On the asymptotic behavior of the second moment of the Fourier transform of a random measure

The behavior at infinity of the Fourier transform of the random measures that appear in the theory of multiplicative chaos of Mandelbrot, Peyrière, and Kahane is an area quite unexplored. For context and further reference, we first present an overview of this theory and then the result, which is the main objective of this work, generalizing a result previously announced by Kahane. We establish an estimate for the asymptotic behavior of the second moment of the Fourier transform of the limit random measure in the theory of multiplicative chaos. After looking at the behavior at infinity of the Fourier transform of some remarkable functions and measures, we prove a formula essentially due to Frostman, involving the Riesz kernels

Integration of post-quantum cryptography in the TLS protocol (LWE Option)

Dissertação de mestrado em Computer ScienceWith the possibility of quantum computers making an appearance, possibly capable of breaking several well established and widespread crytposystems (especially those that implement public key cryptography), necessity has arisen to create new cryptographic algorithms which remain safe even against adversaries using quantum computers. Several algorithms based on different mathematical problems have been proposed which are considered to be hard to solve with quantum computers. In recent years, a new lattice-based mathematical problem called Learning With Errors (and its variant Ring - Learning With Errors) was introduced, and several cryptosystems based on this problem were introduced, some of which are becoming practical enough to compete with traditional schemes that have been used for decades. The primary focus in this work is the implementation of two Ring - Learning With Errors based schemes (one key exchange mechanism and one digital signature scheme) on the TLS protocol via the OpenSSL library as a way of checking their overall viability in real-world scenarios, by comparing them to classical schemes implementing the same functionalities.Com a possibilidade do surgimento dos primeiros computadores quânticos, possivelmente capazes de quebrar muitos dos cripto-sistemas bem difundidos e considerados seguros, tornou-se necessário tomar precauções com a criação de novas técnicas criptográficas que visam manter as suas propriedades de segurança mesmo contra adversários que usem computadores quânticos. Existem já muitas propostas de algoritmos baseados em problemas matemáticos distintos que são considerados difíceis de resolver recorrendo a computadores quânticos. Recentemente, foi introduzido um novo problema baseado em reticulados denominado de Learning With Errors (e a sua variante Ring - Learning With Errors), e consequentemente foram propostos vários cripto-sistemas baseados nesse problema, alguns dos quais começam já a ser utilizáveis ao ponto de poderem ser comparados com os esquemas clássicos usados há décadas. O foco principal neste trabalho é a implementação de dois esquemas baseados no problema Ring - Learning With Errors (mais precisamente, um esquema de troca de chaves e uma assinatura digital) no protocolo TLS através da sua integração no OpenSSL como forma de verificar a sua viabilidade em contextos reais, comparando-os com esquemas clássicos que implementem as mesmas funcionalidades

Young adult Brazilian beauty consumers perception of Lancôme and the effectiveness of social media relationhips with local celebrities on their purchase intention

The aim of this research is to evaluate if a premium beauty brand, in this case, Lancôme, can influence positively the purchase intention from Brazilian young adults, between 18 and 29 years old, consumers of beauty products, by initiating a relationship with a local celebrity or “it” girl on social media. This hypothesis has not been tested, and this research is a first attempt of evaluating it. Additionally, the consumer behavior, brand preferences and social media activeness of this age segment in Brazil are further studied as important insights for beauty brands to conquer these consumers. Results did not confirm the positive influence of local celebrities on this age segment’s purchase intention but several suggestions are made for future research to revisit this topic. Furthermore, there is a significant brand love for M.A.C., an international Lancôme competitor, amongst this target, as well as a probable price sensitivity facing premium beauty brands

Examples of financial market models obtained by euler discretization of continuous models

This work was done under partial financial support of RFBR (Grant n. 19-01-00451).We present a methodology to study discrete time financial models with one risky asset and a risk free asset that may thought to result as a discretization of a suitable continuous time model. In a numerical example we compare the pricing results, obtained with these models, with results obtained from the related continuous time models. Our approach relies on some known important results describing a particular class of discrete time models – the conditionally Gaussian models – a class that, regardless of its particular definition, contains many interesting instances. We aim at a better understanding of the implications of the discretization procedures which are inevitable, both at the parameter estimation and derivative price computation moments, by reason of the observational and computational limitations. We also present a preliminary study of a a model of stochastic differential equations for commodity spot and futures prices that may be studied with the proposed methodology. For that purpose we summarize a naive theory of Ito integration in Hilbert space.publishersversionpublishe

Some Double Diffusion Models For Stock Prices

UID/MAT/00297/2020Regime switching diffusion processes with one or two thresholds and regime switching occurring by a change in the diffusion drift and/or volatility functions parameters of a stochastic differential equation, whose solution defines a continuous time diffusion process, were defined in previous works; the change in regime occurring whenever the trajectory of the process crosses a threshold, possibly with some delay. In this paper we generalise the previous results by allowing the underlying diffusion process to change from one family of diffusions in one regime to an entirely different one in the other regime; these families of diffusions are characterised by specific functional forms for drift and volatility coefficients depending on parameters. We propose an estimation procedure for all the parameters, namely the thresholds, the delay and, for both regimes, diffusion’s parameters and we apply the introduced estimation procedure to both simulated and real data.publishersversionpublishe

