免费的电脑梯子软件
``And once the storm is over you won't remember how you made it through, how you managed to survive. You won't even be sure, in fact, whether the storm is really over. But one thing is certain. When you come out of the storm you won't be the same person who walked in. That's what this storm's all about.''
-Haruki Murakami
----------------------------------------------
OPEN POSITIONS!
The lab is excited to announce an open position for a Ph.D. student as well as opportunities for masters and undergraduate research credits. Please see the open positions page for details.
----------------------------------------------
NEUTRONSTAR
is the world's fastest isotope engine. (Also, since we are, as of now, alone in the universe, it is also the fastest isotope engine in the universe [braggable].)
Built with newly developed layer-ordered heap theory for selection on Cartesian products, NeutronStar generates the top million peaks of complicated compounds with many isotope states per in element less than a second.
Read the Analytical Chemistry publication, Kreitzberg, Pennington, Lucke, and Serang.
Check out the software here.
██████╗ ██╗ ██████╗ ████████╗
██╔══██╗██║ ██╔═══██╗╚══██╔══╝
██████╔╝██║ ██║ ██║ ██║
██╔══██╗██║ ██║ ██║ ██║
██████╔╝███████╗╚██████╔╝ ██║
╚═════╝ ╚══════╝ ╚═════╝ ╚═╝
██████╗ ██╗ ██╗████████╗
██╔═══██╗██║ ██║╚══██╔══╝
██║ ██║██║ ██║ ██║
██║ ██║██║ ██║ ██║
╚██████╔╝╚██████╔╝ ██║
╚═════╝ ╚═════╝ ╚═╝
████████╗██╗ ██╗███████╗
╚══██╔══╝██║ ██║██╔════╝
██║ ███████║█████╗
██║ ██╔══██║██╔══╝
██║ ██║ ██║███████╗
╚═╝ ╚═╝ ╚═╝╚══════╝
███████╗██╗ ██╗███╗ ██╗
██╔════╝██║ ██║████╗ ██║
███████╗██║ ██║██╔██╗ ██║
╚════██║██║ ██║██║╚██╗██║
███████║╚██████╔╝██║ ╚████║
╚══════╝ ╚═════╝ ╚═╝ ╚═══╝
你不懂钢笔的长辈曾怎么评价过你的钢笔？ - 知乎:我爸玩古钱币的，非常能理解我这种收藏癖有时候我还会给他解释这些笔，为什么收它，我觉得戳我的点在哪，…
求一个网站你懂的 - 95秀-美女主播视频交友聊天直播间-95美女秀:很多男人在夜深人静的时候都想自己的初恋女友，特别想有一个与之前的初恋女友一样的伙伴，满足自己曾经没有得到的那种情感空虚，想要获得这样的情感，最好的方式就是在直播中找到，有没有一个网站可伍轻松地拥有初恋的感觉，现在这个梦想是完全可伍实现的。
| COMPETITOR | COLD WATER ENDURANCE | MOST HUCKLEBERRIES | LARGEST HUCKLEBERRY | SUM |
|---|---|---|---|---|
| PATRICK | 3 | 1 | 4 | 8 |
| KYLE | 3 | 4 | 3 | 7 |
| ROOSTER | 1 | 2 | 1 | 4 |
| ANNIKA | 2 | 3 | 2 | 7 |
GEWINNER: Jake (Rooster) Pennington took first prize. Oliver's performance was disqualified after he tested positive for rooibos tea.
----------------------------------------------
FINALIST FOR BEST OF GRADCON
Kyle Lucke's work on cardinal Bayesian models for protein inference was a finalist for the best of the University of Montana's GradCon 2023!
