A note on generalized Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalities

The main result of this paper supports a conjecture by C. P\'erez and E. Rela about the properties of the weight appearing in their recent self-improving result of generalized inequalities of Poincar\'e-type in the Euclidean space. The result we obtain does not need any condition on the weight, but still is not fully satisfactory, even though the result by P\'erez and Rela is obtained as a corollary of ours. Also, we extend the conclusions of their theorem to the range $p<1$. As an application of our result, we give a unified vision of weighted improved Poincar\'e-type inequalities in the Euclidean setting, which gathers both weighted improved classical and fractional Poincar\'e inequalities within an approach which avoids any representation formula. We obtain results related to some already existing results in the literature and furthermore we improve them in some aspects. Finally, we also explore analog inequalities in the context of metric spaces by means of the already known self-improving results in this setting.La Caixa gran

Improved fractional Poincaré type inequalities in John domains

We obtain improved fractional Poincaré inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $\mu$ under some mild regularity conditions on the measure $\mu$. We also give sufficient conditions on a bounded domain to support fractional Poincaré type inequalities in this setting.Universidad Nacional de La Plata, under grant 11/X805 Universidad de Buenos Aires, under grant 20020120100050BA Agencia Nacional de Promoción Científica y Tecnológica, under grant PICT 2014-177

On Bloom type estimates for iterated commutators of fractional integrals

In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse domination that we provide as well in this paper and also in techniques de- veloped in the recent paper [22]. We extend as well the necessity established in [15] to iterated commutators providing a new proof. As a consequence of the preceding results we recover the one weight estimates in [7, 1] and es- tablish the sharpness in the iterated case. Our result provides as well a new characterization of the BMO space

On the BBM-Phenomenon in Fractional Poincaré–Sobolev Inequalities with Weights

In this paper, we unify and improve some of the results of Bourgain, Brezis, and Mironescu and the weighted Poincaré–Sobolev estimate by Fabes, Kenig, and Serapioni. More precisely, we get weighted counterparts of the Poincaré–Sobolev-type inequality and also of the Hardy type inequality in the fractional case under some mild natural restrictions. A main feature of the results we obtain is the fact that we keep track of the behavior of the constants involved when the fractional parameter approaches to 1. Our main method is based on techniques coming from harmonic analysis related to the self-improving property of generalized Poincaré inequalities

MAXIMAL OPERATORS ON THE INFINITE-DIMENSIONAL TORUS

We study maximal operators related to bases on the infinite- dimensional torus Tω. For the normalized Haar measure dx on Tω it is known that MR0, the maximal operator associated with the dyadic basis R0, is of weak type (1,1), but MR, the operator associated with the natural general basis R, is not. We extend the latter result to all q ∈ [1, ∞). Then we find a wide class of intermediate bases R0 ⊂ R′ ⊂ R, for which maximal functions have controlled, but sometimes very peculiar behavior. Precisely, for given q0 ∈ [1, ∞) we construct R′ such that M R′ is of restricted weak type (q, q) if and only if q belongs to a predetermined range of the form (q0,∞] or [q0,∞]. Finally, we study the weighted setting, considering the Muckenhoupt ARp (Tω) and reverse Hölder RHRr (Tω) classes of weights associated with R. For each p ∈ (1,∞) and each w ∈ ARp (Tω) we obtain that MR is not bounded on Lq(w) in the whole range q ∈ [1, ∞). Since we are able to show that ARp (Tω)= RHRr (Tω), p∈(1,∞) r∈(1,∞) the unboundedness result applies also to all reverse Hölder weights

In vivo CRISPR/Cas9 targeting of fusion oncogenes for selective elimination of cancer cells

