Public Articles
Graph Theory
Benchmark study on the electronic structure properties of polyoxometalate Keggin-like structures and Carbon substrates
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Análise de medidas em grafos para conectividade funcional em redes de modo padrão na demência da doença de Alzheimer leve utilizando técnicas de aprendizado de máquina.
A doença de Alzheimer (DA) é uma doença neurodegenerativa que surge, em geral, após a sétima década de vida, e acarreta alterações cognitivas como déficit de memória episódica, nomeação e outros déficits de linguagem, habilidades visuo-esoaciais, praxias e funções executivas.
Estima-se que, em todo o mundo, mais de 27 milhões de pessoas sofram de DA \cite{Wimo_2006}. E é a principal causa de demência na população idosa, responsável por cerca de 60 a 70% de todas as demências.
Sua prevalência tem aumentado progressivamente devido, uma das causas é o envelhecimento da população mundial. A prevalência da doença dobra, a cada 5 anos, em média, passando de 1% aos 60 anos e chegando a mais de 40% da população com mais de 85 anos de idade \cite{Cummings_2002}. Com o avanço tecnológico e científico, a expectativa de vida média vêm aumentando a cada ano, e estima-se que em 2050 serão cerca de 100 milhões de casos da DA em todo o mundo \cite{Wimo_2013}.
Existem alguns fatores de risco conhecidos para a DA de início tardio, como idade, doenças vasculares e fatores genéticos como a presença do alelo ϵ4 da apolipoproteína E(APOE4), uma proteína carreadora de colesterol envolvida no metabolismo das placas neuríticas (PN) \cite{Poirier_2001}.
Existem 5 alelos para a APOE, numerados de ϵ1 a ϵ5, sendo o mais comum o ϵ3 (cerca de 90% da população caucasiana com 1 alelo e 60% com 2 alelos), o ϵ2, cuja presença pode conferir proteção contra o depósito de peptídeo β-amilóide (βA) e o ϵ4, com cerca de 30 % da população com 1 alelo \cite{Corder_1998}.
Do ponto de vista anátomo-patológico, as PN e os emaranhados neurofibrilares (ENF) são as características mais marcantes da DA.
O estudo da fisiopatologia do βA levou ao desenvolvimento de novas propostas terapêuticas, como a inibição da atividade das enzimas γ e β-secretase e/ou estimulação da atividade da α-secretase, ou ainda, imunoterapia com anticorpos anti-βA. Porém, apenas o depósito do βA não explica toda a fisiopatologia da DA, além de apresentar pouca correlação com a gravidade da demência \cite{Eckman_2007}, \cite{Poirier_2001}.
Os ENF contém FHP originados da hiperfosforilação da proteína tau. Algumas áreas cerebrais são mais vulneráveis a esse processo patológico, como os hipocampos e os córtices frontais. É comum ocorrer nessas regiões FHP contendo proteína tau anormalmente fosforilada, de peso molecular maior que o habitual, conhecida como proteína associada a DA \cite{Poirier_2001}. Esse fenômeno pode justificar a maior correlação clínica dos sintomas cognitivos com a presença dos ENF.
Existem outros fatores causais para a DA, como resposta inflamatória local, disfunção mitocondrial, alteração de neurotransmissores secundária a perda dos neurônios colinérgicos do núcleo basal de Meynert e serotoninérgicos dos núcleos da rafe, além de perda sináptica precoce. Essa perda sináptica é a variável neuropatológica com maior correlação com o grau de demência \cite{Scheff_2003}.
Dessa forma, DA possui múltiplas causas, e é possível que cada um desses fatores fisiopatológicos contribua de forma diferente para a origem dos sintomas cognitivos. É possível que em um futuro próximo, a DA poss ser tratada precocemente, levando em conta o perfil genético e molecular de cada indivíduo.
