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L^1 limit solutions in impulsive control [article]

Monica Motta, Caterina Sartori
2017 arXiv   pre-print
We consider a nonlinear control system depending on two controls u and v, with dynamics affine in the (unbounded) derivative of u, and v appearing initially only in the drift term. Recently, motivated by applications to optimization problems lacking coercivity, [1] proposed a notion of generalized solution x for this system, called limit solution, associated to measurable u and v, and with u of possibly unbounded variation in [0,T]. As shown in [1], when u and x have bounded variation, such a
more » ... lution (called in this case BV simple limit solution) coincides with the most used graph completion solution (see e.g. [6]). This correspondence has been extended in [24] to BV_loc u and trajectories (with bounded variation just on any [0,t] with t<T). Starting with an example of optimal control where the minimum does not exist in the class of limit solutions, we propose a notion of extended limit solution x, for which such a minimum exists. As a first result, we prove that extended and original limit solutions coincide in the special cases of BV and BV_loc inputs u (and solutions). Then we consider dynamics where the ordinary control v also appears in the non-drift terms. For the associated system we prove that, in the BV case, extended limit solutions coincide with graph completion solutions.
arXiv:1706.00229v1 fatcat:dhzqis6duvfkvmvjie4fdcblxi

Unbounded variation and solutions of impulsive control systems [article]

Monica Motta, Caterina Sartori
2017 arXiv   pre-print
We consider a control system with dynamics which are affine in the (unbounded) derivative of the control u. We introduce a notion of generalized solution x on [0,T] for controls u of bounded total variation on [0,t] for every t<T, but of possibly infinite variation on [0,T]. This solution has a simple representation formula based on the so-called graph completion approach, originally developed for BV controls. We prove the well-posedness of this generalized solution by showing that x is a limit
more » ... solution, that is the pointwise limit of regular trajectories of the system. In particular, we single out the subset of limit solutions which is in one-to-one correspondence with the set of generalized solutions. The controls that we consider provide the natural setting for treating some questions on the controllability of the system and some optimal control problems with endpoint constraints and lack of coercivity.
arXiv:1705.01724v1 fatcat:bzzw52l7nbhnln3ogbpeat37de

Asymptotic problems in optimal control with a vanishing Lagrangian and unbounded data [article]

Monica Motta, Caterina Sartori
2014 arXiv   pre-print
In this paper we give a representation formula for the limit of the fnite horizon problem as the horizon becomes infinite, with a nonnegative Lagrangian and unbounded data. It is related to the limit of the discounted infinite horizon problem, as the discount factor goes to zero. We give sufficient conditions to characterize the limit function as unique nonnegative solution of the associated HJB equation. We also briefly discuss the ergodic problem.
arXiv:1406.7655v1 fatcat:5m55tkhm6bdhtitjqfoqtc2twa

Lack of BV bounds for impulsive control systems

Monica Motta, Caterina Sartori
2018 Journal of Mathematical Analysis and Applications  
For a nonlinear impulsive control system, we extend the so-called graph completion approach and introduce a notion of generalized solution x associated to a control u whose total variation is bounded on [0, t] for every t < T , but possibly unbounded on [0, T ]. We prove existence, consistency with classical solutions and well-posedness of this solution. In particular, we characterize it as a pointwise limit of certain regular solutions. The notion that we consider provides the natural setting
more » ... or controllability questions and for some non-coercive optimal control problems, where chattering phenomena at the final time are expected. More in general, it is well suited to describe the evolution of control systems subject to a train of impulses where no a-priori bounds on the number and the amplitude of the impulses are imposed.
doi:10.1016/j.jmaa.2018.01.019 fatcat:yw43p237tvgwlp74cnapukrfau

Nascita e sviluppo della Rete LTER-Italia [article]