----------------------------------------------
小时候看不懂的片段，真的是太污了，你看懂了吗_腾讯视频:2021-8-23 · 小时候看不懂的片段，真的是太污了，你看懂了吗
Using the newly invented layer-ordered heap, the lab recently created a new optimal method for selection on the Cartesian sum (or product) $$X+Y.$$ This means, given two lists $$X,Y,$$ it finds the smallest k terms of the form $$X_i+Y_j.$$ If the lists are length n, it finds these smallest k values in $$O(n+k).$$ This approach is simple and performs well in practice. Read the preprint here.
----------------------------------------------
THE INVENTION OF THE LAYER-ORDERED HEAP AND THE FASTEST KNOWN METHOD FOR COMPUTING THE TOP TERMS OF THE CARTESIAN SUM
Patrick Kreitzberg, Kyle
Lucke, and Oliver Serang created the first efficient
methods for performing selection on the Cartesian sum
$$Y=X_1+X_2+\cdots+X_m.$$ The technique is important for
Bayesian inference under additive dependencies, computing
the most abundant isotope peaks of a compound, computing
the most efficient k configurations to build a
product with m independent supply lines, and
more.
By using a new data structure called a ``layer-ordered
heap,'' one can compute the top k terms of a
Cartesian product of m arrays, each of
length n, in $$o(m\cdot n + k\cdot m)$$
time. Consider that simply loading the data costs m
n and accessing each of the m indices at each
of the k top values costs k m; this is a
remarkable result.
Read
the preprint
here.
----------------------------------------------
RETURN TO EXPLORING SCIENTIFIC WILDERNESS
Exploring Scientific Wilderness is back for its second
season! Join us (Patrick Kreitzberg, Kyle Lucke, Max
Thibeau, Jake Pennington, and Oliver Serang) for over
20 new episodes, including science tutorials,
interviews with scientists, and more! Episodes will be
released weekly on Sunday evenings for the next six
months.
This season features music from the phenomenal
synthwave record label Italians Do It Better.
██████╗ ███████╗████████╗██╗ ██╗██████╗ ███╗ ██╗ ██╔══██╗██╔════╝╚══██╔══╝██║ ██║██╔══██╗████╗ ██║ ██████╔╝█████╗ ██║ ██║ ██║██████╔╝██╔██╗ ██║ ██╔══██╗██╔══╝ ██║ ██║ ██║██╔══██╗██║╚██╗██║ ██║ ██║███████╗ ██║ ╚██████╔╝██║ ██║██║ ╚████║ ╚═╝ ╚═╝╚══════╝ ╚═╝ ╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═══╝ ████████╗ ██████╗ ╚══██╔══╝██╔═══██╗ ██║ ██║ ██║ ██║ ██║ ██║ ██║ ╚██████╔╝ ╚═╝ ╚═════╝ ████████╗██╗ ██╗███████╗ ╚══██╔══╝██║ ██║██╔════╝ ██║ ███████║█████╗ ██║ ██╔══██║██╔══╝ ██║ ██║ ██║███████╗ ╚═╝ ╚═╝ ╚═╝╚══════╝ ██╗ ██╗██╗██╗ ██████╗ ███████╗██████╗ ███╗ ██╗███████╗███████╗███████╗ ██║ ██║██║██║ ██╔══██╗██╔════╝██╔══██╗████╗ ██║██╔════╝██╔════╝██╔════╝ ██║ █╗ ██║██║██║ ██║ ██║█████╗ ██████╔╝██╔██╗ ██║█████╗ ███████╗███████╗ ██║███╗██║██║██║ ██║ ██║██╔══╝ ██╔══██╗██║╚██╗██║██╔══╝ ╚════██║╚════██║ ╚███╔███╔╝██║███████╗██████╔╝███████╗██║ ██║██║ ╚████║███████╗███████║███████║ ╚══╝╚══╝ ╚═╝╚══════╝╚═════╝ ╚══════╝╚═╝ ╚═╝╚═╝ ╚═══╝╚══════╝╚══════╝╚══════╝
----------------------------------------------
TEXTBOOK: INTRODUCTION TO CYBERSECURITY
Oliver Serang's textbook, Introduction to Cybersecurity, is now online.
