A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation

In this note we formulate a sufficient condition for the quasiconvexity at $x \mapsto \lambda x$ of certain functionals $I(u)$ which model the stored-energy of elastic materials subject to a deformation $u$. The materials we consider may cavitate, and so we impose the well-known technical condition (INV), due to M\"{u}ller and Spector, on admissible deformations. Deformations obey the condition $u(x)= \lambda x$ whenever $x$ belongs to the boundary of the domain initially occupied by the material. In terms of the parameters of the models, our analysis provides an explicit upper bound on those $\lambda>0$ such that $I(u) \geq I(u_{\lambda})$ for all admissible $u$, where $u_{\lambda}$ is the linear map $x \mapsto \lambda x$ applied across the entire domain. This is the quasiconvexity condition referred to above

The Strong Law of Demand

We show that a demand function is derived from maximizing a quasilinear utility function subject to a budget constraint if and only if the demand function is cyclically monotone. On finite data sets consisting of pairs of market prices and consumption vectors, this result is equivalent to a solution of the Afriat inequalities where all the marginal utilities of income are equal. We explore the implications of these results for maximization of a random quasilinear utility function subject to a budget constraint and for representative agent general equilibrium models. The duality theory for cyclically monotone demand is developed using the Legendre-Fenchel transform. In this setting, a consumer's surplus is measured by the conjugate of her utility function.Permanent income hypothesis, Afriat's theorem, Law of demand, Consumer's surplus, Testable restrictions

Rationalizing and Curve-Fitting Demand Data with Quasilinear Utilities

In the empirical and theoretical literature a consumer's utility function is often assumed to be quasilinear. In this paper we provide necessary and sufficient conditions for testing if the consumer acts as if she is maximizing a quasilinear utility function over her budget set. If the consumer's choices are inconsistent with maximizing a quasilinear utility function over her budget set, then we compute the "best" quasilinear rationalization of her choices.Quasilinear utilities, Afriat inequalities, Curve-fitting

Distinct subsets of unmyelinated primary sensory fibers mediate behavioral responses to noxious thermal and mechanical stimuli

Behavioral responses to painful stimuli require peripheral sensory neurons called nociceptors. Electrophysiological studies show that most C-fiber nociceptors are polymodal (i.e., respond to multiple noxious stimulus modalities, such as mechanical and thermal); nevertheless, these stimuli are perceived as distinct. Therefore, it is believed that discrimination among these modalities only occurs at spinal or supraspinal levels of processing. Here, we provide evidence to the contrary. Genetic ablation in adulthood of unmyelinated sensory neurons expressing the G protein-coupled receptor Mrgprd reduces behavioral sensitivity to noxious mechanical stimuli but not to heat or cold stimuli. Conversely, pharmacological ablation of the central branches of TRPV1+ nociceptors, which constitute a nonoverlapping population, selectively abolishes noxious heat pain sensitivity. Combined elimination of both populations yielded an additive phenotype with no additional behavioral deficits, ruling out a redundant contribution of these populations to heat and mechanical pain sensitivity. This double-dissociation suggests that the brain can distinguish different noxious stimulus modalities from the earliest stages of sensory processing

Adaptive template matching algorithm based on SWAD for robust target tracking

The sum of absolute differences (SAD) is widely used in video coding and disparity computation for its simplicity. However, SAD is not very common in tracking applications owing to issues like partial occlusion and target changes, which can dramatically affect its performance. Presented is a novel adaptive template matching algorithm for target tracking, based on a sum of weighted absolute differences (SWAD). The target template is updated using an infinite impulse response filter, while a weighting kernel is adopted to reduce the effects of partial occlusion. Simulation results demonstrate that the proposed tracker outperforms conventional SAD in terms of efficiency and accuracy, and its performance is comparable with more complex trackers, such as the mean shift algorith

The Chicago Family Case Management Demonstration: Developing a New Model for Serving "Hard to House" Public Housing Families

Describes the design, development, and implementation of an initiative to provide families with enhanced case management, including relocation services, workforce support, and financial literacy training. Presents baseline findings from a resident survey

AN ANALYSIS OF NONIGNORABLE NONRESPONSE IN A SURVEY WITH A ROTATING PANEL DESIGN

Missing values to income questions are common in survey data. When the probabilities of nonresponse are assumed to depend on the observed information and not on the underlining unobserved amounts, the missing income values are missing at random (MAR), and methods such as sequential multiple imputation can be applied. However, the MAR assumption is often considered questionable in this context, since missingness of income is thought to be related to the value of income itself, after conditioning on available covariates. In this article we describe a sensitivity analysis based on a pattern-mixture model for deviations from MAR, in the context of missing income values in a rotating panel survey. The sensitivity analysis avoids the well-known problems of underidentification of parameters of non-MAR models, is easy to carry out using existing sequential multiple imputation software and has a number of novel features

The Strong Law of Demand

We show that a demand function is derived from maximizing a quasilinear utility function subject to a budget constraint if and only if the demand function is cyclically monotone. On finite data sets consisting of pairs of market prices and consumption vectors, this result is equivalent to a solution of the Afriat inequalities where all the marginal utilities of income are equal. We explore the implications of these results for maximization of a random quasilinear utility function subject to a budget constraint and for representative agent general equilibrium models. The duality theory for cyclically monotone demand is developed using the Legendre-Fenchel transform. In this setting, a consumer’s surplus is measured by the conjugate of her utility function