Mariangela Ravaioli, Giorgio Matteucci, Maria Grazia Mazzocchi, Caterina Bergami, Alessandro Campanaro, Lucilla Capotondi, Bruno Cataletto, Andrea Lami, Renzo Motta, Bruno Petriccione, Alessandra Pugnetti
2021 Zenodo  
The long-term ecological research (LTER) aims at understanding, analyzing and monitoring environmental and biological processes over periods of several decades to understand the natural changes of ecosystems, distinguishing them from the modifications that can be induced by humans, at a local and global scale. Between the end of the 20th and the beginning of the 21st century, a large part of LTER research has been organized in networks of sites and platforms, distributed on the global (LTER
more » ... rnational, ILTER: www.ilter.network), European (LTER- Europe: http://www.lter-europe.net/) and national scales. The LTER-Italy network, whose promotion and organizational phases began in the middle of the 1990s, belongs to ILTER and LTER-Europe since 2006, when it was formalized after a long process that started at the VII Congress of the Italian Society of Ecology (SItE) held in Naples in 1996. The establishment of the LTER network in Italy begun with the creation of a promoting group, made up of researchers from the CNR and Universities, officials of the former National Forest Service (CFS), now Carabinieri (Dpt. for protection of Biodiversity and Parks) and representatives of the SItE, and it was sustained as well by the participation and support of many researchers from other organizations, institutes and scientific societies (SBI, SISEF, AIOL, SIBM). The Network of Excellence ALTER-Net (A Long-Term Biodiversity, Ecosystem and Awareness Research Network), was the European framework for the consolidation of the LTER initiative. At the end of 2004, the CFS, three CNR institutes (IBAF, ISE and ISMAR) and the former Marine Biology Laboratory of Aurisina (Trieste) signed a memorandum of understanding that founded the LTER-Italy network by establishing the statute of the network. This statute provides the governance of the network, which is based on a Coordinating Committee, on a Technical-Scientific Committee and on the site manager Assembly.
doi:10.5281/zenodo.5570323 fatcat:m2iv2iujzfhdnecgko3urbdo2a

Prospettive per il futuro della Rete Lter-Italia [article]

Giorgio Matteucci, Caterina Bergami, Alessandro Campanaro, Lucilla Capotondi, Bruno Cataletto, Andrea Lami, Renzo Motta, Alessandra Pugnetti, Mariangela Ravaioli, Maria Grazia Mazzocchi
2021 Zenodo  
In sintesi, la Rete LTER-Italia e la sua futura trasformazione in infrastruttura di ricerca dovranno riuscire a divenire, in modo sempre più efficace e consolidato, uno strumento essenziale per fronteggiare le sfide ambientali e socio-ecologiche attuali e quelle che ci attendono nei prossimi anni, in particolare riguardo alla crisi della biodiversità, alla mitigazione e all'adattamento ai cambiamenti climatici. Nell'attuale contesto storico, appare necessario che la Rete contribuisca anche a
more » ... tenere un cambiamento etico dei nostri modi di vivere e a realizzare una profonda trasformazione dei nostri sistemi socio-economici. A tale scopo sarà necessario avviare e sostenere azioni congiunte che includano i cittadini, le imprese, le parti sociali e la comunità della ricerca, nonché l'attivazione di forti partenariati a livello locale, regionale, nazionale ed europeo, per la realizzazione, in modo innovativo, integrato, etico e responsabile, dei piani e delle strategie ambientali per le prossime decadi (EU Biodiversity Strategy, Green Deal, Next Generation EU, Piano Nazionale di ripresa e resilienza-PNRR).
doi:10.5281/zenodo.5589840 fatcat:rvcj32x3qjbyxj5e25w354s764

LTER Italia: la Rete di Ricerca Ecologica a Lungo Termine [article]

