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In this paper, we consider stochastic weakly convex optimization problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient estimate of the smoothed function. We prove convergence at a similar rate as state of the art methods, however with a larger constant, and report some numerical results showing the effectiveness of the approach.

Cooperative control of Unmanned Aerial Vehicles (UAVs) is currently being researched for a wide range of applications. Applicability of aerial unmanned systems might be increased by formation flight. After a necessary overview of quadrotor flight dynamics and linear quadratic control fundamentals, this control technique is applied to the full quadrotor dynamics. Then the more recent and challenging neural networks based control strategy is introduced from a theoretical perspective and applied to the quadrotor vertical dynamics; the results are compared with the relevant linear quadratic controlled behaviour. Finally, based on the developed single-quadrotor control architectures, a practical leader-follower formation concept is simulated, both for the linear quadratic and the neural networks based approach.

Marianecci C, Rinaldi F, Di Marzio L, et al. Int J Nanomedicine. 2014;9(1):635–651. The Editor and Publisher of International Journal of Nanomedicine wish to retract the published article. Concerns were raised regarding the alleged duplication of TEM images in Figure 1. Specifically, * Figure 1A, F1, appears to have been duplicated with the same image for Figure 1C, F3 and Figure 1D, F3AG. The authors did respond to our queries but were unable to explain how the duplication of images occurred, nor were they able to provide the original TEM images from the reported study. The decision was made to retract the article and the authors were notified of this. Our decision-making was informed by our policy on publishing ethics and integrity and the COPE guidelines on retraction. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as “Retracted”. This retraction relates to this paper

In this paper, we propose new linesearch-based methods for nonsmooth constrained optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence toward stationary points, using the Clarke--Jahn directional derivative. In the second part, we consider inequality constrained optimization problems where both objective function and constraints can possibly be nonsmooth. In this case, we first split the constraints into two subsets: difficult general nonlinear constraints and simple bound constraints on the variables. Then, we use an exact penalty function to tackle the difficult constraints and we prove that the original problem can be reformulated as the bound-constrained minimization of the proposed exact penalty function. Finally, we use the framework developed for the bound-constrained case to solve the penalized problem. Moreover, we prove that every accumulation point, under standard assumptions on the search directions, of the generated sequence of iterates is a stationary point of the original constrained problem. In the last part of the paper, we report extended numerical results on both bound-constrained and nonlinearly constrained problems, showing that our approach is promising when compared to some state-of-the-art codes from the literature. [PUBLICATION ABSTRACT]

Clinical and/or neuroimaging evidence of disease reactivation has been described in multiple sclerosis (MS) patients after a break from natalizumab. Whether fingolimod might be a therapeutic option following natalizumab needs to be evaluated. Twenty-two relapsing remitting MS patients having JC virus antibodies (JCVAb+) in serum were shifted from natalizumab to fingolimod after a three-month washout period. Neurological evaluation with the Expanded Disability Status Scale (EDSS) was performed monthly for a mean follow-up period of nine months. In 20/22 patients, brain magnetic resonance imaging (MRI) was obtained within one month after therapy initiation. Disease reactivation was observed in 11/22 (50%) patients: clinical relapses in six patients (four patients within the first month of therapy) and MRI activity in a further five patients (three patients within the first month of therapy). Clinical and/or MRI signs suggestive of disease rebound were observed in three patients. Our data indicate that fingolimod does not exert clinical activity quickly enough to stop MS reactivation after a break from natalizumab.

The objective of the present paper is the study of a one-dimensional Hamiltonian with the interaction term given by the sum of two nonlocal attractive δ ′ -interactions of equal strength and symmetrically located with respect to the origin. We use the procedure known as renormalisation of the coupling constant in order to rigorously achieve a self-adjoint determination for this Hamiltonian. This model depends on two parameters, the interaction strength and the distance between the centre of each interaction and the origin. Once we have the self-adjoint determination, we obtain its discrete spectrum showing that it consists of two negative eigenvalues representing the energy levels. We analyse the dependence of these energy levels on the above-mentioned parameters. We investigate the possible resonances of the model. Furthermore, we analyse in detail the limit of our model as the distance between the supports of the two δ ′ interactions vanishes.

