Exact value of 3 color weak Rado number

For integers k, n, c with k, n ≥ 1 and c ≥ 0, the n color weak Rado number W Rk(n, c) is defined as the least integer N, if it exists, such that for every n coloring of the set {1, 2, ..., N}, there exists a monochromatic solution in that set to the equation x1 + x2 + ... + xk + c = xk+1, such that xi = xj when i = j. If no such N exists, then W Rk(n, c) is defined as infinite. In this work, we consider the main issue regarding the 3 color weak Rado number for the equation x1 + x2 + c = x3 and the exact value of the W R2(3, c) = 13c + 22 is established

3-color Schur numbers

Let k ≥ 3 be an integer, the Schur number Sk(3) is the least positive integer, such that for every 3-coloring of the integer interval [1, Sk(3)] there exists a monochromatic solution to the equation x1+ · · · + xk= xk+1, where xi , i = 1, . . . , k need not be distinct. In 1966, a lower bound of Sk(3) was established by Znám (1966). In this paper, we determine the exact formula of Sk(3) = k 3 + 2k 2 − 2, finding an upper bound which coincides with the lower bound given by Znám (1966). This is shown in two different ways: in the first instance, by the exhaustive development of all possible cases and in the second instance translating the problem into a Boolean satisfiability problem, which can be handled by a SAT solver

Effects of a 12-week Vivifrail exercise program on intrinsic capacity among frail cognitively impaired community-dwelling older adults: secondary analysis of a multicentre randomised clinical trial

Introduction: The World Health Organisation recently defined the construct of intrinsic capacity (IC), a function-based marker of older adult’s health encompassing all mental and physical capacities of the individual. Multicomponent physical exercise (MCE) is a potential intervention capable to maintain/increase IC at older age; however, evidence is scarce on the effects of MCE on IC in cognitively impaired pre-frail/frail older adults. Methods: Secondary analyses of a randomised clinical trial. One hundred and eighty-eight older outpatients (age = 84.06 ± 4.77, 70.2% women) presenting with pre-frailty/frailty (according to Fried Criteria) and mild cognitive impairment (MCI)/mild dementia were recruited in the Geriatric clinics of three tertiary hospitals in Spain. Subjects were randomised to participate in the 12-week home-based individualised Vivifrail MCE or usual care. An IC index was created based on the z-score of the locomotion (Short Physical Performance Battery), cognitive (Montreal Cognitive Assessment), psychology (15-item Geriatric Depression Scale Yesavage) and vitality (handgrip strength) domains. Results: After the 3-month intervention, linear mixed models showed significant between-group differences in the evolution of the IC composite score (β=0.48; 95% confidence interval [CI] = 0.24, 0.74; P < 0.001), IC Locomotion (β = 0.42; 95% CI = 0.10, 0.74; P < 0.001), IC Cognition (β = 0.45; 95% CI = 0.03, 0.87; P < 0.05) and IC Vitality domains (β = 0.50; 95% CI = 0.25, 0.74 at 3-month) favouring the MCE group. Conclusions: The 12-week Vivifrail multicomponent exercise program is an effective strategy to enhance IC, especially in terms of locomotion, cognition and vitality IC domains in community-dwelling older adults with pre-frailty/frailty and MCI/mild dementia, compared to usual care.This study has been funded by a Gobierno de Navarra project grant and FEDER Funds (426/2016,del 30 September28/16)

Castillo

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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

Project-based learning using scientific poster as a tool for learning and acquisition of skills in physics subjects of engineering bachelor’s degrees

This article shows the experience of working on project-based learning using scientific posters, on the study of the mass geometry of matter, with students of various Physics subjects of Degrees in Engineering of the School of Design Engineering of the Polytechnic University of Valencia. The development of this work has been carried out with a dual purpose: on the one hand, to improve the teachinglearning process of mass geometry; and, on the other hand, to improve the acquisition of skills by students. This matter, which is studied in the Physics subjects of the first year of the degree, forms part of the basis of the studies of resistance of materials and theory of mechanisms of subsequent courses. The inclusion of two sessions of laboratory practices, as an extension of the work carried out in the theory and classroom practice sessions, has allowed us to study more deeply the theoretical concepts of mass geometry and their application to a real project, improving the learning by the students. In addition, the presentation of the project through the scientific poster has facilitated the acquisition of cross-curricular competencies such as application and practical thinking, teamwork, effective communication, and critical thinking

A Critical Gap in Seagrass Protection: Impact of Anthropogenic Off-Shore Nutrient Discharges on Deep Posidonia oceanica Meadows

In the Mediterranean, anthropogenic pressures (specifically those involving nutrient loads) have been progressively moved to deeper off-shore areas to meet current policies dealing with the protection of marine biodiversity (e.g., European Directives). However, conservation efforts devoted to protecting Posidonia oceanica and other vulnerable marine habitats against anthropogenic pressures have dedicated very little attention to the deepest areas of these habitats. We studied the remote influence of off-shore nutrient discharge on the physiology and structure of deep P. oceanica meadows located nearest to an urban sewage outfall (WW; 1 km) and an aquaculture facility (FF; 2.5 km). Light reduction and elevated external nutrient availability (as indicated by high δ15N, total N and P content and N uptake rates of seagrass tissues) were consistent with physiological responses to light and nutrient stress. This was particularly evident in the sites located up to 2.5 km from the WW source, where carbon budget imbalances and structural alterations were more evident. These results provide evidence that anthropogenic nutrient inputs can surpass critical thresholds for the species, even in off-shore waters at distances within the km scale. Therefore, the critical distances between this priority habitat and nutrient discharge points have been underestimated and should be corrected to achieve a good conservation status.J.-C.J.’s PhD was funded by a grant from the University of Alicante. This research was funded by the POSINET2 project (Monitoring network of Posidonia oceanica meadow and climate change of the Murcia Region) of the Spanish Institute of Oceanography (CN IEO-CSIC), the Department of Fishery and Aquaculture of the Regional Ministry of Agriculture and Water of the Murcia Region and by the UMBRAL project (Responses of marine benthic macrophytes to stress: critical transitions, resilience and management opportunities) financed by the National Plan of Research of the Spanish Government (CTM2017-86695-C3-2-R) to R.J.M. The research was also supported by project 19-ESMARES2-ANG funded by the Ministry of Ecological Transition and Demographic Challenge of the Spanish government for the application of the Marine Strategy Framework Directive (MSFD) in Spanish waters