Giorgio Matteucci, Caterina Bergami, Alessandro Campanaro, Lucilla Capotondi, Bruno Cataletto, Andrea Lami, Renzo Motta, Alessandro Oggioni, Bruno Petriccione, Alessandra Pugnetti, Mariangela Ravaioli, Maria Grazia Mazzocchi
2021 Zenodo  
The Italian Network for Long-Term Ecological Research (LTER-Italy) is currently made of 79 sites organized in 25 parent sites, distributed all over the Italian territory in terrestrial, freshwater, transitional and marine water environments; it also includes 7 extraterritorial sites in Antarctica and in the Himalayas LTER-Italy management is regulated according to a Statute that identify an Assembly of sites' managers, an elected Coordinator, a Coordination Committee, and a Technical-Scientific
more » ... Secretariat. Its development and consolidation have been closely linked to that of LTER-Europe, to which the Network belongs since 2006. LTER-Italy researches are supported by numerous Scientific Institutions, Universities and Territorial Agencies. Furthermore, LTER-Italy has important connections with other European research infrastructures as well as with the Regional Authority. Its activities span over multiple scientific fields, with a socio-ecological approach on biodiversity, climate change, training and education and the environmental challenges that engage our society. LTER-Italy was conceived and implemented as a shared ecological research platform, which favors the comparison of results and the data conservation, with the aim of creating a wealth of information and observations accessible and usable for future generations. The members of LTER-Italy study ecosystems, their dynamics and their evolution, the relationships between biodiversity and ecological functionality, and the environmental responses to natural and anthropic drivers. Within this network, fruitful scientific collaborations are initiated and maintained, interdisciplinary activities and cross-sectional(dominion?) research on ecosystems are encouraged and the valorization of long-term ecological data is promoted. Since 2015, LTER Italia is working at the integration within the nascent eLTER-RI European infrastructure (European Long-Term Ecosystem, critical zone and socio-ecological Research Infrastructure).
doi:10.5281/zenodo.5570326 fatcat:fv274kekffea7bh4z5vjuuzyju

On \begin{document} ${\mathcal L}^1$ \end{document} limit solutions in impulsive control

Monica Motta, Caterina Sartori
2018 Discrete and Continuous Dynamical Systems. Series S  
Impulsive control systems, generalized solutions, pointwisely defined measurable solutions, non commutative control systems, impulsive optimal control problems. 1201 1202 MONICA MOTTA AND CATERINA SARTORI  ... 
doi:10.3934/dcdss.2018068 fatcat:z2mbtd2j5rhahbfzimstjhhbye

Disability and Fatigue Can Be Objectively Measured in Multiple Sclerosis

Caterina Motta, Eduardo Palermo, Valeria Studer, Marco Germanotta, Giorgio Germani, Diego Centonze, Paolo Cappa, Silvia Rossi, Stefano Rossi, Sreeram V. Ramagopalan
2016 PLoS ONE  
The available clinical outcome measures of disability in multiple sclerosis are not adequately responsive or sensitive. Objective To investigate the feasibility of inertial sensor-based gait analysis in multiple sclerosis. Methods A cross-sectional study of 80 multiple sclerosis patients and 50 healthy controls was performed. Lower-limb kinematics was evaluated by using a commercially available magnetic inertial measurement unit system. Mean and standard deviation of range of motion (mROM,
more » ... for each joint of lower limbs were calculated in one minute walking test. A motor performance index (E) defined as the sum of sROMs was proposed. Results We established two novel observer-independent measures of disability. Hip mROM was extremely sensitive in measuring lower limb motor impairment, being correlated with muscle strength and also altered in patients without clinically detectable disability. On the other hand, E index discriminated patients according to disability, being altered only in patients with moderate and severe disability, regardless of walking speed. It was strongly correlated with fatigue and patient-perceived health status. Conclusions Inertial sensor-based gait analysis is feasible and can detect clinical and subclinical disability in multiple sclerosis.
doi:10.1371/journal.pone.0148997 pmid:26863109 pmcid:PMC4749243 fatcat:q2zkqmyea5en7c5ihss5z555zy

