Fuzzy upper bounds in groupoids.
Ontology highlight
ABSTRACT:
SUBMITTER: Ahn SS
PROVIDER: S-EPMC4058160 | biostudies-other | 2014
REPOSITORIES: biostudies-other
Similar Datasets
Project description:BackgroundPremature discontinuation and other forms of noncompliance with treatment assignment can complicate causal inference of treatment effects in randomized trials. The intent-to-treat analysis gives unbiased estimates for causal effects of treatment assignment on outcome, but may understate potential benefit or harm of actual treatment. The corresponding upper confidence limit can also be underestimated.PurposeTo compare estimates of the hazard ratio and upper bound of the two-sided 95% confidence interval from causal inference methods that account for noncompliance with those from the intent-to-treat analysis.MethodsWe used simulations with parameters chosen to reflect cardiovascular safety trials of diabetes drugs, with a focus on upper bound estimates relative to 1.3, based on regulatory guidelines. A total of 1000 simulations were run under each parameter combination for a hypothetical trial of 10,000 total subjects randomly assigned to active treatment or control at 1:1 ratio. Noncompliance was considered in the form of treatment discontinuation and cross-over at specified proportions, with an assumed true hazard ratio of 0.9, 1, and 1.3, respectively. Various levels of risk associated with being a non-complier (independent of treatment status) were evaluated. Hazard ratio and upper bound estimates from causal survival analysis and intent-to-treat were obtained from each simulation and summarized under each parameter setting.ResultsCausal analysis estimated the true hazard ratio with little bias in almost all settings examined. Intent-to-treat was unbiased only when the true hazard ratio = 1; otherwise it underestimated both benefit and harm. When upper bound estimates from intent-to-treat were ≥1.3, corresponding estimates from causal analysis were also ≥1.3 in almost 100% of the simulations, regardless of the true hazard ratio. When upper bound estimates from intent-to-treat were <1.3 and the true hazard ratio = 1, corresponding upper bound estimates from causal analysis were ≥1.3 in up to 66% of the simulations under some settings.LimitationsSimulations cannot cover all scenarios for noncompliance in real randomized trials.ConclusionCausal survival analysis was superior to intent-to-treat in estimating the true hazard ratio with respect to bias in the presence of noncompliance. However, its large variance should be considered for safety upper bound exclusion especially when the true hazard ratio = 1. Our simulations provided a broad reference for practical considerations of bias-variance trade-off in dealing with noncompliance in cardiovascular safety trials of diabetes drugs. Further research is warranted for the development and application of causal inference methods in the evaluation of safety upper bounds.
| S-EPMC4420771 | biostudies-literature
Project description:BACKGROUND: Enumeration of chemical graphs satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics since it leads to a variety of useful applications including structure determination of novel chemical compounds and drug design. RESULTS: In this paper, we consider the problem of enumerating all tree-like chemical graphs from a given set of feature vectors, which is specified by a pair of upper and lower feature vectors, where a feature vector represents the frequency of prescribed paths in a chemical compound to be constructed. This problem can be solved by applying the algorithm proposed by Ishida et al. to each single feature vector in the given set, but this method may take much computation time because in general there are many feature vectors in a given set. We propose a new exact branch-and-bound algorithm for the problem so that all the feature vectors in a given set are handled directly. Since we cannot use the bounding operation proposed by Ishida et al. due to upper and lower constraints, we introduce new bounding operations based on upper and lower feature vectors, a bond constraint, and a detachment condition. CONCLUSIONS: Our proposed algorithm is useful for enumerating tree-like chemical graphs with given upper and lower bounds on path frequencies.
| S-EPMC3287468 | biostudies-literature
Project description:MotivationReticulate network is a model for displaying and quantifying the effects of complex reticulate processes on the evolutionary history of species undergoing reticulate evolution. A central computational problem on reticulate networks is: given a set of phylogenetic trees (each for some region of the genomes), reconstruct the most parsimonious reticulate network (called the minimum reticulate network) that combines the topological information contained in the given trees. This problem is well-known to be NP-hard. Thus, existing approaches for this problem either work with only two input trees or make simplifying topological assumptions.ResultsWe present novel results on the minimum reticulate network problem. Unlike existing approaches, we address the fully general problem: there is no restriction on the number of trees that are input, and there is no restriction on the form of the allowed reticulate network. We present lower and upper bounds on the minimum number of reticulation events in the minimum reticulate network (and infer an approximately parsimonious reticulate network). A program called PIRN implements these methods, which also outputs a graphical representation of the inferred network. Empirical results on simulated and biological data show that our methods are practical for a wide range of data. More importantly, the lower and upper bounds match for many datasets (especially when the number of trees is small or reticulation level is low), and this allows us to solve the minimum reticulate network problem exactly for these datasets.AvailabilityA software tool, PIRN, is available for download from the web page: http://www.engr.uconn.edu/~ywu.Supplementary informationSupplementary data is available at Bioinformatics online.
| S-EPMC2881383 | biostudies-literature
Project description:Using the orthogonal rank of the tensor, a new estimation method for the upper bounds on the nuclear norms is presented and some new tight upper bounds on the nuclear norms are established. Taking into account the structure information of the tensor, an important factor affecting the upper bounds is discussed and some corresponding properties related to the nuclear norms are given. Meanwhile, some new results of the upper bounds on the nuclear norms are obtained.
