Von Neumann-Morgenstern solution and convex descompositions of TU games

We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas¿ five player game with a unique stable set different from the core, are reckoning and analyzed.

Von Neumann-Morgenstern solution and convex descompositions of TU games

We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas¿ five player game with a unique stable set different from the core, are reckoning and analyzed.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Caution, children crossing: Heterogeneity of victim's cost of care and negligence rule

The paper deals with a bilateral accident situation in which victims haveheterogeneous costs of care. With perfect information,efficient care bythe injurer raises with the victim's cost. When the injurer cannot observeat all the victim's type, and this fact can be verified by Courts, first-bestcannot be implemented with the use of a negligence rule based on thefirst-best levels of care. Second-best leads the injurer to intermediate care,and the two types of victims to choose the best response to it. This second-bestsolution can be easily implemented by a negligence rule with second-best as duecare. We explore imperfect observation of the victim's type, characterizing theoptimal solution and examining the different legal alternatives when Courts cannotverify the injurers' statements. Counterintuitively, we show that there is nodifference at all between the use by Courts of a rule of complete trust and arule of complete distrust towards the injurers' statements. We then relate thefindings of the model to existing rules and doctrines in Common Law and Civil Lawlegal systems.

Comment to "Weak instruments robust tests in GMM and the New Keynesian Phillips curve" by Frank Kleibergen and Sophocles Mavroeidis

I discuss the identifiability of a structural New Keynesian Phillips curve when it is embedded in a small scale dynamic stochastic general equilibrium model. Identification problems emerge because not all the structural parameters are recoverable from the semi-structural ones and because the objective functions I consider are poorly behaved. The solution and the moment mappings are responsible for the problems.

Brane-world creation and black holes

An inflating brane world can be created from ``nothing'' together with its anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap m=(3/2)H, where H is the Hubble rate. We consider the analogue of the Nariai solution and argue that it describes the pair production of ``black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing or the production of AdS black holes in the vicinity of a pre-existing inflating brane world. The Lorentzian evolution of the brane world after creation is briefly discussed. An additional ``integration constant'' in the Friedmann equation-accompanying a term which dilutes like radiation-describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. In general, this could be a 5-dimensional black hole or a ``parallel'' brane world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the AdS/CFT correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.

Poly(butylene terephthalate-co-5-tert-butyl isophthalate) Copolyesters: Synthesis, Characterization and Properties

A series of poly(butylene terephthalate) copolyesters containing 5-tert-butyl isophthalate units up to 50%-mole, as well as the homopolyester entirely made of these units, were prepared by polycondensation from the melt. The microstructure of the copolymers was determined by NMR to be at random for the whole range of compositions. The effect exerted by the 5-tert-butyl isophthalate units on thermal, tensile and gas transport properties was evaluated. Both Tm and crystallinity as well as the mechanical moduli were found to decrease steadily with copolymerization whereas Tg increased and the polyesters became more brittle. Permeability and solubility sligthly increased also with the content in substituted units whereas the diffusion coefficient remained practically constant. For the homopolyester poly(5-tert-butyl isophthalate), all these properties were found to deviate significantly from the general trend displayed by copolyesters suggesting that a different chain mode of packing in the amorphous phase is likely adopted in this case.

Introducció experimental a la biotecnologia amb clavellina: cultiu in vitro

Treball de recerca realitzat per una alumna d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. Es tracta d’una recerca experimental en la que s’han assajat vuit tècniques de cultiu in vitro amb clavellina. El material vegetal s’ha esterilitzat per immersió en una solució diluïda de lleixiu i s’ha manipulat de manera estèril. En tots els casos el medi de cultiu utilitzat ha estat el MS amb una concentració de sacarosa i reguladors de creixement variable segons l’experiment. La incubació dels cultius s’han dut a terme en una cambra amb control de fotoperíode durant 4 setmanes. Els diferents reguladors de creixement han mostrat un clar efecte sobre les seccions de tija. Els explants cultivats en medi lliure d’hormones han crescut menys que els exposats a diverses concentracions de NAA i BA. Aquests tractaments hormonals han originat símptomes de creixement anòmals (engruiximents a la base i vitrificació). La presencia de 2,4-D ha afavorit la formació de cal•lus i d’arrels per organogènesi adventícia indirecta. L’obtenció de plàntules per germinació in vitro de llavors ha permès reduir notablement les pèrdues per contaminació, mentre que el subcultiu d’aquestes ha donat unes tases de micropropagació de 7.2 seccions/plàntula. Ha estat possible aclimatar aquestes vitroplantes per tal d’adaptar-les a les condicions de camp. No hem pogut obtenir organogènesis adventícia ni embriogènesi somàtica a partir d anteres ni hem pogut iniciar un cultiu de cèl•lules a partir dels cal•lus. Tot i la complexitat d’aquestes tècniques, és possible dur-les a terme en un laboratori escolar.

Simultaneous Nash bargaining with consistent beliefs

We propose and analyze a new solution concept, the R solution, for three-person, transferable utility, cooperative games. In the spirit of the Nash Bargaining Solution, our concept is founded on the predicted outcomes of simultaneous, two-party negotiations that would be the alternative to the grand coalition. These possibly probabilistic predictions are based on consistent beliefs. We analyze the properties of the R solution and compare it with the Shapley value and other concepts. The R solution exists and is unique. It belongs to the bargaining set and to the core whenever the latter is not empty. In fact, when the grand coalition can simply execute one of the three possible bilateral trades, the R solution is the most egalitarian selection of the bargaining set. Finally, we discuss how the R solution changes important conclusions of several well known Industrial Organization models.

