Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

The Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a non-intrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations.

A Bayesian method for detecting stellar flares

We present a Bayesian-odds-ratio-based algorithm for detecting stellar flares in light-curve data. We assume flares are described by a model in which there is a rapid rise with a half-Gaussian profile, followed by an exponential decay. Our signal model also contains a polynomial background model required to fit underlying light-curve variations in the data, which could otherwise partially mimic a flare. We characterize the false alarm probability and efficiency of this method under the assumption that any unmodelled noise in the data is Gaussian, and compare it with a simpler thresholding method based on that used in Walkowicz et al. We find our method has a significant increase in detection efficiency for low signal-to-noise ratio (S/N) flares. For a conservative false alarm probability our method can detect 95 per cent of flares with S/N less than 20, as compared to S/N of 25 for the simpler method. We also test how well the assumption of Gaussian noise holds by applying the method to a selection of 'quiet' Kepler stars. As an example we have applied our method to a selection of stars in Kepler Quarter 1 data. The method finds 687 flaring stars with a total of 1873 flares after vetos have been applied. For these flares we have made preliminary characterizations of their durations and and S/N.

Spindle assembly checkpoint protein expression correlates with cellular proliferation and shorter time to recurrence in ovarian cancer.

Ovarian carcinoma (OC) is the most lethal of the gynecological malignancies, often presenting at an advanced stage. Treatment is hampered by high levels of drug resistance. The taxanes are microtubule stabilizing agents, used as first-line agents in the treatment of OC that exert their apoptotic effects through the spindle assembly checkpoint. BUB1-related protein kinase (BUBR1) and mitotic arrest deficient 2 (MAD2), essential spindle assembly checkpoint components, play a key role in response to taxanes. BUBR1, MAD2, and Ki-67 were assessed on an OC tissue microarray platform representing 72 OC tumors of varying histologic subtypes. Sixty-one of these patients received paclitaxel and platinum agents combined; 11 received platinum alone. Overall survival was available for all 72 patients, whereas recurrence-free survival (RFS) was available for 66 patients. Increased BUBR1 expression was seen in serous carcinomas, compared with other histologies (P = .03). Increased BUBR1 was significantly associated with tumors of advanced stage (P = .05). Increased MAD2 and BUBR1 expression also correlated with increased cellular proliferation (P < .0002 and P = .02, respectively). Reduced MAD2 nuclear intensity was associated with a shorter RFS (P = .03), in ovarian tumors of differing histologic subtype (n = 66). In this subgroup, for those women who received paclitaxel and platinum agents combined (n = 57), reduced MAD2 intensity also identified women with a shorter RFS (P < .007). For the entire cohort of patients, irrespective of histologic subtype or treatment, MAD2 nuclear intensity retained independent significance in a multivariate model, with tumors showing reduced nuclear MAD2 intensity identifying patients with a poorer RFS (P = .05).

Stabilisation of MAD2 expression through inhibition of miR-433; A novel mechanism for restoring chemo-responsiveness in ovarian tumours

Epithelial ovarian carcinoma (EOC) is characterised by late diagnosis and recurrences, both of which contribute to the high morbidity and mortality of this cancer. Unfortunately, EOC has an innate susceptibility to become chemo-resistant. Specifically, up to 30% of patients may not respond to current standard chemotherapy (paclitaxel and platinum in combination) and of those who have an initial response, some patients relapse within a few months. Therefore, in order to improve patient outcome it is crucial to establish what factors influence a patients' individualised response to chemotherapy. We analysed MAD2 protein expression in a patient cohort of 35 ovarian tumours and a panel of 5 ovarian cancer cell lines. We have demonstrated that low nuclear MAD2 expression intensity was significantly associated with chemo-resistant ovarian tumours (p=0.0136). Moreover, in vitro studies of the 5 ovarian cancer cell lines revealed that reduced MAD2 expression was associated with paclitaxel resistance. In silico analysis identified a putative miR-433 binding domain in the MAD2 3′UTR and expression profiling of miR-433 in the ovarian cancer cell lines showed that low MAD2 protein expression was associated with high miR-433 levels. In vitro over-expression of miR-433 attenuated MAD2 protein expression with a concomitant increase in cellular resistance to paclitaxel. Over-expression of a morpholino oligonucleotide that blocks miR-433 binding to MAD2 3′UTR stabilised MAD2 protein expression and protects from miR-433 induced degradation. Furthermore, miR-433 expression analysis in 35 ovarian tumour samples revealed that high miR-433 expression was associated with advanced stage presentations (p=0.0236). In conclusion, ovarian tumours that display low nuclear MAD2 intensity are chemo-resistant and stabilising MAD2 expression by antagonising miR-433 activity is a potential mechanism for restoring chemo-responsiveness in these tumours.

