Abstract. When seeking to understand how computation is carried out in the cell to maintain itself in its environment, process signals and make decisions, the continuous nature of protein interaction processes forces us to consider also analog computation models and mixed analog-digital computation programs. However, recent results in the theory of analog computability and complexity establish fundamental links with classical programming. In this paper, we derive from these results the strong (uniform computability) Turing completeness of chemical reaction networks over a finite set of molecular species under the differential semantics, solving a long standing open problem. Furthermore we derive from the proof a compiler of mathematical functions into elementary chemical reactions. We illustrate the reaction code generated by our compiler on trigonometric functions, and on various sigmoid functions which can serve as markers of presence or absence for implementing program control instructions in the cell and imperative programs. Then we start comparing our compiler-generated circuits to the natural circuit of the MAPK signaling network, which plays the role of an analog-digital converter in the cell with a Hill type sigmoid input/output functions.

Compressive light field photography enables light field acquisition using a single sensor by utilizing a color coded mask. This approach is very cost effective since consumer-level digital cameras can be turned into light field cameras by simply placing a coded mask between the sensor and the aperture plane. This paper describes a deep learning architecture for compressive light field acquisition using a color coded mask and a sensor with Color Filter Array (CFA). Unlike previous methods where a fixed mask pattern is used, our deep network learns the optimal distribution of the color coded mask pixels. The proposed solution enables end-to-end learning of the color-coded mask distribution and the reconstruction network, taking into account the sensor CFA. Consequently, the resulting network can efficiently perform joint demosaicing and light field reconstruction of images acquired with color-coded mask and a CFA sensor. Compared to previous methods based on deep learning with monochrome sensors, as well as traditional compressive sensing approaches using CFA sensors, we obtain superior color reconstruction of the light fields.

Compressed sensing using color-coded masks has been recently considered for capturing light fields using a small number of measurements. Such an acquisition scheme is very practical, since any consumer-level camera can be turned into a light field acquisition camera by simply adding a coded mask in front of the sensor. We present an efficient and mathematically grounded deep learning model to reconstruct a light field from a set of measurements obtained using a color-coded mask and a color filter array (CFA). Following the promising trend of unrolling optimization algorithms with learned priors, we formulate our task of light field reconstruction as an inverse problem and derive a principled deep network architecture from this formulation. We also introduce a closed-form extraction of information from the acquisition, while similar methods found in the recent literature systematically use an approximation. Compared to similar deep learning methods, we show that our approach allows for a better reconstruction quality. We further show that our approach is robust to noise using realistic simulations of the sensing acquisition process.