Coexistence of stable limit cycles in a generalized Curie-Weiss model with dissipation

In this paper, we modify the Langevin dynamics associated to the generalized Curie-Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site distribution, the dynamics in the thermodynamic limit can be described by a finite set of ODEs. Depending on the form of the interaction function, the system can have several phase transitions at different critical temperatures. Because of the dissipation effect, not only the magnetization of the systems displays a self-sustained periodic behavior at sufficiently low temperature, but, in certain regimes, any (finite) number of stable limit cycles can exist. We explore some of these peculiarities with explicit examples

The dynamics of critical fluctuations in asymmetric Curie-Weiss models

We study the dynamics of fluctuations at the critical point for two time-asymmetric version of the Curie-Weiss model for spin systems that, in the macroscopic limit, undergo a Hopf bifurcation. The fluctuations around the macroscopic limit reflect the type of bifurcation, as they exhibit observables whose fluctuations evolve at different time scales. The limiting dynamics of fluctuations of slow observable is obtained via an averaging principle.Comment: 27 page

Self-sustained periodic behaviors in interacting systems: macroscopic limits and fluctuations

In this thesis we study the appearance of self-sustained periodic behavior in the macroscopic dynamics of some interacting systems and related critical phenomena. The thesis is organized as follows. In Chapter 1 we focus on the emergence of periodicity in cooperative mean field models whose interaction potential undergoes a dissipative evolution. We define a generalized Curie-Weiss model with dissipation and we analyse its macroscopic dynamics: we show that not only a periodic behavior is present at sufficiently low temperature, but also that, in certain regimes, any (finite) number of stable limit cycles can coexist. Chapter 2 is concerned with a two-population Curie-Weiss model: we define two types of microscopic dynamics, one with delay and the other without. We identify configurations of the interaction network which can enhance macroscopic oscillations in the case without delay; we also show that delay allows the appearance of a collective periodic behavior in configurations in which periodicity was otherwise absent. In Chapter 3 we consider again the mechanism of dissipation, this time dropping the mean field hypothesis. We study a short-range interacting system obtained introducing dissipation in a 1-dimensional Ising model. We prove that, in a suitable zero-temperature infinite-volume limit, the total magnetization of the system displays regular oscillations between polarized phases. Finally, Chapter 4 is dedicated to the analysis of critical fluctuations for systems exhibiting a Hopf bifurcation in the dynamics of the macroscopic law. The behavior of critical fluctuations around the macroscopic limit reflects the type of bifurcation and the observables display fluctuations evolving at different time scales. We identify the slow and the fast variable and we obtain the convergence of the slow variable to its limiting dynamics via an averaging principle

Rhythmic behavior of an Ising Model with dissipation at low temperature

In this paper we consider the Glauber dynamics for the one-dimensional Ising model with dissipation, in a mesoscopic regime obtained by letting inverse temperature and volume go to infinity with a suitable scaling. In this limit the magnetization has a periodic behavior. Self-organized collective periodicity has been shown for many mean-field models but, to our knowledge, this is the first example with short-range interaction. This supports the view that self-organized periodicity is not linked with the mean-field assumption but it is a thermodynamic phenomenon compatible with short range interactions.Comment: 28 page

Systemic pro-inflammatory response identifies patients with cancer with adverse outcomes from SARS-CoV-2 infection: the OnCovid Inflammatory Score

