Sharp weighted estimates for approximating dyadic operators

We give a new proof of the sharp weighted $L^2$ inequality ||T||_{L^2(w)} \leq c [w]_{A_2} where $T$ is the Hilbert transform, a Riesz transform, the Beurling-Ahlfors operator or any operator that can be approximated by Haar shift operators. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner to estimate the oscillation of dyadic operators.Comment: To appear in the Electronic Research Announcements in Mathematical Science

Electroencephalographic Brain Dynamics of Memory Encoding in Emotionally Arousing Context

Emotional content/context enhances declarative memory through modulation of encoding and retrieval mechanisms. At encoding, neurophysiological data have consistently demonstrated the subsequent memory effect in theta and gamma oscillations. Yet, the existing studies were focused on the emotional content effect and let the emotional context effect unexplored. We hypothesized that theta and gamma oscillations show higher evoked/induced activity during the encoding of visual stimuli when delivered in an emotionally arousing context. Twenty-five healthy volunteers underwent evoked potentials (EP) recordings using a 21 scalp electrodes montage. They attended to an audiovisual test of emotional declarative memory being randomly assigned to either emotionally arousing or neutral context. Visual stimulus presentation was used as the time-locking event. Grand-averages of the EP and evoked spectral perturbations were calculated for each volunteer. EP showed a higher negative deflection from 80 to 140 ms for the emotional condition. Such effect was observed over central, frontal and prefrontal locations bilaterally. Evoked theta power was higher in left parietal, central, frontal, and prefrontal electrodes from −50 to 300 ms in the emotional condition. Evoked gamma power was higher in the emotional condition with a spatial distribution that overlapped at some points with the theta topography. The early theta power increase could be related to expectancy induced by auditory information processing that facilitates visual encoding in emotional contexts. Together, our results suggest that declarative memory enhancement for both emotional content and emotional context are supported by similar neural mechanisms at encoding, and offer new evidence about the brain processing of relevant environmental stimuli

Neutrophil Role in Periodontal Disease

Oral tissues are constantly exposed to damage from the mechanical effort of eating and from the invasion of foreign microorganisms such as bacteria, fungi, and virus. In healthy oral tissues, there is a balance between symbiotic bacteria and cells from the innate immune system, mainly neutrophils. When this balance is broken, inflammation appears and more immune cells are recruited to the gingiva. Neutrophils form a barrier against dysbiotic bacteria. However, when neutrophils are insufficient, bacteria thrive causing periodontitis, a chronic inflammatory disease that destroys the tooth‐supporting tissues or periodontium. Damage of periodontal tissues leads to tooth loss, and in severe cases, it can also affect systemic health by increasing a person\u27s risk for atherosclerosis, rheumatoid arthritis, diabetes, and even cancer. The mechanisms neutrophil employ to keep a balance with bacteria in order to maintain healthy oral tissues is the focus of this chapter. We discuss how neutrophil antimicrobial functions keep bacteria at check and how some dysbiotic bacteria block neutrophils to promote an inflammatory state. Also, novel therapeutic approaches for periodontitis are discussed

Neutrophil Activation by Antibody Receptors

Neutrophils, the most abundant leukocytes in blood, are relevant cells of both the innate and the adaptive immune system. Immunoglobulin (Ig) G antibody molecules are crucial activators of neutrophils. IgGs identify many types of pathogens via their two Fab portions and are in turn detected through their Fc portion by specific Fcγ receptors (FcγRs) on the membrane of neutrophils. Thus, antibodies bring the specificity of the adaptive immune response to the potent antimicrobial and inflammatory functions of neutrophils. Two types of FcγRs with several polymorphic variants exist on the human neutrophil. These receptors are considered to be redundant in inducing cell responses. Yet, new evidence presented in recent years on how the particular IgG subclass and the glycosylation pattern of the antibody modulate the IgG–FcγR interaction has suggested that a particular effector function may in fact be activated in response to a specific type of FcγR. In this chapter, we describe the main types of FcγRs on neutrophils and our current view on how particular FcγRs activate various signaling pathways to promote unique effector cell functions, including phagocytosis, activation of integrins, nuclear factor activation, and formation of neutrophil extracellular traps (NETs)

Sharp weighted estimates for classical operators

We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner to estimate the oscillation of dyadic operators. Our method is flexible enough to prove the corresponding sharp one-weight norm inequalities for some operators of harmonic analysis: the maximal singular integrals associated to $T$, Dyadic square functions and paraproducts, and the vector-valued maximal operator of C. Fefferman-Stein. Also we can derive a very sharp two-weight bump type condition for $T$.Comment: We improve different parts of the first version, in particular we show the sharpness of our theorem for the vector-valued maximal functio

Estimación bayesiana de una proporción bajo error de estimación asimétrico

El proceso de estimación de una proporción relacionada con una pregunta que puede ser altamente sensible para el encuestado, puede generar respuestas que no necesariamente coinciden con la realidad. Para reducir la probabilidad de respuestas falsas a este tipo de preguntas algunos autores han propuesto técnicas de respuesta aleatorizada asumiendo un error de observación asimétrico. En este artículo se presenta una generalización al caso donde se asume un error simétrico lo cual puede ser un supuesto poco realista en la práctica. Se deduce la función de verosimilitud bajo el supuesto de error de estimación asimétrico.El proceso de estimación de una proporción relacionada con una pregunta que puede ser altamente sensible para el encuestado, puede generar respuestas que no necesariamente coinciden con la realidad. Para reducir la probabilidad de respuestas falsas a este tipo de preguntas algunos autores han propuesto técnicas de respuesta aleatorizada asumiendo un error de observación asimétrico. En este artículo se presenta una generalización al caso donde se asume un error simétrico lo cual puede ser un supuesto poco realista en la práctica. Se deduce la función de verosimilitud bajo el supuesto de error de estimación asimétrico

Two weight extrapolation via the maximal operator

We give several extrapolation theorems for pairs of weights of the form (w, Mkw) and (w, (Mw/w)r w), where w is any non-negative function, r>1, and Mk is the kth iterate of the Hardy–Littlewood maximal operator. As an application we show that our results can be used to extend and sharpen results for square functions and singular integral operators by Chang et al. (1985, Comment. Math. Helv.60, 217–246), Chanillo and Wheeden (1987, Indiana Univ. Math. J.36, 277–294), Wilson (1987, Duke Math. J.55, 879–887; 1989, Trans. Amer. Math. Soc.314, 661–692; 1989, Illinois J. Math.33, 361–366), and Uchiyama (1995, Studia Math.115, 135–149). In the process we prove a conjecture due to Wilson.Dirección General de Investigación Científica y Técnic