On the degree of regularity of a certain quadratic Diophantine equation

We show that, for every positive integer r, there exists an integer b = b(r) such that the 4-variable quadratic Diophantine equation (x1 − y1)(x2 − y2) = b is r-regular. Our proof uses Szemerédi’s theorem on arithmetic progressions

Equation-regular sets and the Fox–Kleitman conjecture

Given k ≥ 1, the Fox–Kleitman conjecture from 2006 states that there exists a nonzero integer b such that the 2k-variable linear Diophantine equation ∑k i=1 (xi − yi) = b is (2k − 1)-regular. This is best possible, since Fox and Kleitman showed that for all b ≥ 1, this equation is not 2k-regular. While the conjecture has recently been settled for all k ≥ 2, here we focus on the case k = 3 and determine the degree of regularity of the corresponding equation for all b ≥ 1. In particular, this independently confirms the conjecture for k = 3. We also briefly discuss the case k = 4

Numerical semigroups of Szemerédi type

Given any length k ≥ 3 and density 0 < δ ≤ 1, we introduce and study the set Sz(k, δ) consisting of all positive integers n such that every subset of {1, 2, . . . , n} of density at least δ contains an arithmetic progression of length k. A famous theorem of Szemerédi guarantees that this set is not empty. We show that Sz(k, δ)∪{0} is a numerical semigroup and we determine it for (k, δ) = (4, 1/2) and for more than thirty pairs (3, δ) with δ > 1/5

Vascular Dysfunction in a Transgenic Model of Alzheimer's Disease: Effects of CB1R and CB2R Cannabinoid Agonists

There is evidence of altered vascular function, including cerebrovascular, in Alzheimer's disease (AD) and transgenic models of the disease. Indeed vasoconstrictor responses are increased, while vasodilation is reduced in both conditions. β-Amyloid (Aβ) appears to be responsible, at least in part, of alterations in vascular function. Cannabinoids, neuroprotective and anti-inflammatory agents, induce vasodilation both in vivo and in vitro. We have demonstrated a beneficial effect of cannabinoids in models of AD by preventing glial activation. In this work we have studied the effects of these compounds on vessel density in amyloid precursor protein (APP) transgenic mice, line 2576, and on altered vascular responses in aortae isolated ring. First we showed increased collagen IV positive vessels in AD brain compared to control subjects, with a similar increase in TgAPP mice, which was normalized by prolonged oral treatment with the CB1/CB2 mixed agonist WIN 55,212-2 (WIN) and the CB2 selective agonist JWH-133 (JWH). In Tg APP mice the vasoconstriction induced by phenylephrine and the thromboxane agonist U46619 was significantly increased, and no change in the vasodilation to acetylcholine (ACh) was observed. Tg APP displayed decreased vasodilation to both cannabinoid agonists, which were able to prevent decreased ACh relaxation in the presence of Aβ. In summary, we have confirmed and extended the existence of altered vascular responses in Tg APP mice. Moreover, our results suggest that treatment with cannabinoids may ameliorate the vascular responses in AD-type pathology.This work was supported by the Council of Madrid (S- BIO/0170/2006 and P2010/BMD-2349 to MLC) and by Instituto de Salud Carlos III/FISS (PI12/00590 to TT). AM received a fellowship from the Spanish Ministry of Education and Science and JN-D from FISS. Dr. R. Martínez-Murillo is acknowledged for preliminary EM experiments.Peer reviewedPeer Reviewe

On the finiteness of some n-color Rado numbers

For integers k, n, c with k, n ≥ 1, the n-color Rado number Rk(n, c) is defined to be the least integer N if any, or infinity otherwise, such that for every n-coloring of the set {1, 2, . . . , N}, there exists a monochromatic solution in that set to the linear equation x1 + x2 + · · · + xk + c = xk+1. A recent conjecture of ours states that Rk(n, c) should be finite if and only if every divisor d ≤ n of k−1 also divides c. In this paper, we complete the verification of this conjecture for all k ≤ 7. As a key tool, we first prove a general result concerning the degree of regularity over subsets of Z of some linear Diophantine equations

