Optimal Number Of States Research Articles

Uncovering the Interplay of Oscillatory Processes During Creative Problem Solving: A Dynamic Modeling Approach

ABSTRACT To solve a new problem, people spontaneously engage multiple cognitive processes. Previous work has identified a diverse set of oscillatory components critical at different stages of creative problem solving. In this project, we use hidden state modeling to untangle the roles of oscillation processes over time as people solve puzzles. Building on earlier work, we further developed analytical methods, such as incorporating source separating techniques and identifying the optimal number of states using cross-validation. We extracted brain states characterized by spatio-spectral topographies from time-resolved EEG spectral powers. The data driven approach allowed us to infer the dynamic, trial-by-trial, state sequences, and provided a comprehensive depiction of how various oscillation components interact recurrently throughout the trial. The properties of the states suggest their dissociable cognitive functions. For example, we identified three states with dominant activation in alpha bands but having distinct spatial distributions. People were differentially engaged in these states depending on the stages (e.g., onset or response) and outcomes of the trials (solved with insight or analysis). The current approach, applicable to many tasks requiring extended trial duration, can potentially reconcile findings from previous EEG studies and drive new hypotheses to further our understanding of the complex creative process.

Altered dynamic functional network connectivity in levodopa-induced dyskinesia of Parkinson's disease.

The aim of this study was to clarify the dynamic neural activity of levodopa-induced dyskinesia (LID) in Parkinson's disease (PD). Using dynamic functional network connectivity (dFNC) analysis, we evaluated 41 PD patients with LID (LID group) and 34 PD patients without LID (No-LID group). Group spatial independent component analysis and sliding-window approach were employed. Moreover, we applied a k-means clustering algorithm on windowed functional connectivity (FC) matrices to identify reoccurring FC patterns (i.e., states). The optimal number of states was determined to be five, the so-called State 1, 2, 3, 4, and 5. In ON phase, compared with No-LID group, LID group occurred more frequently and dwelled longer in strongly connected State 1, characterized by strong positive connections between visual network (VIS) and sensorimotor network (SMN). When switching from OFF to ON phase, LID group occurred less frequently in State 3 and State 4. Meanwhile, LID group dwelled longer in State 2 and shorter in State 3. No-LID group occurred more frequently in State 5 and less frequently in State 3. Additionally, correlation analysis demonstrated that dyskinesia's severity was associated with frequency of occurrence and dwell time in State 2, dominated by inferior frontal cortex in cognitive executive network (CEN). Using dFNC analysis, we found that dyskinesia may be related to the dysfunctional inhibition of CEN on motor loops and excessive excitation of VIS and SMN, which provided evidence of the changes in brain dynamics associated with the occurrence of dyskinesia.

A new efficiency relaxation model for rigorous stage number optimization of distillation columns

Determining the optimal state number in distillation column design is a mixed-integer nonlinear programming (MINLP) problem, which is difficult to solve. One strategy to solve this problem is relaxing integer stage numbers into continuous variables and solving an easier nonlinear programming (NLP) problem. However, the existing relaxation model often converges to non-integer stage numbers or poor local optima in practical applications, which motivates this paper to develop a new relaxation model. The proposed relaxation model employs an interpolation function to relax the discrete decision on the existence of a stage by varying interphase mass and heat transfer rate between zero and equilibrium state. By adjusting a shape parameter in the interpolation function, the interpolation function shape and its penalty extent of non-integer stage can be manipulated. The results of three distillation column optimization cases show that the proposed model can effectively avoid converges to non-integer stage numbers or poor optima.

A Classification-Based Approach to Estimate the Number of Resting Functional Magnetic Resonance Imaging Dynamic Functional Connectivity States.

