First-order Approach Research Articles

Existence and non-existence in the moral hazard problem

We provide a new class of counter-examples to existence in a simple moral hazard problem in which the first-order approach is valid. In contrast to the Mirrlees example, unbounded likelihood ratios on the signal technology are not central. Rather, our examples center around the behavior of the utility function as utility diverges to negative infinity. For any utility function, such as ln(w), in which utility diverges to negative infinity at a finite wealth level, existence will fail for some specifications of the agentʼs cost of effort. When utility diverges to negative infinity only as wealth does as well, existence holds for all specifications of the agentʼs cost of effort if and only if the agent continues to dislike risk as wealth diverges to negative infinity. When there is a finite lower bound on utility, existence is assured. For those cases where existence fails, we characterize the limit of near optimal contracts.

Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot’s and multiple scattering models

This article quantitatively investigates ultrasound propagation in numerical anisotropic porous media with finite-difference simulations in 3D. The propagation media consist of clusters of ellipsoidal scatterers randomly distributed in water, mimicking the anisotropic structure of cancellous bone. Velocities and attenuation coefficients of the ensemble-averaged transmitted wave (also known as the coherent wave) are measured in various configurations. As in real cancellous bone, one or two longitudinal modes emerge, depending on the micro-structure. The results are confronted with two standard theoretical approaches: Biot’s theory, usually invoked in porous media, and the Independent Scattering Approximation (ISA), a classical first-order approach of multiple scattering theory. On the one hand, when only one longitudinal wave is observed, it is found that at porosities higher than 90% the ISA successfully predicts the attenuation coefficient (unlike Biot’s theory), as well as the existence of negative dispersion. On the other hand, the ISA is not well suited to study two-wave propagation, unlike Biot’s model, at least as far as wave speeds are concerned. No free fitting parameters were used for the application of Biot’s theory. Finally we investigate the phase-shift between waves in the fluid and the solid structure, and compare them to Biot’s predictions of in-phase and out-of-phase motions.

Contingent Fixed Contracts

For the classic agency model (Holmstrom, 1979), under different assumptions, we offer a completely different solution than the standard solution in the literature. Our optimal contract has a closed form, offers a contingent fixed payment, and is efficient. In contrast, the standard contract in the literature is implicitly determined by four equations except for one special case, is based on the unreliable first-order approach, and is inefficient.

Modeling the die-off of E. coli and Ascaris in wastewater-irrigated vegetables: implications for microbial health risk reduction associated with irrigation cessation.

This study assessed the die-off of Escherichia coli (E. coli) and Ascaris suum on lettuce (Great Lakes 118) and cabbage (Brassica oleracea var capitata) in wastewater-irrigated fields using comparative mathematical die-off models. The study revealed that none of the survival curves of E. coli and A. suum was best fitted with the log-linear model, indicating that the classical first-order kinetic approach is inadequate in many cases. The biphasic die-off model best described the die-off of E. coli on lettuce (kmax1 = 2.62 day(-1) and kmax2 = 0.22 day(-1)) and cabbage (kmax1 = 1.06 day(-1) and kmax2 = 0.53 day(-1)). The die-off of A. suum on lettuce was best described by the biphasic model (kmax1 = 0.48 day(-1) and kmax2 = 0.01 day(-1)) and best described by log linear + tail (kmax = 0.44) on cabbage. A comparative health risk assessment associated with the consumption of lettuce showed significant underestimation of the number of days of irrigation cessation required to achieve E. coli O157:H7 and Ascaris tolerable annual infection risk when using biphasic die-off rates compared with other die-off rates. The study stresses the need to test different die-off models as inputs for quantitative microbial risk assessment (QMRA) particularly for interventions associated with health risk reduction.

On the moral hazard problem without the first-order approach

We study the moral hazard problem without the first-order approach or other common structure. We present sufficient conditions under which the shadow value of simultaneously tightening the minimum payment and individual rationality constraints has a simple and intuitive expression. We then show how this expression can be used to perform comparative statics exercises in which we study (i) the effect of a change in the agentʼs wealth on the well-being of the principal; and (ii) the effects of the outside option and minimum payment on the effort level optimally implemented.

