Joint source-channel coding (JSCC) has emerged to be a major field of research recently. Channel optimized vector quantization (COVQ) is a simple feasible JSCC scheme introduced for communication over practical channels. In ...

Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this thesis, we introduce the notion of a ...

In this work, I will describe a new statistical tool: the canonical bicoherence, which is a combination of the canonical coherence and the bicoherence. I will provide its definitions, properties, estimation by multitaper ...

In this thesis we describe how the balancing of the $\operatorname{Tor}$ functor can be used to compute the minimal free resolution of a graded module $M$ over the polynomial ring $B=\mathbb{K}[X_0,\dots,X_m]$ ($\mathbb{K}$ ...

In this thesis is initiated a more systematic geometric exploration of energy shaping. Most of the previous results have been dealt wih particular cases and neither the existence nor the space of solutions has been discussed ...

Experiments have demonstrated that DNA molecules can compute like a machine to solve mathematical problems, which is significant because of their parallel computation ability. However, due to the nature of biochemical ...

Linear programming (LP) decoding of low-density parity-check codes was introduced by Feldman et al. in [1]. In his formulation it is assumed that communication takes place over a memoryless channel and that the source is ...