Aim: To determine the optimal number of connectivity states in dynamic functional connectivity analysis. Introduction: Recent work has focused on the study of dynamic (vs. static) brain connectivity in resting functional magnetic resonance imaging data. In this work, we focus on temporal correlation between time courses extracted from coherent networks called functional network connectivity (FNC). Dynamic FNC is most commonly estimated using a sliding window-based approach to capture short periods of FNC change. These data are then clustered to estimate transient connectivity patterns or states. Determining the number of states is a challenging problem. The elbow criterion is one of the widely used approaches to determine the connectivity states. Materials and Methods: In our work, we present an alternative approach that evaluates classification (e.g., healthy controls [HCs] vs. patients) as a measure to select the optimal number of states (clusters). We apply different classification strategies to perform classification between HCs and patients with schizophrenia for different numbers of states (i.e., varying the model order in the clustering algorithm). We compute cross-validated accuracy for different model orders to evaluate the classification performance. Results: Our results are consistent with our earlier work which shows that overall accuracy improves when dynamic connectivity measures are used separately or in combination with static connectivity measures. Results also show that the optimal model order for classification is different from that using the standard k-means model selection method, and that such optimization improves cross-validated accuracy. The optimal model order obtained from the proposed approach also gives significantly improved classification performance over the traditional model selection method. Conclusion: The observed results suggest that if one's goal is to perform classification, using the proposed approach as a criterion for selecting the optimal number of states in dynamic connectivity analysis leads to improved accuracy in hold-out data.

Graph-theoretical analysis identifies transient spatial states of resting-state dynamic functional network connectivity and reveals dysconnectivity in schizophrenia

BackgroundDynamic functional network connectivity (dFNC) summarizes associations among time-varying brain networks and is widely used for studying dynamics. However, most previous studies compute dFNC using temporal variability while spatial variability started receiving increasing attention. It is hence desirable to investigate spatial variability and the interaction between temporal and spatial variability. New methodWe propose to use an adaptive variant of constrained independent vector analysis to simultaneously capture temporal and spatial variability, and introduce a goal-driven scheme for addressing a key challenge in dFNC analysis---determining the number of transient states. We apply our methods to resting-state functional magnetic resonance imaging data of schizophrenia patients (SZs) and healthy controls (HCs). ResultsThe results show spatial variability provides more features discriminative between groups than temporal variability. A comprehensive study of graph-theoretical (GT) metrics determines the optimal number of spatial states and suggests centrality as a key metric. Four networks yield significantly different levels of involvement in SZs and HCs. The high involvement of a component that relates to multiple distributed brain regions highlights dysconnectivity in SZ. One frontoparietal component and one frontal component demonstrate higher involvement in HCs, suggesting a more efficient cognitive control system relative to SZs. Comparison with existing methodsSpatial variability is more informative than temporal variability. The proposed goal-driven scheme determines the optimal number of states in a more interpretable way by making use of discriminative features. ConclusionGT analysis is promising in dFNC analysis as it identifies distinctive transient spatial states of dFNC and reveals unique biomedical patterns in SZs.

A Nested MCMC Method Incorporated With Atmospheric Process Decomposition for Photovoltaic Power Simulation

Large-scale photovoltaic (PV) generation's uncertainties significantly affect power system planning and operations. Thus, a stochastic PV power simulation method, which can accurately capture such uncertainties, is urgently needed to provide a foundation for further uncertain studies on power systems with PV stations. This paper proposes a nested Markov chain Monte Carlo (MCMC) method incorporated with atmospheric process decomposition (APD) for PV power simulation. First, an imaginary clear-sky model matching the local actual clear-sky atmosphere is designed to convert PV power to an attenuation coefficient (AC). Second, a nested AC Markov chain (MC) is proposed based on APD to distinguish the macroscale and meso-microscale ACs while consider their coupling relationship. Third, an improved MCMC method is developed to simulate this MC's each layer in a nested manner for stochastically synthesizing AC time series; this method can improve synthesizing accuracy thanks to the adoption of an optimal state number decision-making model to ensure the MCMC model's quality and a 3D transition probability matrix to capture the dynamics of transition probabilities with respect to state duration. Finally, synthetic AC time series are reconverted to PV power time series. The results validate the proposed method's accuracy over previous ones in reproducing PV power characteristics.