Background: Patients with cancer are particularly susceptible to SARS-CoV-2 infection. The systemic inflammatory response is a pathogenic mechanism shared by cancer progression and COVID-19. We investigated systemic inflammation as a driver of severity and mortality from COVID-19, evaluating the prognostic role of commonly used inflammatory indices in SARS-CoV-2-infected patients with cancer accrued to the OnCovid study. Methods: In a multicenter cohort of SARS-CoV-2-infected patients with cancer in Europe, we evaluated dynamic changes in neutrophil:lymphocyte ratio (NLR); platelet:lymphocyte ratio (PLR); Prognostic Nutritional Index (PNI), renamed the OnCovid Inflammatory Score (OIS); modified Glasgow Prognostic Score (mGPS); and Prognostic Index (PI) in relation to oncological and COVID-19 infection features, testing their prognostic potential in independent training (n=529) and validation (n=542) sets. Results: We evaluated 1071 eligible patients, of which 625 (58.3%) were men, and 420 were patients with malignancy in advanced stage (39.2%), most commonly genitourinary (n=216, 20.2%). 844 (78.8%) had ≥1 comorbidity and 754 (70.4%) had ≥1 COVID-19 complication. NLR, OIS, and mGPS worsened at COVID-19 diagnosis compared with pre-COVID-19 measurement (p<0.01), recovering in survivors to pre-COVID-19 levels. Patients in poorer risk categories for each index except the PLR exhibited higher mortality rates (p<0.001) and shorter median overall survival in the training and validation sets (p<0.01). Multivariable analyses revealed the OIS to be most independently predictive of survival (validation set HR 2.48, 95% CI 1.47 to 4.20, p=0.001; adjusted concordance index score 0.611). Conclusions: Systemic inflammation is a validated prognostic domain in SARS-CoV-2-infected patients with cancer and can be used as a bedside predictor of adverse outcome. Lymphocytopenia and hypoalbuminemia as computed by the OIS are independently predictive of severe COVID-19, supporting their use for risk stratification. Reversal of the COVID-19-induced proinflammatory state is a putative therapeutic strategy in patients with cancer

Determinants of enhanced vulnerability to coronavirus disease 2019 in UK patients with cancer: a European study

Despite high contagiousness and rapid spread, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to heterogeneous outcomes across affected nations. Within Europe (EU), the United Kingdom (UK) is the most severely affected country, with a death toll in excess of 100,000 as of January 2021. We aimed to compare the national impact of coronavirus disease 2019 (COVID-19) on the risk of death in UK patients with cancer versus those in continental EU. Methods: We performed a retrospective analysis of the OnCovid study database, a European registry of patients with cancer consecutively diagnosed with COVID-19 in 27 centres from 27th February to 10th September 2020. We analysed case fatality rates and risk of death at 30 days and 6 months stratified by region of origin (UK versus EU). We compared patient characteristics at baseline including oncological and COVID-19-specific therapy across UK and EU cohorts and evaluated the association of these factors with the risk of adverse outcomes in multivariable Cox regression models. Findings: Compared with EU (n = 924), UK patients (n = 468) were characterised by higher case fatality rates (40.38% versus 26.5%, p < 0.0001) and higher risk of death at 30 days (hazard ratio [HR], 1.64 [95% confidence interval {CI}, 1.36-1.99]) and 6 months after COVID-19 diagnosis (47.64% versus 33.33%; p < 0.0001; HR, 1.59 [95% CI, 1.33-1.88]). UK patients were more often men, were of older age and have more comorbidities than EU counterparts (p < 0.01). Receipt of anticancer therapy was lower in UK than in EU patients (p < 0.001). Despite equal proportions of complicated COVID-19, rates of intensive care admission and use of mechanical ventilation, UK patients with cancer were less likely to receive anti-COVID-19 therapies including corticosteroids, antivirals and interleukin-6 antagonists (p < 0.0001). Multivariable analyses adjusted for imbalanced prognostic factors confirmed the UK cohort to be characterised by worse risk of death at 30 days and 6 months, independent of the patient's age, gender, tumour stage and status; number of comorbidities; COVID-19 severity and receipt of anticancer and anti-COVID-19 therapy. Rates of permanent cessation of anticancer therapy after COVID-19 were similar in the UK and EU cohorts. Interpretation: UK patients with cancer have been more severely impacted by the unfolding of the COVID-19 pandemic despite societal risk mitigation factors and rapid deferral of anticancer therapy. The increased frailty of UK patients with cancer highlights high-risk groups that should be prioritised for anti-SARS-CoV-2 vaccination. Continued evaluation of long-term outcomes is warranted