Pulled-to-par returns for zero coupon bonds : historical simulation value at risk

Due to bond prices pull-to-par, zero coupon bonds historical returns are not stationary, as they tend to zero as time to maturity approaches. Given that the historical simulation method for computing Value at Risk (VaR) requires a stationary sequence of historical returns, zero coupon bonds historical returns can not be used to compute VaR by historical simulation. Their use would systematically overestimate VaR, resulting in invalid VaR sequences. In this paper we propose an adjustment of zero coupon bonds historical returns. We call the adjusted returns “pulled-to- par" returns. We prove that when the zero coupon bonds continuously compounded yields to maturity are stationary the adjusted pulled-to-par returns allow VaR computation by historical simulation. We first illustrate the VaR computation in a simulation scenario, then we apply it to real data on euro zone STRIPS.info:eu-repo/semantics/publishedVersio

Open markov type population models: From discrete to continuous time

Funding Information: Funding: For the second author, this work was done under partial financial support of RFBR (Grant n. 19-01-00451). For the first and third author this work was partially supported through the project of the Centro de Matemática e Aplicações, UID/MAT/00297/2020 financed by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology). The APC was funded by the insurance company Fidelidade.We address the problem of finding a natural continuous time Markov type process—in open populations—that best captures the information provided by an open Markov chain in discrete time which is usually the sole possible observation from data. Given the open discrete time Markov chain, we single out two main approaches: In the first one, we consider a calibration procedure of a continuous time Markov process using a transition matrix of a discrete time Markov chain and we show that, when the discrete time transition matrix is embeddable in a continuous time one, the calibration problem has optimal solutions. In the second approach, we consider semi-Markov processes—and open Markov schemes—and we propose a direct extension from the discrete time theory to the continuous time one by using a known structure representation result for semi-Markov processes that decomposes the process as a sum of terms given by the products of the random variables of a discrete time Markov chain by time functions built from an adequate increasing sequence of stopping times.publishersversionpublishe

Screening of Aflatoxin B1 in Laboratory Rat Feed

Many hazards can interfere with the safety of the feeding stuffs intended to provide nutrients to experimental  animals. Chemical and biological contaminants of laboratory animal feed can be a problem for toxicological  and immunological research. Aflatoxin B1 (AFB1) is a secondary toxic metabolite, produced by  the ubiquitous fungal genera, Aspergillus. AFB1 is particularly dangerous for health, inducing cancer of the  urinary tract or liver carcinoma. The aim of this preliminary screening was to evaluate the presence of AFB1  in 31 samples of laboratory rat feed using a method validated in-house, then separated by High Pressure  Liquid Chromatography (HPLC) coupled to a fluorescence detector. The detection limit (limit of detection:  LOD) and the quantification limit (LOQ) were 0.2 and 0.4 ìg/kg respectively. Recoveries ranged from 58.0  to 74.5% for spiked samples. The immunoaffinity approach was significantly faster than methods employing  conventional chromatography clean-up (Sep-Pak Classic Florisil and Sep-Pak ClassicC18 cartridges).  Aflatoxins were not detected in any analysed sample.

The multi-compartment si(Rd) model with regime switching: An application to covid-19 pandemic

Grant No. 19-01-00451 UID/MAT/00297/2020We study—with existence and unicity results—a variant of the SIR model for an infectious disease incorporating both the possibility of a death outcome—in a short period of time—and a regime switch that can account for the mitigation measures used to control the spreading of the infections, such as a total lockdown. This model is parametrised by three parameters: the basic reproduction number, the mortality rate of the infected, and the duration of the disease. We discuss a particular example of application to Portuguese COVID-19 data in two short periods just after the start of the epidemic in 4 March 2020, with the first two cases dated that day. We propose a simple and effective method for the estimation of the main parameters of the disease, namely, the basic reproduction number and the mortality rate of the infected. We correct these estimated values to take into account the asymptomatic non-diagnosed members of the population. We compare the outcome of the model in the cases of the existence, or not, of a regime switch, and under three different scenarios, with a remarkable agreement between model and data deaths in the case of our basis scenario. In a final short remark, we deal with the existence of symmetries for the proposed model.publishersversionpublishe

On a parallelised diffusion induced stochastic algorithm with pure random search steps for global optimisation

Funding Information: Funding: For the second author, this work was undertaken with partial financial support of RFBR (Grant n. 19-01-00451). For the first and third author, this work was partially supported through the project of the Centro de Matemática e Aplicações, UID/MAT/00297/2020, financed by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology). The APC was by supported the New University of Lisbon through the PhD program in Statistics and Risk Management of the FCT Nova Faculty.We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step.publishersversionpublishe