Folate status in type 2 diabetic patients with and without retinopathy

Giulia Malaguarnera, Caterina Gagliano, Salvatore Salomone, Maria Giordano, Claudio Bucolo, Antonio Pappalardo, Filippo Caraci, Filippo Drago, Teresio Avitabile, Massimo Motta
2015 Clinical Ophthalmology  
Folate deficiency is associated with cardiovascular disease, megaloblastic anemia, and with hyperhomocysteinemia. This study has been undertaken to investigate the role of folate status during the progression of the diabetic retinopathy. We measured the plasma levels of homocysteine, folic acid, and red cell folate in 70 diabetic type 2 patients with nonproliferative diabetic retinopathy (NPDR), 65 with proliferative diabetic retinopathy (PDR), 96 without diabetic retinopathy, and 80 healthy
more » ... jects used as a control group. We found higher plasma levels of homocysteine in the NPDR group compared to the control group (P<0.001) and in the PDR group compared to control group (P<0.001) and NPDR group (P<0.01). The severity of diabetic retinopathy was associated with lower folic acid and red cell folate levels, and a significant difference was observed between PDR and NPDR groups (P<0.05). The folate status could play a role in the development and progression of diabetic retinopathy.
doi:10.2147/opth.s77538 pmid:26300625 pmcid:PMC4536839 fatcat:pvvorg425fbihps43eyoheo2ya

Lipoprotein(a) Serum Levels in Diabetic Patients with Retinopathy

Giulia Malaguarnera, Caterina Gagliano, Claudio Bucolo, Marco Vacante, Salvatore Salomone, Michele Malaguarnera, Daniela Giovanna Leonardi, Massimo Motta, Filippo Drago, Teresio Avitabile
2013 BioMed Research International  
Background. Atherogenic lipoproteins, such as total cholesterol, LDL cholesterol, oxidized low density lipoprotein, and triglycerides, are associated with progression of retinopathy.Aim. To evaluate the relationship between lipoprotein(a) and retinopathy in patients with type 2 diabetes mellitus.Materials and Methods. We enrolled 145 diabetic consecutive patients (82 females, 63 males; mean age66.8±12years, mean duration of diabetes9.4±6.8years). Presence and severity of retinopathy were
more » ... ed. Serum lipid profile, including Lp(a) level, was assessed.Results. High Lp(a) levels have been observed in 54 (78.3%) subjects and normal levels in 13 (18.85%) subjects as regards diabetic patients with retinopathy. Lp(a) levels were high in 15 subjects (21.75%) and normal in 63 subjects (91.35%) as regards patients without retinopathy.Conclusions. Lp(a) levels are increased in a significant percentage of patients with retinopathy compared to diabetic patients without retinopathy. The impact of Lp(a) levels on diabetic retinopathy needs to be further investigated.
doi:10.1155/2013/943505 pmid:23862162 pmcid:PMC3687764 fatcat:okekklyo3zapjmerxxvil3g7n4

LTP-like cortical plasticity predicts conversion to dementia in patients with memory impairment