Probabilistic Inference in Credal Networks: New Complexity Results

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove an analogous result for inference in Naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and Naive Bayes networks are used in real applications of imprecise probability.

On the complexity of solving polytree-shaped limited memory influence diagrams with binary variables

Influence diagrams are intuitive and concise representations of structured decision problems. When the problem is non-Markovian, an optimal strategy can be exponentially large in the size of the diagram. We can avoid the inherent intractability by constraining the size of admissible strategies, giving rise to limited memory influence diagrams. A valuable question is then how small do strategies need to be to enable efficient optimal planning. Arguably, the smallest strategies one can conceive simply prescribe an action for each time step, without considering past decisions or observations. Previous work has shown that finding such optimal strategies even for polytree-shaped diagrams with ternary variables and a single value node is NP-hard, but the case of binary variables was left open. In this paper we address such a case, by first noting that optimal strategies can be obtained in polynomial time for polytree-shaped diagrams with binary variables and a single value node. We then show that the same problem is NP-hard if the diagram has multiple value nodes. These two results close the fixed-parameter complexity analysis of optimal strategy selection in influence diagrams parametrized by the shape of the diagram, the number of value nodes and the maximum variable cardinality.

On the Complexity of Strong and Epistemic Credal Networks

Credal networks are graph-based statistical models whose parameters take values on a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The result of inferences with such models depends on the irrelevance/independence concept adopted. In this paper, we study the computational complexity of inferences under the concepts of epistemic irrelevance and strong independence. We strengthen complexity results by showing that inferences with strong independence are NP-hard even in credal trees with ternary variables, which indicates that tractable algorithms, including the existing one for epistemic trees, cannot be used for strong independence. We prove that the polynomial time of inferences in credal trees under epistemic irrelevance is not likely to extend to more general models, because the problem becomes NP-hard even in simple polytrees. These results draw a definite line between networks with efficient inferences and those where inferences are hard, and close several open questions regarding the computational complexity of such models.

Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks

Semi-qualitative probabilistic networks (SQPNs) merge two important graphical model formalisms: Bayesian networks and qualitative probabilistic networks. They provide a very general modeling framework by allowing the combination of numeric and qualitative assessments over a discrete domain, and can be compactly encoded by exploiting the same factorization of joint probability distributions that are behind the Bayesian networks. This paper explores the computational complexity of semi-qualitative probabilistic networks, and takes the polytree-shaped networks as its main target. We show that the inference problem is coNP-Complete for binary polytrees with multiple observed nodes. We also show that inferences can be performed in linear time if there is a single observed node, which is a relevant practical case. Because our proof is constructive, we obtain an efficient linear time algorithm for SQPNs under such assumptions. To the best of our knowledge, this is the first exact polynomial-time algorithm for SQPNs. Together these results provide a clear picture of the inferential complexity in polytree-shaped SQPNs.

Generalized loopy 2U: A new algorithm for approximate inference in credal networks

Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.