| S-EPMC6208618 | biostudies-other
Project description:Although the energetics of grain boundaries are more or less understood, their mechanical description remains challenging primarily because of very fast dynamics in the atomic length scale. By contrast, granular dynamics are extraordinarily sluggish. In this study, two dimensional centripetal packings of macroscopic granular particles are employed to investigate the role of geometric aspects of grain boundary formation. Using a novel sampling scheme, the extensive configuration space is well represented by a few prominent structures. Our results suggest that cohesive effects "iron out" any disorder present and enforce a transition towards a "fixed point" basin associated with a universal high density jammed hexagonal structure. Two main conjectures are advanced: (i) the appearance of grain boundary like structures is the manifestation of the kinetic instabilities of the densification process and has its origin in the structural rearrangement and (ii) the departure from six-fold coordination in the final packing is bounded from above by a sixth of the angular dispersion present in the initial configuration. If similar predictive consequences are further developed for three dimensional cases, this may have far reaching consequences in many areas of science and technology.
| S-EPMC4887881 | biostudies-literature
Project description:Uncertain data are observations that cannot be uniquely mapped to a referent. In the case of uncertainty due to incompleteness, possibility theory can be used as an appropriate model for processing such data. In particular, granular counting is a way to count data in presence of uncertainty represented by possibility distributions. Two algorithms were proposed in literature to compute granular counting: exact granular counting, with quadratic time complexity, and approximate granular counting, with linear time complexity. This paper extends approximate granular counting by computing bounds for exact granular count. In this way, the efficiency of approximate granular count is combined with certified bounds whose width can be adjusted in accordance to user needs.
| S-EPMC7274672 | biostudies-literature
Project description:Interpretability is the dominant feature of a fuzzy model in security-oriented fields. Traditionally fuzzy models based on expert knowledge have obtained well interpretation innately but imprecisely. Numerical data based fuzzy models perform well in precision but not necessarily in interpretation. To utilize the expert knowledge and numerical data in a fuzzy model synchronously, this paper proposed a hybrid fuzzy c-means (FCM) clustering algorithm and Fuzzy Network (FN) method-based model for prediction. The Mamdani rule-based structure of the proposed model is identified based on FCM algorithm from data and by expert-system method from expert knowledge, both of which are combined by FN method. Particle swarm optimization (PSO) algorithm is utilized to optimize the fuzzy set parameters. We tested the proposed model on 6 real datasets comparing the results with the ones obtained by using FCM algorithm. The results showed that our model performed best in interpretability, transparency, and accuracy.
| S-EPMC9523042 | biostudies-literature
Project description:The ability to intervene in disease progression given a person's disease history has the potential to solve one of society's most pressing issues: advancing health care delivery and reducing its cost. Controlling disease progression is inherently associated with the ability to predict possible future diseases given a patient's medical history. We invoke an information-theoretic methodology to quantify the level of predictability inherent in disease histories of a large electronic health records dataset with over half a million patients. In our analysis, we progress from zeroth order through temporal informed statistics, both from an individual patient's standpoint and also considering the collective effects. Our findings confirm our intuition that knowledge of common disease progressions results in higher predictability bounds than treating disease histories independently. We complement this result by showing the point at which the temporal dependence structure vanishes with increasing orders of the time-correlated statistic. Surprisingly, we also show that shuffling individual disease histories only marginally degrades the predictability bounds. This apparent contradiction with respect to the importance of time-ordered information is indicative of the complexities involved in capturing the health-care process and the difficulties associated with utilising this information in universal prediction algorithms.
| S-EPMC4493571 | biostudies-literature
Project description:Dynamical spectral estimation is a well-established numerical approach for estimating eigenvalues and eigenfunctions of the Markov transition operator from trajectory data. Although the approach has been widely applied in biomolecular simulations, its error properties remain poorly understood. Here we analyze the error of a dynamical spectral estimation method called "the variational approach to conformational dynamics" (VAC). We bound the approximation error and estimation error for VAC estimates. Our analysis establishes VAC's convergence properties and suggests new strategies for tuning VAC to improve accuracy.
| S-EPMC8336423 | biostudies-literature
Project description:A recently developed lower bound theory for Coulombic problems (E. Pollak, R. Martinazzo, J. Chem. Theory Comput. 2021, 17, 1535) is further developed and applied to the highly accurate calculation of the ground-state energy of two- (He, Li+, and H-) and three- (Li) electron atoms. The method has been implemented with explicitly correlated many-particle basis sets of Gaussian type, on the basis of the highly accurate (Ritz) upper bounds they can provide with relatively small numbers of functions. The use of explicitly correlated Gaussians is developed further for computing the variances, and the necessary modifications are here discussed. The computed lower bounds are of submilli-Hartree (parts per million relative) precision and for Li represent the best lower bounds ever obtained. Although not yet as accurate as the corresponding (Ritz) upper bounds, the computed bounds are orders of magnitude tighter than those obtained with other lower bound methods, thereby demonstrating that the proposed method is viable for lower bound calculations in quantum chemistry applications. Among several aspects, the optimization of the wave function is shown to play a key role for both the optimal solution of the lower bound problem and the internal check of the theory.
| S-EPMC8796283 | biostudies-literature