Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Crystalline Confinement

We show that exotic phases arise in generalized lattice gauge theories known as quantum link models in which classical gauge fields are replaced by quantum operators. While these quantum models with discrete variables have a finite-dimensional Hilbert space per link, the continuous gauge symmetry is still exact. An efficient cluster algorithm is used to study these exotic phases. The (2+1)-d system is confining at zero temperature with a spontaneously broken translation symmetry. A crystalline phase exhibits confinement via multi stranded strings between chargeanti-charge pairs. A phase transition between two distinct confined phases is weakly first order and has an emergent spontaneously broken approximate SO(2) global symmetry. The low-energy physics is described by a (2 + 1)-d RP(1) effective field theory, perturbed by a dangerously irrelevant SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. This model is an ideal candidate to be implemented in quantum simulators to study phenomena that are not accessible using Monte Carlo simulations such as the real-time evolution of the confining string and the real-time dynamics of the pseudo-Goldstone boson.

Stringy origin of diboson and dijet excesses at the LHC

Very recently, the ATLAS and CMS Collaborations reported diboson and dijet excesses above standard model expectations in the invariant mass region of 1.8–2.0 TeV. Interpreting the diboson excess of events in a model independent fashion suggests that the vector boson pair production searches are best described by WZ or ZZ topologies, because states decaying into W+W− pairs are strongly constrained by semileptonic searches. Under the assumption of a low string scale, we show that both the diboson and dijet excesses can be steered by an anomalous U(1) field with very small coupling to leptons. The Drell–Yan bounds are then readily avoided because of the leptophobic nature of the massive Z′ gauge boson. The non-negligible decay into ZZ required to accommodate the data is a characteristic footprint of intersecting D-brane models, wherein the Landau–Yang theorem can be evaded by anomaly-induced operators involving a longitudinal Z. The model presented herein can be viewed purely field-theoretically, although it is particularly well motivated from string theory. Should the excesses become statistically significant at the LHC13, the associated Zγ topology would become a signature consistent only with a stringy origin.

Simulation in vascular access surgery training.

Rapidly growing technical developments and working time constraints call for changes in trainee formation. In reality, trainees spend fewer hours in the hospital and face more difficulties in acquiring the required qualifications in order to work independently as a specialist. Simulation-based training is a potential solution. It offers the possibility to learn basic technical skills, repeatedly perform key steps in procedures and simulate challenging scenarios in team training. Patients are not at risk and learning curves can be shortened. Advanced learners are able to train rare complications. Senior faculty member's presence is key to assess and debrief effective simulation training. In the field of vascular access surgery, simulation models are available for open as well as endovascular procedures. In this narrative review, we describe the theory of simulation, present simulation models in vascular (access) surgery, discuss the possible benefits for patient safety and the difficulties of implementing simulation in training.

Global models of planet formation and evolution

Despite the strong increase in observational data on extrasolar planets, the processes that led to the formation of these planets are still not well understood. However, thanks to the high number of extrasolar planets that have been discovered, it is now possible to look at the planets as a population that puts statistical constraints on theoretical formation models. A method that uses these constraints is planetary population synthesis where synthetic planetary populations are generated and compared to the actual population. The key element of the population synthesis method is a global model of planet formation and evolution. These models directly predict observable planetary properties based on properties of the natal protoplanetary disc, linking two important classes of astrophysical objects. To do so, global models build on the simplified results of many specialized models that address one specific physical mechanism. We thoroughly review the physics of the sub-models included in global formation models. The sub-models can be classified as models describing the protoplanetary disc (of gas and solids), those that describe one (proto)planet (its solid core, gaseous envelope and atmosphere), and finally those that describe the interactions (orbital migration and N-body interaction). We compare the approaches taken in different global models, discuss the links between specialized and global models, and identify physical processes that require improved descriptions in future work. We then shortly address important results of planetary population synthesis like the planetary mass function or the mass-radius relationship. With these statistical results, the global effects of physical mechanisms occurring during planet formation and evolution become apparent, and specialized models describing them can be put to the observational test. Owing to their nature as meta models, global models depend on the results of specialized models, and therefore on the development of the field of planet formation theory as a whole. Because there are important uncertainties in this theory, it is likely that the global models will in future undergo significant modifications. Despite these limitations, global models can already now yield many testable predictions. With future global models addressing the geophysical characteristics of the synthetic planets, it should eventually become possible to make predictions about the habitability of planets based on their formation and evolution.

Calibrating a CGE model with NTBs that Incorporates Standard Models of Modern Trade Theory

We propose a way to incorporate NTBs for the four workhorse models of the modern trade literature in computable general equilibrium models (CGEs). CGE models feature intermediate linkages and thus allow us to study global value chains (GVCs). We show that the Ethier-Krugman monopolistic competition model, the Melitz firm heterogeneity model and the Eaton and Kortum model can be defined as an Armington model with generalized marginal costs, generalized trade costs and a demand externality. As already known in the literature in both the Ethier-Krugman model and the Melitz model generalized marginal costs are a function of the amount of factor input bundles. In the Melitz model generalized marginal costs are also a function of the price of the factor input bundles. Lower factor prices raise the number of firms that can enter the market profitably (extensive margin), reducing generalized marginal costs of a representative firm. For the same reason the Melitz model features a demand externality: in a larger market more firms can enter. We implement the different models in a CGE setting with multiple sectors, intermediate linkages, non-homothetic preferences and detailed data on trade costs. We find the largest welfare effects from trade cost reductions in the Melitz model. We also employ the Melitz model to mimic changes in Non tariff Barriers (NTBs) with a fixed cost-character by analysing the effect of changes in fixed trade costs. While we work here with a model calibrated to the GTAP database, the methods developed can also be applied to CGE models based on the WIOD database.