Motivation Preview from problem set 2, question 4: (link to original file) This gives a reduction: [submodular welfare maximization] <= [maximize a monotone submodular function s.t. matroid constarint]. Remarks: hardness & approximation of the problem [submodular welfare maximization] >= [maximize a monotone submodular function s.t. matroid constarint] (Is it true though?). maximize monotone submodular function is hard. Because, for instance, one can reduce Partition problem to it. That’s why we started looking at submodular maximization s.t. matroid constraint in last week. To begin with, ...

Following the news of Amazon’s lawsuits and after skimming through the complaints, here are my thoughts. price do go up | 羊毛出在羊身上 There’s no free lunch. While prices may seem lower on Amazon, the market is interconnected. Amazon’s attempt of achieving lower price would backfire. Amazon’s power forces sellers to comply with its Buy Box rules, meaning they must keep prices equal or higher across all channels to access Amazon’s vast demand. However, because Amazon charges high commissions, sellers often decide to raise prices across the board. ...

Following yesterday’s coverage on Amazon’s series of trouble with antitrust regulators, I digged into the filing complaint of CA v Amazon and the orginal complaint and amended complaint of FTC v Amazon. We can obtain quite a bit of interesting information about Amazon’s Buy Box: (at least, from the perspective of regulators…) first, Amazon chose to make purchasing outside the Buy Box hard: Nearly 98% of Amazon sales are made through the Buy Box. ...

Here are recent news about Amazon Buy Box’s into antitrust trouble: California sues Amazon | September, 2022 Timeline: Sept. 2022: Attorney General Bonta sued Amazon in the Superior Court of California. The lawsuit basically focused on accusing Amazon penalizing sellers for listing products at the lower price on other selling channels—that if Amazon spots a product listed elsewhere cheaper, it will often remove the seller from the Buy Box on Amazon. ...

people in academia are generally too good at procrastinating. doing things at last minute isn’t entirely wrong. like, some job scheduling algorithms do look like they are procrastinating. plus there is the infamous structured procrastination… but at the end of the day, procrastination makes one think inefficiently in a rush, raise anxiety level and occasionally, blow up deadlines. so here’s an effort of trying to battle my procrastinating tendency during bloggings: ...

Recap of week 2, and motivation for this week’s Part I: In an economy of $n$ agents and $m$ indivisible items, if all agents’ value functions are Gross-Substitute, the economy has a Walrasian Equilibrium $(\vec S, \vec p)$. The Walrasian Tatônnement process can find the equilibrium efficiently. The allocation also maximizes social welfare. But one subtle thing to notice about Walrasian Tatônnement is that it converges to an equilibrium. So here’s another way of solving it: ...

👏🤦🏻‍♀️👏🤦🏻‍♀️👏🤦🏻‍♀️ 50-years of open problem closed. Proteins are essentially correctly folded and well-functioning polypeptide chains. So theoretically, protein 3D structures are determined by the sequence of amino acids in the polypeptide chain. The Nobel Prize in Chemistry (1972) was awarded to C. Anfinsen for this finding. amino acids make up proteins essentially like LEGOS. importantly, proteins function only when they are folded and form their structure in the right way ...

Much to almost everyone’s surprise, the Nobel Price in Physics 2024 is awarded to John Hopfield and Geoffrey Hinton, for their foundational discoveries and inventions in ML: When we talk about artificial intelligence, we often mean machine learning using artificial neural networks. This technology was originally inspired by the structure of the brain. In an artificial neural network, the brain’s neurons are represented by nodes that have different values. These nodes influence each other through con­nections that can be likened to synapses and which can be made stronger or weaker. The network is trained, for example by developing stronger connections between nodes with simultaneously high values. This year’s laureates have conducted important work with artificial neural networks from the 1980s onward. ...

The official performance of 7 selected songs from Ariana Grande’s 7th album eternal sunshine is out. They are: intro (end of the world) don’t wanna break up again eternal sunshine supernatural yes, and? we can’t be friends imperfect for you My favourite is supernatural, Ari’s vocal is accurate and almost flawless: Editor Katia Temkin seems to be in favor of her weird hand-held camera angle that moves back and forth in an annoyingly unstable way. Editing is also clueless. It’s very disappointing to see this level of unprofessionalism in industry production. ...

Mastery of techinuqe, sweet cockyness, and looking like to be having so much fun—here’s Marianela Núñez’s Kitri in Don Quixote: