Aubry sets for weakly coupled systems of Hamilton--Jacobi equations

We introduce a notion of Aubry set for weakly coupled systems of Hamilton--Jacobi equations on the torus and characterize it as the region where the obstruction to the existence of globally strict critical subsolutions concentrates. As in the case of a single equation, we prove the existence of critical subsolutions which are strict and smooth outside the Aubry set. This allows us to derive in a simple way a comparison result among critical sub and supersolutions with respect to their boundary data on the Aubry set, showing in particular that the latter is a uniqueness set for the critical system. We also highlight some rigidity phenomena taking place on the Aubry set.Comment: 35 pages v.2 the introduction has been rewritten and shortened. Some proofs simplified. Corrections and references added. Corollary 5.3 added stating antisymmetry of the Ma\~n\'e matrix on points of the Aubry set. Section 6 contains a new example

On the fourth root prescription for dynamical staggered fermions

With the aim of resolving theoretical issues associated with the fourth root prescription for dynamical staggered fermions in Lattice QCD simulations, we consider the problem of finding a viable lattice Dirac operator D such that (det D_{staggered})^{1/4} = det D. Working in the flavour field representation we show that in the free field case there is a simple and natural candidate D satisfying this relation, and we show that it has acceptable locality behavior: exponentially local with localisation range vanishing ~ (a/m)^{1/2} for lattice spacing a -> 0. Prospects for the interacting case are also discussed, although we do not solve this case here.Comment: 29 pages, 2 figures; some revision and streamlining of the discussions; results unchanged; to appear in PR

Collodial particles at a range of fluid-fluid particles

The study of solid particles residing at fluid-fluid interfaces has become an established area in surface and colloid science recently experiencing a renaissance since around 2000. Particles at interfaces arise in many industrial products and processes like anti-foam formulations, crude oil emulsions, aerated foodstuffs and flotation. Although they act in many ways like traditional surfactant molecules, they offer distinct advantages also and the area is now multi-disciplinary involving research in the fundamental science and potential applications. In this Feature Article, a flavour of some of this interest is given based on recent work from our own group and includes the behaviour of particles at oil-water, air-water, oil-oil, air-oil and water-water interfaces. The materials capable of being prepared by assembling various kinds of particles at fluid interfaces include particle-stabilised emulsions, particle-stabilised aqueous and oil foams, dry liquids, liquid marbles and powdered emulsions

Low Dirac Eigenmodes and the Topological and Chiral Structure of the QCD Vacuum

Several lattice calculations which probe the chiral and topological structure of QCD are discussed. The results focus attention on the low-lying eigenmodes of the Dirac operator in typical gauge field configurations.Comment: Talk presented at the DPF2000 Conferenc

Does"good government"draw foreign capital ? Explaining China's exceptional foreign direct investment inflow

China is now the world's largest destination of foreign direct investment (FDI), despite assessments highlighting its institutional deficiencies. But this FDI inflow corresponds closely to predicted FDI flows into China from a model that predicts FDI inflow based on government quality indicators and controls and is estimated across a sample of other weak-institution countries. The only real discrepancy is that, if government quality is measured by constraints on executive power, China receives somewhat more FDI than the model predicts. This might reflect an underestimation of the strength of these constraints in China, a unique institutional setting for FDI operations, FDI based on expected future institutional improvements, or a unique Chinese model of development. The authors conclude that Ockham's razor disfavors the last. They also note that FDI may be elevated because Chinese institutions protect foreign firms better than domestic ones.Foreign Direct Investment,Economic Theory&Research,Legal Products,Investment and Investment Climate,Parliamentary Government

A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some reference

Receiver Architectures for MIMO-OFDM Based on a Combined VMP-SP Algorithm

Iterative information processing, either based on heuristics or analytical frameworks, has been shown to be a very powerful tool for the design of efficient, yet feasible, wireless receiver architectures. Within this context, algorithms performing message-passing on a probabilistic graph, such as the sum-product (SP) and variational message passing (VMP) algorithms, have become increasingly popular. In this contribution, we apply a combined VMP-SP message-passing technique to the design of receivers for MIMO-ODFM systems. The message-passing equations of the combined scheme can be obtained from the equations of the stationary points of a constrained region-based free energy approximation. When applied to a MIMO-OFDM probabilistic model, we obtain a generic receiver architecture performing iterative channel weight and noise precision estimation, equalization and data decoding. We show that this generic scheme can be particularized to a variety of different receiver structures, ranging from high-performance iterative structures to low complexity receivers. This allows for a flexible design of the signal processing specially tailored for the requirements of each specific application. The numerical assessment of our solutions, based on Monte Carlo simulations, corroborates the high performance of the proposed algorithms and their superiority to heuristic approaches

Firms' Main Market, Human Capital and Wages

Recent international trade literature emphasizes two features in characterizing the current patterns of trade: efficiency heterogeneity at the firm level and quality differentiation. This paper explores human capital and wage differences across firms in that context. We build a partial equilibrium model predicting that firms selling in more-remote markets employ higher human capital and pay higher wages to employees within each education group. The channel linking these variables is firms’ endogenous choice of quality. Predictions are tested using Spanish employer-employee matched data that classify firms according to four main destination markets: local, national, European Union, and rest of the World. Employees’ average education is increasing in the remoteness of firm’s main output market. Market–destination wage premia are large, increasing in the remoteness of the market, and increasing in individual education. These results suggest that increasing globalization may play a significant role in raising wage inequality within and across education groups

Management of Agitation During the COVID-19 Pandemic

The coronavirus disease 2019 (COVID-19) pandemic caused by the coronavirus SARS-CoV-2 has radically altered delivery of care in emergency settings. Unprecedented hardship due to ongoing fears of exposure and threats to personal safety, along with societal measures enacted to curb disease transmission, have had broad psychosocial impact on patients and healthcare workers alike. These changes can significantly affect diagnosing and managing behavioral emergencies such as agitation in the emergency department. On behalf of the American Association for Emergency Psychiatry, we highlight unique considerations for patients with severe behavioral symptoms and staff members managing symptoms of agitation during COVID-19. Early detection and treatment of agitation, precautions to minimize staff hazards, coordination with security personnel and psychiatric services, and avoidance of coercive strategies that cause respiratory depression will help mitigate heightened risks to safety caused by this outbreak