Optimal Dynamic Procurement Policies for a Storable Commodity with L\'evy Prices and Convex Holding Costs

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal procurement problem as a singular stochastic control problem in which controls are nondecreasing processes and represent the cumulative investment made by the firm in the spot market (a so-called stochastic "monotone follower problem"). We assume a general exponential L\'evy process for the commodity's spot price, rather than the commonly used geometric Brownian motion, and general convex holding costs. We obtain necessary and sufficient first order conditions for optimality and we provide the optimal procurement policy in terms of a "base inventory" process; that is, a minimal time-dependent desirable inventory level that the firm's manager must reach at any time. In particular, in the case of linear holding costs and exponentially distributed demand, we are also able to obtain the explicit analytic form of the optimal policy and a probabilistic representation of the optimal revenue. The paper is completed by some computer drawings of the optimal inventory when spot prices are given by a geometric Brownian motion and by an exponential jump-diffusion process. In the first case we also make a numerical comparison between the value function and the revenue associated to the classical static "newsvendor" strategy.Comment: 28 pages, 3 figures; improved presentation, added new results and section

Ventilation strategies to minimise the airborne virus transmission in indoor environments

A key challenge to fight the Covid-19 pandemic is to minimise the airborne transmission of the SARS-CoV-2 virus. Highly crowded indoor environments, such as schools, become possible hotspots for virus spreading because the basic non-pharmaceutical mitigation measures applied until now are not effective in reducing the virus airborne transmission mode, which is the principal one in indoor environments and requires improved ventilation. In the present study, a mass balance equation was applied to typical school scenarios to evaluate (i) required air exchange rates for mechanically-ventilated classrooms and (ii) adequate airing procedures for naturally ventilated classrooms. In the case of naturally ventilated classrooms, a feedback control strategy was evaluated using the measurements of indoor CO2. Our results show how these procedures can be applied in real life to support continued in-person instruction during a pandemic.publishedVersio

Increasing ventilation reduces SARS-CoV-2 airborne transmission in schools: A retrospective cohort study in Italy's Marche region

IntroductionWhile increasing the ventilation rate is an important measure to remove inhalable virus-laden respiratory particles and lower the risk of infection, direct validation in schools with population-based studies is far from definitive.MethodsWe investigated the strength of association between ventilation and SARS-CoV-2 transmission reported among the students of Italy's Marche region in more than 10,000 classrooms, of which 316 were equipped with mechanical ventilation. We used ordinary and logistic regression models to explore the relative risk associated with the exposure of students in classrooms.Results and discussionFor classrooms equipped with mechanical ventilation systems, the relative risk of infection of students decreased at least by 74% compared with a classroom with only natural ventilation, reaching values of at least 80% for ventilation rates >10 L s−1 student−1. From the regression analysis we obtained a relative risk reduction in the range 12%15% for each additional unit of ventilation rate per person. The results also allowed to validate a recently developed predictive theoretical approach able to estimate the SARS-CoV-2 risk of infection of susceptible individuals via the airborne transmission route. We need mechanical ventilation systems to protect students in classrooms from airborne transmission; the protection is greater if ventilation rates higher than the rate needed to ensure indoor air quality (>10 L s−1 student−1) are adopted. The excellent agreement between the results from the retrospective cohort study and the outcome of the predictive theoretical approach makes it possible to assess the risk of airborne transmission for any indoor environment

numerical simulation of ultrafine particle dispersion in urban street canyons with the spalart allmaras turbulence model

The increased traffic emissions and reduced ventilation of urban street canyons lead to the formation of high particle concentrations as a function of the related flow field and geometry. In this context, the use of advanced modelling tools, able to evaluate particle concentration under different traffic and meteorological conditions, may be helpful. In this work, a numerical scheme based on the non-commercial fully explicit AC-CBS algorithm, and the one-equation Spalart-Allmaras turbulence model, was developed to perform numerical simulations of fluid flow and ultrafine particle dispersion in different street canyon configurations and under different wind speed and traffic conditions. The proposed non-commercial numerical tool was validated through a comparison with data drawn from the scientific literature. The results obtained from ultrafine particle concentration simulations show that as the building height increases the dispersion of particles in the canyon becomes weaker, due to the restricted interaction between the flow field in the street canyon and the undisturbed flow. Higher values of approaching wind speed facilitate the dispersion of the particles. The traffic effect has been evaluated by imposing different values of particles emission, depending on the vehicles type, with the lowest concentration values obtained for the Euro 6 vehicles, and the highest for High Duty Vehicles. A parametric analysis was also performed concerning the exposure to particles of pedestrians in different positions at the road level as a function of street canyon geometry, traffic mode, and wind speed. The worst exposure (1.25 × 10 6 part./cm 3 ) was found at the leeward side for an aspect ratio H/W = 1, wind speed of 5 m/s when High Duty Vehicles traffic was considered