New Complexity Results for MAP in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. It is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure), which extends previous complexity results. Furthermore, a Fully Polynomial Time Approximation Scheme for MAP in networks with bounded treewidth and bounded number of states per variable is developed. Approximation schemes were thought to be impossible, but here it is shown otherwise under the assumptions just mentioned, which are adopted in most applications.

Solving Limited Memory Influence Diagrams

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and 10^64 solutions. We show that the problem is NP-hard even if the underlying graph structure of the problem has small treewidth and the variables take on a bounded number of states, but that a fully polynomial time approximation scheme exists for these cases. Moreover, we show that the bound on the number of states is a necessary condition for any efficient approximation scheme.

The Complexity of Approximately Solving Influence Diagrams

Influence diagrams allow for intuitive and yet precise description of complex situations involving decision making under uncertainty. Unfortunately, most of the problems described by influence diagrams are hard to solve. In this paper we discuss the complexity of approximately solving influence diagrams. We do not assume no-forgetting or regularity, which makes the class of problems we address very broad. Remarkably, we show that when both the treewidth and the cardinality of the variables are bounded the problem admits a fully polynomial-time approximation scheme.

New Results for the MAP Problem in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure). Such proofs extend previous complexity results for the problem. Inapproximability results are also derived in the case of trees if the number of states per variable is not bounded. Although the problem is shown to be hard and inapproximable even in very simple scenarios, a new exact algorithm is described that is empirically fast in networks of bounded treewidth and bounded number of states per variable. The same algorithm is used as basis of a Fully Polynomial Time Approximation Scheme for MAP under such assumptions. Approximation schemes were generally thought to be impossible for this problem, but we show otherwise for classes of networks that are important in practice. The algorithms are extensively tested using some well-known networks as well as random generated cases to show their effectiveness.

Generalized Loopy 2U: A New Algorithm for Approximate Inference in Credal Networks

Credal nets generalize Bayesian nets by relaxing the requirement of precision of probabilities. Credal nets are considerably more expressive than Bayesian nets, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal nets. The algorithm is based on an important representation result we prove for general credal nets: that any credal net can be equivalently reformulated as a credal net with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal net is updated by L2U, a loopy approximate algorithm for binary credal nets. Thus, we generalize L2U to non-binary credal nets, obtaining an accurate and scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences is evaluated by empirical tests.

Modelling the fresh properties of self-compacting concrete using support vector machine approach

The main objective of the study presented in this paper was to investigate the feasibility using support vector machines (SVM) for the prediction of the fresh properties of self-compacting concrete. The radial basis function (RBF) and polynomial kernels were used to predict these properties as a function of the content of mix components. The fresh properties were assessed with the slump flow, T50, T60, V-funnel time, Orimet time, and blocking ratio (L-box). The retention of these tests was also measured at 30 and 60 min after adding the first water. The water dosage varied from 188 to 208 L/m3, the dosage of superplasticiser (SP) from 3.8 to 5.8 kg/m3, and the volume of coarse aggregates from 220 to 360 L/m3. In total, twenty mixes were used to measure the fresh state properties with different mixture compositions. RBF kernel was more accurate compared to polynomial kernel based support vector machines with a root mean square error (RMSE) of 26.9 (correlation coefficient of R2 = 0.974) for slump flow prediction, a RMSE of 0.55 (R2 = 0.910) for T50 (s) prediction, a RMSE of 1.71 (R2 = 0.812) for T60 (s) prediction, a RMSE of 0.1517 (R2 = 0.990) for V-funnel time prediction, a RMSE of 3.99 (R2 = 0.976) for Orimet time prediction, and a RMSE of 0.042 (R2 = 0.988) for L-box ratio prediction, respectively. A sensitivity analysis was performed to evaluate the effects of the dosage of cement and limestone powder, the water content, the volumes of coarse aggregate and sand, the dosage of SP and the testing time on the predicted test responses. The analysis indicates that the proposed SVM RBF model can gain a high precision, which provides an alternative method for predicting the fresh properties of SCC.