Interannual variability of the early summer circulation around the Balearic Islands: Driving factors and potential effects on the marine ecosystem

Six summer surveys conducted from 2001 to 2005 and in 2012 by the Spanish Institute of Oceanography (IEO) reveal that the hydrographic early summer scenarios around the Balearic Islands are related to the winter atmospheric forcing in the northwestern Mediterranean Sea. The Balearic Islands (western Mediterranean Sea) lie at the transition between the southern, fresher, newly arrived Atlantic Waters (AWs) and the northern, saltier, resident AW. The meridional position of the salinity driven oceanic density front separating the new from the resident AW is determined by the presence/absence of Western Intermediate Water (WIW) in the Mallorca and Ibiza channels. When WIW is present in the channels, the oceanic density front is found either at the south of the islands, or along the Emile Baudot escarpment. In contrast, when WIW is absent, new AW progresses northwards crossing the Ibiza channel and/or the Mallorca channel. In this later scenario, the oceanic density front is closer to the Balearic Islands. A good correspondence exists between standardized winter air temperature anomaly in the Gulf of Lions and the presence of WIW in the channels. We discuss the use of a regional climatic index based on these parameters to forecast in a first-order approach the position of the oceanic front, as it is expected to have high impact on the regional marine ecosystem.

The first-order approach to the principal–agent problems under inequality aversion

This paper considers the principal–agent problems under inequality aversion. We identify sufficient conditions for the first-order approach to be valid. Our results suggest that the first-order approach is restricted in the presence of inequality aversion.

Correlated four-component EPR g-tensors for doublet molecules

The first correlated ab initio four-component calculations of electron paramagnetic resonance (EPR) g-tensors for doublet radicals are reported. We have implemented a first-order degenerate perturbation theory approach based on the four-component Dirac-Coulomb Hamiltonian and fully relativistic configuration interaction wave functions in the DIRAC program package. We find that the correlation effects on the g-tensors can be sufficiently well described with manageable basis sets of triple-zeta quality and manageable configuration spaces. The new fully relativistic EPR module in DIRAC should be useful for benchmarking density functional theory approaches, however, with future optimization of the code we believe it will also be useful for applications.

Theoretical and experimental analysis of the forced LacI-AraC oscillator with a minimal gene regulatory model

Oscillatory dynamics have been observed in multiple cellular functions and synthetic constructs; and here, we study the behavior of a synthetic oscillator under temporal perturbations. We use a minimal model, involving a single transcription factor with delayed self-repression and enzymatic degradation, together with a first-order perturbative approach, to derive an analytical expression for the power spectrum of the system, which characterizes its response to external forces and molecular noise. Experimentally, we force and monitor the dynamics of the LacI-AraC oscillator in single cells during long time intervals by constructing a microfluidics device. Pulse dynamics of IPTG with different periods serve to perturb this system. Due to the resonance of the system, we predict theoretically and confirm experimentally the dependence on the forcing frequency of the variability in gene expression with time and the synchronization of the population to the input signal. The reported results show that the engineering of gene circuits can provide test cases for dynamical models, which could be further exploited in synthetic biology.

Strain-engineering of graphene's electronic structure beyond continuum elasticity

We present a new first-order approach to strain-engineering of graphene's electronic structure where no continuous displacement field u(x,y) is required. The approach is valid for negligible curvature. The theory is directly expressed in terms of atomic displacements under mechanical load, such that one can determine if mechanical strain is varying smoothly at each unit cell, and the extent to which sublattice symmetry holds. Since strain deforms lattice vectors at each unit cell, orthogonality between lattice and reciprocal lattice vectors leads to renormalization of the reciprocal lattice vectors as well, making the K and K′ points shift in opposite directions. From this observation we conclude that no K-dependent gauges enter on a first-order theory. In this formulation of the theory the deformation potential and pseudo-magnetic field take discrete values at each graphene unit cell. We illustrate the formalism by providing strain-generated fields and local density of electronic states on graphene membranes with large numbers of atoms. The present method complements and goes beyond the prevalent approach, where strain engineering in graphene is based upon first-order continuum elasticity.

