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First-order iterative optimization methods play a fundamental role in large scale optimization and machine learning. This paper presents control interpretations for such optimization methods. First, we give loop-shaping interpretations for…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
Obtaining first-order regret bounds -- regret bounds scaling not as the worst-case but with some measure of the performance of the optimal policy on a given instance -- is a core question in sequential decision-making. While such bounds…
Reset elements are nonlinear filters that improve control performance beyond linear time-invariant (LTI) limits but introduce higher-order harmonics that complicate design. Although frequency-domain tools like describing functions (DFs) and…
We study the performance of first- and second-order optimization methods for l1-regularized sparse least-squares problems as the conditioning of the problem changes and the dimensions of the problem increase up to one trillion. A rigorously…
In this contribution, a design of a synthetic calibration genetic circuit to characterize the relative strength of different sensing promoters is proposed and its specifications and performance are analyzed via an effective mathematical…
Mixed feedback loops combining transcriptional and post-transcriptional regulations are common in cellular regulatory networks. They consist of two genes, encoding a transcription factor and a small non-coding RNA (sRNA), which mutually…
Cells receive a wide variety of cellular and environmental signals, which must be processed combinatorially to generate specific and timely genetic responses. We present here a theoretical study on the combinatorial control and integration…
Synthetic biology sets out to implement new functions in cells, and to develop a deeper understanding of biological design principles. In 2000, Elowitz and Leibler showed that by rational design of the reaction network, and using existing…
Machine learning models are generally vulnerable to adversarial examples, which is in contrast to the robustness of humans. In this paper, we try to leverage one of the mechanisms in human recognition and propose a bio-inspired…
Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been…
To handle the control difficulties caused by high-order dynamics, a control structure based on fractional order [proportional integral] (PI) controller and fractional order Smith-like predictor for a class of high order systems in the type…
We consider controller design for robust output tracking and disturbance rejection for continuous-time periodic linear systems with periodic reference and disturbance signals. As our main results we present four different controllers: A…
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of…
Dynamical control of biological systems is often restricted by the practical constraint of unidirectional parameter perturbations. We show that such a restriction introduces surprising complexity to the stability of one-dimensional map…
The genetic repressilator circuit consists of three transcription factors, or repressors, which negatively regulate each other in a cyclic manner. This circuit was synthetically constructed on plasmids in {\it Escherichia coli} and was…
Mixed positive and negative feedback loops are often found in biological systems which support oscillations. In this work we consider a prototype of such systems, which has been recently found at the core of many genetic circuits showing…
Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges…
In this paper the following three control systems for first-order time-delay plants are studied and compared: the feedback proportional-integral controller (PI), the Smith Predictor (SP) and a proposed variable structure consisting of two…
The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale information, past studies in the area have proposed recovering…