Partition Regularity of Nonlinear Diophantine Equations

Ramsey Theory and partition regularity problems are interesting settings of combinatorics that investigate structural properties of families of sets. More precisely, a collection of a sets of A, namely F, is partition regular on the set A if, whenever A is finitely partitioned in C_1,...,C_r, then there exists an index j in {1,...,r} and an element of F contained in C_j. Our interest is focused on diophantine equations. In particular we answer to the following question: given a polynomial P, is P partition regular over the natural numbers? This means: given a finite partition (or colouring) of natural numbers, can we find monochromatic solutions of P? The thesis is structured in four chapters. The first chapter lays the foundations of the rest of the thesis. It starts with the theory of ultrafilters which are important and multifaced mathematical objects, whose definition can be formulated in several languages: from set theory, as maximal families of closed under finite intersection sets, to measure theory, as {0,1}-valued finitely additive measures on a given space, to algebra as maximal ideals of ring of function F^I. The chapter continues with a brief dissertation about nonstandard analysis that was created in the early 1960s by the mathematician Abraham Robinson. In particular we focus on hypernatural numbers and their properties to prove the main results of this thesis. We show that the theory of ultrafilters and nonstandard analysis are strictly connected, and they have many applications in other fields of mathematics, as combinatorics or topology. Though this, in the second chapter we can prove some important well-known results that concern partition regularity. We focus our attention on Ramsey Theory, a branch of combinatorics that studies the conditions under which order must appear. Typically, Ramsey problems are connected to questions of the form: how many elements of a given structure should there be to make true a particular property? The begin of this theory is dated back to 1928 when Frank Plumpton Ramsey published his paper "On a problem of formal logic". The paper has led to a large area of combinatorics now known as Ramsey Theory and several important results arose from it in the last century. The most important results that are relevant to our purposes are: Schur's Theorem (1916), Rado's Theorem (1933) that gives a characterisation of the homogeneous systems to which a monochromatic solution can be found in any finite colouring of the natural numbers, Van der Waerden's Theorem (1927), Hindman’s Theorem (1974), and Milliken-Taylor's Theorem (1975). Rado's Theorem completely settled the characterisation of partition regularity of the linear polynomials, and it is the starting point from which the heart of this thesis develops: the partition regularity of nonlinear equations. Actually, the third chapter is dedicated to proving the partition regularity of a few particular equations. Furthermore we give necessary conditions to say when a polynomial is partition regular. These conditions depend on Rado's Theorem and on the degree of the nonlinear variables. In the last fourth chapter we investigate the non-partition regularity of large classes of nonlinear equations. Starting from two simple non partition regular polynomials, x^2+y^2-z and x+y-z^2, we aim at extending these examples. The first step toward the generalisation is to modify the exponents: we prove that the equations x^n+y^n=z^k and x^n+y^m=z^k with n,m,k mutually distinct are non-partition regular. Subsequently we increase the numbers of variables and we prove that also the following equations are non-partition regular: x_1^n+...+x_m^n = y^k with m>1 and kn and there exists a prime p that divides m and p^{k-n} does not divide m; x_1^n+...+x_m^n = y^{n+1}. In the end considering polynomials with coefficients c_j not equal to 1, under suitable conditions on the c_j, we have that the two following equations are non-partition regular: c_1x_1^n+...+c_nx_m^n = y^k, with k1; c_1x_1^n+...+c_nx_m^n = y^{n+1}, with m>1

Chained activation of the motor system during language understanding

Two experiments were carried out to investigate whether and how one important characteristic of the motor system, that is its goal-directed organization in motor chains, is reflected in language processing. This possibility stems from the embodied theory of language, according to which the linguistic system re-uses the structures of the motor system. The participants were presented with nouns of common tools preceded by a pair of verbs expressing grasping or observational motor chains (i.e., grasp-to-move, grasp-to-use, look-at-to-grasp, and look-at-to-stare). They decided whether the tool mentioned in the sentence was the same as that displayed in a picture presented shortly after. A primacy of the grasp-to-use motor chain over the other motor chains in priming the participants' performance was observed in both the experiments. More interestingly, we found that the motor information evoked by the noun was modulated by the specific motor-chain expressed by the preceding verbs. Specifically, with the grasping chain aimed at using the tool, the functional motor information prevailed over the volumetric information, and vice versa with the grasping chain aimed at moving the tool (Experiment 2). Instead, the functional and volumetric information were balanced for those motor chains that comprise at least an observational act (Experiment 1). Overall our results are in keeping with the embodied theory of language and suggest that understanding sentences expressing an action directed toward a tool drives a chained activation of the motor system