Bayesian inference of chromatin structure ensembles from population-averaged contact data

Mounting experimental evidence suggests a role for the spatial organization of chromatin in crucial processes of the cell nucleus such as transcription regulation. Chromosome conformation capture techniques allow us to characterize chromatin structure by mapping contacts between chromosomal loci on a genome-wide scale. The most widespread modality is to measure contact frequencies averaged over a population of cells. Single-cell variants exist, but suffer from low contact numbers and have not yet gained the same resolution as population methods. While intriguing biological insights have already been garnered from ensemble-averaged data, information about three-dimensional (3D) genome organization in the underlying individual cells remains largely obscured because the contact maps show only an average over a huge population of cells. Moreover, computational methods for structure modeling of chromatin have mostly focused on fitting a single consensus structure, thereby ignoring any cell-to-cell variability in the model itself. Here, we propose a fully Bayesian method to infer ensembles of chromatin structures and to determine the optimal number of states in a principled, objective way. We illustrate our approach on simulated data and compute multistate models of chromatin from chromosome conformation capture carbon copy (5C) data. Comparison with independent data suggests that the inferred ensembles represent the underlying sample population faithfully. Harnessing the rich information contained in multistate models, we investigate cell-to-cell variability of chromatin organization into topologically associating domains, thus highlighting the ability of our approach to deliver insights into chromatin organization of great biological relevance.

Beszédfelismerő hatékonysági vizsgálata különböző állapotszámú rejtett Markov-modellekkel

A beszédfelismerés az a folyamat, melynek során a beszédfelismerő gép azonosítja a kiejtett beszédjeleket és átalakítja ezeket szöveggé, vagy más, számítógép által feldolgozható adattá. Beszédjelek alatt természetesen érthetünk akusztikus vagy akár vizuális jeleket is (gesztikulációk, arcmimika, szájmozgás). Az általam betanított beszédfelismerő viszont az akusztikus jeleket fogja figyelembe venni, azaz magát a beszédhangot, amit szöveggé fog átalakítani. Vizsgálataim a lényegkiemelés alapját képező rejtett Markov-modellek állapotszámának optimális megválasztását helyezik középpontba.

Akusztikus beszédfeldolgozó egység hatékonysági vizsgálata különböző zajok esetén

Az ember-gép kommunikáció során az egyik legfontosabb kritérium a megbízhatóság. Ez az elvárás magába foglalja azt, hogy az észlelt információ megegyezzen a küldő által kibocsátott jel információtartalmával. Tudjuk, hogy ez emberek közötti kommunikáció egyik legalapvetőbb eszköze, és egyben legegyszerűbb és legtermészetesebb módja a beszéd. Ezen állítást szem előtt tartva az ember régi vágya, hogy az általa konstruált gépekkel, berendezésekkel emberi nyelven, a beszéd eszközével tudjon hatékonyan és megbízhatóan kommunikálni. Munkám során teszteléseket fogok végezni egy rejtett Markov-modelleken alapuló beszédfelismerőn, ahol különböző zajokkal terhelt tanító és tesztelő anyagok hatékonyságra gyakorolt hatásait fogom vizsgálni.

Fitting Markovian binary trees using global and individual demographic data

We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arrival process (TMAP). We develop methods for estimating the parameters of the TMAP by using either age-specific averages of reproduction and mortality rates, or age-specific individual demographic data. Depending on the degree of detail of the available information, we follow a weighted non-linear regression or a maximum likelihood approach. We discuss several criteria to determine the optimal number of states in the underlying TMAP. Our results improve the fit of an existing MBT model for human demography, and provide insights for the future conservation management of the threatened Chatham Island black robin population.

