Monge assignment games

Un juego de asignación se define por una matriz A; donde cada fila representa un comprador y cada columna un vendedor. Si el comprador i se empareja a un vendedor j; el mercado produce aij unidades de utilidad. Estudiamos los juegos de asignación de Monge, es decir, aquellos juegos bilaterales de asignación en los cuales la matriz satisface la propiedad de Monge. Estas matrices pueden caracterizarse por el hecho de que en cualquier submatriz 2x2 un emparejamiento óptimo está situado en la diagonal principal. Para mercados cuadrados, describimos sus núcleos utilizando sólo la parte central tridiagonal de elementos de la matriz. Obtenemos una fórmula cerrada para el reparto óptimo de los compradores dentro del núcleo y para el reparto óptimo de los vendedores dentro del núcleo. Analizamos también los mercados no cuadrados reduciéndolos a matrices cuadradas apropiadas.

On the nucleolus of 2 x 2 assignment games

[spa] En este artículo hallamos fórmulas para el nucleolo de juegos de asignación arbitrarios con dos compradores y dos vendedores. Se analizan cinco casos distintos, dependiendo de las entradas en la matriz de asignación. Los resultados se extienden a los casos de juegos de asignación de tipo 2 x m o m x 2.

An axiomatization of the nucleolus of the assignment game

[cat] En el domini dels jocs bilaterals d’assignació, es presenta una axiomàtica del nucleolus com l´unica solució que compleix les propietats de consistència respecte del joc derivat definit per Owen (1992) i monotonia de les queixes dels sectors respecte de la seva cardinalitat. Com a conseqüència obtenim una caracterització geomètrica del nucleolus mitjançant una propietat de bisecció més forta que la que satisfan els punts del kernel (Maschler et al, 1979).

Symmetrically multilateral-bargained allocations in multi-sided assignment markets

[cat] Aquest treball tracta d’extendre la noció d’equilibri simètric de negociació bilateral introduït per Rochford (1983) a jocs d’assignació multilateral. Un pagament corresponent a un equilibri simètric de negociación multilateral (SMB) és una imputación del core que garanteix que qualsevol agent es troba en equilibri respecte a un procés de negociación entre tots els agents basat en allò que cadascun d’ells podria rebre -i fer servir com a amenaça- en un ’matching’ òptim diferent al que s’ha format. Es prova que, en el cas de jocs d’assignació multilaterals, el conjunt de SMB és sempre no buit i que, a diferència del cas bilateral, no sempre coincideix amb el kernel (Davis and Maschler, 1965). Finalment, responem una pregunta oberta per Rochford (1982) tot introduïnt un conjunt basat en la idea de kernel, que, conjuntament amb el core, ens permet caracteritzar el conjunt de SMB.

Complements and substitutes in multilateral assignment markets

[cat] En aquest treball provo que, en mercats d’assignació amb més de dos costats, agents de diferents sectors poden no ser complementaris mentre que agents del mateix sector poden no ser substituts. Shapley (1962) va provar que això mai pot succeïr quan el mercat d’assignació només té dos costats. No obstant, demostro que existeixen condicions suficients que garanteixen la substitutabilitat i la complementarietat entre agents en aquests tipus de mercats. A més, provo que, quan els béns al mercat son homogenis, el resultat de Shapley (1962) es manté.

Ubiquitin-specific protease 2-45 (Usp2-45) binds to epithelial Na+ channel (ENaC)-ubiquitylating enzyme Nedd4-2.

Regulation of the epithelial Na(+) channel (ENaC) by ubiquitylation is controlled by the activity of two counteracting enzymes, the E3 ubiquitin-protein ligase Nedd4-2 (mouse ortholog of human Nedd4L) and the ubiquitin-specific protease Usp2-45. Previously, Usp2-45 was shown to decrease ubiquitylation and to increase surface function of ENaC in Xenopus laevis oocytes, whereas the splice variant Usp2-69, which has a different N-terminal domain, was inactive toward ENaC. It is shown here that the catalytic core of Usp2 lacking the N-terminal domain has a reduced ability relative to Usp2-45 to enhance ENaC activity in Xenopus oocytes. In contrast, its catalytic activity toward the artificial substrate ubiquitin-AMC is fully maintained. The interaction of Usp2-45 with ENaC exogenously expressed in HEK293 cells was tested by coimmunoprecipitation. The data indicate that different combinations of ENaC subunits, as well as the α-ENaC cytoplasmic N-terminal but not C-terminal domain, coprecipitate with Usp2-45. This interaction is decreased but not abolished when the cytoplasmic ubiquitylation sites of ENaC are mutated. Importantly, coimmunoprecipitation in HEK293 cells and GST pull-down of purified recombinant proteins show that both the catalytic domain and the N-terminal tail of Usp2-45 physically interact with the HECT domain of Nedd4-2. Taken together, the data support the conclusion that Usp2-45 action on ENaC is promoted by various interactions, including through binding to Nedd4-2 that is suggested to position Usp2-45 favorably for ENaC deubiquitylation.