Recovering Euclidean deformable models from stereo-motion

In this paper we present a novel structure from motion (SfM) approach able to infer 3D deformable models from uncalibrated stereo images. Using a stereo setup dramatically improves the 3D model estimation when the observed 3D shape is mostly deforming without undergoing strong rigid motion. Our approach first calibrates the stereo system automatically and then computes a single metric rigid structure for each frame. Afterwards, these 3D shapes are aligned to a reference view using a RANSAC method in order to compute the mean shape of the object and to select the subset of points on the object which have remained rigid throughout the sequence without deforming. The selected rigid points are then used to compute frame-wise shape registration and to extract the motion parameters robustly from frame to frame. Finally, all this information is used in a global optimization stage with bundle adjustment which allows to refine the frame-wise initial solution and also to recover the non-rigid 3D model. We show results on synthetic and real data that prove the performance of the proposed method even when there is no rigid motion in the original sequence

KAM theory for conformally symplectic systems

We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the system is close to integrable, but we use an a-posteriori format. Our unknowns are a parameterization of the solution and a parameter. We show that if there is a sufficiently approximate solution of the invariance equation, which also satisfies some explicit non–degeneracy conditions, then there is a true solution nearby. We present results both in Sobolev norms and in analytic norms. The a–posteriori format has several consequences: A) smooth dependence on the parameters, including the singular limit of zero dissipation; B) estimates on the measure of parameters covered by quasi–periodic solutions; C) convergence of perturbative expansions in analytic systems; D) bootstrap of regularity (i.e., that all tori which are smooth enough are analytic if the map is analytic); E) a numerically efficient criterion for the break–down of the quasi–periodic solutions. The proof is based on an iterative quadratically convergent method and on suitable estimates on the (analytical and Sobolev) norms of the approximate solution. The iterative step takes advantage of some geometric identities, which give a very useful coordinate system in the neighborhood of invariant (or approximately invariant) tori. This system of coordinates has several other uses: A) it shows that for dissipative conformally symplectic systems the quasi–periodic solutions are attractors, B) it leads to efficient algorithms, which have been implemented elsewhere. Details of the proof are given mainly for maps, but we also explain the slight modifications needed for flows and we devote the appendix to present explicit algorithms for flows.

Discrimination in Bankruptcy Situations

In a bankruptcy situation, not all claimants are affected in the same way. In particular, some depositors may enter into a situation of personal bankruptcy if they lose part of their investments. Events of this kind may lead to a social catastrophe. We propose discrimination among the claimants as a possible solution. A fact considered in the American bankruptcy law (among others) that establishes some discrimination on the claimants, or the Santander Bank that in the Madoff’s case reimbursed only the deposits to its particular customers. Moreover, the necessity of discriminating has already been mentioned in different contexts by Young (1988), Bossert (1995), Thomson (2003) and Pulido et al. (2002, 2007), for instance. In this paper, we take a bankruptcy solution as the reference point. Given this initial allocation, we make transfers from richer to poorer with the purpose of distributing not only the personal incurred losses as evenly as possible but also the transfers in a progressive way. The agents are divided into two groups depending on their personal monetary value (wealth, net-income, GDP or any other characteristic). Then, we impose a set of Axioms that bound the maximal transfer that each net-contributor can make and each net-receiver can obtain. Finally, we define a value discriminant solution, and we characterize it by means of the Lorenz criterion. Endogenous convex combinations between solutions are also considered. Keywords: Bankruptcy, Discrimination, Compensation, Rules JEL classification: C71, D63, D71.

Optimum power allocation for parallel Gaussian channels with arbitrary input distributions

The mutual information of independent parallel Gaussian-noise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signalling constellations with limited peak-to-average ratios (m-PSK, m-QAM, etc) are used in lieu of the ideal Gaussian signals. This paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions. Such policy admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition. The relationship between mutual information of Gaussian channels and nonlinear minimum mean-square error proves key to solving the power allocation problem.

Contribution biplots

In order to interpret the biplot it is necessary to know which points usually variables are the ones that are important contributors to the solution, and this information is available separately as part of the biplot s numerical results. We propose a new scaling of the display, called the contribution biplot, which incorporates this diagnostic directly into the graphical display, showing visually the important contributors and thus facilitating the biplot interpretation and often simplifying the graphical representation considerably. The contribution biplot can be applied to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. In the contribution biplot one set of points, usually the rows of the data matrix, optimally represent the spatial positions of the cases or sample units, according to some distance measure that usually incorporates some form of standardization unless all data are comparable in scale. The other set of points, usually the columns, is represented by vectors that are related to their contributions to the low-dimensional solution. A fringe benefit is that usually only one common scale for row and column points is needed on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot legible. Furthermore, this version of the biplot also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important, when they are in fact contributing minimally to the solution.

Endogenous bargaining power

We present a novel approach to N-person bargaining, based on the idea thatthe agreement reached in a negotiation is determined by how the directconflict resulting from disagreement would be resolved. Our basic buildingblock is the disagreement function, which maps each set of feasible outcomesinto a disagreement point. Using this function and a weak axiom basedon individual rationality we reach a unique solution: the agreement inthe shadow of conflict, ASC. This agreement may be construed as the limitof a sequence of partial agreements, each of which is reached as a functionof the parties relative power. We examine the connection between ASC andasymmetric Nash solutions. We show the connection between the power ofthe parties embodied in the ASC solution and the bias in the SWF thatwould select ASC as an asymmetric Nash solution.