Francesco Di Lorenzo, Caterina Motta, Elias Paolo Casula, Sonia Bonnì, Martina Assogna, Carlo Caltagirone, Alessandro Martorana, Giacomo Koch
2020 Brain Stimulation  
New diagnostic criteria consider Alzheimer's disease (AD) as a clinico-biological entity identifiable in vivo on the presence of specific patterns of CSF biomarkers. Here we used transcranial magnetic stimulation to investigate the mechanisms of cortical plasticity and sensory-motor integration in patients with hippocampal-type memory impairment admitted for the first time in the memory clinic stratified according to CSF biomarkers profile. Seventy-three patients were recruited and divided in
more » ... ree groups according to the new diagnostic criteria: 1) Mild Cognitive Impaired (MCI) patients (n=21); Prodromal AD (PROAD) patients (n=24); AD with manifest dementia (ADD) patients (n=28). At time of recruitment all patients underwent CSF sampling for diagnostic purposes. Repetitive and paired-pulse transcranial magnetic stimulation protocols were performed to investigate LTP-like and LTD-like cortical plasticity, short intracortical inhibition (SICI) and short afferent inhibition (SAI). Patients were the followed up during three years to monitor the clinical progression or the conversion to dementia. MCI patients showed a moderate but significant impairment of LTP-like cortical plasticity, while ADD and PROAD groups showed a more severe loss of LTP-like cortical plasticity. No differences were observed for LTD-like cortical plasticity, SICI and SAI protocols. Kaplan-Meyer analyses showed that PROAD and MCI patients converting to dementia had weaker LTP-like plasticity at time of first evaluation. LTP-like cortical plasticity could be a novel biomarker to predict the clinical progression to dementia in patients at with memory impairment at prodromal stages of AD identifiable with the new diagnostic criteria based on CSF biomarkers.
doi:10.1016/j.brs.2020.05.013 pmid:32485235 fatcat:nxtssb5wejghtmf5pfgcpholou

The value function of a finite fuel problem for a new class of singular stochastic controls

Monica Motta, Caterina Sartori
2008 2008 47th IEEE Conference on Decision and Control  
Motta where Dv and D 2 v denote the gradient and the matrix of the second derivatives of the function v = v(t, k, x) with respect to the x variable, F (t, x, p, S) . = − A(t, x), p − l 0 (t, x) − 1  ... 
doi:10.1109/cdc.2008.4739504 dblp:conf/cdc/MottaS08 fatcat:ucopqbc2mnf75insytmx67bkmy

Centenarians and supercentenarians: a black swan. Emerging social, medical and surgical problems

Marco Vacante, Velia D'Agata, Massimo Motta, Giulia Malaguarnera, Antonio Biondi, Francesco Basile, Michele Malaguarnera, Caterina Gagliano, Filippo Drago, Salvatore Salamone
2012 BMC Surgery  
The Black Swan Theory was described by Nassim Nicholas Taleb in his book "The Black Swan". This theory refers to "high-impact, hard-to-predict, and rare events beyond the realm of normal expectations". According to Taleb's criteria, a Black Swan Event is a surprise, it has a major impact and after the fact, the event is rationalized by hindsight, as if it had been expected. For most of human history centenarians were a rare and unpredictable phenomenon. The improvements of the
more » ... al conditions, of medical care, and the quality of life caused a general improvement of the health status of the population and a consequent reduction of the overall morbidity and mortality, resulting in an overall increase of life expectancy. The study of centenarians and supercentenarians had the objective to consider this black swan and to evaluate the health, welfare, social and economic consequences of this phenomenon.
doi:10.1186/1471-2482-12-s1-s36 pmid:23173707 pmcid:PMC3499197 fatcat:qdjjlhr2yjeq7eatlwjiju4lwi

Homocysteine Serum Levels in Diabetic Patients with Non Proliferative, Proliferative and without Retinopathy

Giulia Malaguarnera, Caterina Gagliano, Maria Giordano, Salvatore Salomone, Marco Vacante, Claudio Bucolo, Filippo Caraci, Michele Reibaldi, Filippo Drago, Teresio Avitabile, Massimo Motta
2014 BioMed Research International  
Homocysteine has been associated with extracellular matrix changes. The diabetic retinopathy is a neurovascular complication of diabetes mellitus and it is the leading cause of vision loss among working adults worldwide. In this study, we evaluate the role of homocysteine in diabetic retinopathy analyzing the plasma levels of homocysteine in 63 diabetic type 2 patients with nonproliferative retinopathy (NPDR), 62 patients with proliferative diabetic retinopathy (PDR), 50 healthy subjects used as control group, and 75 randomly selected patients.
doi:10.1155/2014/191497 pmid:24877066 pmcid:PMC4022262 fatcat:upd6p7pwczeffpcmfobuseomxy
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