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A mathematician known for Strassen's algorithm and contributions to efficient algorithms.^[ref]

Wayne Rasband developed NIH Image and ImageJ, tools that make quantitative image processing available through an interactive program and extensible code. The ImageJ project's biography records forty years at the US National Institutes of Health and retirement in 2010. It dates the start of NIH Image to 1987 and ImageJ to 1997, when Rasband explored implementing the earlier program in Java.^[ref]

This progression mattered because the same recorded digital image could become input to many explicit measurements. Selecting a region of interest, applying image thresholding and measuring an area are separate operations; each makes a choice that affects the result. ImageJ User Guide by Tiago Ferreira and Wayne Rasband records the program's image representations, selections, analysis commands and scripting facilities.^[ref]

For a small original measurement example, take four stored grayscale valuesSelect values at least 128, obtaining the binary image $(0,0,1,1)$. If each complete pixel represents a rectangle of calibrated width $\Delta x=0.5\mu \mathrm{m}$ and height $\Delta y=0.5\mu \mathrm{m}$, the area from a calibrated pixel count isThe chosen threshold determines which pixels contribute; the pixel pitch determines the physical area assigned to each. An attractive display alone supplies neither of these measurement choices. The calculation assumes complete selected pixel cells and a uniform rectangular calibration; it is not a measured specimen area.

Rasband's contribution also includes maintaining a community around the software: the project profile describes improvements supplied through user feedback, bug reports, code and documentation. That process connects a general algorithm to the concrete representations and measurement conventions needed for a repeatable analysis.^[ref]

Worst-case analysis measures the largest resource use of a specified algorithm among inputs of the same size. If $T(x)$ counts operations on input $x$, the worst-case function isThe cost model and meaning of input size $n$ are part of the definition. A big O notation bound describes growth of this function, rather than a claim about how often the difficult input occurs.^[ref]

For linear search of $n$ entries, looking for an absent item requires $n$ equality tests; finding the first item needs just one. Thus the worst-case comparison count is $n$, even if many actual queries finish earlier. This supplies a guarantee for every allowed input, while an average-case analysis requires a stated distribution over inputs.

A computer scientist working on game theory, algorithms and computational complexity theory. Co-author with Christos Papadimitriou of On the Complexity of Cooperative Solution Concepts by Xiaotie Deng and Christos Papadimitriou, which studies induced subgraph games.

Primary profile: Peking University profile identifying Xiaotie Deng and his research interests.

Two shared programming/algorithms/proof-systems papers, discrete mathematics and probability, introduction to philosophy, and philosophical topics in logic and probability.

Algorithms and data structures, models of computation, group design practical, and options; philosophy teaching continues.

Core mathematics and computer science, including algorithms and data structures, models of computation and a group design practical; options from both subjects.

Yihong Wu coauthored information-theory notes with Yury Polyanskiy. Their account links probabilistic quantities with limits on coding and statistical inference, separating what an algorithm achieves from what any algorithm can achieve.^[ref]

Yu. Ofman coauthored the 1962 paper Multiplication of many-digital numbers by automatic computers by A. Karatsuba and Yu. Ofman. The work reduces a multiplication of large integers to three smaller multiplications rather than four, yielding the divide-and-conquer recurrence behind Karatsuba multiplication. It is an early example where an algebraic rearrangement changes an algorithm's asymptotic cost.^[ref]