The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered

The extreme core allocations of the assignment game

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal contribution to a certain reduced game played by his predecessors. We prove that the whole set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is the set of extreme points of the core of the assignment game

Uniform-price assignment markets

Uniform-price assignment games are introduced as those assignment markets with the core reduced to a segment. In these games, for all active agents, competitive prices are uniform although products may be non-homogeneous. A characterization in terms of the assignment matrix is given. The only assignment markets where all submarkets are uniform are the Bohm-Bawerk horse markets. We prove that for uniform-price assignment games the kernel, or set of symmetrically-pairwise bargained allocations, either coincides with the core or reduces to the nucleolus

All assignment games with the same core have the same nucleolus

There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyer-seller exact representative

The epithelial sodium channel mediates the directionality of galvanotaxis in human keratinocytes.

Cellular directional migration in an electric field (galvanotaxis) is one of the mechanisms guiding cell movement in embryogenesis and in skin epidermal repair. The epithelial sodium channel (ENaC), in addition to its function of regulating sodium transport in kidney, has recently been found to modulate cell locomotory speed. Here we tested whether ENaC has an additional function of mediating the directional migration of galvanotaxis in keratinocytes. Genetic depletion of ENaC completely blocks only galvanotaxis and does not decrease migration speed. Overexpression of ENaC is sufficient to drive galvanotaxis in otherwise unresponsive cells. Pharmacologic blockade or maintenance of the open state of ENaC also decreases or increases, respectively, galvanotaxis, suggesting that the channel open state is responsible for the response. Stable lamellipodial extensions formed at the cathodal sides of wild-type cells at the start of galvanotaxis; these were absent in the ENaC knockout keratinocytes, suggesting that ENaC mediates galvanotaxis by generating stable lamellipodia that steer cell migration. We provide evidence that ENaC is required for directional migration of keratinocytes in an electric field, supporting a role for ENaC in skin wound healing.

Functional analysis of altered channel-activating protease-1 (CAP1) expression in the skin

Summary : The skin is a complex organ that protects the body against entry of pathogens and supplies a relatively dry and impermeable barrier to water loss. This barrier function is mainly provided by the epidermis, which is the outermost layer of the skin. Serine proteases are involved in skin physiology and it is known that mutations or alterations in their expression can lead to skin diseases. In order to investigate the importance of the regulated expression of CAPI/Prss8, a membrane bound serine protease expressed in the epidermis, we developed transgenic mice ectopically expressing CAPI/Prss8 in the skin. These animals exhibited a phenotype characterized by scaly skin, epidermal hypertrophy, inflammation and scratching behavior. This phenotype could be completely abolished in mice lacking the proteinase activated receptor 2 (PAR2) revealing PAR2 as a potential in vivo downstream target of CAP 1 /Prss8. We could also provide evidence of a CAP1 /Prss8 function independent of its catalytic activity. Additionally, mice ectopically expressing PAR2 in the skin developed a skin phenotype very similar to CAPI/Prss8 transgenic animals, supporting the hypothesis of PAR2 activation by CAPI/Prss8. We could furthermore demonstrate an inhibitory effect of the serine protease inhibitor nexin-I on CAPI/Prss8, since nexin-1 transgenic expression negated the skin phenotype observed in CAPI/Prss8 transgenic mice. CAP1/Prss8 and PAR2 transgenic animals, and the understanding of the interaction between CAPl/Prss8 and PAR2, can be helpful in developing potential CAPI/Prss8 and PAR2 inhibitory molecules that may be used as drugs to treat ichthyoses-like skin diseases. Résumé : La peau est un organe complexe qui protège le corps contre l'entrée des pathogènes et forme une barrière imperméable qui empêche la déshydratation. Cette fonction de barrière est surtout fournie par l'épiderme, la couche la plus superficielle de la peau. Le bon fonctionnement de cet organe est permis, entre autres, par les protéases à sérine qui sont des enzymes dont l'altération peut causer des maladies de la peau. Pour étudier l'importance de la régulation de CAP1/Prss8, une protéase à sérine exprimée au niveau de l'épiderme, des souris génétiquement modifiées, dans lesquelles CAP1/Prss8 est exprimé d'une manière ectopique dans la peau, ont été générées. Les animaux transgéniques pour CAP1/Prss8 présentent une peau squameuse, un épiderme hypertrophique, des processus inflammatoires et se grattent. Ce phénotype a pu être complètement guéri lorsque le gène de PAR2, un récepteur qui règle l'activité des cellules de l'épiderme, est inactivé chez la souris. Ceci montre que PAR2 est une cible de CAP1/Prss8 dans le système étudié. Des études expérimentales suggèrent de plus que l'effet de CAP1/Prss8 dans ce modèle ne dépend pas de son activité enzymatique. En dernière analyse, il a été démontré que l'expression transgénique de nexin-1, un inhibiteur des protéases à sérine exprimé dans la peau, a la capacité d'améliorer la peau squameuse et l'épiderme hypertrophique causés par CAP1/Prss8 transgénique. Les animaux transgéniques pour CAP1/Prss8 et PAR2, et la compréhension du mécanisme d'interaction entre eux, pourraient aider à développer et à tester des molécules inhibitrices de CAP1 /Prss8 et PARI qui pourraient alors être utilisées comme médicaments pour traiter des maladies de la peau comme les ichthyoses.

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.