For a Boolean function $f:\{0,1\}^n \to \{0,1\}$ computed by a circuit $C$ over a finite basis $\cal{B}$, the energy complexity of $C$ (denoted by $\mathbf{EC}_{{\cal B}}(C)$) is the maximum over all inputs $\{0,1\}^n$ the numbers of gates of the circuit $C$ (excluding the inputs) that output a one. Energy Complexity ... more >>>

In this paper, we study the Boolean function parameters sensitivity ($\mathbf{s}$), block sensitivity ($\mathbf{bs}$), and alternation ($\mathbf{alt}$) under specially designed affine transforms and show several applications. For a function $f:\mathbb{F}_2^n \to \{0,1\}$, and $A = Mx+b$ for $M \in \mathbb{F}_2^{n \times n}$ and $b \in \mathbb{F}_2^n$, the result of the ... more >>>

Scaling problems have a rich and diverse history, and thereby have found numerous
applications in several fields of science and engineering. For instance, the matrix scaling problem
has had applications ranging from theoretical computer science to telephone forecasting,
economics, statistics, optimization, among many other fields. Recently, a generalization of matrix
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