Optimal prize allocations in group contests

We characterize the optimal prize allocation, namely the allocation that maximizes a group's effectiveness, in a model of contests. The model has the following features: (i) it allows for heterogeneity between and within groups; (ii) it classifies contests as "easy" and "hard" depending on whether the marginal costs are concave or convex. Thus, we show that in an "easy" contest the optimal prize allocation assigns the entire prize to one group member, the most skilled one. Conversely, all group members receive a positive share of the prize when the contest is "hard" and players have unbounded above marginal productivities. If the contest is "hard" and the marginal productivities are bounded above, then only the most skilled group members are certain of receiving a positive share of the prize for any distribution of abilities. Finally, we study the effects of a change in the distribution of abilities within a group. Our analysis shows that if the contest is either "easy" or a particular subset of "hard", then the more the heterogeneity within a group, the higher its probability of winning the prize

Study and characterisation of different metal alloys processed through Laser Powder Bed Fusion

Additive Manufacturing (AM) techniques inspired a substantial revolution in the way of concept and produce metal components for industry. Among all the available AM processes, Laser Powder Bed Fusion (LPBF) inspired a noticeable series of investments, studies and standardisation routes since the great interested it acquired in several industrial sectors. In the past years numerous researchers demonstrated how this process produces metal components with innovative and unprecedented microstructures and mechanical properties, disclosing new horizons in the scientific and industrial research. This thesis took under investigation the study and characterisation of three different metal alloys, A357 aluminium alloy, Ti-6Al-4V titanium alloy and pure copper, respectively, all processed by LPBF. Furthermore, the investigation of different post-processing heat treatments was took under study. The processed samples, as well the metal powders used, were characterised by microscopic and macroscopic analyses. The study on A357 aluminium alloy processed by LPBF investigated the process parameters necessary to build full dense components for industrial applications. By correctly combining hatching distance and scanning speed it was possible to fabricate completely dense specimens keeping a good productivity rate. Moreover, the effects of different heat treatments on specimens microstructure and mechanical properties were studied. Particularly, a stress relieving and a subsequent T6 precipitation hardening treatment were performed on the full dense LPBF parts, investigating the effects of different temperatures and durations in the case of T6 treatment. Longer solution treatments enabled to obtain higher hardness values and to reduce the time required to reach peak hardening conditions during ageing. While stress relieving strongly softened the material, a maximum hardness comparable to as-built parts conditions was obtained after subsequent 8 h solution treatment, water quenching and 3 h ageing treatment. Stress reliving treatment slightly modified the as-built microstructure by favouring the diffusion of Si but did not removed the melt pool structures present, furthermore it noticeably increased the elongation at break to detriment of tensile strength. Further T6 treatment modified the tensile properties to values comparable with the as-built conditions eliminating melt pools anisotropic features. The study on Ti-6Al-4V titanium alloy investigated the microstructural, tensile and fatigue properties of the LPBF fabricated parts, produced with two different gas atomised powders. The two powders contained two level of oxygen inside the chemical composition, a low and a high amount, in order to simulate the LPBF processing of Ti-6Al-4V ELI and Ti-6Al-4V grade 5, respectively. Two different building orientations, vertical and horizontal, were chosen for the specimens fabrication and moreover three different testing conditions were considered: after stress relieving, after stress relieving plus heat treatment and after stress relieving plus Hot Isostatic Pressing (HIP). Processing a subsequent heat treatment after stress relieving reduced tensile strength and increased ductility by coarsening α + β lamellar structure while β columnar grains faded. HIP post-processing closed the major part of porosities and defects and enabled to greatly increase both ductility and fatigue resistance. Pores and defects were detected as the most influencing factors upon the fatigue properties, rather than building orientation and oxygen content, which mostly influenced tensile strength. Only stress relieved and HIPped samples resisted more than the chosen endurance limit of 107 cycles at high applied strength than the other specimens. The study carried out on pure copper investigated the feasibility of processing such material with LPBF using a commercial machine equipped with an infrared 200 W fibre laser. The specimens fabricated did not exceed the 83 % of density due to the low absorptivity of copper to infrared radiation, but Diffuse Reflectance Spectroscopy (DRS) analysis demonstrated how modifying the laser radiation from infrared wavelengths to the green ones, the powder bed absorption raised. As-built samples did not present oxides traces inside the microstructure and were constituted by α-Cu phase. The microstructure was constituted by both equiassic and elongated grains depending on the heat fluxes generated inside the material in the horizontal and vertical cross sections

