Sistemes lineals: una aproximació a algun dels seus conceptes i problemes rellevants

L'objectiu que m'he proposat al preparar aquesta exposicióha estat el de mostrar. per una banda, com alguns delsproblemes bàsics de la teoria de Sistemes Dinàmics Linealstenen una resposta senzilla en termes de l' Álgebra lineal i,d'altra, com alguns problemes importants d'aquesta teorias'entronquen amb conceptes i tècniques bàsiques de la geometriai la topologia

Modelos dinámicos en finanzas

El problema de la modelización dinámica enfinanzas tiene mucho que ver con el tipo deproblema que se pretende estudiar. Es preciso teneren cuenta el subyacente así como las magnitudesque se pretende estimar para elegir el modeloadecuado.-

Characterizing the connectome in schizophrenia with diffusion spectrum imaging.

Schizophrenia is a complex psychiatric disorder characterized by disabling symptoms and cognitive deficit. Recent neuroimaging findings suggest that large parts of the brain are affected by the disease, and that the capacity of functional integration between brain areas is decreased. In this study we questioned (i) which brain areas underlie the loss of network integration properties observed in the pathology, (ii) what is the topological role of the affected regions within the overall brain network and how this topological status might be altered in patients, and (iii) how white matter properties of tracts connecting affected regions may be disrupted. We acquired diffusion spectrum imaging (a technique sensitive to fiber crossing and slow diffusion compartment) data from 16 schizophrenia patients and 15 healthy controls, and investigated their weighted brain networks. The global connectivity analysis confirmed that patients present disrupted integration and segregation properties. The nodal analysis allowed identifying a distributed set of brain nodes affected in the pathology, including hubs and peripheral areas. To characterize the topological role of this affected core, we investigated the brain network shortest paths layout, and quantified the network damage after targeted attack toward the affected core. The centrality of the affected core was compromised in patients. Moreover the connectivity strength within the affected core, quantified with generalized fractional anisotropy and apparent diffusion coefficient, was altered in patients. Taken together, these findings suggest that the structural alterations and topological decentralization of the affected core might be major mechanisms underlying the schizophrenia dysconnectivity disorder. Hum Brain Mapp, 36:354-366, 2015. © 2014 Wiley Periodicals, Inc.

Uric acid and cardio-metabolic risk factors : an epidemiological approach

The role of serum uric acid (SUA) in cardio-metabolic conditions has long been contentious. It is still unclear if SUA is an independent risk factor or marker of cardio-metabolic conditions and most observed associations are not necessarily causal. This study aimed to further understand and explore the causal role of SUA in cardio-metabolic conditions using genetic and non-genetic epidemiological methods in population-based data. In the first part of this study, we found moderate to high heritability estimates for SUA and fractional excretion of urate (FEUA) suggesting the role of genetic factors in the etiology of hyperuricemia. With regards to the role of SUA on inflammatory markers (IMs), a strong positive association of SUA with C-reactive protein (CRP) and a weaker positive association with tumor necrosis factor alpha (TNF-α) and interleukin 6 (IL-6) was observed, which was in part mediated by body mass index (BMI). These findings suggest that SUA may have a role in sterile inflammation. In view of the inconsistency surrounding the causal nature and direction of the relation between SUA and adiposity, we applied a bidirectional Mendelian randomization approach using genetic variants to decipher the association. The finding that elevated SUA is a consequence rather than a cause of adiposity was not totally unexpected and is compatible with the hypothesis that hyperinsulinemia, accompanying obesity, enhances renal proximal tubular reabsorption of uric acid. The fourth part of this study examined the relationship between SUA and blood pressure (BP) in young adults. The association between SUA and BP, significant only in females, was strongly attenuated upon adjustment for BMI. The possibility that BMI lies in the causal pathway may explain the attenuation observed in the associations of SUA with BP and IMs. Finally, a significant hockey-stick shaped association of SUA with social phobia in our data suggests a protective effect of SUA only up to a certain concentration. Although our study findings have shed some light on the uncertainty underlying the pathophysiology of SUA, more compelling evidence using longitudinal designs, randomized controlled trials and the use of robust genetic tools is warranted to increase our understanding of the clinical significance of SUA.

