Andante cantabile(It.) is a direction often used by composers. In general, it means flowing and songlike. The andante tempo is known as the walking pace, and the pacing and energy should generally feel like a nice stroll. Cantabile [kanˈtaːbile], an Italian word, means literally “singable” or “songlike”. In instrumental music, it is a particular style of playing designed to imitate the human voice. To a large section of the public, however, it means one work, the 2nd movt., andante cantabile, of Tchaikovsky’s str. qt. No.1 in D (1871), Op.11. ...

Prologue In the highly competitive coffee market, a fierce price war erupted with the introduction of the ¥9.9 (~1.37USD) coffee, leading to dramatic changes for two major players: COTTI Coffee and luckin Coffee. Over the span of a year, this aggressive pricing strategy have caused COTTI’s slowing down in its pace of expansion, while luckin Coffee also saw its profits plummet, transitioning from profitability to significant losses. By Xu Qing | Edited by Jin Za ...

Here’s a professional, in-depth intepretation of the Liederabend performance of Changyong Liao, originally in Chinese, available here. The program selected works from Italy, Germany-Austria, and China, each with distinct artistic themes. It included classic Italian art songs by Paolo Tosti such as “The Last Song,” “I Love You No More,” and “Melancholy,” totaling five pieces. The repertoire also featured twelve Chinese art songs, including “Three Wishes of the Rose,” “Spring Thoughts,” and “The River Flows Eastward,” as well as Gustav Mahler’s song cycle “Songs of a Wayfarer.” ...

A two-day series on Lieder Today I had the privilege of attending a concert curated and performed by Changyong Liao, alongside his long-time collaborator, German pianist Hartmut Höll. The duo masterfully arranged a series of Lieder (aka, art songs) titled Three Wishes of the Rose: 16 Chinese Lieders. Witnessing these original composers interpret these songs was a profound experience, filled with a rich tapestry of emotions and beauty. The encore ’the seek of Prunus mume on a snowey day’. Watch here for the up-stairs version, and here for the front-seat version. ...

Lieder in a nutshell The plural German noun Lieder (singular Lied) simply means “songs” – any kind of songs. But for classical music enthusiasts, the word signifies songs with piano accompaniment circa 1800–1900 – the birth of the form which coincided with the rise of the poetry-enjoying European middle classes in the wake of the French Revolution. Explainer: What Are Lieder? by Graham Johnson OBE. Lieder represents perhaps the most expressive sub-genre within classical music. These compositions, typically performed in relaxed afternoon salons, are based on poetry and sung with a freedom that contrasts with the rigid structures of concertos. ...

Working as a teaching assistant for college mathematics or general mathematically inclined courses turns out to be not as trivial a task as I’ve thought it to be. This semester I’m TAing for Advanced Optimization –– an obligatory course for sophomore students. I’ve also took last year. Moreover, I took an even more advanced version of it (convex optimization) while I was visiting Stanford last summer. Still, teaching and tutoring turns out not to be something that comes out of thin air. I thought I can just do the assignments and gradings within minutes, give the recitation session without any efforts or too much investment in preparing––turns out the truth is quite the opposite. ...

Dynamic Programming (DP) serves as a foundational approach in computational algorithms, especially effective in environments with complete knowledge of state transitions and rewards, described within the Markov Decision Process (MDP) framework. However, the real-world often presents scenarios where such comprehensive information is unavailable. Here, Reinforcement Learning (RL) steps in with model-free methods that leverage DP principles but operate without the need for explicit transition probabilities or rewards. Markov Decision Process (MDP) Framework An MDP is a mathematical framework used to describe an environment in decision-making problems where outcomes are partly random and partly under the control of a decision-maker. MDPs are defined by the following components: ...

a stochastic calculus crash course for Financial Engineering. Building on Kolmogorov’s axiomatic probability theory, define continuous time stochastic process, for time $\mathcal T = [0,\infty)$ a sample path is essentially $$ {X_t : t\ge 0} $$ Brownian Motion History anecdote: In 1828, British Botanist R. Brown observed the random movement exhibited by plant pollens suspended in water. In 1905, A. Einstein proposed the first quantitative model of Brownian motion in terms of a Gaussian process, which explains some principles of molecular movements. ...

reading write-up: How Food Affects the Mind and Body December 20, 2022, The Economist the trend The take-out delivery industry is booming, paralleling the general food industry’s growth in Shanghai. The United States has been facing serious obesity problem for decades, and now East Asia, particularly Shanghai, appears to be catching up. This trend is rooted in macroeconomic factors. The general decline in growth rate has increased stress levels, causing people to lower their consumption standards. In such times, easily accessible, unhealthy, yet delicious food becomes a cheap dopamine booster. The phrase “happiness is the same price as Red-Bottoms” holds true only if one can afford them. The economic downturn has led capital to venture into the general food industry, especially in Shanghai, where bakeries are flourishing. ...

The Timeless Tchaikovsky: best known, and much loved, with his epic work of ballets and symphonies. Among one of his most cherished ballet compositions is the Miniature Overture from The Nutcracker, a masterpiece of delicate orchestration and intricate musical storytelling. For a stellar rendition of this celebrated piece, listen to the 2010 performance conducted by Sir Simon Rattle and recorded by the Berliner Philharmoniker. Listen here on YouTube or on Apple Music which provides the Lossless fidelity. ...