Traffic flow prediction based on optimized hidden Markov model

In order to alleviate the current urban traffic congestion pressure and provide accurate and reliable traffic condition information, it is difficult to select the optimal state parameters for the original Hidden Markov model (HMM) and the state number redundancy determined during the training process leads to the model over-provisioning. The problem of weak is integration and generalization. An improved Hidden Markov Model for traffic flow prediction is proposed to more effectively fit the actual urban road intersection traffic flow. In the calculation of the negative log-likelihood function, an Akaike information criterion (AIC) or a Bayesian information criterion (BIC) penalty term is added, and the Baum-Welch algorithm is combined to optimize the optimal state number of the model. Experiments are carried out based on the collected real traffic flow and GPS feature data. The results show that the optimized hidden Markov model is superior to the original model in the accuracy and generalization ability of traffic flow prediction.

Regime Heteroskedasticity in Bitcoin: A Comparison of Markov Switching Models

In response to Molnar and Thies (2018) demonstrating that the price data of Bitcoin contained structural breaks, we identify the optimal number of states for a Markov regime-switching (MRS) model to capture the regime heteroskedasticity of Bitcoin. We determined that the restricted 5-state MRS model provided the best goodness-of-fit scores (-AIC, -BIC, -HQIC) for the fitted sample. In addition, we found evidence of stylised characteristics in the price data of Bitcoin, namely: volatility clustering; volatility jumps; asymmetric volatility transitions; and the persistence of shocks.

Residual Chart with Hidden Markov Model to Monitoring the Auto-Correlated Processes

Autocorrelations exist in real production extensively, and special statistical tools are needed for process monitoring. Residual charts based on autoregressive integrated moving average (ARIMA) models are typically used. However, ARIMA models need a quite amount of experience, which sometimes causes inconveniences in the implementation. With a good performance under less experience or even none, hidden Markov models (HMMs) were proposed. Since ARIMA models have many different performances in positive and negative autocorrelations, it is interesting and essential to study how HMMs affect the performances of residual charts in opposite autocorrelations, which has not been studied yet. Therefore, we extend HMMs to negatively auto-correlated observations. The cross-validation method is used to select the relatively optimal state number. The experiment results show that HMMs are more stable than Auto-Regressive of order one (AR(1) models) in both cases of positive and negative autocorrelations. For detecting abnormalities, the performance of HMMs approach is much better than AR(1) models under positive autocorrelations while under negative autocorrelations both methods have similar performances.

Hidden Markov Model for Stock Trading

Hidden Markov model (HMM) is a statistical signal prediction model, which has been widely used to predict economic regimes and stock prices. In this paper, we introduce the application of HMM in trading stocks (with S&P 500 index being an example) based on the stock price predictions. The procedure starts by using four criteria, including the Akaike information, the Bayesian information, the Hannan Quinn information, and the Bozdogan Consistent Akaike Information, in order to determine an optimal number of states for the HMM. The selected four-state HMM is then used to predict monthly closing prices of the S&P 500 index. For this work, the out-of-sample R OS 2 , and some other error estimators are used to test the HMM predictions against the historical average model. Finally, both the HMM and the historical average model are used to trade the S&P 500. The obtained results clearly prove that the HMM outperforms this traditional method in predicting and trading stocks.

Distributed Voting/Ranking With Optimal Number of States per Node

Considering a network with n nodes, where each node initially votes for one (or more) choices out of K possible choices, we present a distributed multichoice voting/ranking (DMVR) algorithm to determine either the choice with maximum vote (the voting problem) or to rank all the choices in terms of their acquired votes (the ranking problem). The algorithm consolidates node votes across the network by updating the states of interacting nodes using two key operations: the union and the intersection. The proposed algorithm is simple, independent from network size, and easily scalable in terms of the number of choices K, using only K × 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K-1</sup> nodal states for voting, and K × K! nodal states for ranking. We prove the number of states to be optimal in the ranking case; this optimality is conjectured to also apply to the voting case. The time complexity of the algorithm is analyzed in complete graphs. We show that the time complexity for both ranking and voting is O(log(n)) for given vote percentages, and is inversely proportional to the minimum of the vote percentage differences among various choices.

