Rusalka is undoubtedly Dvořák’s most celebrated opera. Like many operas, its fame largely stems from one iconic excerpt: the hauntingly beautiful “Song to the Moon.” This piece, with its ethereal melody, has been adapted in countless forms—including a harp version I found to be a soothing lullaby… A Story That Echoes Through Time Rusalka, like the mermaids or willies of folklore, embodies the tragic figure of a woman wronged by love—mournful, otherworldly, and sometimes vengeance towards mankind. These entities appear frequently in Slavic mythology and have inspired countless modern adaptations, often drawing parallels with the archetype of the mermaid. ...

The biggest musical production of 2024 is out. Directed by Jon Chu, music by Stephem Schwartz and Holzman. Original broadway cast was Idina Menzel (center) and Kristin Chenoweth More information (and spoiler) can be found here at its Wikipedia. Check out its box office performance here. I will update its movie review later, after I submitted all of my applications…

This post follows up on the Online Bipartite Matching series, specifically building on the primal-dual techniques discussed in Part II. Recently, I attended a talk by Yiding Feng at SJTU that introduced a fascinating application of these techniques in a broader context, as detailed in their paper. Batching and Optimal Multi-stage Bipartite Allocations Yiding Feng and Rad Niazadeh In several applications of real-time matching of demand to supply in online marketplaces, the platform allows for some latency to batch the demand and improve the efficiency of the resulting matching. Motivated by these applications, we study the optimal trade-off between batching and inefficiency in the context of designing robust online allocations. As our base model, we consider K-stage variants of the classic vertex weighted bipartite b-matching in the adversarial setting, where online vertices arrive stage-wise and in K batches — in contrast to online arrival. Our main result for this problem is an optimal 1−(1−1/K)^K- competitive (fractional) matching algorithm, improving the classic (1 − 1/e) competitive ratio bound known for its online variant (Mehta et al., 2007; Aggarwal et al., 2011). We also extend this result to the rich model of multi-stage configuration allocation with free-disposals (Devanur et al., 2016), which is motivated by the display advertising application in the context of video streaming platforms. ...

China’s higher education system employs a unique postgraduate enrollment mechanism called “recommendation for postgraduate studies,” or “保研” (Bao-Yan) in Chinese. Due to its structure and timing, commitments between students and universities are often made and then broken, leading to a chaotic landscape of mutual defaults. This admission process has evolved into a disturbing game between students and admissions offices. Colloquially, students refer to the act of reneging on commitments as “鸽” (ge), meaning “to pigeon,” a playful nod to the widespread practice. Here’s a breakdown of the admission process, an analysis of its complications, and a proposed solution. ...

To use more colors in Overleaf LaTeX, one can do the following: at header \usepackage[dvipsnames]{xcolor} Then the following named color can be accessed: [dvipsnames] provided colors One can access colors by \color{RoyalBlue} Or, in a more fancy way, define the commands at header \newcommand{\note}[1]{{\color{Rhodamine}\noindent\textbf{\{}{#1}\textbf{\}}}} For more information, check out Overleaf’s tutorial here: Using colors in LaTeX.

Continuing the discussion on online matching algorithms, the first post here discussed the online bipartite matching model and a greedy (deterministic) algorithm that achieves a 1/2-competitive ratio. Today, we explore randomized algorithms for the online bipartite matching problem: Stealing a page from Professor Tang’s slide. One side of the bipartite graph is fixed and known in advance, the other side with edges arrives one-by-one in an online fashion. ...

The G20 2024 took place Nov. 18 and 19 in Rio, Brazil. G20 for Group of Twenty, is a club of the world’s largest economies, representing about 85% of global GDP, 75% of international trade, and two-thirds of the world’s population. It started in 1999 as a meeting of finance ministers and central bank governors, but it wasn’t until the 2008 global financial crisis that it became a platform for world leaders to gather. ...

Professor Tang’s online seminar course today covers online matching. (very short) motivation The (offline) maximum matching problem is a well-studied area in graph theory, even though some cases (e.g., on general graphs with weights) can be NP-hard. Classic algorithms have provided efficient solutions for specific cases: Bipartite matching: Solved using the Ford-Fulkerson Algorithm for maximum flow. Weighted bipartite matching: Uses the Hungarian Algorithm to find an optimal match. Unweighted general graphs: Solved by Edmonds’ Blossom Algorithm, which extends matching theory to handle odd-length cycles. These problems have wide applications, from job assignments to network design. Here’s a snapshot of real-world examples: ...

The closing performance of the Shanghai International Art Festival, by Tugan Sokhiev and the Munich Philharmonic was nothing short of extraordinary! While high-quality recordings can provide an astonishingly immersive experience for solo or chamber works—especially with a decent set of headphones. But only live orchestral performances can achieve the stunning scale and acoustic intricacies of a grand compositions. The emotional depth of Tchaikovsky’s Piano Concerto No. 1 and the vivid storytelling in Rimsky-Korsakov’s Scheherazade were rendered with such mastery that no recording could ever hope to capture their full impact. This performance was a reminder of why orchestras like this exist: to make music alive, dynamic, and immersive. ...

Tomorrow (Nov. 17) marks the grand finale of the Shanghai International Art Festival. The closing performance features the esteemed Munich Philharmonic, led by Tugan Sokhiev, with the brilliant pianist Haochen Zhang gracing the stage. Tugan Sokhiev: the man with a baton and a plan. The program offers a sumptuous feast of late-Romantic repertoire, showcasing three well-loved classics: Tchaikovsky | Polonaise from Eugene Onegin Tchaikovsky | Piano Concerto No.1 Rimsky-Korsakov | Scheherazade Interestingly, Tchaikovsky’s Polonaise also made an appearance as an encore during the opening performance in September, presented by the Shanghai Symphony Orchestra under Long Yu: ...