Project description:In this paper, we discuss parameterized algorithms for variants of the partial vertex cover problem. Recall that in the classical vertex cover problem (VC), we are given a graph
Project description:We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata.
Project description:Learning from demonstration (LfD) enables a robot to emulate natural human movement instead of merely executing preprogrammed behaviors. This article presents a hierarchical LfD structure of task-parameterized models for object movement tasks, which are ubiquitous in everyday life and could benefit from robotic support. Our approach uses the task-parameterized Gaussian mixture model (TP-GMM) algorithm to encode sets of demonstrations in separate models that each correspond to a different task situation. The robot then maximizes its expected performance in a new situation by either selecting a good existing model or requesting new demonstrations. Compared to a standard implementation that encodes all demonstrations together for all test situations, the proposed approach offers four advantages. First, a simply defined distance function can be used to estimate test performance by calculating the similarity between a test situation and the existing models. Second, the proposed approach can improve generalization, e.g., better satisfying the demonstrated task constraints and speeding up task execution. Third, because the hierarchical structure encodes each demonstrated situation individually, a wider range of task situations can be modeled in the same framework without deteriorating performance. Last, adding or removing demonstrations incurs low computational load, and thus, the robot's skill library can be built incrementally. We first instantiate the proposed approach in a simulated task to validate these advantages. We then show that the advantages transfer to real hardware for a task where naive participants collaborated with a Willow Garage PR2 robot to move a handheld object. For most tested scenarios, our hierarchical method achieved significantly better task performance and subjective ratings than both a passive model with only gravity compensation and a single TP-GMM encoding all demonstrations.
Project description:Many applications in protein engineering require optimizing multiple protein properties simultaneously, such as binding one target but not others or binding a target while maintaining stability. Such multistate design problems require navigating a high-dimensional space to find proteins with desired characteristics. A model that relates protein sequence to functional attributes can guide design to solutions that would be hard to discover via screening. In this work, we measured thousands of protein-peptide binding affinities with the high-throughput interaction assay amped SORTCERY and used the data to parameterize a model of the alpha-helical peptide-binding landscape for three members of the Bcl-2 family of proteins: Bcl-xL, Mcl-1, and Bfl-1. We applied optimization protocols to explore extremes in this landscape to discover peptides with desired interaction profiles. Computational design generated 36 peptides, all of which bound with high affinity and specificity to just one of Bcl-xL, Mcl-1, or Bfl-1, as intended. We designed additional peptides that bound selectively to two out of three of these proteins. The designed peptides were dissimilar to known Bcl-2-binding peptides, and high-resolution crystal structures confirmed that they engaged their targets as expected. Excellent results on this challenging problem demonstrate the power of a landscape modeling approach, and the designed peptides have potential uses as diagnostic tools or cancer therapeutics.
Project description:The mutation-selection model of coding sequence evolution has received renewed attention for its use in estimating site-specific amino acid propensities and selection coefficient distributions. Two computationally tractable mutation-selection inference frameworks have been introduced: One framework employs a fixed-effects, highly parameterized maximum likelihood approach, whereas the other employs a random-effects Bayesian Dirichlet Process approach. While both implementations follow the same model, they appear to make distinct predictions about the distribution of selection coefficients. The fixed-effects framework estimates a large proportion of highly deleterious substitutions, whereas the random-effects framework estimates that all substitutions are either nearly neutral or weakly deleterious. It remains unknown, however, how accurately each method infers evolutionary constraints at individual sites. Indeed, selection coefficient distributions pool all site-specific inferences, thereby obscuring a precise assessment of site-specific estimates. Therefore, in this study, we use a simulation-based strategy to determine how accurately each approach recapitulates the selective constraint at individual sites. We find that the fixed-effects approach, despite its extensive parameterization, consistently and accurately estimates site-specific evolutionary constraint. By contrast, the random-effects Bayesian approach systematically underestimates the strength of natural selection, particularly for slowly evolving sites. We also find that, despite the strong differences between their inferred selection coefficient distributions, the fixed- and random-effects approaches yield surprisingly similar inferences of site-specific selective constraint. We conclude that the fixed-effects mutation-selection framework provides the more reliable software platform for model application and future development.
Project description:We applied the high-throughput interaction assay SORTCERY to measure thousands of protein-peptide binding affinities and used the data to parameterize models of the peptide-binding landscape for three members of the Bcl-2 family of proteins. We applied the models to design peptides that bound with high affinity and specificity to just one of Bcl-xL, Mcl-1, or Bfl-1. We designed additional peptides that bound selectively to two out of three of these proteins. The raw data provided are the multiplexed fastq files that serve as inputs to our analysis pipeline. Additional detail is available in our corresponding publication and at the following github repository. https://github.com/KeatingLab/sortcery_design
Project description:We refine and clinically parameterize a mathematical model of the humoral immune response against Shigella, a diarrheal bacteria that infects 80-165 million people and kills an estimated 600,000 people worldwide each year. Using Latin hypercube sampling and Monte Carlo simulations for parameter estimation, we fit our model to human immune data from two Shigella EcSf2a-2 vaccine trials and a rechallenge study in which antibody and B-cell responses against Shigella's lipopolysaccharide (LPS) and O-membrane proteins (OMP) were recorded. The clinically grounded model is used to mathematically investigate which key immune mechanisms and bacterial targets confer immunity against Shigella and to predict which humoral immune components should be elicited to create a protective vaccine against Shigella. The model offers insight into why the EcSf2a-2 vaccine had low efficacy and demonstrates that at a group level a humoral immune response induced by EcSf2a-2 vaccine or wild-type challenge against Shigella's LPS or OMP does not appear sufficient for protection. That is, the model predicts an uncontrolled infection of gut epithelial cells that is present across all best-fit model parameterizations when fit to EcSf2a-2 vaccine or wild-type challenge data. Using sensitivity analysis, we explore which model parameter values must be altered to prevent the destructive epithelial invasion by Shigella bacteria and identify four key parameter groups as potential vaccine targets or immune correlates: 1) the rate that Shigella migrates into the lamina propria or epithelium, 2) the rate that memory B cells (BM) differentiate into antibody-secreting cells (ASC), 3) the rate at which antibodies are produced by activated ASC, and 4) the Shigella-specific BM carrying capacity. This paper underscores the need for a multifaceted approach in ongoing efforts to design an effective Shigella vaccine.
Project description:Studies of economic mobility summarize the distribution of offspring incomes for each level of parent income. Mitnik and Grusky (2020) highlight that the conventional intergenerational elasticity (IGE) targets the geometric mean and propose a parametric strategy for estimating the arithmetic mean. We decompose the IGE and their proposal into two choices: (1) the summary statistic for the conditional distribution and (2) the functional form. These choices lead us to a different strategy-visualizing several quantiles of the offspring income distribution as smooth functions of parent income. Our proposal solves the problems Mitnik and Grusky highlight with geometric means, avoids the sensitivity of arithmetic means to top incomes, and provides more information than is possible with any single number. Our proposal has broader implications: the default summary (the mean) used in many regressions is sensitive to the tail of the distribution in ways that may be substantively undesirable.