SARS-CoV-2 omicron (B.1.1.529)-related COVID-19 sequelae in vaccinated and unvaccinated patients with cancer: results from the OnCovid registry

Background COVID-19 sequelae can affect about 15% of patients with cancer who survive the acute phase of SARS-CoV-2 infection and can substantially impair their survival and continuity of oncological care. We aimed to investigate whether previous immunisation affects long-term sequelae in the context of evolving variants of concern of SARS-CoV-2. Methods OnCovid is an active registry that includes patients aged 18 years or older from 37 institutions across Belgium, France, Germany, Italy, Spain, and the UK with a laboratory-confirmed diagnosis of COVID-19 and a history of solid or haematological malignancy, either active or in remission, followed up from COVID-19 diagnosis until death. We evaluated the prevalence of COVID-19 sequelae in patients who survived COVID-19 and underwent a formal clinical reassessment, categorising infection according to the date of diagnosis as the omicron (B.1.1.529) phase from Dec 15, 2021, to Jan 31, 2022; the alpha (B.1.1.7)-delta (B.1.617.2) phase from Dec 1, 2020, to Dec 14, 2021; and the pre-vaccination phase from Feb 27 to Nov 30, 2020. The prevalence of overall COVID-19 sequelae was compared according to SARS-CoV-2 immunisation status and in relation to post-COVID-19 survival and resumption of systemic anticancer therapy. This study is registered with ClinicalTrials.gov, NCT04393974. Findings At the follow-up update on June 20, 2022, 1909 eligible patients, evaluated after a median of 39 days (IQR 24-68) from COVID-19 diagnosis, were included (964 [ 50 center dot 7%] of 1902 patients with sex data were female and 938 [49 center dot 3%] were male). Overall, 317 (16 center dot 6%; 95% CI 14 center dot 8-18 center dot 5) of 1909 patients had at least one sequela from COVID-19 at the first oncological reassessment. The prevalence of COVID-19 sequelae was highest in the prevaccination phase (191 [19 center dot 1%; 95% CI 16 center dot 4-22 center dot 0] of 1000 patients). The prevalence was similar in the alpha-delta phase (110 [16 center dot 8%; 13 center dot 8- 20 center dot 3] of 653 patients, p=0 center dot 24), but significantly lower in the omicron phase (16 [6 center dot 2%; 3 center dot 5-10 center dot 2] of 256 patients, p<0 center dot 0001). In the alpha- delta phase, 84 (18 center dot 3%; 95% CI 14 center dot 6-22 center dot 7) of 458 unvaccinated patients and three (9 center dot 4%; 1 center dot 9- 27 center dot 3) of 32 unvaccinated patients in the omicron phase had sequelae. Patients who received a booster and those who received two vaccine doses had a significantly lower prevalence of overall COVID-19 sequelae than unvaccinated or partially vaccinated patients (ten [7 center dot 4%; 95% CI 3 center dot 5-13 center dot 5] of 136 boosted patients, 18 [9 center dot 8%; 5 center dot 8-15 center dot 5] of 183 patients who had two vaccine doses vs 277 [ 18 center dot 5%; 16 center dot 5-20 center dot 9] of 1489 unvaccinated patients, p=0 center dot 0001), respiratory sequelae (six [4 center dot 4%; 1 center dot 6-9 center dot 6], 11 [6 center dot 0%; 3 center dot 0-10 center dot 7] vs 148 [9 center dot 9%; 8 center dot 4- 11 center dot 6], p= 0 center dot 030), and prolonged fatigue (three [2 center dot 2%; 0 center dot 1-6 center dot 4], ten [5 center dot 4%; 2 center dot 6-10 center dot 0] vs 115 [7 center dot 7%; 6 center dot 3-9 center dot 3], p=0 center dot 037)