Desalination brine effects beyond excess salinity: Unravelling specific stress signaling and tolerance responses in the seagrass Posidonia oceanica

Desalination has been proposed as a global strategy for tackling freshwater shortage in the climate change era. However, there is a concern regarding the environmental effects of high salinity brines discharged from desalination plants on benthic communities. In this context, seagrasses such as the Mediterranean endemic and ecologically important Posidonia oceanica have shown high vulnerability to elevated salinities. Most ecotoxicological studies regarding desalination effects are based on salinity increments using artificial sea salts, although it has been postulated that certain additives within the industrial process of desalination may exacerbate a negative impact beyond just the increased salinities of the brine. To assess the potential effect of whole effluent brines on P. oceanica, mesocosm experiments were conducted within 10 days, simulating salinity increment with either artificial sea salts or brines from a desalination plant (at 43 psμ, 6 psμ over the natural 37 psμ). Morphometrical (growth and necrosis), photochemical (PSII chlorophyll a fluorometry), metabolic, such as hydrogen peroxide (H2O2), thiobarbituric reactive substances (TBARS) and ascorbate/dehydroascorbate (ASC/DHA), and molecular (expression of key tolerance genes) responses were analyzed in each different treatment. Although with a still positive leaf growth, associated parameters decreased similarly for both artificial sea salt and brine treatments. Photochemical parameters did not show general patterns, although only P. oceanica under brines demonstrated greater energy release through heat (NPQ). Lipid peroxidation and upregulation of genes related to oxidative stress (GR, MnSOD, and FeSOD) or ion exclusion (SOS3 and AKT2/3) were similarly incremented on both hypersalinity treatments. Conversely, the ASC/DHA ratio was significantly lower, and the expression of SOS1, CAT, and STRK1 was increased under brine influence. This study revealed that although metabolic and photochemical differences occurred under both hypersalinity treatments, growth (the last sign of physiological detriment) was similarly compromised, suggesting that the potential effects of desalination are mainly caused by brine-associated salinities and are not particularly related to other industrial additives.This investigation was funded by Marie Skłodowska-Curie Action (888415) granted to C.A. Sáez. F. Blanco-Murillo was supported by a grant from Universidad de Alicante (Grant ID: FPUUA98). F. Rodríguez-Rojas was financed by the ANID project FONDECYT 11220425. C.A. Sáez was also financed by project ANID InES I+D 2021 (INID210013)

Role of drug transporters in the sensitivity of acute myeloid leukemia to sorafenib

[EN]Chemoresistance often limits the success of the pharmacological treatment in acute myeloid leukemia (AML) patients. Although positive results have been obtained with tyrosine kinase inhibitors (TKIs), such as sorafenib, especially in patients with Fms-like tyrosine kinase 3 (FLT3)-positive AML, the success of chemotherapy is very heterogeneous.The sensitivity to sorafenib-induced cell death (MTT test and anexin V/7-AAD method) was evaluated in five different cell lines: MOLM-13, OCI-AML2, HL-60, HEL and K-562. The transportome was characterized by measuring mRNA using RT-qPCR. Drug uptake/efflux was determined by flow cytometry using specific substrates and inhibitors. The cytostatic response to sorafenib was: MOLM-13»OCI-AML2>HL- 60>HEL≈K-562. Regarding efflux pumps, MDR1 was highly expressed in HEL>K- 562≈MOLM-13, but not in OCI-AML2 and HL-60. BCRP and MPR3 expression was low in all cell lines, whereas MRP4 and MRP5 expression was from moderate to high. Flow cytometry studies demonstrated that MRP4, but not MRP5, was functional

Mechanically reconfigurable linear phased array antenna based on single-block waveguide reflective phase shifters with tuning screws

This work presents the design and prototyping of a reconfigurable phased array in Ku band (16 to 18 GHz) implemented in waveguide technology. The design is based on the use of a novel seamless waveguide module integrating four reconfigurable phase shifters to adjust the relative phase shift between the unitary elements of a linear array, which are illuminated uniformly by a corporate waveguide feeding network. The phase shifters are implemented by a 90º hybrid coupler in waveguide technology where two of its ports are loaded with a tunable reactive load, implemented in this proof of concept with a tuning screw. The four phase shifters have been manufactured in a single part using direct metal laser sintering, avoiding the losses related to bad electric contacts and misalignments associated to multipart devices. This also simplifies the assembly of the full phased array, leading to a modular approach with three parts whose design can be addressed separately. The experimental results for the complete array antenna show great performance and demonstrate that the main-lobe of the radiation pattern can be effectively scanned continuously between the angles - 25º and 25º, with a high efficiency in the whole design band thanks to the proposed waveguide implementationThis work was supported by the Spanish Government, Agencia Estatal de Investigación, Fondo Europeo de Desarrollo Regional: AEI/FEDER, UE, under Grant TEC2016-76070-C3-1-