Predicting mortality among patients with liver cirrhosis in electronic health records with machine learning

OBJECTIVE: Liver cirrhosis is a leading cause of death and effects millions of people in the United States. Early mortality prediction among patients with cirrhosis might give healthcare providers more opportunity to effectively treat the condition. We hypothesized that laboratory test results and other related diagnoses would be associated with mortality in this population. Our another assumption was that a deep learning model could outperform the current Model for End Stage Liver disease (MELD) score in predicting mortality. MATERIALS AND METHODS: We utilized electronic health record data from 34,575 patients with a diagnosis of cirrhosis from a large medical center to study associations with mortality. Three time-windows of mortality (365 days, 180 days and 90 days) and two cases with different number of variables (all 41 available variables and 4 variables in MELD-NA) were studied. Missing values were imputed using multiple imputation for continuous variables and mode for categorical variables. Deep learning and machine learning algorithms, i.e., deep neural networks (DNN), random forest (RF) and logistic regression (LR) were employed to study the associations between baseline features such as laboratory measurements and diagnoses for each time window by 5-fold cross validation method. Metrics such as area under the receiver operating curve (AUC), overall accuracy, sensitivity, and specificity were used to evaluate models. RESULTS: Performance of models comprising all variables outperformed those with 4 MELD-NA variables for all prediction cases and the DNN model outperformed the LR and RF models. For example, the DNN model achieved an AUC of 0.88, 0.86, and 0.85 for 90, 180, and 365-day mortality respectively as compared to the MELD score, which resulted in corresponding AUCs of 0.81, 0.79, and 0.76 for the same instances. The DNN and LR models had a significantly better f1 score compared to MELD at all time points examined. CONCLUSION: Other variables such as alkaline phosphatase, alanine aminotransferase, and hemoglobin were also top informative features besides the 4 MELD-Na variables. Machine learning and deep learning models outperformed the current standard of risk prediction among patients with cirrhosis. Advanced informatics techniques showed promise for risk prediction in patients with cirrhosis

Modal Logics with Hard Diamond-free Fragments

We investigate the complexity of modal satisfiability for certain combinations of modal logics. In particular we examine four examples of multimodal logics with dependencies and demonstrate that even if we restrict our inputs to diamond-free formulas (in negation normal form), these logics still have a high complexity. This result illustrates that having D as one or more of the combined logics, as well as the interdependencies among logics can be important sources of complexity even in the absence of diamonds and even when at the same time in our formulas we allow only one propositional variable. We then further investigate and characterize the complexity of the diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers' comments. Accepted at LFCS 201

Intuitionistic implication makes model checking hard

We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic FPL, and Jankov's logic KC. We show that the model checking problem is P-complete for the implicational fragments of all these intuitionistic logics. For BPL and FPL we reach P-hardness even on the implicational fragment with only one variable. The same hardness results are obtained for the strictly implicational fragments of their modal companions. Moreover, we investigate whether formulas with less variables and additional connectives make model checking easier. Whereas for variable free formulas outside of the implicational fragment, FPL model checking is shown to be in LOGCFL, the problem remains P-complete for BPL.Comment: 29 pages, 10 figure

The Computational Complexity of Generating Random Fractals

In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential; it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation that can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.Comment: 28 pages, LATEX, 8 Postscript figures available from [email protected]

Molecular profile of synovial fibroblasts in rheumatoid arthritis depends on the stage of proliferation

The aim of this study was to explore the molecular profile of proliferating rheumatoid arthritis synovial fibroblasts (RA-SF). Total RNA was extracted from two cultures of RA-SF (low-density [LD] proliferating cells and high-density [HD] nonproliferating cells) and suppression subtractive hybridization was performed to compare differential gene expression of these two cultures. Subtracted cDNA was subcloned, and nucleotide sequences were analyzed to identify each clone. Differential expression of distinct clones was confirmed by semiquantitative RT-PCR. The expression of certain genes in synovial tissues was examined by in situ hybridization. In both LD and HD cells, 44 clones were upregulated. Of the 88 total clones, 46 were identical to sequences that have previously been characterized. Twenty-nine clones were identical to cDNAs that have been identified, but with unknown functions so far, and 13 clones did not show any significant homology to sequences in GenBank (NCBI). Differential expression of distinct clones was confirmed by RT-PCR. In situ hybridization showed that certain genes, such as S100A4, NFAT5, unr and Fbx3, were also expressed predominantly in synovial tissues from patients with RA but not from normal individuals. The expression of distinct genes in proliferating RA-SF could also be found in RA synovium, suggesting that these molecules are involved in synovial activation in RA. Most importantly, the data indicate that the expression of certain genes in RA-SF depends on the stage of proliferation; therefore, the stage needs to be considered in any analysis of differential gene expression in SF

On the Complexity of Query Result Diversification

Query result diversification is a bi-criteria optimization problem for ranking query results. Given a database D, a query Q and a positive integer k, it is to find a set of k tuples from Q(D) such that the tuples are as relevant as possible to the query, and at the same time, as diverse as possible to each other. Subsets of Q(D) are ranked by an objective function defined in terms of relevance and diversity. Query result diversification has found a variety of applications in databases, information retrieval and operations research. This paper studies the complexity of result diversification for relational queries. We identify three problems in connection with query result diversification, to determine whether there exists a set of k tuples that is ranked above a bound with respect to relevance and diversity, to assess the rank of a given k-element set, and to count how many k-element sets are ranked above a given bound. We study these problems for a variety of query languages and for three objective functions. We establish the upper and lower bounds of these problems, all matching, for both combined complexity and data complexity. We also investigate several special settings of these problems, identifying tractable cases. 1

Flow Phase Diagram for the Helium Superfluids

The flow phase diagram for He II and $^3$He-B is established and discussed based on available experimental data and the theory of Volovik [JETP Letters {\bf{78}} (2003) 553]. The effective temperature - dependent but scale - independent Reynolds number $Re_{eff}=1/q=(1+\alpha')/\alpha$, where $\alpha$ and $\alpha'$ are the mutual friction parameters and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram allows identification of experimentally observed turbulent states I and II in counterflowing He II with the turbulent regimes suggested by Volovik.Comment: 2 figure

Does Treewidth Help in Modal Satisfiability?

Many tractable algorithms for solving the Constraint Satisfaction Problem (CSP) have been developed using the notion of the treewidth of some graph derived from the input CSP instance. In particular, the incidence graph of the CSP instance is one such graph. We introduce the notion of an incidence graph for modal logic formulae in a certain normal form. We investigate the parameterized complexity of modal satisfiability with the modal depth of the formula and the treewidth of the incidence graph as parameters. For various combinations of Euclidean, reflexive, symmetric and transitive models, we show either that modal satisfiability is FPT, or that it is W[1]-hard. In particular, modal satisfiability in general models is FPT, while it is W[1]-hard in transitive models. As might be expected, modal satisfiability in transitive and Euclidean models is FPT.Comment: Full version of the paper appearing in MFCS 2010. Change from v1: improved section 5 to avoid exponential blow-up in formula siz