SARS-CoV-2 omicron (B.1.1.529)-related COVID-19 sequelae in vaccinated and unvaccinated patients with cancer: results from the OnCovid registry

Background COVID-19 sequelae can affect about 15% of patients with cancer who survive the acute phase of SARS-CoV-2 infection and can substantially impair their survival and continuity of oncological care. We aimed to investigate whether previous immunisation affects long-term sequelae in the context of evolving variants of concern of SARS-CoV-2. Methods OnCovid is an active registry that includes patients aged 18 years or older from 37 institutions across Belgium, France, Germany, Italy, Spain, and the UK with a laboratory-confirmed diagnosis of COVID-19 and a history of solid or haematological malignancy, either active or in remission, followed up from COVID-19 diagnosis until death. We evaluated the prevalence of COVID-19 sequelae in patients who survived COVID-19 and underwent a formal clinical reassessment, categorising infection according to the date of diagnosis as the omicron (B.1.1.529) phase from Dec 15, 2021, to Jan 31, 2022; the alpha (B.1.1.7)-delta (B.1.617.2) phase from Dec 1, 2020, to Dec 14, 2021; and the pre-vaccination phase from Feb 27 to Nov 30, 2020. The prevalence of overall COVID-19 sequelae was compared according to SARS-CoV-2 immunisation status and in relation to post-COVID-19 survival and resumption of systemic anticancer therapy. This study is registered with ClinicalTrials.gov, NCT04393974. Findings At the follow-up update on June 20, 2022, 1909 eligible patients, evaluated after a median of 39 days (IQR 24-68) from COVID-19 diagnosis, were included (964 [ 50 center dot 7%] of 1902 patients with sex data were female and 938 [49 center dot 3%] were male). Overall, 317 (16 center dot 6%; 95% CI 14 center dot 8-18 center dot 5) of 1909 patients had at least one sequela from COVID-19 at the first oncological reassessment. The prevalence of COVID-19 sequelae was highest in the prevaccination phase (191 [19 center dot 1%; 95% CI 16 center dot 4-22 center dot 0] of 1000 patients). The prevalence was similar in the alpha-delta phase (110 [16 center dot 8%; 13 center dot 8- 20 center dot 3] of 653 patients, p=0 center dot 24), but significantly lower in the omicron phase (16 [6 center dot 2%; 3 center dot 5-10 center dot 2] of 256 patients, p<0 center dot 0001). In the alpha- delta phase, 84 (18 center dot 3%; 95% CI 14 center dot 6-22 center dot 7) of 458 unvaccinated patients and three (9 center dot 4%; 1 center dot 9- 27 center dot 3) of 32 unvaccinated patients in the omicron phase had sequelae. Patients who received a booster and those who received two vaccine doses had a significantly lower prevalence of overall COVID-19 sequelae than unvaccinated or partially vaccinated patients (ten [7 center dot 4%; 95% CI 3 center dot 5-13 center dot 5] of 136 boosted patients, 18 [9 center dot 8%; 5 center dot 8-15 center dot 5] of 183 patients who had two vaccine doses vs 277 [ 18 center dot 5%; 16 center dot 5-20 center dot 9] of 1489 unvaccinated patients, p=0 center dot 0001), respiratory sequelae (six [4 center dot 4%; 1 center dot 6-9 center dot 6], 11 [6 center dot 0%; 3 center dot 0-10 center dot 7] vs 148 [9 center dot 9%; 8 center dot 4- 11 center dot 6], p= 0 center dot 030), and prolonged fatigue (three [2 center dot 2%; 0 center dot 1-6 center dot 4], ten [5 center dot 4%; 2 center dot 6-10 center dot 0] vs 115 [7 center dot 7%; 6 center dot 3-9 center dot 3], p=0 center dot 037)

Self-sustained periodic behaviors in interacting systems: macroscopic limits and fluctuations

