Comments for Calvin Café: The Simons Institute Blog https://blog.simons.berkeley.edu What's New at the Simons Institute for the Theory of Computing. Sun, 01 Oct 2023 15:41:22 +0000 hourly 1 https://wordpress.org/?v=6.1.1 Comment on Theory at the Institute and Beyond, July 2023 by Jual Kambing Purwokerto https://blog.simons.berkeley.edu/2023/07/theory-at-the-institute-and-beyond-july-2023/#comment-23096 Sun, 01 Oct 2023 15:41:22 +0000 https://blog.simons.berkeley.edu/?p=949#comment-23096 It’s fascinating to see how the Simons Institute remains abuzz with activity during what is typically a quieter period on university campuses. The mention of the ongoing programs in Analysis and TCS, as well as Quantum Computing, highlights the institute’s commitment to fostering cutting-edge research and collaboration.

The historical perspective on the Simons Institute’s past programs, such as Real Analysis in Computer Science in 2013, underscores the institute’s role in shaping and advancing various fields of computer science. The evolution of the field over the past decade, with the emergence of new themes like global hypercontractivity and spectral independence, as well as the incorporation of innovative methodologies, demonstrates the dynamic nature of computer science research.

Furthermore, the focus on Quantum Computing and its emphasis on noisy intermediate-scale quantum (NISQ) devices is particularly intriguing. NISQ devices are at the forefront of quantum technology, and the pursuit of quantum advantage in the absence of error correction presents unique challenges and exciting opportunities for theoretical research.

In summary, the Simons Institute’s dedication to facilitating groundbreaking research in Analysis, TCS, and Quantum Computing is commendable, and it’s evident that these programs are contributing significantly to the advancement of their respective fields. The institute’s role in fostering collaboration between theory and practice is vital, especially in areas as cutting-edge and rapidly evolving as quantum computing.

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Comment on Theory at the Institute and Beyond, July 2023 by Betul Aydın https://blog.simons.berkeley.edu/2023/07/theory-at-the-institute-and-beyond-july-2023/#comment-21952 Sun, 16 Jul 2023 21:54:43 +0000 https://blog.simons.berkeley.edu/?p=949#comment-21952 It was a pleasant article. Thanks…

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Comment on Mechanisms: Inside or In-Between? by Sanny https://blog.simons.berkeley.edu/2023/05/mechanisms-inside-or-in-between/#comment-21097 Thu, 04 May 2023 18:10:41 +0000 https://blog.simons.berkeley.edu/?p=920#comment-21097 It is interesting to note how the different uses of “causal mechanism” can lead to confusion and misinterpretation of results in causal inference. The in-between sense of causal mechanisms is focused on the chain of causal relations between a triggering event and outcome, while the inside sense is concerned with the constituents of the triggering variable that give it its causal powers. While both uses are important, the inside sense is crucial for developing accurate causal models. Understanding the innards of each relata designated by a variable name and their connections to other variables can help researchers to create more robust and reliable models.

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Comment on The Blooming of the \(c^3\) LTC Flowers by Teknik Telekomunikasi https://blog.simons.berkeley.edu/2022/09/the-blooming-of-the-c3-ltc-flowers/#comment-18421 Fri, 28 Oct 2022 10:31:08 +0000 https://blog.simons.berkeley.edu/?p=677#comment-18421 Wow this is an amazing and spectacular code discovery!

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Comment on The Blooming of the \(c^3\) LTC Flowers by Inquisitor https://blog.simons.berkeley.edu/2022/09/the-blooming-of-the-c3-ltc-flowers/#comment-18294 Wed, 19 Oct 2022 06:37:42 +0000 https://blog.simons.berkeley.edu/?p=677#comment-18294 What is L in the definition of the Schrier graph?

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Comment on Fine-grained hardness of lattice problems: Open questions by Divesh Aggarwal https://blog.simons.berkeley.edu/2020/05/fine-grained-hardness-of-lattice-problems-open-questions/#comment-5682 Wed, 30 Sep 2020 17:50:25 +0000 https://blog.simons.berkeley.edu/?p=164#comment-5682 Just to add to Huck’s comment above, I think that the algorithm from [ADS15] that starts with 2^{n+o(n)} vectors in D_{L,s} for large enough s, and repeatedly takes average of pairs of vectors in the same coset in L/2L seems like a reasonable candidate that solves CVP_p in 2^{n+o(n)} time.

I have no clue how to go about proving this, though.

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Comment on Lattice Blog Reduction – Part II: Slide Reduction by Lattice Blog Reduction – Part III: Self-Dual BKZ | Calvin Café: The Simons Institute Blog https://blog.simons.berkeley.edu/2020/05/lattice-blog-reduction-part-ii-slide-reduction/#comment-5541 Fri, 28 Aug 2020 11:58:39 +0000 https://blog.simons.berkeley.edu/?p=260#comment-5541 […] ← Previous […]

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Comment on Lattice Blog Reduction – Part I: BKZ by Lattice Blog Reduction – Part III: Self-Dual BKZ | Calvin Café: The Simons Institute Blog https://blog.simons.berkeley.edu/2020/04/lattice-blog-reduction-part-i-bkz/#comment-5540 Fri, 28 Aug 2020 11:56:58 +0000 https://blog.simons.berkeley.edu/?p=146#comment-5540 […] is the third and last entry in a series of posts about lattice block reduction. See here and here for the first and second part, resp. In this post I will assume you have read the other […]

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Comment on Lattice Blog Reduction – Part I: BKZ by Lattice Blog Reduction – Part II: Slide Reduction | Calvin Café: The Simons Institute Blog https://blog.simons.berkeley.edu/2020/04/lattice-blog-reduction-part-i-bkz/#comment-5074 Tue, 12 May 2020 10:45:27 +0000 https://blog.simons.berkeley.edu/?p=146#comment-5074 […] is the second entry in a series of posts about lattice block reduction. See here for the first part. In this post I will assume you have read the first one, so if you haven’t, […]

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Comment on Fine-grained hardness of lattice problems: Open questions by Huck Bennett https://blog.simons.berkeley.edu/2020/05/fine-grained-hardness-of-lattice-problems-open-questions/#comment-5071 Thu, 07 May 2020 00:23:43 +0000 https://blog.simons.berkeley.edu/?p=164#comment-5071 In reply to Huck Bennett.

Hi Thijs,

RE, Frodo, thanks for the correction! I’ve updated the post.

I’m not at all sure about kissing numbers in l_p norms, but the maximum number of closest vectors is known and is fairly straightforward for all l_p norms: the maximum possible number of closest vectors for 1 < p < infinity is 2^n and is unbounded for l_1 and l_infinity (even in two dimensions).

For 1 < p < infinity, the integer lattice together with the all (1/2)s vector as a target yields a lower bound of 2^n, and the upper bound follows by a pigeonhole/coset averaging argument. Namely, suppose that there are 2^n + 1 closest lattice vectors to a given target. Then, there must be two such closest vectors v, w that lie in the same coset mod twice the lattice. But then (v + w)/2 is also a lattice vector, and, by the strict convexity of the l_p norm for 1 < p < infinity, it is strictly closer to the target than v or w, which is a contradiction.

Accordingly, it might be reasonable to guess that the “right” time complexity of CVP_p for 1 < p < infinity is 2^n. This would match our lower bound for all such p that are not even integers.

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