How to Reform the Italian Domestic Adoptions System Through a Centralized Market Design

Using an innovative variation of the standard Matching Market Design framework, this draft aims to provide inputs useful to drive the reform of the current Italian Domestic Adoption System (Italian families that desire to adopt an Italian child). The problem addressed in this draft, concern how to match the relative small number of waiting children to the large number of waiting families in the most rational and efficient way: each year, the adoptions system is not able to place the 20% of the children in foster care, despite the fact that the number of children (supply side) is very small respect the total amount of families (demand side) willing to adopt. This project is oriented to solve the inefficiencies characterizing the current adoption program, substituting the actual decentralized setup with a more efficient centralized matching market criteriaMatching Market Design, Adoptions System, Matching Algorithm

Oligopolistic Non-Linear Pricing and Size Economies

The effects of non-linear pricing are determined by the relationship between the demand and the technological structure of the market. This paper focuses on a model in which firms supply a homogeneous product in two different sizes. Information about consumers' reservation prices is incomplete and the production technology is characterized by size economies. Four equilibrium regions are identified depending on the relative intensity of size economies with respect to consumers' evaluation of a second unit of the good. The desirability of non-linear pricing varies across different equilibrium regions.non-linear pricing, size economies, supply technology.

Mechanosensing in myosin filament solves a 60 years old conflict in skeletal muscle modeling between high power output and slow rise in tension

Almost 60 years ago Andrew Huxley with his seminal paper \cite{Huxley1957} laid the foundation of modern muscle modeling, linking chemical events to mechanical performance. He described mechanics and energetics of muscle contraction through the cyclical attachment and detachment of myosin motors to the actin filament with ad hoc assumptions on the dependence of the rate constants on the strain of the myosin motors. That relatively simple hypothesis is still present in recent models, even though with several modifications to adapt the model to the different experimental constraints which became subsequently available. However, already in that paper, one controversial aspect of the model became clear. Relatively high attachment and detachment rates of myosin to the actin filament were needed to simulate the high power output at intermediate velocity of contraction. However, these rates were incompatible with the relatively slow rise in tension after activation, despite the rise should be generated by the same rate functions. This discrepancy has not been fully solved till today, despite several hypotheses have been forwarded to reconcile the two aspects. Here, using a conventional muscle model, we show that the recently revealed mechanosensing mechanism of recruitment of myosin motors \cite{Linarietal2015} can solve this long standing problem without any further ad-hoc hypotheses

A note on the uniqueness of the canonical connection of a naturally reductive space

We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie group with a bi-invariant metric or its symmetric dual. In particular, the canonical connection is unique for the hyperbolic space when the dimension is different from three. We also prove that the canonical connection on the sphere is unique for the symmetric presentation. Finally, we compute the full isometry group (connected component) of a compact and locally irreducible naturally reductive space.Comment: 7 page