A Cloud-based Vehicle Collision Avoidance Strategy for Unmanned Aircraft System Traffic Management (UTM) in Urban Areas

Unmanned Aircraft Systems are increasingly used to monitor and sense our cities and the diffusion of UAS will require a Traffic Management System to coordinate UAS in the low-altitude airspace. In this paper we propose a collision avoidance strategy to be implemented in an Unmanned Aircraft System Traffic Management (UTM). The proposed strategy relies on a Cloud-based architecture that monitors and manages the low-altitude airspace, as well as coordinating the fleet of UAS. The strategy uses a Priority-based Model Predictive Control approach to define the optimal trajectory of the UAS, avoiding obstacles and other UAS with higher priority. The optimal trajectory is shared with other UAS to communicate the own motion track to be avoided by other UAS. The suggested method is implemented and tested in simulations with three UAS with conflicting trajectories. Preliminary results positively support the proposed approach

Changes in Plasma \u3b2-NGF and Its Receptors Expression on Peripheral Blood Monocytes During Alzheimer\u2019s Disease Progression

Alzheimer\u2019s disease (AD), the most common cause of dementia, is characterized by the deposition of extracellular amyloid-\u3b2 (A\u3b2) plaques and intracellular neurofibrillary tangles, and by neuroinflammation. During the pathogenesis of AD, monocyte-macrophage lineage cells become increasingly ineffective in clearing A\u3b2 deposits, less able to differentiate, and shift toward pro-inflammatory processes. Beta-nerve growth factor (\u3b2-NGF) and its receptors, TrKA and p75NTR, produce several biological responses, including cell apoptosis and survival, and inflammation. In the central nervous system, the involvement of these receptors in several critical hallmarks of AD is well known, but their role in circulating monocytes during the progression of dementia is unclear. We investigated the relationship between plasma \u3b2-NGF concentration and TrkA/p75NTR receptor expression in monocytes of patients with mild cognitive impairment (MCI), mild AD, and severe AD. We observed that plasma \u3b2-NGF concentration was increased with a higher expression of TrKA, but not of p75NTR, in monocytes from patients with MCI and mild AD, whereas \u3b2-NGF concentration and TrKA expression were decreased and p75NTR expression was increased, associated with caspase 3-mediated apoptosis, in patients with severe AD. In our study, we show evidence of variation in plasmatic \u3b2-NGF and monocytic TrkA/p75NTR receptor expression during the progression of dementia. These novel findings add evidence to support the hypothesis for the involvement of \u3b2-NGF and its receptors on monocytes during AD progression

Case report: Pragmatic impairment in multiple sclerosis after worsening of clinical symptoms

Pragmatics, defined as the ability to integrate language and context to communicate effectively, may be impaired in Multiple Sclerosis (MS). We present the case of a patient with active secondary progressive MS who, after a first neuropsychological assessment that evidenced only a slight pragmatic impairment, suffered a sudden worsening of her clinical conditions, treated with corticosteroids. After this clinical worsening, her pragmatic abilities declined markedly, both in comprehension and production. This worsening was accompanied by a decline only in one attention task, in the context of an overall stable cognitive functioning. We conclude that pragmatics may be a domain particularly susceptible to cognitive worsening, highlighting the importance of its assessment in clinical practice

HA PEGylated Filler in Association with an Infrared Energy Device for the Treatment of Facial Skin Aging: 150 Day Follow-Up Data Report

Background: The face is the area most exposed to the normal course of skin aging, both intrinsically and extrinsically. The aim of the study was to evaluate the cellular and clinical response of a therapeutic protocol aimed at countering facial skin aging. Materials and methods: Twenty female patients with facial skin laxity and photodamage underwent combined therapy including mesotherapy using non-cross-linked hyaluronic acid with calcium hydroxyapatite and an infrared energy-based device treatment with subsequent implementation of PEG-cross-linked hyaluronic acid soft tissue fillers. To evaluate the benefits, patients underwent histological, immunological, and biomechanical evaluations before the treatment and at 21 and 150 days after the treatment. Results: The histological results at 21 days and 150 days after the procedure showed an increase in the number of fibroblasts and angiogenesis. As for the immunological aspect, it was shown that the treatment has an immunomodulating action, avoiding the activation of CD4 and CD8 cells. Biomechanical data showed that, at 150 days after treatment, the average changes in skin elasticity increased by 72% and the skin hydration increased by 49%. Conclusions: A combination of an infrared energy-based device treatment with both non-cross-linked hyaluronic acid and novel PEG-cross-linked hyaluronic acid leads to numerous positive cutaneous changes after histological, immunological, and biomechanical evaluations

Multiparametric magnetic resonance imaging and clinical variables: Which is the best combination to predict reclassification in active surveillance patients?

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