Desse modo, um dos ramos mais ativos na pesquisa sobre DDA hoje é baseado na busca de biomarcadores que possam antecipar seu diagnóstico, e espera-se que em um futuro próximo haja terapias farmacológicas que possam interromper sua progressão. Neste contexto, surgiu o conceito de Comprometimento Cognitivo Leve (CCL), que é o termo clínico usado para pacientes com alterações cognitivas, porém sem prejuízo significativo em atividades diárias (ou seja, sem que sejam preenchidos critérios para diagnóstico de demência) \cite{21514249}. Embora não haja um critério universalmente aceito, a maioria dos pesquisadores considera necessários: uma queixa cognitiva, comumente memória episódica e preferencialmente confirmada por uma pessoa próxima; comprometimento cognitivo objetivo, com desempenho inferior em testes neuropsicológicos quando comparados a pessoas da mesma faixa etária e escolaridade; Além de atividades de vida diária preservadas ou minimamente comprometidas.
Energy dependence of Net-kaon Multiplicity Distributions at RHIC
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Blog Post 7
1 $\underline{\text{Public Key Cryptography}}$
Public key cryptography (from the Greek roots “crypto” and “graphon,” meaning “hidden writing”) is perhaps the most discreet application of discrete mathematics (Benjamin, 2009). The most famous method for public key cryptography is called the RSA method. This method was discovered in 1977 by three mathematicians Rivest, Shamier, and Adleman.
To carry out this method, one would begin by defining n to be the product of two primes p and q. We must also choose a private key, as it is called, and we will name this d. Then, we compute ϕ(n) which is equivalent to (p − 1)(q − 1). As long as d is relatively prime to ϕ(n), we can set up the equation de − ϕ(n)f = 1 and solve for e and f using the Euclidean Algorithm. The value for e is made public. Therefore, the information that is published is n and e while all other values are kept private.
The message that is sent is $M^e \equiv C \pmod{n}$ where the original message is denoted M and the encrypted message is C. To decrypt our message, one would compute $C^d \equiv M \pmod{n}$.
Graph Theory
The Chinese Remainder Theorem
Serendipity
and 4 collaborators
Modular Arithmetic
Blog Post 6
1 $\underline{\text{Card Shuffling}}$ In discrete mathematics, a riffle shuffle is a shuffling of cards in which the top half is placed in one hand and the other half lies in the opposite hand. The cards are then alternatively interlaced with one another. There are two different types of riffle shuffles that will be the topic of discussion: the out-shuffle and the in-shuffle. An out-shuffle keeps the top card on top and the bottom card on bottom. When the top card is, instead, placed in the second position we have an in-shuffle.
Consider a typical 52 card deck. If we name and order the cards 0, 1, 2, 3, 4..., then after an out-shuffle we receive the order 0, 26, 1, 27, 2, 28.... After an in-shuffle, the cards appear as 26, 0, 27, 1, 28, 2.... Note that the first card is in the 0 position. To return to the original order, we must make 8 out-shuffles. Interestingly enough, however, it takes 52 in-shuffles.
Fermat's Little Theorem
Enabling a muscle-based gesture interface for an Air Guitar game.
With the advancement of technology and the decline of manual labor, humans try to improve their quality of life using any innovation that they can think of. Technology makes our lives easier and more efficient. In turn, efficiency implies that we can allot the saved time for other tasks. For example, the evolution of buttons to touch screen. This evolution saved precious time by introducing dynamic menus, faster input, and a lot of flexibility. However, evolution does not stop there. With the introduction of electromyography (EMG), or the technique of evaluating and recording muscle activity through either a needle (intramuscular) or electrodes on muscles (surface), another form of input was made. It’s unclear if it provides a substantial increase in efficiency compared to traditional touch screens. However, having different options for certain situations are favorable. Other forms of input are: speech recognition, eye gaze trackers, and computer vision. These three other forms of input however, are unfavorable in certain situations; electromyography may be used for those situations. Surface EMG may be preferred over intramuscular EMG because it’s too professional and expensive. One device that’s able to conduct surface EMG is the Myo armband.
Recollimation boundary layers as X-ray sources in young stellar jets
and 2 collaborators
Young stars accrete mass from circumstellar disks and in many cases, the accretion coincides with a phase of massive outflows, which can be highly collimated. Those jets emit predominantly in the optical and IR wavelength range. However, in several cases X-ray and UV observations reveal a weak but highly energetic component in those jets. X-rays are observed both from stationary regions close to the star and from knots in the jet several hundred AU from the star. In this article we show semi-analytically that a fast stellar wind which is recollimated by the pressure from a slower, more massive disk wind can have the right properties to power stationary X-ray emission. The size of the shocked regions is compatible with observational constraints. Our calculations support a wind-wind interaction scenario for the high energy emission near the base of YSO jets. For the specific case of DG Tau, a stellar wind with a mass loss rate of 5 ⋅ 10−10 M⊙ yr−1 and a wind speed of 800 km s−1 reproduces the observed X-ray spectrum. We conclude that a stellar wind recollimation shock is a viable scenario to power stationary X-ray emission close to the jet launching point.