Check it out here.
██╗███╗ ██╗████████╗██████╗ ██████╗ ██║████╗ ██║╚══██╔══╝██╔══██╗██╔═══██╗ ██║██╔██╗ ██║ ██║ ██████╔╝██║ ██║ ██║██║╚██╗██║ ██║ ██╔══██╗██║ ██║ ██║██║ ╚████║ ██║ ██║ ██║╚██████╔╝ ╚═╝╚═╝ ╚═══╝ ╚═╝ ╚═╝ ╚═╝ ╚═════╝ ████████╗ ██████╗ ╚══██╔══╝██╔═══██╗ ██║ ██║ ██║ ██║ ██║ ██║ ██║ ╚██████╔╝ ╚═╝ ╚═════╝ ██████╗██╗ ██╗██████╗ ███████╗██████╗ ██╔════╝╚██╗ ██╔╝██╔══██╗██╔════╝██╔══██╗ ██║ ╚████╔╝ ██████╔╝█████╗ ██████╔╝ ██║ ╚██╔╝ ██╔══██╗██╔══╝ ██╔══██╗ ╚██████╗ ██║ ██████╔╝███████╗██║ ██║ ╚═════╝ ╚═╝ ╚═════╝ ╚══════╝╚═╝ ╚═╝ ███████╗███████╗ ██████╗██╗ ██╗██████╗ ██╗████████╗██╗ ██╗ ██╔════╝██╔════╝██╔════╝██║ ██║██╔══██╗██║╚══██╔══╝╚██╗ ██╔╝ ███████╗█████╗ ██║ ██║ ██║██████╔╝██║ ██║ ╚████╔╝ ╚════██║██╔══╝ ██║ ██║ ██║██╔══██╗██║ ██║ ╚██╔╝ ███████║███████╗╚██████╗╚██████╔╝██║ ██║██║ ██║ ██║ ╚══════╝╚══════╝ ╚═════╝ ╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝
让我听懂你的语言电视剧剧情介绍,演员表,大结局_搜视网:2021-3-12 · 搜视网为您提供让我听懂你的语言电视剧全集的详细介绍，包括剧情介绍、演员表、大结局、剧照、主题曲、电视台播出时间 ...
PROTEIN INFERENCE TOURNAMENT 2023
Lab members each chose a set of present human proteins, and these were used to simulate an MS/MS data set. Using only target-decoy information and intuition, lab members built models and performed protein inference. Using the secret present proteins from each data set, the participants' submissions were ranked (via AUC of the ROC at a q-value <0.1). The participant with the best sum of ranks over the data sets was named the winner.
FINAL STANDINGS:
| COMPETITOR | JAKE DATA | KYLE DATA | SEAN DATA | PATRICK DATA | MAX DATA | SUM |
|---|---|---|---|---|---|---|
| JAKE | ---- | 2 | 2 | 2 | 1 | 7 |
| KYLE | 3 | ---- | 1 | 1 | 3 | 8 |
| SEAN | 4 | 4 | ---- | 3 | 2 | 13 |
| PATRICK | 2 | 1 | 3 | ---- | 4 | 10 |
| MAX | 1 | 3 | 4 | 4 | ---- | 12 |
GEWINNER: Jake Pennington took first prize (Little Debbie chocolate cupcakes) with Kyle Lucke in a photo-finish for second prize (Little Debbie powdered sugar donuts).
----------------------------------------------
KREITZBERG ET AL.
Congratulations to Patrick Kreitzberg for the publication for his first first-author paper (Kreitzberg, Bern, Shu, Yang, and Serang) on the topic of his masters thesis!
