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What is the inverse of repeated square and multiply algorithm?

H. Gopalkrishna Gadiyar, K. M. Sangeeta Maini, R. Padma, Mario Romsy (2009)

Colloquium Mathematicae

It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm and what is its time compexity. The technical hitch is in fixing the right sign of the square root and this is the heart of the discrete logarithm problem over finite fields of characteristic not equal to 2. In this paper a couple of probabilistic algorithms to compute the discrete...

Wildfires identification: Semantic segmentation using support vector machine classifier

Pecha, Marek, Langford, Zachary, Horák, David, Tran Mills, Richard (2023)

Programs and Algorithms of Numerical Mathematics

This paper deals with wildfire identification in the Alaska regions as a semantic segmentation task using support vector machine classifiers. Instead of colour information represented by means of BGR channels, we proceed with a normalized reflectance over 152 days so that such time series is assigned to each pixel. We compare models associated with 𝓁 1 -loss and 𝓁 2 -loss functions and stopping criteria based on a projected gradient and duality gap in the presented benchmarks.

WWW-based Boolean function minimization

Sebastian Tomaszewski, Ilgaz Celik, George Antoniou (2003)

International Journal of Applied Mathematics and Computer Science

In this paper a Boolean minimization algorithm is considered and implemented as an applet in Java. The application is based on the Quine-McCluskey simplification technique with some modifications. The given application can be accessed on line since it is posted on the World Wide Web (WWW), with up to four variables, at the URL http://www.csam.montclair.edu/~antoniou/bs. After extensive testing, the performance of the algorithm has been found to be excellent. The proposed application is a useful...

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