[section] [section] [section] [section] [section] Optimal Predictors: A Bayesian Notion of Approximation Algorithm
Modular Arithmetic
Blog Post 5
1 $\underline{\text{Binary Notation}}$
We define binary numbers as the powers of two that lay the foundation for the additive building blocks of positive integers. Note that the word binary comes from “Bi” meaning two. In this system, integers are expressed in terms of only 0s and 1s. The values that represent each integer are calculated by finding the sum of the powers of two that make up the given number. We pull out the amount of times that each power of two occurs. For example, the decimal number ten is written as “1010” because it is $\underline{1}$ ⋅ $2^3+ \underline{0} $ ⋅ $2^2 + \underline{1} \cdot 2^1 + \underline{0} \cdot 2^0 $. Notice that this starts with the largest power of two. We read “1010” as “one-zero-one-zero” as opposed to one thousand and ten. The binary representation of the first few natural numbers are shown in the table below.
Euclidean Algorithm
The Euclidean Algorithm, also known as Euclid’s Algorithm, is
used in discrete mathematics to find the greatest common divisor of two natural
numbers, namely \(a\) and \(b\). The greatest common divisor is typically denoted as \(gcd\left(a,b\right).\) In general, the Euclidean Algorithm is used
within numerous applications like solving Diophantine equations, constructing
continued fractions, and is even used when dividing in modular arithmetic.
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On the evolution of Cold Classical Kuiper Belt Objects
At a region between 39.4 AU and 47.8 AU, the Kuiper Belt contains planetesimals thought to remnants of the protoplanetary disk in the early Solar System. There are 3 types of object which occupy the Kuiper Belt: Scattered Objects, Hot Classicals, and Cold Classicals.
Scattered Objects have highly eccentric and inclined orbits, not constrained to the 40-50 AU region, believed to be due to Neptune’s early migration outwards when Jupiter and Saturn entered a 2:1 resonance, derived from the Nice Model. This migration scattered the primordial Kuiper Belt which had occupied the region where Neptune orbits today.
Hot Classicals are objects which were believed to have been scattered by Neptune but not to the extent of the Scattered Objects. These objects would’ve had their eccentricities and inclinations increased, but ultimately would find stable orbits within the region bounded by 2:3 and 1:2 resonances with Neptune, thus being deemed “Classical”
Cold Classicals are objects which are believed to be unaffected by Neptune’s early migration, being formed between 39.4 AU and 47.8 AU with low eccentricities and inclinations (with e ≈ 0.02, i ≈ 0.02), and remaining stable within the region bounded by 2:3 and 1:2 resonances with Neptune, with perturbations in orbits being due to self-scattering.
Since the Cold Classical Kuiper Belt Objects (CCKBOs) presumably are only affected by self-scattering, by understanding that process it would be possible to simulate these objects over the age of the Solar System to see if that alone can reproduce the observed orbital properties of CCKBOs. The process in question is the combined effect of Viscous Stirring and Dynamical Friction.
Viscous Stirring involves multiple encounters of multiple objects over time, which lead to a wider spread of velocity distribution, which leads to an increase of eccentricity and inclination of objects. Dynamical Friction involves gravitational encounters with masses of different velocities. Large mass objects are dragged by low mass objects, while low mass objects are gravitationally assisted by large mass objects. This leads to a general decrease of velocity for large masses and an increase for low masses.
Ohtsuki & Stewart (2002, Icarus 155, 436-453, hereafter O&S) obtained evolution rates of eccentricity and inclination using Viscous Stirring and Dynamical Friction rates where the coordinates are referred to a reference point that moves in a circular orbit with semimajor axis a0 at the Keplerian angular velocity Ω = (GM⊙/a03)1/2, and described them for a system of 2 planetesimal components, with object masses m1 and m2
[!HD-episode!] Gogglebox S7 E2 On'line Free Full
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