----------------------------------------------
面试碰到不懂的问题怎么办？ - 知乎 - Zhihu:2021-5-7 · 第一招——坦言相告，切勿乱编答案 我发现身边的朋友都存在一个误区，就是特别容易把面试当成考试，还是文科考试。 仔细想一想大家在高中作答文史哲等试卷时，是不是不管这个问题的答案，我知不知道，先写上字再说。
Having won its bid for the 2023 Serang Lab Olympics, Missoula hosted competitors at Bonner Park to compete in a triathlon of lab events: The first event is the longest frisbee throw with successful catch. Participants select a partner of choice, who gets a four second head start running before the competitor throws. Completed catches are marked with sparkling water (competitor's flavor of choice), and the best of three throws was used for scoring. The second event was the egg toss. In this case, competitors must work together. Each completed throw results in one step back for all remaining competitors, until only one egg remains. The last event is the crab walk race. Going to the telephone pole would be too easy (You know what else is easy? TV dinners! For once, ask the most of yourself!): competitors must go around the telephone pole and return.
FINAL STANDINGS:
| COMPETITOR | 你懂的vnp2022 | 搜罗vnp | CRAB RANK | RANK SUM |
|---|---|---|---|---|
| MAX | 1 | 3 | 4 | 8 |
| JAKE | 3 | 2 | 8 | 13 |
| SEAN | 4 | 2 | 1 | 7 |
| SARAH | 5 | 1 | 5 | 11 |
| KYLE | 6 | 1 | 6 | 13 |
| BLAKE | 6 | 3 | 3 | 12 |
| PATRICK | 6 | 1 | 3 | 12 |
| OLIVER | -- | -- | -- | -- |
GEWINNER: Sean Rice wins the Strawberry-Watermelon bubble yum. Oliver Serang was disqualified due to his suspiciously good performance after testing positive for peppermint tea.
----------------------------------------------
NSF CAREER GRANT AWARD
Oliver Serang has received an NSF CAREER award! This
grant will fund the development of new combinatorics
methods, K-12 curriculum on teaching mathematics and
computer science, and a new season of the Exploring
Scientific Wilderness podcast.
You can follow the fruits of this grant
on this page.
----------------------------------------------
ASMS 2023
Patrick Kreitzberg and Oliver Serang presented at ASMS
2023 in Atlanta, where Patrick got his first taste of
Szechuan food in his life.
To read Patrick's masters thesis (on computing de
novo neutral loss alphabets from mass spectra),
click here. To
get the code (MIT licese),
visit http://bitbucket.org/orserang/peak-bagger.
To see Kyle Lucke et al.'s poster (which was
presented by Oliver) on the the hitchhiking proteins
during protein inference, click here.
----------------------------------------------
PATRICK KREITZBERG MASTERS THESIS DEFENSE
Patrick Kreitzberg will defend his Masters Thesis on Wednesday, June 19th at 1PM in Social Sciences 362. Read his thesis here!
----------------------------------------------
搜罗vnp
小时候看不懂的片段，真的是太污了，你看懂了吗_腾讯视频:2021-8-23 · 小时候看不懂的片段，真的是太污了，你看懂了吗
----------------------------------------------
SECOND ANNUAL UM CS STABLE MARRIAGE TRIVIA CONTEST
----------------------------------------------
FINALIST FOR BEST OF GRADCON
Patrick Kreitzberg's work on meta de novo mass spectrometry methods, "The Alphabet Projection of Mass Spectrometry Data", was a finalist for the best of the University of Montana's GradCon 2023!
----------------------------------------------
WELCOME WINTER 2023!
To celebrate the new year, lab members jumped into the snowy Clark Fork and then everyone went to warm up with some ramen and then cool back down with a quick game of Race for the Galaxy over ice cream.
Only 170 days until the days start getting shorter again!
小时候看不懂的片段，真的是太污了，你看懂了吗_腾讯视频:2021-8-23 · 小时候看不懂的片段，真的是太污了，你看懂了吗
AUTUMN 2018
你不懂钢笔的长辈曾怎么评价过你的钢笔？ - 知乎:我爸玩古钱币的，非常能理解我这种收藏癖有时候我还会给他解释这些笔，为什么收它，我觉得戳我的点在哪，…
This cozy season, which is viewed as the time when the veil between the living and the dead is its thinnest, proved to be a perfect time to introduce everyone to "cheese dogs".
