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Research Project
Center for Mathematics, Fundamental Applications and Operations Research
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Fractal calculus on fractal interpolation functions
Publication . Gowrisankar, Arulprakash; Khalili Golmankhaneh, Alireza; Serpa, Cristina
In this paper, fractal calculus, which is called F α -calculus, is reviewed. Fractal calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non differentiable and non-integrable in the sense of ordinary calculus. Graphical representations of fractal calculus of fractal interpolation functions and Weierstrass functions are presented.
Herpesviruses serology distinguishes different subgroups of patients from the United Kingdom myalgic encephalomyelitis/chronic fatigue syndrome biobank
Publication . Domingues, Tiago Dias; Grabowska, Anna D.; Lee, Ji-Sook; Ameijeiras-Alonso, Jose; Westermeier, Francisco; Scheibenbogen, Carmen; Cliff, Jacqueline M.; Nacul, Luis; Lacerda, Eliana M.; Mouriño, Helena; Sepulveda, Nuno
The evidence of an association between Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS) and chronic herpesviruses infections remains inconclusive. Two reasons for the lack of consistent evidence are the large heterogeneity of the patients’ population with different disease triggers and the use of arbitrary cutoffs for defining seropositivity. In this work we re-analyzed previously published serological data related to 7 herpesvirus antigens. Patients with ME/CFS were subdivided into four subgroups related to the disease triggers: S0-42 patients who did not know their disease trigger; S1-43 patients who reported a non-infection trigger; S2-93 patients who reported an infection trigger, but that infection was not confirmed by a lab test; and S3-48 patients who reported an infection trigger and that infection was confirmed by a lab test. In accordance with a sensitivity analysis, the data were compared to those from 99 healthy controls allowing the seropositivity cutoffs to vary within a wide range of possible values. We found a negative association between S1 and seropositivity to Epstein-Barr virus (VCA and EBNA1 antigens) and Varicella-Zoster virus using specific seropositivity cutoff. However, this association was not significant when controlling for multiple testing. We also found that S3 had a lower seroprevalence to the human cytomegalovirus when compared to healthy controls for all cutoffs used for seropositivity and after adjusting for multiple testing using the Benjamini-Hochberg procedure. However, this association did not reach statistical significance when using Benjamini-Yekutieli procedure. In summary, herpesviruses serology could distinguish subgroups of ME/CFS patients according to their disease trigger, but this finding could be eventually affected by the problem of multiple testing.
Fractal analysis and ferroelectric properties of Nd(Zn-1/Ti-2(1)/(2))O-3(NZT)
Publication . Khamoushi, Kouros; Serpa, Cristina
The challenges in productivity of satellite mobile devices are growing rapidly to overcome the question of miniaturization. The intention is to supply the electrical and microwave properties of materials by discovering their outstanding electronic properties. Neodymium Zinc Titanate (NZT) can be a promising ferroelectric material due to its stable dielectric and microwave properties. The grain size and shape of NZT have a strong influence on overall material performances. Therefore, shape, reconstruction and property of the coming compound take an important part and can be predicted before being utilized in the devices. The significant of this research is to define ferroelectric properties of NZT and to characterize it by using Fractal Nature Analysis (FNA). FNA is a powerful mathematical technique that could be applied to improve the grain shape and interface reconstruction. The fractal structure is identified by its self-similarity. The self-similarity of an object means a repetition of shapes in smaller scales. A measure of this structure is computed using the Hausdorff dimension. It is for the first time in this investigation the Fractal analysis method is applied for the microwave materials microstructure reconstruction which makes this research an innovative work and will open the door for Curie-Weiss law fractal correction. In connection to our previous research for dielectric properties fractalization, we had some characterization and reconstruction data which include the Hausdorff dimension (HD).
Mixed Hodge structures on character varieties of nilpotent groups
Publication . A. A. Florentino, Carlos; Lawton, Sean; Silva, Jaime
Let Hom0(Ƭ, G) be the connected component of the identity of the variety of representations of a finitely generated nilpotent group into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the representation variety Hom0(Ƭ, G) and on the character variety Hom0(Ƭ, G)//G. We obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomial of these representation and character varieties.
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Funding agency
Fundação para a Ciência e a Tecnologia
Funding programme
6817 - DCRRNI ID
Funding Award Number
UIDB/04561/2020