Adam A. Smith

Clustered alignments of gene-expression time series data

Motivation: Characterizing and comparing temporal gene-expression responses is an important computational task for answering a variety of questions in biological studies. Algorithms for aligning time series represent a valuable approach for such analyses. However, previous approaches to aligning gene-expression time series have assumed that all genes should share the same alignment. Our work is motivated by the need for methods that identify sets of genes that differ in similar ways between two time series, even when their expression profiles are quite different. Results: We present a novel algorithm that calculates clustered alignments; the method finds clusters of genes such that the genes within a cluster share a common alignment, but each cluster is aligned independently of the others. We also present an efficient new segment-based alignment algorithm for time series called SCOW (shorting correlation-optimized warping). We evaluate our methods by assessing the accuracy of alignments computed with sparse time series from a toxicogenomics dataset. The results of our evaluation indicate that our clustered alignment approach and SCOW provide more accurate alignments than previous approaches. Additionally, we apply our clustered alignment approach to characterize the effects of a conditional Mop3 knockout in mouse liver. Availability: Source code is available at http://www.biostat.wisc.edu/∼aasmith/catcode. Contact: aasmith@cs.wisc.edu

Similarity Queries for Temporal Toxicogenomic Expression Profiles

We present an approach for answering similarity queries about gene expression time series that is motivated by the task of characterizing the potential toxicity of various chemicals. Our approach involves two key aspects. First, our method employs a novel alignment algorithm based on time warping. Our time warping algorithm has several advantages over previous approaches. It allows the user to impose fairly strong biases on the form that the alignments can take, and it permits a type of local alignment in which the entirety of only one series has to be aligned. Second, our method employs a relaxed spline interpolation to predict expression responses for unmeasured time points, such that the spline does not necessarily exactly fit every observed point. We evaluate our approach using expression time series from the Edge toxicology database. Our experiments show the value of using spline representations for sparse time series. More significantly, they show that our time warping method provides more accurate alignments and classifications than previous standard alignment methods for time series.

Fast multisegment alignments for temporal expression profiles.

We present two heuristics for speeding up a time series alignment algorithm that is related to dynamic time warping (DTW). In previous work, we developed our multisegment alignment algorithm to answer similarity queries for toxicogenomic time-series data. Our multisegment algorithm returns more accurate alignments than DTW at the cost of time complexity; the multisegment algorithm is O(n(5)) whereas DTW is O(n(2)). The first heuristic we present speeds up our algorithm by a constant factor by restricting alignments to a cone shape in alignment space. The second heuristic restricts the alignments considered to those near one returned by a DTW-like method. This heuristic adjusts the time complexity to O(n(3)). Importantly, neither heuristic results in a loss in accuracy.

The effects of meridional motion on the determination of rotation by tracer tracking

We explore a systematic error that arises in feature-tracking measurements of time-average rotation. It stems from the flows of features across latitudes, and as these flows vary with the solar activity cycle, the error has a pattern of variation which mocks the torsional oscillation. We develop a series expansion for this error and evaluate the leading terms for the example case of cycle 21. It grows with the time lag; for a 30 day lag it is ≲1%, depending on how the correlations are done and interpreted. We conclude that the mock pattern cannot, however, account for the magnetic-rotation torsional oscillations pattern found in recent analyses of magnetograms from Kitt Peak and Mount Wilson. For the 1-day time lag in the Kitt Peak study, the error is negligible, and for the ∼30-day time lag in the Mount Wilson study, it represents at most about 30% of the signal.

Making a Hash of Things

A dobe, Ashley Madison, Snapchat, Target, Yahoo!, and Zappos: These are just a few of the well-known companies that have been hacked in the past year or two. If you have an account with any of these services, you probably received a message warning you to change your password. Does this mean a dastardly hacker has your old password? Maybe . . . or maybe not. Smart websites don’t store big lists of passwords; that would be asking for trouble. Instead, they store your user name and a hashed version of your password. A hashed password has been transformed by a hash function—a function that transforms a string of characters (such as your password) into a string of fixed length. For example, if your password was Il0vemath, a website might store the hexadecimal number 0940a51639174af39ec5d5c1069fb2554453 f76017c70426cde3aec984301158. If your password was the more enthusiastic Il0vemath!, the same website would store e8b690ca2dba3d4d45c c99fa52e326ae446e4acda0a7f277ac3d8e a068b0b415. The original passwords are similar, but the hashed versions don’t look anything alike! What makes a good hash function? A key feature for password storage is preimage resistance. That means that it should be hard for a hacker who has stolen a hashed phrase to guess the original input. Ideally, the hacker’s only way to find your password would be a giant game of guess and check—plugging phrases into the hash function until he hits on a working password. If you’re familiar with cryptography, preimage resistance may remind you of the quest for one-way functions, which are invertible functions that are easy to compute but hard to invert. Such functions are highly useful in encrypting secret messages. Hash functions are different, however, because they Making a Hash of Things

Hidden Markov models and mouse ultrasonic vocalizations

An introduction to Markov models, their significance, and an explanation of how a hidden Markov model can be used to model the ultrasonic calls made by mice.