----------------------------------------------
TEXTBOOK: ALGORITHMS IN PYTHON
Oliver Serang's textbook, Algorithms in Python is now online.
Check it out here.
█████╗ ██╗ ██████╗ ██████╗ ██████╗ ██╗████████╗██╗ ██╗███╗ ███╗███████╗ ██╔══██╗██║ ██╔════╝ ██╔═══██╗██╔══██╗██║╚══██╔══╝██║ ██║████╗ ████║██╔════╝ ███████║██║ ██║ ███╗██║ ██║██████╔╝██║ ██║ ███████║██╔████╔██║███████╗ ██╔══██║██║ ██║ ██║██║ ██║██╔══██╗██║ ██║ ██╔══██║██║╚██╔╝██║╚════██║ ██║ ██║███████╗╚██████╔╝╚██████╔╝██║ ██║██║ ██║ ██║ ██║██║ ╚═╝ ██║███████║ ╚═╝ ╚═╝╚══════╝ ╚═════╝ ╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝╚═╝ ╚═╝╚══════╝ ██╗███╗ ██╗ ██████╗ ██╗ ██╗████████╗██╗ ██╗ ██████╗ ███╗ ██╗ ██║████╗ ██║ ██╔══██╗╚██╗ ██╔╝╚══██╔══╝██║ ██║██╔═══██╗████╗ ██║ ██║██╔██╗ ██║ ██████╔╝ ╚████╔╝ ██║ ███████║██║ ██║██╔██╗ ██║ ██║██║╚██╗██║ ██╔═══╝ ╚██╔╝ ██║ ██╔══██║██║ ██║██║╚██╗██║ ██║██║ ╚████║ ██║ ██║ ██║ ██║ ██║╚██████╔╝██║ ╚████║ ╚═╝╚═╝ ╚═══╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═════╝ ╚═╝ ╚═══╝
----------------------------------------------
THE OFFICIAL GOLDEN DOODLE OF UM
During an afternoon of Patrick and Oliver playing fetch with Patrick's dog Butters, Butters was recorded in a video that is slated for use in offial promotion for the University of Montana.
让我听懂你的语言电视剧剧情介绍,演员表,大结局_搜视网:2021-3-12 · 搜视网为您提供让我听懂你的语言电视剧全集的详细介绍，包括剧情介绍、演员表、大结局、剧照、主题曲、电视台播出时间 ...
COBRE GRANT AWARD
看完这篇，别说你还不懂Hinton大神的胶囊网络，capsule ...:2021-10-15 · 在讲胶囊网络之前，首先我伊回顾一下我伊熟悉的CNN。CNN做了什么事情呢? 假设这里有一个卷积核（左图），除了曲线轨迹上的值很大，其他的值都是零，所伍这个卷积核对旁边这种曲线（右图）就有很高的输出，也就是说对这种曲线有很高的识别，而对其他的曲线类型输出就低。
----------------------------------------------
UM PILOT PROJECT GRANT AWARD
图解两会数字：45万亿怎么花？ 一图读懂与你有关的“国家 ...:2021-5-25 · 图解两会数字：45万亿怎么花？ 一图读懂与你有关的“国家账本”
----------------------------------------------
TEXTBOOK: CODE OPTIMIZATION IN C++11
Oliver Serang's textbook, Code Optimization in C++11 is now online.
Check it out vnp 加速.
图解两会数字：45万亿怎么花？ 一图读懂与你有关的“国家 ...:2021-5-25 · 图解两会数字：45万亿怎么花？ 一图读懂与你有关的“国家账本”
----------------------------------------------
THE LAUNCH OF EXPLORING SCIENTIFIC WILDERNESS
Exploring Scientific Wilderness is a new podcast miniseries with short and sweet pieces of scientific brain candy.
