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Experimental design trade-offs for gene regulatory network inference: an in silico study of the yeast Saccharomyces cerevisiae cell cycle Markdahl, Johan ; Colombo, Nicolo ; Thunberg, Johan et al in Proceedings of the 56th IEEE Conference on Decision and Control (2017, December) Time-series of high throughput gene sequencing data intended for gene regulatory network (GRN) inference are often short due to the high costs of sampling cell systems. Moreover, experimentalists lack a ... [more ▼] Time-series of high throughput gene sequencing data intended for gene regulatory network (GRN) inference are often short due to the high costs of sampling cell systems. Moreover, experimentalists lack a set of quantitative guidelines that prescribe the minimal number of samples required to infer a reliable GRN model. We study the temporal resolution of data vs.quality of GRN inference in order to ultimately overcome this deficit. The evolution of a Markovian jump process model for the Ras/cAMP/PKA pathway of proteins and metabolites in the G1 phase of the Saccharomyces cerevisiae cell cycle is sampled at a number of different rates. For each time-series we infer a linear regression model of the GRN using the LASSO method. The inferred network topology is evaluated in terms of the area under the precision-recall curve (AUPR). By plotting the AUPR against the number of samples, we show that the trade-off has a, roughly speaking, sigmoid shape. An optimal number of samples corresponds to values on the ridge of the sigmoid. [less ▲] Detailed reference viewed: 115 (10 UL)An Iterative Projection method for Synchronization of Invertible Matrices Over Graphs Thunberg, Johan ; Colombo, Nicolo ; Yue, Zuogong et al in 22nd International Symposium on Mathematical Theory of Networks and Systems (2016) This paper addresses synchronization of invertible matrices over graphs. The matrices represent pairwise transformations between n euclidean coordinate systems. Synchronization means that composite ... [more ▼] This paper addresses synchronization of invertible matrices over graphs. The matrices represent pairwise transformations between n euclidean coordinate systems. Synchronization means that composite transformations over loops are equal to the identity. Given a set of measured matrices that are not synchronized, the synchronization problem amounts to fining new synchronized matrices close to the former. Under the assumption that the measurement noise is zero mean Gaussian with known covariance, we introduce an iterative method based on linear subspace projection. The method is free of step size determination and tuning and numerical simulations show significant improvement of the solution compared to a recently proposed direct method as well as the Gauss-Newton method. [less ▲] Detailed reference viewed: 129 (10 UL)Global Optimality Bounds for ICA Algorithms Colombo, Nicolo ; Thunberg, Johan ; Goncalves, Jorge in 22nd International Symposium on Mathematical Theory of Networks and Systems (2016) Independent Component Analysis is a popular statistical method for separating a multivariate signal into additive components. It has been shown that the signal separation problem can be reduced to the ... [more ▼] Independent Component Analysis is a popular statistical method for separating a multivariate signal into additive components. It has been shown that the signal separation problem can be reduced to the joint diagonalization of the matrix slices of some higher-order cumulants of the signal. In this approach, the unknown mixing matrix can be computed directly from the obtained joint diagonalizer. Various iterative algorithms for solving the non-convex joint diagonalization problem exist, but they usually lack global optimality guarantees. In this paper, we introduce a procedure for computing an optimality gap for local optimal solutions. The optimality gap is then used to obtain an empirical error bound for the estimated mixing matrix. Finally, a class of simultaneous matrix decomposition problems that admit such relaxation procedure is identified. [less ▲] Detailed reference viewed: 167 (9 UL)Expression of the Parkinson’s Disease-Associated Gene Alpha-Synuclein is Regulated by the Neuronal Cell Fate Determinant TRIM32 Pavlou, Maria Angeliki ; Colombo, Nicolo ; et al in Molecular Neurobiology (2016) Detailed reference viewed: 223 (13 UL)FastMotif: Spectral Sequence Motif Discovery Colombo, Nicolo ; Vlassis, Nikos in Bioinformatics (2015) Motivation: Sequence discovery tools play a central role in several fields of computational biology. In the framework of Transcription Factor binding studies, most of the existing motif finding algorithms ... [more ▼] Motivation: Sequence discovery tools play a central role in several fields of computational biology. In the framework of Transcription Factor binding studies, most of the existing motif finding algorithms are computationally demanding, and they may not be able to support the increasingly large datasets produced by modern high-throughput sequencing technologies. Results: We present FastMotif, a new motif discovery algorithm that is built on a recent machine learning technique referred to as Method of Moments. Based on spectral