Orlicz-Sobolev spaces associated with Young functions fulfilling the \Delta_2-condition, and, as shown by counterexamples, it may fail if this condition is dropped. This is a joint work with Andrea Cianchi, Lubos Pick and Lenka Slavikova.

We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young functions, of the Bourgain-Brezis-Mironescu theorem on the limit as s ->1^-, and of the Maz'ya-Shaposhnikova theorem on the limit as s->0^-, dealing with classical fractional Sobolev spaces. As regards the limit as s ->1^-, Young functions with an asymptotic linear growth are also considered in connection with the space of functions of bounded variation. Concerning the limit as s->0^+, Young functions fulfilling the \Delta_2-condition are admissible. Indeed, counterexamples show that our result may fail if this condition is dropped. This is a joint work with Andrea Cianchi, Lubos Pick and Lenka Slavikova.

The optimal Orlicz target space and the optimal rearrangement-invariant tar- get space are exhibited for embeddings of fractional-order Orlicz-Sobolev spaces W^{s,A}(R^n). Related Hardy type inequalities are proposed as well. Versions for frac- tional Orlicz-Sobolev seminorms of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^- and of the Maz'ya-Shaposhnikova theorem on the limit as s ->0^+ are established. This is a joint work with Andrea Cianchi, Lubos Pick and Lenka Slavikova.

The existence of eigenfunctions for a class of fully anisotropic elliptic equations is established. The relevant equations are associated with constrained minimization problems for integral func- tionals depending on the gradient of competing functions through general anisotropic Young functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called \Delta_2-condition. In particular, our analysis requires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces. This is a joint work with G. di Blasio and F. Feo.

Optimal embeddings for fractional-order Orlicz{Sobolev spaces into Campanato type s- paces are offered. This is a joint work in progress with Andrea Cianchi, Lubos Pick and Lenka Slavikova.

The existence of eigenfunctions for a class of fully anisotropic elliptic equations is estab- lished. The relevant equations are associated with constrained minimization problems for inte- gral functionals depending on the gradient of competing functions through general anisotropic Young functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called 2-condition. In particular, our analysis re- quires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces. This is a joint work with G. di Blasio and F. Feo [1].

Compact embeddings on domain for fractional Orlicz-Sobolev spaces are exhibited.

The present work is motivated by the development of a mathematical model mimicking the mechanisms observed in lab-on-chip experiments, made to reproduce on microfluidic chips the in vivo reality. Here we consider the Cancer-on-Chip experiment where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment attracting multiple immune cell species. The in silico model here proposed goes towards the construction of a "digital twin" of the experimental immune cells in the chip environment to better understand the complex mechanisms of immunosurveillance. To this aim, we develop a tumor-immune microfluidic hybrid PDE-ODE model to describe the concentration of chemicals in the Cancer-on-Chip environment and immune cells migration. The development of a trustable simulation algorithm, able to reproduce the immunocompetent dynamics observed in the chip, requires an efficient tool for the calibration of the model parameters. In this respect, the present paper represents a first methodological work to test the feasibility and the soundness of the calibration technique here proposed, based on a multidimensional spline interpolation technique for the time-varying velocity field surfaces obtained from cell trajectories.

Over the last decade, significant attention has been devoted to Closed-Loop Supply Chain (CLSC) design problems. As such, this review aims at assessing whether the current modelling approaches for CLSC problems can support the transition towards a Circular Economy at a supply chain level. The paper comprehensively assesses the extent to which existing modelling approaches evaluate the performance of supply chains across the complete spectrum of sustainability dimensions. Also, the capability of the current approaches of incorporating strategic, tactical, and operational decisions is considered, along with adopted solution methodologies. As a result, a comprehensive analysis was performed on 254 selected articles. This paper emphasises how most of the current literature in the field is affected by a disconnection between supply chain design and the founding principles of Circular Economy. Specifically, the CLSC literature exhibits a reductionist interpretation of the Circular Economy. CLSC studies focusing on all three dimensions of sustainability are relatively rare, and performance measurement approaches appear to be very much focused on monetary issues. While methodological contributions appear adequate to focus on the non-deterministic nature of CLSC design problems, there is paucity of empirically-grounded research. Coherently, a research agenda is proposed, in order to address the mentioned gaps and increase the relevance of this research field to practice.

Recently, many European local authorities have set up Urban Consolidation Centres (UCC) for dealing with challenges arising from the environmental and social impacts of logistical activities in urban contexts through shipment synchronisation and carrier coordination policies. However, the number of successful UCC projects led by local authorities in Europe is low, with most of the UCCs failing to achieve financial sustainability after the initial experimental phase, which is often heavily supported by public funds. In order to propose mechanisms that could favour the economic and financial sustainability of UCC systems, this research develops an adaptation of game-theoretic approaches to the problems of responsibility and cost allocation among stakeholders participating in a UCC delivery network. A solution based on the Shapley Value concept is employed to derive cost allocations; applications of the model to a real-world scenario are evaluated. An extensive sensitivity analysis shows that the proposed cost allocation rules can provide alternative arrangements, based on extended responsibility concepts, which can alleviate the burden on local authorities for the set up of UCCs. As such, results provide useful policy and practice implications on how to safeguard UCCs' viability under different scenarios, including the outsourcing of the last-mile deliveries.

In network analysis, many community detection algorithms have been developed. However, their implementation leaves unaddressed the question of the statistical validation of the results. Here, we present robin (ROBustness In Network), an R package to assess the robustness of the community structure of a network found by one or more methods to give indications about their reliability. The procedure initially detects if the community structure found by a set of algorithms is statistically significant and then compares two selected detection algorithms on the same graph to choose the one that better fits the network of interest. We demonstrate the use of our package on the American College Football benchmark dataset.