███████╗████████╗███████╗██████╗ ██╔════╝╚══██╔══╝██╔════╝██╔══██╗ ███████╗ ██║ █████╗ ██████╔╝ ╚════██║ ██║ ██╔══╝ ██╔═══╝ ███████║ ██║ ███████╗██║ ╚══════╝ ╚═╝ ╚══════╝╚═╝ ██╗███╗ ██╗████████╗ ██████╗ ██║████╗ ██║╚══██╔══╝██╔═══██╗ ██║██╔██╗ ██║ ██║ ██║ ██║ ██║██║╚██╗██║ ██║ ██║ ██║ ██║██║ ╚████║ ██║ ╚██████╔╝ ╚═╝╚═╝ ╚═══╝ ╚═╝ ╚═════╝ ████████╗██╗ ██╗███████╗ ╚══██╔══╝██║ ██║██╔════╝ ██║ ███████║█████╗ ██║ ██╔══██║██╔══╝ ██║ ██║ ██║███████╗ ╚═╝ ╚═╝ ╚═╝╚══════╝ ██╗ ██╗██╗██╗ ██████╗ ███████╗██████╗ ███╗ ██╗███████╗███████╗███████╗ ██║ ██║██║██║ ██╔══██╗██╔════╝██╔══██╗████╗ ██║██╔════╝██╔════╝██╔════╝ ██║ █╗ ██║██║██║ ██║ ██║█████╗ ██████╔╝██╔██╗ ██║█████╗ ███████╗███████╗ ██║███╗██║██║██║ ██║ ██║██╔══╝ ██╔══██╗██║╚██╗██║██╔══╝ ╚════██║╚════██║ ╚███╔███╔╝██║███████╗██████╔╝███████╗██║ ██║██║ ╚████║███████╗███████║███████║ ╚══╝╚══╝ ╚═╝╚══════╝╚═════╝ ╚══════╝╚═╝ ╚═╝╚═╝ ╚═══╝╚══════╝╚══════╝╚══════╝
求一个网站你懂的 - 95秀-美女主播视频交友聊天直播间-95美女秀:很多男人在夜深人静的时候都想自己的初恋女友，特别想有一个与之前的初恋女友一样的伙伴，满足自己曾经没有得到的那种情感空虚，想要获得这样的情感，最好的方式就是在直播中找到，有没有一个网站可伍轻松地拥有初恋的感觉，现在这个梦想是完全可伍实现的。
EVERGREENFOREST INFERENCE ENGINE 0.9
After years of work, the beta version of
EvergreenForest has been released! It includes a fast,
lazy implementation of trimmed convolution trees, a
fast in-house FFT written in C++11 (using the lab's
work on methods for performing bit-reversed
permutation), and lots of other Waldmeister-flavored
goodies to activate your almonds.
You can read more about it and download it
here.
----------------------------------------------
THE INVENTION OF ``TRIMMED'' CONVOLUTION TREES
Trimmed convolution trees use sparsity in the solution
space exploit sparsity in the input priors and
likelihood of a convolution tree to achieve an
algorithmic and practical speedup. For example, when
all input priors are $$X_i \in \{0,1\}$$ and the
likelihood $$Y=X_1 + X_2 + \cdots X_n \in \{0,1\},$$
all posteriors can be solved with trimmed convolution
trees in $$O(n)$$ rather than the $$O(n \log(n)
\log(n))$$ required by non-trimmed convolution
trees.
Trimmed convolution trees generalize this to use
narrower priors and likelihoods, even when some priors
have larger support than others or when the likelihood
distribution has are larger support than all priors,
smaller support, or anything, making the first method
$$\in o(nk \log(nk) \log(n))$$ on some problems with
$$n$$ inputs each with $$k$$ bins.
The paper (in review) includes a demo that uses
trimmed convolution trees to estimate posterior
probabilities for peoples' orders given their total
ice cream bill; the demo is, of course, written using
the menu from
Missoula's
own Big Dipper Ice Cream.
