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

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

Multi-sided Böhm-Bawerk assignment markets: the nucleolus and the core-center

En aquest treball mostrem que, a diferència del cas bilateral, per als mercats multilaterals d'assignació coneguts amb el nom de Böhm-Bawerk assignment games, el nucleolus i el core-center, i. e. el centre de masses del core, no coincideixen en general. Per demostrar-ho provem que donant un m-sided Böhm-Bawerk assignment game les dues solucions anteriors poden obtenir-se respectivament del nucleolus i el core-center d'un joc convex definit en el conjunt format pels m sectors. Encara més, provem que per calcular el nucleolus d'aquest últim joc només les coalicions formades per un jugador o m-1 jugadors són importants. Aquests resultats simplifiquen el càlcul del nucleolus d'un multi-sided ¿¿ohm-Bawerk assignment market amb un número molt elevat d'agents.

The Lorenz-maximal core allocations and the kernel in some classes of assignment games

En aquest treball demostrem que en la classe de jocs d'assignació amb diagonal dominant (Solymosi i Raghavan, 2001), el repartiment de Thompson (que coincideix amb el valor tau) és l'únic punt del core que és maximal respecte de la relació de dominància de Lorenz, i a més coincideix amb la solucié de Dutta i Ray (1989), també coneguda com solució igualitària. En segon lloc, mitjançant una condició més forta que la de diagonal dominant, introduïm una nova classe de jocs d'assignació on cada agent obté amb la seva parella òptima almenys el doble que amb qualsevol altra parella. Per aquests jocs d'assignació amb diagonal 2-dominant, el repartiment de Thompson és l'únic punt del kernel, i per tant el nucleolo.

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.

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

Analysis of an iterative deconvolution approach for estimating the source wavelet during waveform inversion of crosshole ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole georadar data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a time-domain waveform inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little-to-no trade-off between the wavelet estimation and the tomographic imaging procedures.

MDCT arthrography of the hip: value of the adaptive statistical iterative reconstruction technique and potential for radiation dose reduction.

OBJECTIVE: The purpose of this article is to assess the effect of the adaptive statistical iterative reconstruction (ASIR) technique on image quality in hip MDCT arthrography and to evaluate its potential for reducing radiation dose. SUBJECTS AND METHODS: Thirty-seven patients examined with hip MDCT arthrography were prospectively randomized into three different protocols: one with a regular dose (volume CT dose index [CTDIvol], 38.4 mGy) and two with a reduced dose (CTDIvol, 24.6 or 15.4 mGy). Images were reconstructed using filtered back projection (FBP) and four increasing percentages of ASIR (30%, 50%, 70%, and 90%). Image noise and contrast-to-noise ratio (CNR) were measured. Two musculoskeletal radiologists independently evaluated several anatomic structures and image quality parameters using a 4-point scale. They also jointly assessed acetabular labrum tears and articular cartilage lesions. RESULTS: With decreasing radiation dose level, image noise statistically significantly increased (p=0.0009) and CNR statistically significantly decreased (p=0.001). We also found a statistically significant reduction in noise (p=0.0001) and increase in CNR (p≤0.003) with increasing percentage of ASIR; in addition, we noted statistically significant increases in image quality scores for the labrum and cartilage, subchondral bone, overall diagnostic quality (up to 50% ASIR), and subjective noise (p≤0.04), and statistically significant reductions for the trabecular bone and muscles (p≤0.03). Regardless of the radiation dose level, there were no statistically significant differences in the detection and characterization of labral tears (n=24; p=1) and cartilage lesions (n=40; p≥0.89) depending on the ASIR percentage. CONCLUSION: The use of up to 50% ASIR in hip MDCT arthrography helps to reduce radiation dose by approximately 35-60%, while maintaining diagnostic image quality comparable to that of a regular-dose protocol using FBP.

Adaptive statistical iterative reconstruction reduces patient radiation dose in neuroradiology CT studies.

INTRODUCTION: Adaptive statistical iterative reconstruction (ASIR) can decrease image noise, thereby generating CT images of comparable diagnostic quality with less radiation. The purpose of this study is to quantify the effect of systematic use of ASIR versus filtered back projection (FBP) for neuroradiology CT protocols on patients' radiation dose and image quality. METHODS: We evaluated the effect of ASIR on six types of neuroradiologic CT studies: adult and pediatric unenhanced head CT, adult cervical spine CT, adult cervical and intracranial CT angiography, adult soft tissue neck CT with contrast, and adult lumbar spine CT. For each type of CT study, two groups of 100 consecutive studies were retrospectively reviewed: 100 studies performed with FBP and 100 studies performed with ASIR/FBP blending factor of 40 %/60 % with appropriate noise indices. The weighted volume CT dose index (CTDIvol), dose-length product (DLP) and noise were recorded. Each study was also reviewed for image quality by two reviewers. Continuous and categorical variables were compared by t test and free permutation test, respectively. RESULTS: For adult unenhanced brain CT, CT cervical myelography, cervical and intracranial CT angiography and lumbar spine CT both CTDIvol and DLP were lowered by up to 10.9 % (p < 0.001), 17.9 % (p = 0.005), 20.9 % (p < 0.001), and 21.7 % (p = 0.001), respectively, by using ASIR compared with FBP alone. Image quality and noise were similar for both FBP and ASIR. CONCLUSION: We recommend routine use of iterative reconstruction for neuroradiology CT examinations because this approach affords a significant dose reduction while preserving image quality.