Sharp Bounds on Heterogeneous Individual Treatment Responses

This paper discusses how to identify individual-specific causal effects of an ordered discrete endogenous variable. The counterfactual heterogeneous causal information is recovered by identifying the partial differences of a structural relation. The proposed refutable nonparametric local restrictions exploit the fact that the pattern of endogeneity may vary across the level of the unobserved variable. The restrictions adopted in this paper impose a sense of order to an unordered binary endogeneous variable. This allows for a uni.ed structural approach to studying various treatment effects when self-selection on unobservables is present. The usefulness of the identi.cation results is illustrated using the data on the Vietnam-era veterans. The empirical findings reveal that when other observable characteristics are identical, military service had positive impacts for individuals with low (unobservable) earnings potential, while it had negative impacts for those with high earnings potential. This heterogeneity would not be detected by average effects which would underestimate the actual effects because different signs would be cancelled out. This partial identification result can be used to test homogeneity in response. When homogeneity is rejected, many parameters based on averages may deliver misleading information.

Sharp A₂ inequality for haar shift operators

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Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Weak-type estimates for Haar shift operators: Sharp power on the A(p) characteristic

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Positive occipital sharp transients of sleep (POSTS): a reappraisal.

OBJECTIVE: Positive occipital sharp transients of sleep (POSTS) are considered a normal variant seen in non-REM sleep; their asymmetrical presentation and relationship with EEG abnormalities have received scarce attention to date. We analyzed these features in a large prospective EEG recordings' sample. METHODS: In this case-control study, over 6 months we collected consecutive patients showing POSTS on their EEG. They were matched with consecutive control subjects (two for each). Demographical data, asymmetries for POSTS and alpha activity, and lateralized or diffuse occurrence of EEG abnormalities (slowing, epileptiform transients) were compared among these two groups. RESULTS: Out of 1254 EEG studies, 102 (8%) patients showed POSTS. They were younger (p=0.031), and more likely to show EEG abnormalities (p=0.008) - including epileptiform transients (p=0.002) - than controls. However, this relationship was influenced by age and recording length. Thirty nine POSTS recordings (38%) had a consistent amplitude asymmetry, but this was not associated with specific EEG abnormalities or alpha asymmetry. CONCLUSION: POSTS are a normal EEG variant, occurring in less than 10% of unselected EEG recordings, mostly in younger adults, without gender predominance. Amplitude asymmetries are found in over one third of subjects. SIGNIFICANCE: POSTS asymmetry, as opposed to other sleep transients, should be considered as normal.

A sharp Remez inequality for trigonometric polynomials

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Traitement du décollement de rétine du pseudophaque: étude rétrospective comparant la vitrectomie sans indentation au traitement ab-externo [Vitrectomy without scleral buckle versus ab-externo approach for pseudophakic retinal detachment: comparative retrospective study].

PURPOSE: Retinal detachment (RD) is a major complication of cataract surgery, which can be treated by either primary vitrectomy without indentation or the scleral buckling procedure. The aim of this study is to compare the results of these two techniques for the treatment of pseudophakic RD. PATIENTS AND METHODS: The charts of 40 patients (40 eyes) treated with scleral buckling for a primary pseudophakic RD were retrospectively studied and compared to the charts of 32 patients (32 eyes) treated with primary vitrectomy without scleral buckle during the same period by the same surgeons. To obtain comparable samples, patients with giant retinal tears, vitreous hemorrhage, and severe preoperative proliferative vitreoretinopathy (PVR) were not included. Minimal follow-up was 6 months. RESULTS: The primary success rate was 84% in the vitrectomy group and 82.5% in the ab-externo group. Final anatomical success was observed in 100% of cases in the vitrectomy group and in 95% of cases in the ab-externo group. Final visual acuity was 0.5 or better in 44% of cases in the vitrectomy group and 37.5% in the ab-externo group. The duration of the surgery was significantly lower in the ab-externo group, whereas the hospital stay tended to be lower in the vitrectomy group. In the vitrectomy group, postoperative PVR developed in 3 eyes and new or undetected breaks were responsible for failure of the initial procedure in 2 eyes. CONCLUSION: Primary vitrectomy appears to be as effective as scleral buckling procedures for the treatment of pseudophakic RD.

A species delimitation approach in the Trochulus sericeus/hispidus complex reveals two cryptic species within a sharp contact zone.

BACKGROUND: Mitochondrial DNA sequencing increasingly results in the recognition of genetically divergent, but morphologically cryptic lineages. Species delimitation approaches that rely on multiple lines of evidence in areas of co-occurrence are particularly powerful to infer their specific status. We investigated the species boundaries of two cryptic lineages of the land snail genus Trochulus in a contact zone, using mitochondrial and nuclear DNA marker as well as shell morphometrics. RESULTS: Both mitochondrial lineages have a distinct geographical distribution with a small zone of co-occurrence. In the same area, we detected two nuclear genotype clusters, each being highly significantly associated to one mitochondrial lineage. This association however had exceptions: a small number of individuals in the contact zone showed intermediate genotypes (4%) or cytonuclear disequilibrium (12%). Both mitochondrial lineage and nuclear cluster were statistically significant predictors for the shell shape indicating morphological divergence. Nevertheless, the lineage morphospaces largely overlapped (low posterior classification success rate of 69% and 78%, respectively): the two lineages are truly cryptic. CONCLUSION: The integrative approach using multiple lines of evidence supported the hypothesis that the investigated Trochulus lineages are reproductively isolated species. In the small contact area, however, the lineages hybridise to a limited extent. This detection of a hybrid zone adds an instance to the rare reported cases of hybridisation in land snails.

A sharp concentration inequality with applications

We present a new general concentration-of-measure inequality and illustrate its power by applications in random combinatorics. The results find direct applications in some problems of learning theory.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.