On the Lagrange and Markov Dynamical Spectra for Geodesic Flows in Surfaces with Negative Curvature

We consider the Lagrange and the Markov dynamical spectra associated to a geodesic flow on a surface of negative curvature. We show that for a large set of real functions on the unit tangent bundle and for typical metrics with negative curvature and finite volume, both the Lagrange and the Markov dynamical spectra have non-empty interior

Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak

It is well-known that size-adjustments based on Edgeworth expansions for the t-statistic perform poorly when instruments are weakly correlated with the endogenous explanatory variable. This paper shows, however, that the lack of Edgeworth expansions and bootstrap validity are not tied to the weak instrument framework, but instead depends on which test statistic is examined. In particular, Edgeworth expansions are valid for the score and conditional likelihood ratio approaches, even when the instruments are uncorrelated with the endogenous explanatory variable. Furthermore, there is a belief that the bootstrap method fails when instruments are weak, since it replaces parameters with inconsistent estimators. Contrary to this notion, we provide a theoretical proof that guarantees the validity of the bootstrap for the score test, as well as the validity of the conditional bootstrap for many conditional tests. Monte Carlo simulations show that the bootstrap actually decreases size distortions in both cases.

Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak

It is well-known that size-adjustments based on Edgeworth expansions for the t-statistic perform poorly when instruments are weakly correlated with the endogenous explanatory variable. This paper shows, however, that the lack of Edgeworth expansions and bootstrap validity are not tied to the weak instrument framework, but instead depends on which test statistic is examined. In particular, Edgeworth expansions are valid for the score and conditional likelihood ratio approaches, even when the instruments are uncorrelated with the endogenous explanatory variable. Furthermore, there is a belief that the bootstrap method fails when instruments are weak, since it replaces parameters with inconsistent estimators. Contrary to this notion, we provide a theoretical proof that guarantees the validity of the bootstrap for the score test, as well as the validity of the conditional bootstrap for many conditional tests. Monte Carlo simulations show that the bootstrap actually decreases size distortions in both cases.

Hausdorff measures and the Morse-Sard theorem

Let F : U [contained in] Rn --> Rm be a differentiable function and p < m an integer. If k [greater than or equal] 1 is an integer, [alpha] [member of] [0, 1] and F [member of] Ck+([alpha]), if we set Cp(F) = {x [member of] U $r ank(Df(x)) [less than or equal] p} then the Hausdorff measure of dimension [formula] of F(Cp(F)) is zero

An Extremal Problem in the Hypercube and Optimization of Asynchronous Circuits

AbstractWe prove that if m≥ 2, then the minimumk∈N such that the k -cube {0, 1}kcan be decomposed as the disjoint union of m connected adjacent subsets satisfies 2log2m−log2log2m− 1 ≤k≤ 2⌈log2m⌉ − ⌊log2log2m⌋ + 5

Ischemic liver lesions mimicking neoplasm in a patient with severe chronic mesenteric ischemia

Chronic mesenteric ischemia most frequently presents with abdominal pain, weight loss, and food fear. Ischemic involvement of the liver is infrequent because of the dual blood supply via the portal vein and hepatic artery. Hepatic infarction has been associated with embolization, thrombosis, arterial injury, prothrombotic states, and impairment of portal venous flow. We report a patient with chronic mesenteric ischemia and severe mesenteric arterial disease who presented with large liver masses suspicious for neoplasm. Tissue samples from two hepatic biopsies confirmed ischemic lesions. After open surgical mesenteric revascularization, the patient had complete symptom improvement and nearly complete regression of the liver lesions

FRIDA, a Framework for Software Design, Applied in the Treatment of Children with Autistic Disorder.

The “FRIDA” framework is a guide for the agile development of accessible software for users with Autism Spectrum Disorder (ASD), as a tool for strengthening emotional and social skills in the treatment of autism. It is based on the use of accessible software for the development of emotional and social skills, and designed with a focus on the user with intellectual disabilities. A mixed quasi-experimental study is carried out with three focus groups: children with ASD, expert therapists in ASD treatments and software designers adapting the Design Thinking model for the co-creation of the functional characteristics of the software and its use in therapies. The findings and results show that using FRIDA facilitates the agile design of accessible apps by reducing their development time by 94% and increasing their usability level by more than 90%. This facilitates the treatment of people with ASD, especially in the development of emotional self-recognition skills and social adaptation. The experience applied collaborative design thinking models and agile software design methodologies, articulating knowledge between software developers, therapists, and families of users with ASD. Users were characterized separately, and the functionalities required for the software that would be developed and linked in the treatment of autism were identified.post-print5958 K