Supposedly, Mozart once made a joke: “What’s worse than the sound of a flute? - Two flutes.” We’ll never know if it is real. Somehow anecdotally humors turned into being that Mozart hated the flute. But, when one listens to his flute and harp concerto, this seems hard to believe anyway. But it’s true that Mozart seldom offer to write works for flute alone. He said so himself, in a letter to his father. He said he couldn’t abide the sound of a solo flute and found it difficult to compose for a flute. Mozart was struggling to fulfill a commission from an amateur musician for numerous flute works (including his two concertos for the instrument) when he penned those disparaging words to his father; he sounds like a procrastinating student making excuses for not finishing his homework: ...

The music industry is booming in 2024. What a scene. Following Ariana Grande’s eternal sunshine release in March, Taylor Swift’s tenth album in April, Dua Lipa in May. And now Sabrina Carpenter has taken over to begin her campaign for her new project Short n’ Sweet. Sabrina Carpenter’s latest single looks to take her breakout year to an even-higher level. Her season is in full effect. As “Espresso” continues to dominate, “Please Please Please,” the second single from Carpenter’s forthcoming Short n’ Sweet LP, has emerged as yet another smash for the pint-sized pop star. ...

The Beta distribution is a versatile and useful probability distribution with a wide range of applications in statistics, particularly when associated with modelling unknown probabilities and doing Bayesian inference. Here’s a brief overview: definition The Beta distribution, denoted as $ \theta \sim B(\alpha, \beta) $​, is defined by two shape parameters $ \alpha $​ and $ \beta $​. The probability density function (pdf) of the Beta distribution is given by: ...

There are three major shopping festivals in China: double eleven (Nov. 11), double twelve (Dec. 12) and 6.18. It’s somewhat akin to Black Friday yet still slightly different. All these three festivals emerged in the past decade, and are promoted mainly by E-commerce platforms. They are basically artificial festivals tailored for consumerism. Naturally (though still interesting and enjoyable to observe and experience), when online platforms started to offer huge discounts, local retail stores simultaneously begin to offer discounts. And these discounts sometimes don’t match. ...

The song casts a magical spell. The first line of the chorus, with the lyric ’the boy is mine’, masterfully escalates the tension built up from the pre-chorus––however though, by disrupting the tension’s anticipating flow, with a striking and beautiful fermata on the tempo. This innovative technique, rarely seen in recent pop productions, perfectly ignites the song’s whimsical and provocative allure. the music video match the audacious and dramatic flair of the song. Start from here to listen to the editing of the music video that almost completes this avant-garde, iconic production. ...

Ariana Grande’s albums invariably feature at least one so-called ‘bad-girl anthem’. Take her debut album ‘Yours Truly’, arguably the most innocent of her career, which includes the sultry track The Way. This song is a collaboration with her then-boyfriend Mac Miller, and it famously includes the line, “I got a bad boy, you must admit it.” Her subsequent albums—My Everything and Dangerous Woman—further shaped her image as a love-craving icon. Even Sweetener offers R.E.M., which lyrically flirts with: ...

Consider the following RMAB problem instance. (For a review of what is an RMAB, check out here). A platform coordinates a total of $N$ volunteers for various tasks. At each time point, a task $k$ out of $K$ possible tasks arrives randomly with probability $f_k$, and the platform must decide whom to notify (activate) based on the likelihood of acceptance $p_{k, i}, i\in [N]$ and the potential reward for each volunteer incentivized, exogeneously given as $w_k$. ...

Consider an RMAB instance with $N$ arms, where each arm $i \in [N]$ has a finite state space $\mathbb S_i$ and can receive an action $y_i^t \in \{0, 1\}$ (representing not pulling or pulling the arm, respectively) at each time step $t$. The state of arm $i$ at time $t$ is denoted by $s_i^t$. Depending on the action taken, a reward $r_i(s_i^t, y_i^t)$ is accrued. As a decision maker, our objective is to maximize the averaged total reward over an infinite time horizon, under a constraint that only $B$ arms can be pulled at any time step. This setup can be formalized as follows: ...

Decision-making in dynamic environments over time presents unique challenges, particularly when the conditions influencing decisions are constantly changing. In such scenarios, traditional decision-making models often fall short. This is where Restless Multi-Armed Bandits (RMAB) come into play. The method provides a robust framework for modeling and optimizing decisions over time. Here’s a brief introduction of the concept of RMAB and the Whittle Index Policy. understanding Restless Multi-Armed Bandits what are RMAB? The multi-armed bandit problem is a classic version of the problem of optimal allocation of activity under certainty: simply saying, one has $n$ projects, the state of project $i\in [n]$ being denoted by $x_i(t)$​. ...

A memoir of Market Mechanism Design course’s final presentation report, based on: Algorithmic Classification and Strategic Effort Jon Kleinberg and Manish Raghavan | ACM SIGecom Exchanges, Vol. 18, No. 2, November 2020, Pages 53–60 motivation: difference in modelling strategic behavior and objectives–between econ/CS perspectives The principal-agent and strategic machine learning literatures appear to share a common goal: how should one structure a decision-making rule to account for the strategic actions of decision subjects? ...