AKT1 and AKT2 isoforms play distinct roles during breast cancer progression through the regulation of specific downstream proteins

The purpose of this study was to elucidate the mechanisms associated with the specific effects of AKT1 and AKT2 isoforms in breast cancer progression. We modulated the abundance of specific AKT isoforms in IBH-6 and T47D human breast cancer cell lines and showed that AKT1 promoted cell proliferation, through S6 and cyclin D1 upregulation, but it inhibited cell migration and invasion through β1-integrin and focal adhesion kinase (FAK) downregulation. In contrast, AKT2 promoted cell migration and invasion through F-actin and vimentin induction. Thus, while overexpression of AKT1 promoted local tumor growth, downregulation of AKT1 or overexpression of AKT2 promoted peritumoral invasion and lung metastasis. Furthermore, we evaluated The Cancer Genome Atlas (TCGA) dataset for invasive breast carcinomas and found that increased AKT2 but not AKT1 mRNA levels correlated with a worse clinical outcome. We conclude that AKT isoforms play specific roles in different steps of breast cancer progression, with AKT1 involved in the local tumor growth and AKT2 involved in the distant tumor dissemination, having AKT2 a poorer prognostic value and consequently being a worthwhile target for therapy.Fil: Riggio, Marina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Perrone, Maria Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Polo, Maria Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Rodriguez, Maria Jimena. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: May, Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Abba, Martín Carlos. Universidad Nacional de La Plata; ArgentinaFil: Lanari, Claudia Lee Malvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Novaro, Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; Argentin

Should we Set a Formalized Discharge Instruction Education Standard?

Smart AIM: With a more formalized discharge instruction evaluation process for PGY-1s, discharge instructions for specific diagnoses will have less error in a year’s time.https://jdc.jefferson.edu/patientsafetyposters/1035/thumbnail.jp

Zinc oxide nanoparticles as selective killers of proliferating cells

Background: It has recently been demonstrated that zinc oxide nanoparticles (ZnO NPs) induce death of cancerous cells whilst having no cytotoxic effect on normal cells. However, there are several issues which need to be resolved before translation of zinc oxide nanoparticles into medical use, including lack of suitable biocompatible dispersion protocols and a better understanding being needed of the mechanism of their selective cytotoxic action. Methods: Nanoparticle dose affecting cell viability was evaluated in a model of proliferating cells both experimentally and mathematically. The key issue of selective toxicity of ZnO NPs toward proliferating cells was addressed by experiments using a biological model of noncancerous cells, ie, mesenchymal stem cells before and after cell differentiation to the osteogenic lineage. Results: In this paper, we report a biocompatible protocol for preparation of stable aqueous solutions of monodispersed zinc oxide nanoparticles. We found that the threshold of intracellular ZnO NP concentration required to induce cell death in proliferating cells is 0.4 ± 0.02 mM. Finally, flow cytometry analysis revealed that the threshold dose of zinc oxide nanoparticles was lethal to proliferating pluripotent mesenchymal stem cells but exhibited negligible cytotoxic effects to osteogenically differentiated mesenchymal stem cells. Conclusion: Results confirm the ZnO NP selective cytotoxic action on rapidly proliferating cells, whether benign or malignant

No effect of albumin infusion on the prevention of hepatic encephalopathy after transjugular intrahepatic portosystemic shunt

