Poisson Processes and Data Loss

Poisson Processes and Data Loss

There are many applications for counting arrivals over time. Perhaps I want to count the arrivals into a store, or shipments into a postal distribution center, or node failures in a cloud cluster, or hard drive failures in a traditional storage array. It's rare that these events come neatly, one after the other, with a…

Commentary: Technical Debt in Machine Learning

Commentary: Technical Debt in Machine Learning

I recently had the opportunity to be a guest on an episode of the On-Premise IT Roundtable podcast, the topic of which was technical debt. (You can listen to the twenty minute episode here, or watch the video version here.) The conventional definition of technical debt, for both consumer and enterprise technology, is the lagging of upgrades,…

Commentary: On Straight As and Salaries

Commentary: On Straight As and Salaries

(Fair warning: this is a personal account.) The systems were designed well, I think. When we were in school or college, passing was supposed to mean you knew the material, basically. A B showed you were pretty good, and an A was only for the smartest students. Not relatively the smartest, but objectively the smartest.…

Commentary: High Level Data Filtration

Commentary: High Level Data Filtration

The consensus over the last five or so years has converged on a conclusion regarding data: we're drowning in it. We have more than we can possibly monitor with our own eyeballs, and certainly more than we know what to do with intelligently. The motto for data scientists has been "More is better." Well, ask…

On Server Efficiency

On Server Efficiency

For the full text of the paper, including all proofs and supplementary lemmata, click to download  Abstract Editor's note: This paper comprises the second chapter of the PhD dissertation by Rachel Traylor. Cha and Lee defined a mathematical notion of server performance by measuring efficiency defined as the long run average number of jobs completed per…

Commentary: Returning to Fundamentals in Tech

Commentary: Returning to Fundamentals in Tech

I once heard a great analogy about the difference between mathematicians and engineers in their problem-solving approaches. If an engineer and a mathematician are tasked with crossing a river, the engineer will create a set of stepping stones and get you across quickly, and safely in most cases. The mathematician will spend a month examining…

Reduce the Problem: Permutations and Modulo Arithmetic

Reduce the Problem: Permutations and Modulo Arithmetic

We've all seen permutations before. If you have ten distinct items, and rearrange them on a shelf, you've just performed a permutation. A permutation is actually a function that is performing the arrangement on a set of labeled objects. For simplicity, we can just number the objects and work with permuting the numbers.  (more…)

The Gravity of Mathematics: Summary of Tech Field Day at SDC 2017

The Gravity of Mathematics: Summary of Tech Field Day at SDC 2017

Fair warning - this will likely be one of the least technical posts I write. On September 14, I gave a presentation at Tech Field Day that wasn't actually storage related, but rather a call to rekindle the relationship between pure math and industry. Here I'll post the slides from that talk and summarize some of the…

The Central Limit Theorem isn’t a Statistical Silver Bullet

The Central Limit Theorem isn’t a Statistical Silver Bullet

Chances are, if you took anything away from that high school or college statistics class you were dragged into, you remember some vague notion about the Central Limit Theorem. It's likely the most famous theorem in statistics, and the most widely used. Most introductory statistics textbooks state the theorem in broad terms, that as the…

Cauchy Sequences: the Importance of Getting Close

Cauchy Sequences: the Importance of Getting Close

I am an analyst at heart, despite my recent set of algebra posts. Augustin Louis Cauchy can be argued as one of the most influential mathematicians in history, pioneering rigor in the study of calculus, almost singlehandedly inventing complex analysis and real analysis, though he also made contributions to number theory, algebra, and physics.  One…