In this thesis we study the appearance of self-sustained periodic behavior in the macroscopic dynamics of some interacting systems and related critical phenomena. The thesis is organized as follows. In Chapter 1 we focus on the emergence of periodicity in cooperative mean field models whose interaction potential undergoes a dissipative evolution. We define a generalized Curie-Weiss model with dissipation and we analyse its macroscopic dynamics: we show that not only a periodic behavior is present at sufficiently low temperature, but also that, in certain regimes, any (finite) number of stable limit cycles can coexist. Chapter 2 is concerned with a two-population Curie-Weiss model: we define two types of microscopic dynamics, one with delay and the other without. We identify configurations of the interaction network which can enhance macroscopic oscillations in the case without delay; we also show that delay allows the appearance of a collective periodic behavior in configurations in which periodicity was otherwise absent. In Chapter 3 we consider again the mechanism of dissipation, this time dropping the mean field hypothesis. We study a short-range interacting system obtained introducing dissipation in a 1-dimensional Ising model. We prove that, in a suitable zero-temperature infinite-volume limit, the total magnetization of the system displays regular oscillations between polarized phases. Finally, Chapter 4 is dedicated to the analysis of critical fluctuations for systems exhibiting a Hopf bifurcation in the dynamics of the macroscopic law. The behavior of critical fluctuations around the macroscopic limit reflects the type of bifurcation and the observables display fluctuations evolving at different time scales. We identify the slow and the fast variable and we obtain the convergence of the slow variable to its limiting dynamics via an averaging principle.In questa tesi studiamo comportamenti periodici auto-sostenuti che appaiono nella dinamica macroscopica di certi sistemi interagenti e alcuni fenomeni critici collegati a questo comportamento. La tesi è organizzata come segue. Nel primo capitolo ci concentriamo sulla comparsa di periodicità in modelli cooperativi a campo medio il cui potenziale di interazione è soggetto a una dissipazione. Definiamo un modello di Curie-Weiss generalizzato con dissipazione ed analizziamo la sua dinamica limite: mostriamo che non solo il comportamento periodico è presente a temperature sufficientemente basse, ma anche che, in certi regimi, diversi cicli limite stabili possono coesistere, purché in numero finito. Nel secondo capitolo ci occupiamo di un modello di Curie-Weiss bipopolato: definiamo due tipi di dinamiche microscopiche, una con ritardo e l'altra senza. Identifichiamo le configurazioni della rete di interazione che possono dare luogo ad oscillazioni macroscopiche nel caso senza ritardo; mostriamo inoltre che il ritardo permette la comparsa di periodicità in configurazioni nelle quali sarebbe altrimenti assente. Nel terzo capitolo consideriamo nuovamente il meccanismo della dissipazione, questa volta lasciando cadere l'ipotesi di interazione a campo medio. Studiamo un sistema di particelle con interazione a corto raggio ottenuto introducendo la dissipazione in un modello di Ising 1-dimensionale. Mostriamo che, in un opportuno limite di temperatura zero e volume infinito, la magnetizzazione totale del sistema presenta oscillazioni regolari tra fasi polarizzate. Infine, il quarto capitolo è dedicato all'analisi delle fluttuazioni critiche di sistemi che esibiscono una biforcazione di Hopf nella dinamica della legge macroscopica. Il comportamento delle fluttuazioni critiche attorno al limite macroscopico riflette il tipo di biforcazione e gli osservabili mostrano fluttuazioni che evolvono su scale temporali differenti. Identifichiamo la variable lenta e quella veloce ed otteniamo la convergenza della variabile lenta alla sua dinamica limite tramite un averaging principle

The dynamics of critical fluctuations in asymmetric Curie\u2013Weiss models

We study the dynamics of fluctuations at the critical point for two time-asymmetric version of the Curie\u2013Weiss model for spin systems that, in the macroscopic limit, undergo a Hopf bifurcation. The fluctuations around the macroscopic limit reflect the type of bifurcation, as they exhibit observables whose fluctuations evolve at different time scales. The limiting dynamics of fluctuations of slow observable is obtained via an averaging principle