Hepatic encephalopathy (HE) is a major problem in patients submitted to TIPS. Previous studies identified low albumin as a factor associated to post-TIPS HE. In cirrhotics with diuretic-induced HE and hypovolemia, albumin infusion reduced plasma ammonia and improved HE. Our aim was to evaluate if the incidence of overt HE (grade II or more according to WH) and the modifications of venous blood ammonia and psychometric tests during the first month after TIPS can be prevented by albumin infusion. Twenty-three patients consecutively submitted to TIPS were enrolled and treated with 1 g/Kg BW of albumin for the first 2 days after TIPS followed by 0,5 g/Kg BW at day 4th and 7th and then once a week for 3 weeks. Forty-five patients included in a previous RCT (Riggio et al. 2010) followed with the same protocol and submitted to no pharmacological treatment for the prevention of HE, were used as historical controls. No differences in the incidence of overt HE were observed between the group of patients treated with albumin and historical controls during the first month (34 vs 31 %) or during the follow-up (39 vs 48 %). Two patients in the albumin group and three in historical controls needed the reduction of the stent diameter for persistent HE. Venous blood ammonia levels and psychometric tests were also similarly modified in the two groups. Survival was also similar. Albumin infusion has not a role in the prevention of post-TIPS HE

Study of polymorphisms in the promoter region of ovine β-lactoglobulin gene and phylogenetic analysis among the Valle del Belice breed and other sheep breeds considered as ancestors

The aim of this work was to sequence the promoter region of b-lactoglobulin (BLG) gene in four sheep breeds, in order to identify polymorphisms, infer and analyze haplotypes, and phylogenetic relationship among the Valle del Belice breed and the other three breeds considered as ancestors. Sequencing analysis and alignment of the obtained sequences showed the presence of 36 single nucleotide polymorphisms (SNPs) and one deletion. A total of 22 haplotypes found in ‘‘best’’ reconstruction were inferred considering the 37 polymorphic sites identified. Haplotypes were used for the reconstruction of a phylogenetic tree using the Neighbor-Joining algorithm. The number of polymorphisms identified showed high variability within breeds. Analysis of genetic diversity indexes showed that the Sarda breed presented the lowest nucleotide diversity, whereas the Comisana breed presented the highest one. Comparing the nucleotide diversity among breeds, the highest value was obtained between Valle del Belice and Pinzirita breeds, whereas the lowest one was between Valle del Belice and Sarda breeds. Considering that polymorphisms in the promoter region of BLG gene could have a functional role associated with milk composition, the lowest value of nucleotide diversity between Valle del Belice and Sarda breeds may be related to a higher similarity of milk composition of these two breeds compared to the others. Further analyses will be conducted in order to evaluate the possible correlation between the genetic diversity indexes and the BLG content in milk of our breeds

The Emotional Impact of Patient Loss on Brazilian Veterinarians

Simple Summary Unlike human physicians, veterinarians may follow their patients throughout their lifetime, from conception to end-of-life care. Due to the high involvement with the animal, healthcare providers (veterinarians and veterinary staff) are likely to be exposed, together with the caregivers, to the impact of negative events including death and euthanasia. The degree course of veterinary medicine should contain a course that prepares future veterinarians for bad news delivery in order to better handle these challenging situations. Along with the need to further explore this topic, veterinarians should be taught how to recognize psychological fatigue and avoid burnout, seek medical and psychotherapeutic advice, look for ways to lessen these effects and make it easier to identify workers who are most susceptible to burnout early on.Abstract Veterinarians, unlike human physicians, could potentially care for the patient for several years, from conception to end-of-life care. Because of their close relationship with the animal, healthcare providers (for example, veterinarians and staff) are more likely to be affected by bad events and end-of-life care. The purpose of this study was to assess the emotional impact of patients' deaths on Brazilian veterinarians; 549 Brazilian veterinarians (78.3% females) completed a 20-item online questionnaire. Females were more emotionally affected than males by having to talk to the owner about their animal's death and more emotionally affected by the animal's death itself. Furthermore, the emotional impact of an animal's death was heavily influenced by the number of animals euthanized and varied greatly across veterinarians based on their age, with vets over 50 years old being less affected than vets between the ages of 31 and 40. The majority of responders (91.0%) were not trained to deal with grief during their degree. Those who had some training reported being less affected by bereavement. These findings indicate that patient death is a significant emotional concern for veterinarians. Specific education during the degree course, aimed at preparing future veterinarians to deal with death and death communication, is lacking but necessary

