A rewriting system for convex optimization problems

Agrawal, Akshay; Verschueren, Robin; Diamond, Steven; Boyd, Stephen

doi:10.1080/23307706.2017.1397554

Cited by 539 publications

(359 citation statements)

References 52 publications

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“…All simulations are done with the CVXPY package [30] in PYTHON 3. All codes are available on GitHub at https://github.com/Emergent-Behaviors-in-Biology/species-packing-bound.…”

Section: Simulation Detailsmentioning

confidence: 99%

The effect of resource dynamics on species packing in diverse ecosystems

Cui

Marsland

Mehta

2019

Preprint

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The competitive exclusion principle asserts that coexisting species must occupy distinct ecological niches (i.e. the number of surviving species can not exceed the number of resources). An open question is to understand if and how different resource dynamics affect this bound. Here, we analyze a generalized consumer resource model with externally supplied resources and show thatin contrast to self-renewing resources -species can occupy only half of all available environmental niches. This motivates us to construct a new schema for classifying ecosystems based on species packing properties.

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“…All simulations are done with the CVXPY package [30] in PYTHON 3. All codes are available on GitHub at https://github.com/Emergent-Behaviors-in-Biology/species-packing-bound.…”

Section: Simulation Detailsmentioning

confidence: 99%

The effect of resource dynamics on species packing in diverse ecosystems

Cui

Marsland

Mehta

2019

Preprint

View full text Add to dashboard Cite

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“…Moreover, analytical inversion is limited to the oversampled regime, and its breakdown is observed at the Shannon-Nyquist sampling limit [22]. Compressive sensing (CS) extends reconstruction into the undersampling regime under conditions of sparsity, in our work CS was implemented for comparison to DL using the python package "cvxpy" [45]. Spectral reconstruction via DL was implemented using a convolutional neural network (CNN), composed of a series of convolutional layers followed by two fully connected layers of 512 and 256 nodes with dropout regularization using 70% keep probability.…”

Section: Methodsmentioning

confidence: 99%

Deep learning enabled real time speckle recognition and hyperspectral imaging using a multimode fiber array

et al. 2019

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We demonstrate the use of deep learning for fast spectral deconstruction of speckle patterns. The artificial neural network can be effectively trained using numerically constructed multispectral datasets taken from a measured spectral transmission matrix. Optimized neural networks trained on these datasets achieve reliable reconstruction of both discrete and continuous spectra from a monochromatic camera image. Deep learning is compared to analytical inversion methods as well as to a compressive sensing algorithm and shows favourable characteristics both in the oversampling and in the sparse undersampling (compressive) regimes. The deep learning approach offers significant advantages in robustness to drift or noise and in reconstruction speed. In a proof-of-principle demonstrator we achieve real time recovery of hyperspectral information using a multi-core, multi-mode fiber array as a random scattering medium.

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“…Since the problem becomes a Quadratically Constrained Quadratic Program (QCQP), we leave the rest to the CVXPY python package [27,28]. The details of the derivation related to update X can be found in the Supplementary Material C.3.…”

Section: The Netrex-cf Algorithmmentioning

confidence: 99%

Reconstruction of Gene Regulatory Networks by integrating biological model and a recommendation system

Wang

Fear²,

Berger³

et al. 2020

Preprint

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Gene Regulatory Networks (GRNs) control many aspects of cellular processes including cell differentiation, maintenance of cell type specific states, signal transduction, and response to stress. Since GRNs provide information that is essential for understanding cell function, the inference of these networks is one of the key challenges in systems biology. Leading algorithms to reconstruct GRN utilize, in addition to gene expression data, prior knowledge such as Transcription Factor (TF) DNA binding motifs or results of DNA binding experiments. However, such prior knowledge is typically incomplete hence resulting in missing values. Therefore, the integration of such incomplete prior knowledge with gene expression to elucidate the underlying GRNs remains difficult.To address this challenge we introduce NetREX-CF -Regulatory Network Reconstruction using EXpression and Collaborative Filtering -a GRN reconstruction approach that brings together a modern machine learning strategy (Collaborative Filtering model) and a biologically justified model of gene expression (sparse Network Component Analysis based model). The Collaborative Filtering (CF) model is able to overcome the incompleteness of the prior knowledge and make edge recommends for building the GRN. Complementing CF, the sparse Network Component Analysis (NCA) model can use gene expression data to validate the recommended edges. Here we combine these two approaches using a novel data integration method and show that the new approach outperforms the currently leading GRN reconstruction methods.Furthermore, our mathematical formalization of the model has lead to a complex optimization problem of a type that has not been attempted before. Specifically, the formulation contains 0 norm that can not be separated from other variables. To fill this gap, we introduce here a new method Generalized PALM (GPALM) that allows us to solve a broad class of non-convex optimization problems and prove its convergence. NetREX-CF -Method OverviewThe NetREX-CF model is a novel data integration framework for reconstructing GRNs by organically utilizing both gene expression E and a set of prior networks P = {P 1 , ...P d }. The main idea behind the NetREX-CF model is an integration of two complementary optimization strategies: (i) a machine learning component designed based on Collaborative Filtering that is able to identify hidden features from the current observed prior networks P and utilize these features to recommend an improved GRN and (ii) a sparse NCA-based network remodelling component that can refine the topology of a GRN based on given gene expression E. These two computational components operate alternatively. The CF component recommends new edges to the current GRN and the sparse NCA-based network remodelling component screens the recommended edges and keeps the edges that are essential to explain the given gene expression. Once the sparse NCA-based network remodelling component confirms some of the recommended edges, the CF component further utilizes those retained recomm...

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A rewriting system for convex optimization problems

Cited by 539 publications

References 52 publications

The effect of resource dynamics on species packing in diverse ecosystems

The effect of resource dynamics on species packing in diverse ecosystems

Deep learning enabled real time speckle recognition and hyperspectral imaging using a multimode fiber array

Reconstruction of Gene Regulatory Networks by integrating biological model and a recommendation system

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