Decoration of squalenoyl-gemcitabine nanoparticles with squalenyl-hydroxybisphosphonate for the treatment of bone tumors

Therapeutic perspectives of bone tumors such as osteosarcom are main restricted due to the inefficacy of current treatments. We propose here the construction of a novel anticancers qualene-based nanomedicine with bone affinity and retention capacity. A squalenyl-hydroxybisphosphonate molecule was synthetized by chemical conjugation of a 1-hydroxyl-1,1-bi-sphosphonatemoiety to the squalenechain. This amphiphilic compound was inserted onto squalenoyl-gemcitabinenano-particles using the nanoprecipitation method. The co-assemblyled to nanoconstructsof 75 nm, with different morphology and colloidal properties. The presence of squalenyl-hydroxybi-sphosphonate enhanced the nanoparticles binding affinity for hydroxyapatite,a mineral present in the bone. Moreover, the in vitro anticancer activity was preserved when tested in commercial and patient-treated derived pedia tricoste osarcomacells. Furtherin vivo studies will shed lighton the potential of these nano medicines for the treatment of bones arcomas

Whole-Exome sequencing reveals recurrent but heterogeneous mutational profiles in sporadic who grade 1 meningiomas

© 2021 González-Tablas, Prieto, Arandia, Jara-Acevedo, Otero, Pascual, Ruíz, Álvarez-Twose, García-Montero, Orfao and Tabernero.Human WHO grade 1 meningiomas are generally considered benign tumors; despite this, they account for ≈50% of all recurrent meningiomas. Currently, limited data exist about the mutational profiles of grade 1 meningiomas and patient outcome. We investigated the genetic variants present in 32 WHO grade 1 meningiomas using whole exome sequencing, and correlated gene mutational profiles with tumor cytogenetics and patient outcome. Overall, WHO grade 1 meningiomas harbored numerous and heterogeneous genetic variants, which most frequently affected the NF2 (47%) gene and to a less extent the PNMA6A (22%), TIGD1 (16%), SMO (13%), PTEN (13%), CREG2 (9%), EEF1A1 (6%), POLR2A (6%), ARID1B (3%), and FAIM3 (3%) genes. Notably, non-synonymous genetic variants of SMO and POLR2A were restricted to diploid meningiomas, whereas NF2 mutations were only found among tumors that showed -22/22q─ (with or without a complex karyotype). Based on NF2 mutations and tumor cytogenetics, four genetic profiles were defined with an impact on patient recurrence-free survival (RFS). These included (1) two good-prognosis tumor subgroups—diploid meningiomas (n=9) and isolated -22/22q─ associated with NF2 mutation (n=7)—with RFS rates at 10 y of 100%; and (2) two subgroups of poor-prognosis meningiomas—isolated -22/22q─ without NF2 mutation (n=3) and tumors with complex karyotypes (n=11)—with a RFS rate at 10 y of 48% (p=0.003). Our results point out the existence of recurrent but heterogeneous mutational profiles in WHO grade 1 meningiomas which have an impact on patient outcome.This work was supported by grants: IBY 17/00002 from IBSAL (Salamanca, Spain), GRS2132/A2020 from Junta de Castilla y León (Spain), and CB16/12/00400 from CIBER-ONC and FONDOS FEDER (Instituto de Salud Carlos III, Ministerio de Economía y Competitividad, Madrid, Spain)

Ajustes y validación de CropSyst para la determinación del consumo hídrico en el viñedo

