Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations

Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time, robust envy-free, and non-wasteful. It relies on parametric network flows and recent generalizations of the probabilistic serial algorithm. For the subdomain of piecewise uniform valuations, we show that it is also group-strategyproof. Then, we show that there exists an algorithm (MEA) that is polynomial-time, envy-free, proportional, and Pareto optimal. MEA is based on computing a market-based equilibrium via a convex program and relies on the results of Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise uniform valuations. We then present an algorithm CSD and a way to implement it via randomization that satisfies strategyproofness in expectation, robust proportionality, and unanimity for piecewise constant valuations. For the case of two agents, it is robust envy-free, robust proportional, strategyproof, and polynomial-time. Many of our results extend to more general settings in cake cutting that allow for variable claims and initial endowments. We also show a few impossibility results to complement our algorithms.Comment: 39 page

Pareto Optimal Matchings in Many-to-Many Markets with Ties

We consider Pareto-optimal matchings (POMs) in a many-to-many market of applicants and courses where applicants have preferences, which may include ties, over individual courses and lexicographic preferences over sets of courses. Since this is the most general setting examined so far in the literature, our work unifies and generalizes several known results. Specifically, we characterize POMs and introduce the \emph{Generalized Serial Dictatorship Mechanism with Ties (GSDT)} that effectively handles ties via properties of network flows. We show that GSDT can generate all POMs using different priority orderings over the applicants, but it satisfies truthfulness only for certain such orderings. This shortcoming is not specific to our mechanism; we show that any mechanism generating all POMs in our setting is prone to strategic manipulation. This is in contrast to the one-to-one case (with or without ties), for which truthful mechanisms generating all POMs do exist

Neurogenic Inflammation of Guinea-Pig Bladder

Capsaicin, substance P, and ovalbumin, instilled into the bladders of naive and ovalbumin (OVA) sensitized guineapigs caused inflammation, as indicated by increased vascular permeability. Histological changes after exposure to these compounds progressed with time from intense vasodilatation to marginalization of granulocytes followed by interstitial migration of leukocytes. In vitro incubation of guinea-pig bladder tissue with substance P and ovalbumin stimulated release of prostaglandin D2 and leukotrienes. In vitro incubation of bladder tissue with capsaicin, OVA, prostaglandin D2, leukotriene C4, histamine, or calcium ionophore A-23587 all stimulated substance P release. These data suggest that bladder inflammation initiated by a variety of stimuli could lead to a cyclic pattern of release of inflammatory mediators and neuropeptides, which could result in amplification and persistence of cystitis after the inciting cause has subsided

First Powering of the LHC Test String 2

String 2 is a full-size model of a regular cell in an LHC arc. In the first phase, three dipole magnets and two quadrupole magnets have been assembled in String 2 and commissioning started in April 2001. By the beginning of 2002 three pre-series dipole magnets will be added to complete the cell. As for its predecessor String 1, the facility was built to individually validate the LHC systems and to investigate their collective behaviour for normal operation with the magnets at a temperature of 1.9 K, during transients as well as during exceptional conditions. String 2 is a precious milestone before installation and commissioning of the first LHC sector (1/8 of the machine) in 2004, with respect to infrastructure, installation, tooling and assembly procedures, testing and commissioning of individual systems, as well as the global commissioning of the technical systems. This paper describes the commissioning, and retraces the first powering history

Sequential Deliberation for Social Choice

In large scale collective decision making, social choice is a normative study of how one ought to design a protocol for reaching consensus. However, in instances where the underlying decision space is too large or complex for ordinal voting, standard voting methods of social choice may be impractical. How then can we design a mechanism - preferably decentralized, simple, scalable, and not requiring any special knowledge of the decision space - to reach consensus? We propose sequential deliberation as a natural solution to this problem. In this iterative method, successive pairs of agents bargain over the decision space using the previous decision as a disagreement alternative. We describe the general method and analyze the quality of its outcome when the space of preferences define a median graph. We show that sequential deliberation finds a 1.208- approximation to the optimal social cost on such graphs, coming very close to this value with only a small constant number of agents sampled from the population. We also show lower bounds on simpler classes of mechanisms to justify our design choices. We further show that sequential deliberation is ex-post Pareto efficient and has truthful reporting as an equilibrium of the induced extensive form game. We finally show that for general metric spaces, the second moment of of the distribution of social cost of the outcomes produced by sequential deliberation is also bounded

Experiments and cycling at the LHC prototype helf-cell

The first version of the LHC prototype half-cell has been in operation since February 1995. It consists of one quadrupole and three 10-m twin aperture dipole magnets which operate at 1.8 K. This experimental set-up has been used to observe and study phenomena which appear when the systems are assembled in one unit and influence one another. The 18-month long experimental program has validated the cryogenic system and yielded a number of results on cryogenic instrumentation, magnet protection and vacuum in particular under non-standard operating conditions. The program was recently complemented by the cycling experiment: it consisted in powering the magnets following the ramp rates which will be experienced by the magnets during an LHC acceleration. In order to simulate 10 years of routine operation of LHC, more than 2000 1-hour cycles were performed interleaved with provoked quenches. The objective of this experiment was to reveal eventual flaws in the design of components. The prototype half-cell performed to expectations showing no sign of failure of fatigue of components for more than 2000 cycles until one of the dipoles started exhibiting an erratic quench behavior

The Commissioning of the LHC Test String 2

String 2 [1,2] is a full-size model of an LHC cell of the regular part of the arc. It is composed of six dipole magnets with their correctors, two short straight sections with their orbit and lattice corrector magnets, and a cryogenic distribution line running alongside the magnets. The commissioning of String 2 Phase 1, with one half-cell and the following quadrupole, has started in April 2001. As for String 1 [3], the facility was built to individually validate the LHC systems and to investigate their collective behaviour during normal operation (pump-down, cool-down and powering) as well as during exceptional conditions such as quenches. String 2 is a stepping stone towards the commissioning of the first sector (one eight of LHC) planned for 2004. It is expected to yield precious information on the infrastructures, the installation, the tooling and the procedures for the assembly, the testing and the commissioning of the individual systems, as well as the global commissioning of the technical systems. This paper describes the procedures followed for the commissioning and details the preparation for the first cool-down and for the powering

The Preparation of the Cryomagnets and the Assembly of the LHC Test String 2

The numerous complex activities required to prepare the cryomagnets for the installation in String 2 are described. These include the configuration of the mechanical interfaces, thee conditioning of the beam tubes, the installation of beam screens and the instrumentation as well as the final checks. The preparation of the cryomagnets for String 2 has been a dress rehearsal for the preparation that the cryomagnets will undergo before their installation in the tunnel. After a description of the interconnection procedures of the components for String 2, the tests carried-out to release the String for operation are described. A brief account of the lessons learnt is also given

First Results and Status of the LHC Test String 2

After the commissioning of String 2 Phase1 and the powering of the main circuits in autumn 2001, a short yet vigorous experimental program was carried-out to validate the final design choices for the technical systems of LHC. This program included the investigation of thermo-hydraulics of quenches quench propagation, power converter controls and tracking between power converters, as well as the measurement of currents induced in the beam screen after a quench and crossing the interconnects. Parameters significant for the LHC, such as heat loads, were also measured. During the winter shutdown the String was completed to a full cell with the addition of three pre-series dipoles (Phase 2). After a short description of the layout of Phase 1 and Phase 2, the results of the experiments are presented and the future experimental program is outlined