The current work proposes a machine learning (ML)-based HVAC management strategy that shifts heating load to periods of high photovoltaic (PV) output, using demand and generation forecasts, aiming to maximize self-consumption. In this context, the case study of a conditioned warehouse with installed onsite PV panels and dedicated office and storage areas is considered. EnergyPlus is used to simulate building baseline behavior under varying conditions, generating data to train physics-informed ML models that would predict the hour-ahead load of the building. Additionally, PV generation forecasts are obtained from an open-access dataset. The strategy agent receives real-time and short-term forecasts for both building load and PV generation, continuously monitoring their balance. Based on this information, the agent applies slight heating setpoint adjustments, relaxing the setpoints or preheating the indoor environment by one degree, to shift the heating load away from grid reliance and toward periods of high PV availability. The results show that implementing the proposed interventions increases the building’s self-consumption rate by 9% during the targeted intervention periods and by 7.47% over the entire heating season. Likewise, the self-sufficiency rate improves, indicating that a larger share of the building’s energy demand is met by the PV system.

Vitamin E (VitE) may be classified in \"the first line of defense\" against the formation of reactive oxygen species. Its inclusion in nanoemulsions (NEs) is a promising alternative to increase its bioavailability. The aim of this study was to compare O/W NEs including VitE based on Almond or Neem oil, showing themselves antioxidant properties. The potential synergy of the antioxidant activities of oils and vitamin E, co-formulated in NEs, was explored. NEs have been prepared by sonication and deeply characterized evaluating size, ζ-potential, morphology (TEM and SAXS analyses), oil nanodroplet feature, and stability. Antioxidant activity has been evaluated in vitro, in non-tumorigenic HaCaT keratinocytes, and in vivo through fluorescence analysis of transgenic strain. Moreover, on healthy human volunteers, skin tolerability and anti-inflammatory activity were evaluated by measuring the reduction of the skin erythema induced by the application of a skin chemical irritant (methyl-nicotinate). Results confirm that Vitamin E can be formulated in highly stable NEs showing good antioxidant activity on keratinocyte and on . Interestingly, only Neem oil NEs showed some anti-inflammatory activity on healthy volunteers. From the obtained results, Neem over Almond oil is a more appropriate candidate for further studies on this application.

In this work, we study exact continuous reformulations of nonlinear integer programming problems. To this aim, we preliminarily state conditions to guarantee the equivalence between pairs of general nonlinear problems. Then, we prove that optimal solutions of a nonlinear integer programming problem can be obtained by using various exact penalty formulations of the original problem in a continuous space.

Objective: To measure the effects of disease-modifying drugs (DMDs) on the development of cortical lesions (CL) and cortical atrophy in patients with relapsing–remitting multiple sclerosis (RRMS). Methods: RRMS patients (n = 165) were randomized to subcutaneous (sc) interferon (IFN) beta-1a (44 mcg three times weekly), intramuscular (im) IFN beta-1a (30 mcg weekly) or glatiramer acetate (GA; 20 mg daily). The reference population comprised 50 untreated patients. Clinical and MRI examinations were performed at baseline, 12 months and 24 months. Results: One hundred and forty-one treated patients completed the study. After 12 months, 37/50 (74%) of untreated patients developed ≥1 new CL (mean 1.6), compared with 30/47 (64%) of im IFN beta-1a-treated patients (mean 1.2, p = 0.021), 24/48 (50%) of GA-treated patients (mean 0.8, p = 0.001) and 12/46 (26%) of sc IFN beta-1a-treated patients (mean 0.4, p < 0.001). After 24 months, ≥1 new CL was observed in 41/50 (82%) of untreated (mean 3.0), 34/47 (72%) of im IFN beta-1a-treated (mean 1.6, p < 0.001), 30/48 (62%) of GA-treated (mean 1.3, p < 0.001) and 24/46 (52%) of sc IFN beta-1a-treated patients (mean 0.8, p < 0.001). Mean grey matter fraction decrease in DMD-treated patients at 24 months ranged from 0.7 to 0.8 versus 1.0 in untreated patients (p = 0.023). Conclusions: Disease-modifying drugs significantly decreased new CL development and cortical atrophy progression compared with untreated patients, with faster and more pronounced effects seen with sc IFN beta-1a than with im IFN beta-1a or GA.