Coupling-Strength-Independent Long-Period Grating Designs for THz-Bandwidth Optical Differentiators

A novel design of THz-bandwidth all-optical arbitrary-order temporal differentiators using long period fiber/waveguide gratings (LPGs) is proposed and numerically demonstrated. The proposed technique is based on the first-order Born approximation approach in LPGs. We show that an N th-order optical differentiator can be implemented based on an LPG incorporating N π-phase shifts along its length and operating in the cross-coupling mode. The proposed design has a strong tolerance against practical fluctuations in the grating parameters, e.g., as induced during the fabrication process or by environmental fluctuations. In particular, this LPG design solution is essentially insensitive to variations in the grating coupling strength.

Case study: Risk analysis by overtopping of diversion works during dam construction: The La Yesca hydroelectric project, Mexico

A risk analysis-based methodology for the determination of the most economical layout dam–tunnel diversion works is introduced. The aim of the proposed procedure is to identify the least cost layout in terms of the diversion works overtopping risk. The methodology has been built upon the reliability theory advanced first-order second moment approach, and accounts for the probability of the maximum height reached by the upstream water elevation, associated with a design flood (as characterized by its return period), as well as for excavation and lining costs. The proposed procedure has been applied to the La Yesca hydroelectric project in Mexico, currently under operation. It is demonstrated that the use of composite roughness, which consists of lining the floor of the diversion tunnels with hydraulic concrete, while the walls and vault of the tunnels are lined with shotcrete, results in an increase in the discharge capacity of the tunnels, thus leading to a reduction of the overall risk of the project. The importance of economic risk assessments is emphasized and the flexibility of the proposed methodology to account for a suite of risk–cost combinations is shown.

Wave dispersion derived from the square-root Klein–Gordon–Poisson system

AbstractRecently, there has been great interest around quantum relativistic models for plasmas. In particular, striking advances have been obtained by means of the Klein–Gordon–Maxwell system, which provides a first-order approach to the relativistic regimes of quantum plasmas. The Klein–Gordon–Maxwell system provides a reliable model as long as the plasma spin dynamics is not a fundamental aspect, to be addressed using more refined (and heavier) models involving the Pauli–Schrödinger or Dirac equations. In this work, a further simplification is considered, tracing back to the early days of relativistic quantum theory. Namely, we revisit the square-root Klein–Gordon–Poisson system, where the positive branch of the relativistic energy–momentum relation is mapped to a quantum wave equation. The associated linear wave propagation is analyzed and compared with the results in the literature. We determine physical parameters where the simultaneous quantum and relativistic effects can be noticeable in weakly coupled electrostatic plasmas.

Can nucleosomal DNA be described by an elastic model?: Comment on “Sequence-dependent collective properties of DNAs and their role in biological systems” by Pasquale De Santis and Anita Scipioni

Can nucleosomal DNA be described by an elastic model?: Comment on “Sequence-dependent collective properties of DNAs and their role in biological systems” by Pasquale De Santis and Anita Scipioni

Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach

This article studies efficient allocations in a dynamic private information economy with a continuum of idiosyncratic shocks that are persistent. I develop a first-order approach for this environment and show that the problem has a simple recursive structure that relies on only a small number of state variables, making the problem tractable. I find sufficient conditions that guarantee that the first-order approach is valid. To illustrate the first-order approach I numerically compute the efficient allocations in a Mirrleesean economy with productivity shocks that follow a random walk and verify the validity of the first-order approach. I show that persistent shocks create a new trade-off where the social planner decreases the informational rent of the agent today at the cost of providing higher insurance in the future. Copyright 2013, Oxford University Press.

Insurance and Taxation over the Life Cycle

We consider a dynamic Mirrlees economy in a life-cycle context and study the optimal insurance arrangement. Individual productivity evolves as a Markov process and is private information. We use a first-order approach in discrete and continuous time and obtain novel theoretical and numerical results. Our main contribution is a formula describing the dynamics for the labour-income tax rate. When productivity is an AR(1) our formula resembles an AR(1) with a trend where: (i) the auto-regressive coefficient equals that of productivity; (ii) the trend term equals the covariance productivity with consumption growth divided by the Frisch elasticity of labour; and (iii) the innovations in the tax rate are the negative of consumption growth. The last property implies a form of short-run regressivity. Our simulations illustrate these results and deliver some novel insights. The average labour tax rises from 0% to 37% over 40 years, whereas the average tax on savings falls from 12% to 0% at retirement. We compare the second best solution to simple history-independent tax systems, calibrated to mimic these average tax rates. We find that age-dependent taxes capture a sizable fraction of the welfare gains. In this way, our theoretical results provide insights into simple tax systems.