Cardiac raptor deletion impairs adaptive hypertrophy, alters metabolic gene expression and causes heart failure in mice

Background: Mammalian target of rapamycin (mTOR), a central regulator of cell growth, is found in two structurally and functionally distinct multiprotein complexes called mTOR complex (mTORC)1 and mTORC2. The specific roles of each of these branches of mTOR signaling have not been dissected in the adult heart. In the present study, we aimed to bring new insights into the function of cardiac mTORC1-mediated signaling in physiological as well as pathological situations.Methods: We generated mice homozygous for loxP-flanked raptor and positive for the tamoxifen-inducible Cre recombinase (MerCreMer) under control of the α- myosin heavy chain promoter. The raptor gene encodes an essential component of mTORC1. Gene ablation was induced at the age of 10-12 weeks, and two weeks later the raptor cardiac-knockout (raptor-cKO) mice started voluntary cagewheel exercise or were subjected to transverse aortic constriction (TAC) to induce pressure overload.Results: In sedentary raptor-cKO mice, ejection fractions gradually decreased, resulting in significantly reduced values at 38 days (P < 0.001). Raptor-cKO mice started to die during the fifth week after the last tamoxifen injection. At that time, the mortality rate was 36% in sedentary (n = 11) and 64% in exercising (n = 14) mice. TAC-induced pressure overload resulted in severe cardiac dysfunction already at earlier timepoints. Thus, at 7-9 days after surgery, ejection fraction and fractional shortening values were 22.3% vs 43.5% and 10.2% vs 21.5% in raptor-cKO vs wild-type mice, respectively. This was accompanied by significant reductions of ventricular wall and septal thickness as well as an increase in left ventricular internal diameter. Moreover, ventricular weight to tibial length ratios were increased in wild-type, but not in the raptor-cKO TAC mice. Together, this shows that raptor-cKO mice rapidly developed dilated cardiomyopathy without going through a phase of adaptive hypertrophy. Expression of ANP and β-MHC was induced in all raptor-cKO mice irrespective of the cardiac load conditions. Consistent with reduced mTORC1 activity, phosphorylation of ribosomal S6 kinase and 4E-BP1 was blunted, indicating reduced protein synthesis. Moreover, expression of multiple genes involved in the regulation of energy metabolism was altered, and followed by a shift from fatty acid to glucose oxidation.Conclusion: Our study suggests that mTORC1 coordinates protein and energy metabolic pathways in the heart. Moreover, we demonstrate that raptor is essential for the cardiac adaptation to increased workload and importantly, also for normal physiological cardiac function.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences

This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Equacions diferencials i models

En tot cas, jo voldria que aquesta conferència fos això que he dit: una breu lliçó sobre la importància de les equacions diferencials. Parlaré d'elles des de el punt de vista del models, és a dir, dels fenòmens que modelitzeu. I intentaré explicar que malgrat el seu origen antic, totes elles segueixen presentant avui en dia problemes nous i interessants, tant des de el punt de vista teòric com pràctic.

Gestió d'un projecte per optimitzar recursos informàtics

Estudi per verificar la hipòtesis plantejada inicial sobre que moltes empreses implementen nous sistemes integrals i segueixen efectuant tasques rutinàries sense aprofitar aquests nous sistemes, fent duplicitat de tasques i malgastant recursos informàtics.

Evaluation of Gap-Graded Asphalt Concrete Mixtures Part II: Statistical Design and Analysis, HR-157, 1973

This report presents the results of a comparative laboratory study between well- and gap-graded aggregates used in asphalt concrete paving mixtures. A total of 424 batches of asphalt concrete mixtures and 3, 960 Marshall and Hveem specimens were examined. The main thrust of the statistical analysis conducted in this experiment was in the calibration study and in Part I of the experiment. In the former study, the compaction procedure between the Iowa State University Lab and the Iowa Highway Commission Lab was calibrated. By an analysis of the errors associated with the measurements we were able to separate the "preparation" and "determination" errors for both laboratories as well as develop the calibration curve which describes the relationship between the compaction procedures at the two labs. In Part I, the use of a fractional factorial design in a split plot experiment in measuring the effect of several factors on asphalt concrete strength and weight was exhibited. Also, the use of half normal plotting techniques for indicating significant factors and interactions and for estimating errors in experiments with only a limited number of observations was outlined,

Retrieving Cloud Characteristics from Ground-Based Daytime Color All-Sky Images

A discussion is presented of daytime sky imaging and techniques that may be applied to the analysis of full-color sky images to infer cloud macrophysical properties. Descriptions of two different types of skyimaging systems developed by the authors are presented, one of which has been developed into a commercially available instrument. Retrievals of fractional sky cover from automated processing methods are compared to human retrievals, both from direct observations and visual analyses of sky images. Although some uncertainty exists in fractional sky cover retrievals from sky images, this uncertainty is no greater than that attached to human observations for the commercially available sky-imager retrievals. Thus, the application of automatic digital image processing techniques on sky images is a useful method to complement, or even replace, traditional human observations of sky cover and, potentially, cloud type. Additionally, the possibilities for inferring other cloud parameters such as cloud brokenness and solar obstruction further enhance the usefulness of sky imagers

A method for decision making with the OWA operator

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.