----------------------------------------------
FAST C++11 METHODS FOR BIT-REVERSED PERMUATION
The bit-reversed permutation is an important task for
implementing an in-place FFT library. This paper
explores several bit reversal methods on the x86
architecture, including new bit twiddling tricks and a
proposed template-recursive, cache-oblivious method,
which achieves state-of-the-art performance.
The paper draft can be found
here. The
repository (linked in the paper) includes translations
in the mother tongue of each student who participated
(Chinese, German, Turkish, and Spanish) to help
students throughout the world participate in the joy
of scientific computing. So when someone says, ``Bit
reversal? How?'' you can say, ``很好!''
----------------------------------------------
A FASTER, SIMPLER MULTIDIMENSIONAL ARRAY LIBRARY IN C++11
Florian Heyl, who is doing his masters Praktikum in the
group, has just had his first paper accepted for
publication. The paper (Heyl & Serang 2017,
PROGRAMMING) introduces and benchmarks the
``template-recursive iteration over tensors'' (TRIOT)
design pattern in C++11. The method enables easy
vectorizing over tensors of different shaps and does not
require tensor dimensions to be fixed at compile
time.
Download the free header-only
library here.
----------------------------------------------
MORE ACCURATE NUMERIC P-CONVOLUTION
The lab's
second paper on the
topic 你一定要懂的15个法律常识！（情侣必看版） - 知乎:本文转载自微信公众号：一只学霸（ID：bajie203） 鉴于粉丝总有一些奇奇怪怪的问题 又怕你伊在不知不觉中突然被 所伍帅气优秀聪明完美（此处省略一万字）的我贴心地准备了这一篇 接下来我就直接开始了 …
builds upon the original idea, looking at the curve of
(modeled using orthogonal polynomials) of a constant
number of $$L_p$$ spaces. The way that these spaces bend
toward the true maximum can allow us to estimate the
maximum better than any particular numerically stable
p-norm.
The paper highlights the approach with faster prediction
of U.S. unemployment given S&P 500 index data (via a
fast Viterbi path computation).
----------------------------------------------
THE INVENTION OF FAST NUMERIC MAX-CONVOLUTION
Max-convolution, a cousin of standard convolution but on
the semiring $$( \times, \max )$$ (consider multiplying
two polynomials but taking the maximum coefficient for
every term rather than the sum of coefficients for that
term), arises frequently in combinatorics and in
Bayesian inference. In 2006, Bremner et al. discovered
the first solution $$\in o(n^2);$$ theirs is a beautiful
method, but it's only slightly sub-quadratic and relies
on a reduction to APSP, and it is not fast enough for
large-scale use in Bayesian networks. However, this
problem can be approximated numerically by using $$L_p$$
space, where FFT can be used in $$\in O(n
\log(n))$$ (Serang
2015, Journal of Computational Biology). The method
can also be used to improve hidden Markov models (HMMs)
with with k states from $$O(k^2 n)$$ to $$O(k \log(k)~
n),$$ whenever the transition matrix is a Toeplitz
matrix.
Combined with the probabilistic convolution tree, the
method can be used for max-product inverence when $$Y =
X_1 + X_2 + \cdots + X_n.$$ This can be used to solve a
generalization of the knapsack problem on
integer-discretized supports.
----------------------------------------------
A FASTER DYNAMIC PROGRAMMING ALGORITHM
The probabilistic convolution tree (Serang 2014, PLOS ONE) is a new dynamic programming algorithm that solves a class of probabilistic problems, which are equivalent to a generalization of subset-sum on integer-discretized supports. When $$Y = X_1 + X_2 + \cdots + X_n$$ and each $$X_i \in \{0, 1, \ldots k-1\}$$ it computes all marginals simultaneously with a runtime $$\in O(n\cdot k \log(n\cdot k) \log(n)).$$
----------------------------------------------