En las condiciones climáticas dominantes en las principales zonas vitícolas extremeñas la disponibilidad de agua determina en buena medida la productividad del viñedo. La determinación del consumo hídrico en el viñedo es necesaria para una correcta gestión del riego, por lo que el desarrollo de metodologías que ayuden a su determinación sería de gran utilidad para la viticultura. Nuestro estudio evaluó la capacidad del modelo de simulación de cultivo CropSyst (CS) a la hora de predecir el consumo hídrico, el desarrollo vegetativo y el estado hídrico de un viñedo cv. Tempranillo. Para ello, en el año 2010, se realizaron los ajustes paramétricos necesarios del modelo, comparando las salidas de CS (desarrollo vegetativo, consumos hídricos y estado hídrico) con datos obtenidos de una parcela en la que se encontraba un lisímetro de pesada en viña. Tras los ajustes realizados en 2010, se procedió a su validación para los años 2011 y 2012, comparando las salidas ofrecidas por CS con datos obtenidos directamente en campo. Los ajustes de Cs resultaron ser adecuados para determinar la evapotranspiración del cultivo (ETc) y el coeficiente de cultivo (kc), con limitaciones a la hora de simular el desarrollo vegetativo de las cepas, debido, en parte al manejo diferencial de la vegetación en los años objeto de estudio.Comunicación presentada al XXXVII Congreso Nacional de Riegos, celebrado en Don Benito del 4 al 6 de Junio de 2019 y organizada por la Asociación Española de Riegos y Drenajes y la Universidad de Extremadura

Ideal cardiovascular health, handgrip strength, and muscle mass among college students: The fuprecol adults study

The American Heart Association established the 2020 Strategic Impact Goals to define the concept of ideal cardiovascular health (CVH) and the metrics needed to monitor it across populations. The purpose of this study was to investigate the relationship between handgrip strength, muscle mass, and ideal CVH among Colombian college students. Data from 1,835 college students were analyzed (1,128 female). Muscular strength was estimated using a hand-held dynamometer and normalized to body mass (normalized grip strength [NGS]). The percentage of body fat was determined for bioelectrical impedance analysis using tetrapolar whole-body impedance. Ideal CVH was defined as meeting the ideal levels of 4 behaviors (smoking, body mass index, physical activity, and diet adherence) and 3 factors (total cholesterol, fasting glucose, and blood pressure). Higher levels of NGS and muscle mass (relative to body mass) were associated with a higher number of ideal CVH metrics in both sexes (p for trend less than 0.001). For the total ideal CVH metrics scored on a continuous scale from 0 (all 7 poor) to 7 (all 7 ideal), a 1-metric increase was associated with reduced odds of weak NGS (33 and 36%) and low-medium muscle mass (28 and 34%) mass in men and women, respectively (all p less than 0.001). This study indicates that in Colombian college students, both handgrip strength and muscle mass are positively associated with the ideal CVH metrics. To reduce the possible future public health burden of muscular weakness, health professionals need to encourage the public to optimize lifestyle-related risk factors during the young adult stage. © 2019 National Strength and Conditioning Association

Preventive Conservation and Restoration Monitoring of Heritage Buildings Based on Fuzzy Logic

This article discusses the usability of the Art-Risk 3.0 software for research on the conservation of heritage buildings. It is a new and free software based on fuzzy logic, which enables the assessment of preventive conservation and surveillance of the restoration of heritage buildings over a period of time. This artificial intelligence-based tool considers the vulnerability of buildings, their environ ments, and their management to evaluate the necessity of their restoration or preventive con servation. To validate the Art-Risk 3.0, 500 theoretical case studies were analyzed, and a 14th century Mudejar-Gothic-style Church in Seville, Spain was studied both before and after its restora tion to identify post-restoration changes. This proof of concept demonstrates the capability of the Art-Risk 3.0 software to analyze environmental impacts on the vulnerability, risk, and functional service life of buildings, and assess the effectiveness of restoration activities. Additionally, this software identifies the most problematic factors and the necessity of restoration.Ministerio de Economía y Competitividad BIA2015- 64878-R (RETOS)Ministerio de Ciencia e Innovación PID2019-107257RB-I00 (FENIX)Ministerio de Ciencia, Innovación y Universidades EQC2019-005780-P (Ambulab-LAB)Junta de Andalucía PYC20 RE 034 UPO RESILIENT-TOURISMMinisterio de Ciencia e Innovación PTA2019-01688