Mash extends the MinHash dimensionality-reduction technique to include a pairwise mutation distance and P value significance test, enabling the efficient clustering and search of massive sequence collections. Mash reduces large sequences and sequence sets to small, representative sketches, from which global mutation distances can be rapidly estimated. We demonstrate several use cases, including the clustering of all 54,118 NCBI RefSeq genomes in 33 CPU h; real-time database search using assembled or unassembled Illumina, Pacific Biosciences, and Oxford Nanopore data; and the scalable clustering of hundreds of metagenomic samples by composition. Mash is freely released under a BSD license (
 https://github.com/marbl/mash
 ).

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Mash: fast genome and metagenome distance estimation using MinHash.

In this article, we give an overview of efficient algorithms for the approximate and exact nearest neighbor problem. The goal is to preprocess a dataset of objects (e.g., images) so that later, given a new query object, one can quickly return the dataset object that is most similar to the query. The problem is of significant interest in a wide variety of areas.

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Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions

This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.

Parameterized Algorithms

We present an algorithm for the c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time of O\left( {dn^{1/c^2 + o(1)} } \right) and space O\left( {dn + n^{1 + 1/c^2 + o(1)} } \right). This almost matches the lower bound for hashing-based algorithm recently obtained in [27]. We also obtain a space-efficient version of the algorithm, which uses dn+n log^{O(1)} n space, with a query time of dn^{O(1/c^2 )}. Finally, we discuss practical variants of the algorithms that utilize fast bounded-distance decoders for the Leech Lattice.

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Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions

We present two algorithms for the approximate nearest neighbor problem in high dimensional spaces. For data sets of size n living in IR, the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree.

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Approximate Nearest Neighbor: Towards Removing the Curse of Dimensionality

Long-term drift of temperature sensors is critical to applications requiring high reliability. However, documentation and knowledge regarding long-term stability is limited. Usually manufacturers promulgate drift margins down to 10–20 mK/year, while the performance of the sensors might be much better. For some advanced industrial applications, which demand drift rates down to a few mK/year, this information is inadequate. In this paper, we present our investigation of the long-term drift of a few sets of small footprint, off-the-shelf NTC (negative temperature coefficient) temperature sensors, based on an extremely stable test setup guaranteeing stability of better than 1 mK between two calibration intervals. The results show that the SMD type sensor from Murata manufacturing (NCP15XH103D03RC), intriguingly, is the most stable sensor among the sensors tested with a drift rate of 0.492 mK/year peak-to-peak. Most of the other sensors tested have drift rates of lower than 1 mK/year, making them suitable for temperature sensing applications requiring long-term stabilities in the mK range.

Investigation of long-term drift of NTC temperature sensors with less than 1 mK uncertainty

Oscillator-Based Volatile Detection System Using Doubly- Clamped Micromechanical Resonators

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.

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Picture-Hanging Puzzles

We present a nanometer range, closed-loop control study for MEMS stepper actuators. Although generically applicable to other types of stepper motors, the control design presented here was particularly intended for one dimensional shuffle actuators fabricated by surface micromachining technology. The stepper actuator features 50 nm or smaller step sizes. It can deliver forces up to 5 mN (measured) and has a typical range of about 20 μm. The target application is probe storage, where positioning accuracies of about 10 nm are required. The presence of inherent actuator stiction, load disturbances, and other effects make physical modeling and control studies necessary. Performed experiments include measurements with openand closed-loop control, where a positioning accuracy in the order of tens of nm or better is obtained from image data of a conventional fire-wire camera at 30 fps.

Nanometer range closed-loop control of a stepper micro-motor for data storage

The rank problem in succinct data structures asks to preprocess an array A[1..n] of bits into a data structure using as close to n bits as possible, and answer queries of the form rank(k) = Sum_{i=1}^k A[i]. The problem has been intensely studied, and features as a subroutine in a majority of succinct data structures. 
We show that in the cell probe model with w-bit cells, if rank takes t time, the space of the data structure must be at least n + n/w^{O(t)} bits. This redundancy/query trade-off is essentially optimal, matching our upper bound from [FOCS'08].

Mihai Patrascu

Papers

Investigation of long-term drift of NTC temperature sensors with less than 1 mK uncertainty

Oscillator-Based Volatile Detection System Using Doubly- Clamped Micromechanical Resonators

Picture-Hanging Puzzles

Nanometer range closed-loop control of a stepper micro-motor for data storage

A Lower Bound for Succinct Rank Queries