Stabilizing Consensus with Many Opinions

We consider the following distributed consensus problem: Each node in a complete communication network of size $n$ initially holds an \emph{opinion}, which is chosen arbitrarily from a finite set $\Sigma$. The system must converge toward a consensus state in which all, or almost all nodes, hold the same opinion. Moreover, this opinion should be \emph{valid}, i.e., it should be one among those initially present in the system. This condition should be met even in the presence of an adaptive, malicious adversary who can modify the opinions of a bounded number of nodes in every round. We consider the \emph{3-majority dynamics}: At every round, every node pulls the opinion from three random neighbors and sets his new opinion to the majority one (ties are broken arbitrarily). Let $k$ be the number of valid opinions. We show that, if $k \leqslant n^{\alpha}$, where $\alpha$ is a suitable positive constant, the 3-majority dynamics converges in time polynomial in $k$ and $\log n$ with high probability even in the presence of an adversary who can affect up to $o(\sqrt{n})$ nodes at each round. Previously, the convergence of the 3-majority protocol was known for $|\Sigma| = 2$ only, with an argument that is robust to adversarial errors. On the other hand, no anonymous, uniform-gossip protocol that is robust to adversarial errors was known for $|\Sigma| > 2$

Ex vivo Time Evolution of Thrombus Growth through Optical and Electrical Impedance data fusion

We designed a novel sensor specifically aimed at ex vivo measurements of white thrombus volume growth; a white thrombus is induced within an artificial micro-channel where hemostasis takes place starting from whole blood under flow conditions. The advantage of the proposed methodology is to identify the time evolution of the thrombus volume by means of an original data fusion methodology based on 2D optical and electrical impedance data simultaneously processed. On the contrary, the present state of the art optical imaging methodologies allow the thrombus volume estimation only at the end of the hemostatic process

Constraints on feedback processes during the formation of early-type galaxies

Galaxies are found to obey scaling relations between a number of observables. These relations follow different trends at the low- and the high-mass ends. The processes driving the curvature of scaling relations remain uncertain. In this letter, we focus on the specific family of early-type galaxies, deriving the star formation histories of a complete sample of visually classified galaxies from SDSS-DR7 over the redshift range 0.01<z<0.025, covering a stellar mass interval from 10^9 to 3 x 10^11 Msun. Our sample features the characteristic "knee" in the surface brightness vs. mass distribution at Mstar~3 x 10^10 Msun. We find a clear difference between the age and metallicity distributions of the stellar populations above and beyond this knee, which suggests a sudden transition from a constant, highly efficient mode of star formation in high-mass galaxies, gradually decreasing towards the low-mass end of the sample. At fixed mass, our early-type sample is more efficient in building up the stellar content at early times in comparison to the general population of galaxies, with half of the stars already in place by redshift z~2 for all masses. The metallicity-age trend in low-mass galaxies is not compatible with infall of metal-poor gas, suggesting instead an outflow-driven relation.Comment: 12 pages,3 figures, accepted for publication in ApJ

Economics of contests: theory and evidence

This thesis consists of three chapters devoted to the study of the economics of contests. Each chapter can be read independently. A special attention is placed on teams’ behaviour and team-incentive schemes. These questions are particularly important as the way in which institutions reward individuals shapes the inequality of the group to which these individuals belong. Chapter 1. Optimal Prize Allocations in Group Contests. We characterize the optimal prize allocation, namely the allocation that maximizes a group’s effectiveness, in a model of contests. The model has the following features: (i) it allows for heterogeneity between and within groups; (ii) it classifies contests as “easy” and “hard” depending on whether the marginal costs are concave or convex. Thus, we show that in an “easy” contest the optimal prize allocation assigns the entire prize to one group member, the most skilled one. Conversely, all group members receive a positive share of the prize when the contest is “hard” and players have unbounded above marginal productivities. If the contest is “hard” and the marginal productivities are bounded above, then only the most skilled group members are certain of receiving a positive share of the prize for any distribution of abilities. Finally, we study the effects of a change in the distribution of abilities within a group. Our analysis shows that if the contest is either “easy” or a particular subset of “hard”, then the more the heterogeneity within a group, the higher its probability of winning the prize. Chapter 2. Inequalities within Groups: Theory and Evidence. We study the design of a team in multi-team contests. Is it better to distribute prizes among players equally, or to just one player? And is it better to spend a budget on a diverse team with stars and rookies, or on an equal team? First, we study these questions theoretically. We find that depending on the production function, it is either optimal to (i) hire superstars and rookies, and reward superstars the most, or (ii) hire a homogeneous team and reward everyone equally. Then, we test the first set of predictions in the lab. Unlike the theory, superstars or concentrated rewards alone do not help a team win. Both must be used together. Chapter 3. Model of War of Attrition with Outside Options. We study a model of war of attrition with outside options. In a society that allocates rewards via tournaments, individuals decide how much resources dedicate towards winning the prize. Conflicts are of incomplete information and agents’ type consist of their drawn valuation of the prize and valuation of the outside option. We show that this model can be reduced to a standard war of attrition with one signal. Further, we derive the symmetric perfect Bayesian equilibrium of the game and discuss possible applications

Perturbative Approach to Analog Hawking Radiation in dielectric media in subcritical regime

We take into account the subcritical case for dielectric media by exploiting an approximation allowing us to perform perturbative analytical calculations and still not implying low dispersive effects. We show that in the background of a specific soliton-like solution, pair-creation occurs and can display a thermal behaviour governed by an effective temperature. The robustness of the approach is also corroborated by the analysis of the $\phi\psi$-model related to the standard Hopfield model, for which analogous results are obtained.Comment: 22 pages, 6 figure