decompositions, our method is robust to model misspecifications and is not prone to locally optimal solutions. We obtain an algorithm that is extremely fast and designed for the analysis of big sequencing data. On HT-Selex data, FastMotif extracts motif profiles that match those computed by various state-of- the-art algorithms, but one order of magnitude faster. We provide a theoretical and numerical analysis of the algorithm’s robustness and discuss its sensitivity with respect to the free parameters. [less ▲] Detailed reference viewed: 130 (9 UL)Spectral Sequence Motif Discovery Colombo, Nicolo ; Vlassis, Nikos E-print/Working paper (2014) Sequence discovery tools play a central role in several fields of computational biology. In the framework of Transcription Factor binding studies, motif finding algorithms of increasingly high performance ... [more ▼] Sequence discovery tools play a central role in several fields of computational biology. In the framework of Transcription Factor binding studies, motif finding algorithms of increasingly high performance are required to process the big datasets produced by new high-throughput sequencing technologies. Most existing algorithms are computationally demanding and often cannot support the large size of new experimental data. We present a new motif discovery algorithm that is built on a recent machine learning technique, referred to as Method of Moments. Based on spectral decompositions, this method is robust under model misspecification and is not prone to locally optimal solutions. We obtain an algorithm that is extremely fast and designed for the analysis of big sequencing data. In a few minutes, we can process datasets of hundreds of thousand sequences and extract motif profiles that match those computed by various state-of-the-art algorithms. [less ▲] Detailed reference viewed: 56 (3 UL)A minimal BV action for Vasiliev's four-dimensional higher spin gravity ; Colombo, Nicolo ; in Journal of High Energy Physics [=JHEP] (2012) The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to ... [more ▼] The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle. [less ▲] Detailed reference viewed: 100 (1 UL)Higher Spin Gravity Amplitudes From Zero-form Charges Colombo, Nicolo ; E-print/Working paper (2012) We examine zero-form charges in Vasiliev's four-dimensional bosonic higher spin gravities. These are classical observables given by integrals over noncommutative twistor space of adjoint combinations of ... [more ▼] We examine zero-form charges in Vasiliev's four-dimensional bosonic higher spin gravities. These are classical observables given by integrals over noncommutative twistor space of adjoint combinations of the zero-form master fields, including insertions of delta functions in the deformed oscillators serving as gauge invariant regulators. The regularized charges admit perturbative expansions in terms of multi-linear functionals in the Weyl zero-form, which are Bose symmetric and higher spin invariant by construction, and that can be interpreted as basic building blocks for higher spin gravity amplitudes. We compute two- and three-point functions by attaching external legs given by unfolded bulk-to-boundary propagators, and identify the result with the two- and three-current correlation functions in theories of free conformal scalars and fermions in three dimensions. Modulo assumptions on the structure of the sub-leading corrections, and relying on the generalized Hamiltonian off-shell formulation, we are thus led to propose an expression for the free energy as a sum of suitably normalized zero-form charges [less ▲] Detailed reference viewed: 27 (0 UL)Twistor space observables and quasi-amplitudes in 4D higher spin gravity Colombo, Nicolo ; in Journal of High Energy Physics [=JHEP] (2010) Vasiliev equations facilitate globally defined formulations of higher-spin gravity in various correspondence spaces associated with different phases of the theory. In the four-dimensional case this ... [more ▼] Vasiliev equations facilitate globally defined formulations of higher-spin gravity in various correspondence spaces associated with different phases of the theory. In the four-dimensional case this induces a map from a generally covariant formulation in spacetime with higher-derivative interactions to a formulation in terms of a deformed symplectic structure on a noncommutative doubled twistor space, sending spacetime boundary conditions to various sectors of an associative star-product algebra. We look at observables given by integrals over twistor space defining composite zero-forms in spacetime that do not break any local symmetries and that are closed on shell. They can be evaluated locally in spacetime and interpreted as building blocks for dual amplitudes. To regularize potential twistor-space divergencies arising in their curvature expansion, we propose a closed-contour prescription that respects associativity and hence higher-spin gauge symmetry. As a sample calculation, we examine next-to-leading corrections to quasi-amplitudes for twistor-space plane waves, and find cancellations that we interpret using transgression properties in twistor space. [less ▲] Detailed reference viewed: 81 (3 UL) |
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