Detection of genomic regions underlying milk production traits in Valle del Belice dairy sheep using regional heritability mapping

The aim of this study was to identify genomic regions underlying milk production traits in the Valle del Belice dairy sheep using regional heritability mapping (RHM). Repeated measurements for milk yield (MY), fat percentage and yield (F% and FY) and protein percentage and yield (P% and PY), collected over a period of 6 years (2006-2012) on 481 Valle del Belice ewes, were used for the analysis. Animals were genotyped with the Illumina 50k SNP chip. Variance components, heritabilities and repeatabilities within and across lactations were estimated, fitting parity, litter size, season of lambing and fortnights in milk, as fixed; and additive genetic, permanent environment within and across lactations, flock by test-day interaction and residual as random effects. For the RHM analysis, the model included the same fixed and random effects as before, plus an additional regional genomic additive effect (specific for the region being tested) as random. While the whole genomic additive effect was estimated using the genomic relationship matrix (GRM) constructed from all SNPs, the regional genomic additive effect was estimated from a GRM matrix constructed from the SNPs within each region. Heritability estimates ranged between 0.06 and 0.15, with repeatabilities being between 0.14 and 0.24 across lactations and between 0.23 and 0.39 within lactation for all milk production traits. A substantial effect of flock-test-day on milk production traits was also estimated. Significant genomic regions at either genome-wide (p < .05) or suggestive (i.e., one false positive per genome scan) level were identified on chromosome (OAR) 2, 3 and 20 for F% and on OAR3 for P%, with the regions on OAR3 in common between the two traits. Our results confirmed the role of LALBA and AQP genes, on OAR3, as candidate genes for milk production traits in sheep

Quantitative changes of nicotinic receptors in the hippocampus of dystrophin-deficient mice

Lack of dystrophin in Duchenne muscle dystrophy (DMD) and in the mutant mdx mouse results in progressive muscle degeneration, structural changes at the neuromuscular junction, and destabilization of the nicotinic acetylcholine receptors (nAChRs). One-third of DMD patients also present non-progressive cognitive impairments. Considering the role of the cholinergic system in cognitive functions, the number of nAChR binding sites and the mRNA levels of alpha 4, beta 2, and alpha 7 subunits were determined in brain regions normally enriched in dystrophin (cortex, hippocampus and cerebellum) of mdx mice using specific ligands and reverse-transcription polymerase chain reaction assays, respectively. Membrane preparations of these brain regions were obtained from male control and mdx mice at 4 and 12 months of age. the number of [H-3]-cytisine (alpha 4 beta 2) and [I-125]-alpha-bungarotoxin ([I-125]-alpha BGT, alpha 7) binding sites in the cortex and cerebellum was not altered with age or among age-matched control and mdx mice. A significant reduction in [H-3]-cytisine (48%) and [I-125]-alpha BGT (37%) binding sites was detected in the hippocampus of mdx mice at 12 months of age. When compared with the age-matched control groups, the mdx mice did not have significantly altered [H-3]-cytisine binding in the hippocampus, but [I-125]-alpha BGT binding in the same brain region was 52% higher at 4 months and 20% lower at 12 months. mRNA transcripts for the nAChR alpha 4, beta 2, and alpha 7 subunits were not significantly altered in the same brain regions of all animal groups. These results suggest a potential alteration of the nicotinic cholinergic function in the hippocampus of dystrophin-deficient mice, which might contribute to the impairments in cognitive functions, such as learning and memory, that have been reported in the dystrophic murine model and DMD patients. (C) 2012 Elsevier B.V. All rights reserved.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Universidade Federal de São Paulo, Escola Paulista Med, Sect Nat Prod, Dept Pharmacol, São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, Sect Expt Endocrinol, Dept Pharmacol, São Paulo, BrazilUniv Fed Santa Catarina, Dept Pharmacol, Neuropharmacol Lab, Florianopolis, SC, BrazilAmazon Biotechnol Ctr, Lab Pharmacol & Toxicol, Manaus, AM, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, Sect Nat Prod, Dept Pharmacol, São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, Sect Expt Endocrinol, Dept Pharmacol, São Paulo, BrazilWeb of Scienc