General and specific consciousness: a first-order representationalist approach

It is widely acknowledged that a complete theory of consciousness should explain general consciousness (what makes a state conscious at all) and specific consciousness (what gives a conscious state its particular phenomenal quality). We defend first-order representationalism, which argues that consciousness consists of sensory representations directly available to the subject for action selection, belief formation, planning, etc. We provide a neuroscientific framework for this primarily philosophical theory, according to which neural correlates of general consciousness include prefrontal cortex, posterior parietal cortex, and non-specific thalamic nuclei, while neural correlates of specific consciousness include sensory cortex and specific thalamic nuclei. We suggest that recent data support first-order representationalism over biological theory, higher-order representationalism, recurrent processing theory, information integration theory, and global workspace theory.

Restoring Poissonian Images by a Combined First-Order and Second-Order Variation Approach

The restoration of blurred images corrupted by Poisson noise is an important topic in imaging science. The problem has recently received considerable attention in recent years. In this paper, we propose a combined first-order and second-order variation model to restore blurred images corrupted by Poisson noise. Our model can substantially reduce the staircase effect, while preserving edges in the restored images, since it combines advantages of the first-order and second-order total variation. We study the issues of existence and uniqueness of a minimizer for this variational model. Moreover, we employ a gradient descent method to solve the associated Euler-Lagrange equation. Numerical results demonstrate the validity and efficiency of the proposed method for Poisson noise removal problem.

Optimizations Under Uncertainty Using Gradients, Hessians, and Surrogate Models

In this article, a first-order moment method and a kriging surrogate model are used for optimizations under uncertainty applied to two-bar truss designs and two-dimensional lift-constrained drag minimizations. Given uncertainties in statistically independent, random, normally distributed input variables, the two approaches are used to propagate these uncertainties through the mathematical model and to approximate output statistics of interest. To assess the validity of the approximations, the results are compared with full Monte Carlo simulations. When using first-order moment methods for robust optimizations, first-order sensitivity derivatives appear in the objective function and system constraints. Therefore, second-order sensitivity derivatives are needed for gradient-based optimization approaches. When the kriging surrogate model is used to calculate the objective function value and system constraints, it will be shown that a gradient predictor for the kriging model can be successfully used for gradient-based optimizations. Both the kriging and first-order moment method approaches enable predictions of the mean and variance of quantities of interest while at the same time keeping the computational cost for optimization under uncertainty problems manageable. The novelty of this article is the use of a kriging surrogate model for uncertainty propagation in a gradient-based robust optimization framework.

Potential collapse of the upper slope and tsunami generation on the Great Barrier Reef margin, north-eastern Australia

Analysis of high-resolution multibeam bathymetry and seismic profiles in the Noggin Passage region, north-eastern Australia, has identified a small area (Noggin block) in the upper-slope offshore Cairns that may potentially collapse and generate a tsunami wave. The Noggin block extends from 340 to 470 m depth covering a roughly circular (2.4 km long and 3.7 km wide) area of about 5.3 km2. The well-defined margins of the block correspond to different bounding seabed features. These features include steep headscarps, small landslides and a group of aligned circular pockforms up to 500 m wide and 20 m deep. Slope stability simulations indicate that the Noggin block is stable under normal present-day gravitational conditions on the upper slope. However, block failure may result under external loads, such as those produced by earthquakes. Failure modelling shows that critical peak horizontal accelerations of 0.2–0.4 g could lead to the collapse of the Noggin block. In north-eastern Australia, these acceleration values would involve earthquakes generated at short hypocentral distances and short periods. The collapse of the potential sediment slide mass of about 0.86 km3 (162 m average thickness) may lead to the formation of a landslide-generated tsunami wave. Semi-empirical equations indicate the collapse of this mass would yield a 7–11-m high three-dimensional tsunami wave. These waves could reach an estimated run-up height at the coast of 5–7 m. Our first-order approach highlights the potential consequences for nearby coastal communities, the need for better sediment characterisation in the study area, and the systematic identification of other areas prone to slope failures along the Great Barrier Reef margin.