This work was supported by CaixaImpulse (CI18-00017;FuGe) to S.R-P. RT-R. is supported by a postdoctoral fellowship from the Asociación Española Contra el Cáncer (AECC). J.C.S. is supported by the Spanish Cell Therapy cooperative research network (TERCEL)(RD16/0011/0011). P.M. also acknowledges the financial support from the Obra Social La Caixa-Fundaciò Josep Carreras. P.M. is an investigator of the Spanish Cell Therapy cooperative research network (TERCEL). A.M.C. acknowledges funding fromXarxa de Bancs de Tumors de Catalunya (XBTC; sponsored by Pla Director d'Oncologia de Catalunya).Fusion oncogenes (FOs) are common in many cancer types and are powerful drivers of tumor development. Because their expression is exclusive to cancer cells and their elimination induces cell apoptosis in FO-driven cancers, FOs are attractive therapeutic targets. However, specifically targeting the resulting chimeric products is challenging. Based on CRISPR/Cas9 technology, here we devise a simple, efficient and non-patient-specific gene-editing strategy through targeting of two introns of the genes involved in the rearrangement, allowing for robust disruption of the FO specifically in cancer cells. As a proof-of-concept of its potential, we demonstrate the efficacy of intron-based targeting of transcription factors or tyrosine kinase FOs in reducing tumor burden/mortality in in vivo models. The FO targeting approach presented here might open new horizons for the selective elimination of cancer cells

Comparación de distintas estrategias para la predicción de muerte a corto plazo en el paciente anciano infectado

Objective. The aim of this study was to determine the utility of a post hoc lactate added to SIRS and qSOFA score to predict 30-day mortality in older non-severely dependent patients attended for infection in the Emergency Department (ED). Methods. We performed an analytical, observational, prospective cohort study including patients of 75 years of age or older, without severe functional dependence, attended for an infectious disease in 69 Spanish ED for 2-day three seasonal periods. Demographic, clinical and analytical data were collected. The primary outcome was 30-day mortality after the index event. Results. We included 739 patients with a mean age of 84.9 (SD 6.0) years; 375 (50.7%) were women. Ninety-one (12.3%) died within 30 days. The AUC was 0.637 (IC 95% 0.587-0.688; p= 2 and 0.698 (IC 95% 0.635- 0.761; p= 2. Comparing receiver operating characteristic (ROC) there was a better accuracy of qSOFA vs SIRS (p=0.041). Both scales improve the prognosis accuracy with lactate inclusion. The AUC was 0.705 (IC95% 0.652-0.758; p<0.001) for SIRS plus lactate and 0.755 (IC95% 0.696-0.814; p<0.001) for qSOFA plus lactate, showing a trend to statistical significance for the second strategy (p=0.0727). Charlson index not added prognosis accuracy to SIRS (p=0.2269) or qSOFA (p=0.2573). Conclusions. Lactate added to SIRS and qSOFA score improve the accuracy of SIRS and qSOFA to predict short-term mortality in older non-severely dependent patients attended for infection. There is not effect in adding Charlson index

In vivo CRISPR/Cas9 targeting of fusion oncogenes for selective elimination of cancer cells

This work was supported by CaixaImpulse (CI18-00017;FuGe) to S.R-P. RT-R. is supported by a postdoctoral fellowship from the Asociación Española Contra el Cáncer (AECC). J.C.S. is supported by the Spanish Cell Therapy cooperative research network (TERCEL)(RD16/0011/0011). P.M. also acknowledges the financial support from the Obra Social La Caixa-Fundaciò Josep Carreras. P.M. is an investigator of the Spanish Cell Therapy cooperative research network (TERCEL). A.M.C. acknowledges funding fromXarxa de Bancs de Tumors de Catalunya (XBTC; sponsored by Pla Director d'Oncologia de Catalunya).Fusion oncogenes (FOs) are common in many cancer types and are powerful drivers of tumor development. Because their expression is exclusive to cancer cells and their elimination induces cell apoptosis in FO-driven cancers, FOs are attractive therapeutic targets. However, specifically targeting the resulting chimeric products is challenging. Based on CRISPR/Cas9 technology, here we devise a simple, efficient and non-patient-specific gene-editing strategy through targeting of two introns of the genes involved in the rearrangement, allowing for robust disruption of the FO specifically in cancer cells. As a proof-of-concept of its potential, we demonstrate the efficacy of intron-based targeting of transcription factors or tyrosine kinase FOs in reducing tumor burden/mortality in in vivo models. The FO targeting approach presented here might open new horizons for the selective elimination of cancer cells