A dynamical system approach to data assimilation in chaotic models

The Assimilation in the Unstable Subspace (AUS) was introduced by Trevisan and Uboldi in 2004, and developed by Trevisan, Uboldi and Carrassi, to minimize the analysis and forecast errors by exploiting the flow-dependent instabilities of the forecast-analysis cycle system, which may be thought of as a system forced by observations. In the AUS scheme the assimilation is obtained by confining the analysis increment in the unstable subspace of the forecast-analysis cycle system so that it will have the same structure of the dominant instabilities of the system. The unstable subspace is estimated by Breeding on the Data Assimilation System (BDAS). AUS- BDAS has already been tested in realistic models and observational configurations, including a Quasi-Geostrophicmodel and a high dimensional, primitive equation ocean model; the experiments include both fixed and“adaptive”observations. In these contexts, the AUS-BDAS approach greatly reduces the analysis error, with reasonable computational costs for data assimilation with respect, for example, to a prohibitive full Extended Kalman Filter. This is a follow-up study in which we revisit the AUS-BDAS approach in the more basic, highly nonlinear Lorenz 1963 convective model. We run observation system simulation experiments in a perfect model setting, and with two types of model error as well: random and systematic. In the different configurations examined, and in a perfect model setting, AUS once again shows better efficiency than other advanced data assimilation schemes. In the present study, we develop an iterative scheme that leads to a significant improvement of the overall assimilation performance with respect also to standard AUS. In particular, it boosts the efficiency of regime’s changes tracking, with a low computational cost. Other data assimilation schemes need estimates of ad hoc parameters, which have to be tuned for the specific model at hand. In Numerical Weather Prediction models, tuning of parameters — and in particular an estimate of the model error covariance matrix — may turn out to be quite difficult. Our proposed approach, instead, may be easier to implement in operational models.

Essays in nonlinear pricing and rent seeking

This thesis consists of three self-contained essays on nonlinear pricing and rent-seeking. In the first chapter of the thesis, I provide new theoretical insights about non-linear pricing in monopoly and common agency by combining the principal-agent framework with other-regarding preferences. I introduce a new theoretical model that separately characterizes status-seeker and inequity-averse buyers. I show how the buyer’s optimal choice of quality and market inefficiency change when the buyer has other-regarding preferences. In the second chapter, I find the optimal productive rent-seeking and sabotaging efforts when the prize is endogenous. I show that due to the existence of endogeneity, sabotaging the productive rent-seeking efforts causes sabotaging the endogenous part of the prize, which can affect the rent-seeking efforts. Moreover, I introduce social preferences into my model and characterize symmetric productive rent-seeking and sabotaging efforts. In the last chapter, I propose a new theoretical model regarding information disclosure with Bayesian persuasion in rent-seeking contests when the efforts are productive. I show that under one-sided incomplete information, information disclosure decision depends on both the marginal costs of efforts and the marginal benefit of aggregate exerted effort. I find that since the efforts are productive and add a positive surplus on the fixed rent, my model narrows down the conditions for the information disclosure compared to the exogenous model. Under the two-sided incomplete information case, I observe that there is a non-monotone relationship between optimal effort and posterior beliefs. Thus, it might be difficult to conclude whether a contest organizer should disclose any information to contestants.

Pharmacological targeting of P-selectin to halt the progression of myelofibrosis in the Gata1low mouse model

Primary myelofibrosis is a clonal hematopoietic disorder characterized by marked degrees of systemic inflammation. The release of pro-inflammatory factors by clonal hematopoietic cell populations cause the remodeling of a specialized microenvironment, defined niche, in which the hematopoietic stem cells reside. The main source of pro-inflammatory cytokines is represented by malignant megakaryocytes. The bone marrow and spleen from myelofibrosis patients, as well as those from the Gata1low mouse model of the disease, contain increased number of abnormal megakaryocytes. These cells express on their surface high levels of the adhesion receptor P-selectin that, by triggering a pathological megakaryocyte-neutrophil emperipolesis, lead to increased bioavailability of TGF-β1 in the microenvironment and disease progression. Gata1low mice develop with age a phenotype similar to that of patients with myelofibrosis. We previously demonstrated that deletion of the P-selectin gene in Gata1low mice prevented the development of the myelofibrotic phenotype in these mice. In the current study, we tested the hypothesis that pharmacological inhibition of P-selectin may rescue the fibrotic phenotype of Gata1low mice. To test this hypothesis, we have investigated the phenotype expressed by old Gata1low mice treated with the anti-mouse monoclonal antibody against P-selectin RB40.34, alone or in combination with the JAK2 inhibitor Ruxolitinib. The results showed that the combined therapy normalized the phenotype of Gata1low mice with limited toxicity by reducing fibrosis, TGF-β1 and CXCL1 content in the BM and spleen and by restoring hematopoiesis in the bone marrow and the normal architecture of the spleen. In conclusion, pharmacological inhibition of P-selectin was effective in targeting malignant megakaryocytes and the microenvironmental abnormalities that affect the hematopoietic stem cell compartment in this model. These results suggest that P-selectin and JAK1/2 inhibitors in combination may represent a valid therapeutic option for patients with myelofibrosis.