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Constraint Programming (CP) has proven to be an effective platform for constraint based sequence mining. Previous work has focused on standard frequent sequence mining, as well as frequent sequence mining with a maximum ’gap’ between two matching events in a sequence. The main challenge in the latter is that this constraint can not be imposed independently of the omnipresent frequency constraint. Indeed, the gap constraint changes whether a subsequence is included in a sequence, and hence its frequency. In this work, we go beyond that and investigate the integration of timed events and constraining the minimum/maximum gap as well as minimum/maximum span. The latter constrains the allowed time between the first and last matching event of a pattern. We show how the three are interrelated, and what the required changes to the frequency constraint are. Key in our approach is the concept of an extension window defined by gap/span and we develop techniques to avoid scanning the sequences needlessly, as well as using a backtracking-aware data structure. Experiments demonstrate that the proposed approach outperforms both specialized and CP-based approaches in almost all cases and that the advantage increases as the minimum frequency threshold decreases. This paper is an extension of the original manuscript presented at CPAIOR’17 [5].

An uncertainty-oriented cross-scale topology optimization model with global stress reliability constraint, local displacement constraint, and micro-manufacturing control based on evidence theory is presented. The model is oriented to two-dimensional porous material structure, which concurrently designs the material distribution of both the macrostructure and the cell microstructure. During the optimization process, the homogenization method is used to solve the equivalent elastic modulus of the cell microstructure, which is then endowed to the macro-elements for subsequent analysis. The local stress constraints are converted to a global constraint by P-norm to reduce the computational consumption. Considering the uncertainty factors, the evidence theory is utilized to process the uncertainty parameters and evaluate the reliability of the structural strength performance. Minimum length-scale constraint is imposed on the cell microstructure by a density projection method for better manufacturability. Three numerical examples are presented to illustrate the availability of the proposed model.

Despite our continuous improvement in understanding antibiotic resistance, the interplay between natural selection of resistance mutations and the environment remains unclear. To investigate the role of bacterial metabolism in constraining the evolution of antibiotic resistance, we evolved Escherichia coli growing on glycolytic or gluconeogenic carbon sources to the selective pressure of three different antibiotics. Profiling more than 500 intracellular and extracellular putative metabolites in 190 evolved populations revealed that carbon and energy metabolism strongly constrained the evolutionary trajectories, both in terms of speed and mode of resistance acquisition. To interpret and explore the space of metabolome changes, we developed a novel constraint‐based modeling approach using the concept of shadow prices. This analysis, together with genome resequencing of resistant populations, identified condition‐dependent compensatory mechanisms of antibiotic resistance, such as the shift from respiratory to fermentative metabolism of glucose upon overexpression of efflux pumps. Moreover, metabolome‐based predictions revealed emerging weaknesses in resistant strains, such as the hypersensitivity to fosfomycin of ampicillin‐resistant strains. Overall, resolving metabolic adaptation throughout antibiotic‐driven evolutionary trajectories opens new perspectives in the fight against emerging antibiotic resistance. Synopsis Bacterial metabolism constrains the evolution of antibiotic resistance. A modeling approach is developed to interpret the functionality of metabolic rewiring in resistance‐evolving E. coli growing on glycolytic or gluconeogenic carbon sources from metabolomics data. Large‐scale untargeted metabolome profiling reveals metabolic adaptations in 190 evolved antibiotic‐resistant E. coli populations, in part as compensation for consequences of the primary resistance mechanisms. Carbon and energy metabolism strongly constrain the evolutionary trajectories, both in terms of speed and mode of resistance acquisition. A novel constraint‐based modeling approach, together with genome re‐sequencing of resistant populations, identifies condition‐dependent compensatory mechanisms. Graphical Abstract Bacterial metabolism constrains the evolution of antibiotic resistance. A modeling approach is developed to interpret the functionality of metabolic rewiring in resistance‐evolving E. coli growing on glycolytic or gluconeogenic carbon sources from metabolomics data.

We propose a DC (Difference of two Convex functions) formulation approach for sparse optimization problems having a cardinality or rank constraint. With the largest-k norm, an exact DC representation of the cardinality constraint is provided. We then transform the cardinality-constrained problem into a penalty function form and derive exact penalty parameter values for some optimization problems, especially for quadratic minimization problems which often appear in practice. A DC Algorithm (DCA) is presented, where the dual step at each iteration can be efficiently carried out due to the accessible subgradient of the largest-k norm. Furthermore, we can solve each DCA subproblem in linear time via a soft thresholding operation if there are no additional constraints. The framework is extended to the rank-constrained problem as well as the cardinality- and the rank-minimization problems. Numerical experiments demonstrate the efficiency of the proposed DCA in comparison with existing methods which have other penalty terms.

Abstract Rubisco assimilates CO2 to form the sugars that fuel life on earth. Correlations between rubisco kinetic traits across species have led to the proposition that rubisco adaptation is highly constrained by catalytic trade-offs. However, these analyses did not consider the phylogenetic context of the enzymes that were analyzed. Thus, it is possible that the correlations observed were an artefact of the presence of phylogenetic signal in rubisco kinetics and the phylogenetic relationship between the species that were sampled. Here, we conducted a phylogenetically resolved analysis of rubisco kinetics and show that there is a significant phylogenetic signal in rubisco kinetic traits. We re-evaluated the extent of catalytic trade-offs accounting for this phylogenetic signal and found that all were attenuated. Following phylogenetic correction, the largest catalytic trade-offs were observed between the Michaelis constant for CO2 and carboxylase turnover (∼21–37%), and between the Michaelis constants for CO2 and O2 (∼9–19%), respectively. All other catalytic trade-offs were substantially attenuated such that they were marginal (<9%) or non-significant. This phylogenetically resolved analysis of rubisco kinetic evolution also identified kinetic changes that occur concomitant with the evolution of C4 photosynthesis. Finally, we show that phylogenetic constraints have played a larger role than catalytic trade-offs in limiting the evolution of rubisco kinetics. Thus, although there is strong evidence for some catalytic trade-offs, rubisco adaptation has been more limited by phylogenetic constraint than by the combined action of all catalytic trade-offs.