Robot behaviour learning using Topological Gaussian Adaptive Resonance Hidden Markov Model

Behaviour learning by robots is an emerging research field. The robot behaviour learning in realistic environment requires the robot to be able to learn incrementally in order to adapt itself to the dynamic environment. The incremental learning system should be stable and acquire new information without corrupting previous knowledge. Probabilistic approach has become the prevalent epitome in robotic learning systems. In probabilistic learning models, such as Hidden Markov Model, estimating the optimal number of states is difficult which limits the models capabilities by limiting the number of motion patterns to be learned a priori. In this paper, we presented an approach for learning behaviour patterns through continuous observation. We have proposed a novel architecture for learning the spatio-temporal sequences using Topological Gaussian Adaptive Resonance Hidden Markov Model. The proposed model dynamically generates the graph-based structure for the observed patterns through a novel topological mapping architecture. The structure (number of states) of the probabilistic model is not fixed and is adjusted based on the topological map of the acquired motion features. The topological map consists of nodes connected with edges, where each node represents the encoded motion features to adaptively generalize the observed behaviour patterns. The model combines the self-organizing, self-stabilizing properties and time series processing features to learn the spatio-temporal sequences. To demonstrate the properties of the proposed algorithm, we have performed a set of experiments through simulation on DARwIn-OP humanoid robot.

Bull, bear or any other states in US stock market?

A stock market is traditionally considered to shift between bull and bear markets, reflecting the states of high mean and low mean in stock returns, respectively. In this paper, we attempt to detect more different states in a stock market by applying a Bayesian Markov switching model, where the optimal number of states is determined according to the marginal likelihoods. An application to US stock market indicates that there exist four distinguishable states and each state represents different characteristics of US stock market.

The switching relationship between natural gas and crude oil prices

In this analysis we more accurately capture the cointegrating relationship between natural gas and crude oil prices by endogenously incorporating shifts in the cointegrating vector into the estimation of the cointegrating equation. Specifically, we allow the cointegrating equation to switch between m states, according to a first-order Markov process. First, we find evidence that regime-switching exists in the relative pricing relationship, and that two is the optimal number of states. Once we control for shifts in the cointegrating vector, we find that natural gas and crude oil prices are cointegrated, and an error correction model (ECM) of their long-term equilibrium relationship is properly specified. This finding broadens the ECM model of their relationship to longer and more varied sample periods. Also, in a direct comparison of the two and one state cointegrating equations, we found evidence of the potential superiority of the two-state equation, in that it may be robust to shifts in the cointegrating vector which are missed by standard tests for a unit root. Further, our analysis finds evidence that natural gas and crude oil prices did not permanently ‘decouple’ in the early 2000s, but rather experienced a temporary shift in regimes. We find that forecasts of the relative pricing of natural gas and crude oil should be conditioned on state probability.

The Switching Relationship between Natural Gas and Oil Prices

Herein we more accurately capture the cointegrating relationship between natural gas and crude oil prices by controlling for nonstationarity induced by endogenous changes in regime. Specifically, we allow the cointegrating equation to switch between m states, according to a first-order Markov process. First, we find evidence that regime-switching exists in the relative pricing relationship, and that two is the optimal number of states. Once we control for this type of nonstationarity natural gas and crude oil prices are cointegrated, and in an error correction model the state-weighted residuals contain unique information and allow for faster recovery toward equilibrium in response to exogenous shocks. Further, our analysis finds evidence that natural gas and crude oil prices did not permanently ‘decouple’ in the early 2000s, but rather experienced a temporary shift in regimes. We find that forecasts of the relative pricing of natural gas and crude oil should be conditioned on state probability.

Improvement of Set-Covering Weighted Control Model of S3PR

The set-covering approach by Piroddi et al. may reach the optimal number of states among all approaches for a well-known benchmark using a siphon-based approach without reachability analysis. However, the resulting model is a generalized Petri net incurring extra cost in system verification, validation and implementation. The only improvement is to replace two monitors with weighted arcs by two new monitors without weighted arcs. We develop a theory for explaining the cause of state losses and providing the foundation for the above improvement model.