The objective function is important to constraint-based modeling, but setting it has traditionally been subjective, limiting predictive accuracy. We expose the biases of commonly used objective functions and propose a paradigm shift toward unbiased objective functions powered by artificial intelligence, offering a promising avenue for metabolic engineering and biomedical applications. The objective function is important to constraint-based modeling, but setting it has traditionally been subjective, limiting predictive accuracy. We expose the biases of commonly used objective functions and propose a paradigm shift toward unbiased objective functions powered by artificial intelligence, offering a promising avenue for metabolic engineering and biomedical applications.

Additive manufacturing (AM) technologies, such as selective laser sintering (SLS) and fused deposition modeling (FDM), have become the powerful tools for direct manufacturing of complex parts. This breakthrough in manufacturing technology makes the fabrication of new geometrical features and multiple materials possible. Past researches on designs and design methods often focused on how to obtain desired functional performance of the structures or parts, specific manufacturing capabilities as well as manufacturing constraints of AM were neglected. However, the inherent constraints in AM processes should be taken into account in design process. In this paper, the enclosed voids, one type of manufacturing constraints of AM, are investigated. In mathematics, enclosed voids restriction expressed as the solid structure is simplyconnected. We propose an equivalent description of simply-connected constraint for avoiding enclosed voids in structures, named as virtual temperature method (VTM). In this method, suppose that the voids in structure are filled with a virtual heating material with high heat conductivity and solid areas are filled with another virtual material with low heat conductivity. Once the enclosed voids exist in structure, the maximum temperature value of structure will be very high. Based upon this method, the simplyconnected constraint is equivalent to maximum temperature constraint. And this method can be easily used to formulate the simply-connected constraint in topology optimization. The effectiveness of this description method is illustrated by several examples. Based upon topology optimization, an example of 3D cantilever beam is used to illustrate the trade-off between manufacturability and functionality. Moreover, the three optimized structures are fabricated by FDM technology to indicate further the necessity of considering the simply-connected constraint in design phase for AM.

Two ways of implementing unilateral holonomic constraints with piecewise smooth boundaries are considered. Examples are given that testify both in favor of the proposed methods and against them. The sensitivity of the equilibria of a system subjected to holonomic constraints with piecewise smooth boundaries to the way these constraints are implemented is also discussed using examples. Two problems from the mechanics of systems constrained by a pair of inextensible weightless tethers are considered. In one of these problems, which is most likely academic in nature, equilibria are found and small oscillations near these equilibria are studied. Another problem relates to tethered systems deployed near a uniformly rotating celestial body. For it, the relative equilibria of a load suspended on a pair of tethers are found, and sufficient conditions for the stability of these relative equilibria are studied.

A novel trajectory tracking control problem based on constraint modeling and analysis is addressed by the way of constraint-following control for the unmanned tracked vehicle in this paper. The unmanned tracked vehicle system contains time-varying uncertainty which is possibly swift but bounded, and the bound is possibly unknown. First, the coupled dynamics model of unmanned tracked vehicle is established. By taking into account the kinematic characteristics, it makes the motion control of unmanned tracked vehicles more precise. Meanwhile, a 3D virtual prototype model is established for the unmanned tracked vehicle. Second, for the control objective of trajectory tracking, the related problem is converted into a constraint-following problem, and an adaptive robust controller is therefore proposed based on this for the controlled unmanned tracked vehicle system to satisfy the trajectory tracking constraint. Finally, it is proved that the controlled unmanned tracked vehicle system can achieve accurate trajectory tracking with the proposed adaptive robust control, even under the interference of complex time-varying uncertainties. Modeling accurate dynamics and trajectory tracking constraints for unmanned tracked vehicles while designing an adaptive robust controller to realize accurate motion control for unmanned tracked vehicles even under strong external disturbances are the main contributions of this paper.

Metal ions are vital to metabolism, as they can act as cofactors on enzymes and thus modulate individual enzymatic reactions. Although many enzymes have been reported to interact with metal ions, the quantitative relationships between metal ions and metabolism are lacking. Here, we reconstructed a genome-scale metabolic model of the yeast Saccharomyces cerevisiae to account for proteome constraints and enzyme cofactors such as metal ions, named CofactorYeast. The model is able to estimate abundances of metal ions binding on enzymes in cells under various conditions, which are comparable to measured metal ion contents in biomass. In addition, the model predicts distinct metabolic flux distributions in response to reduced levels of various metal ions in the medium. Specifically, the model reproduces changes upon iron deficiency in metabolic and gene expression levels, which could be interpreted by optimization principles (i.e., yeast optimizes iron utilization based on metabolic network and enzyme kinetics rather than preferentially targeting iron to specific enzymes or pathways). At last, we show the potential of using the model for understanding cell factories that harbor heterologous iron-containing enzymes to synthesize high-value compounds such as p-coumaric acid. Overall, the model demonstrates the dependence of enzymes on metal ions and links metal ions to metabolism on a genome scale.