Maximum likelihood estimation for semiparametric regression models with interval-censored multistate data.

Interval-censored multistate data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur over a broad time interval. We relate potentially time-dependent covariates to multistate processes through semiparametric proportional intensity models with random effects. We study nonparametric maximum likelihood estimation under general interval censoring and develop a stable expectation-maximization algorithm. We show that the resulting parameter estimators are consistent and that the finite-dimensional components are asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood. In addition, we demonstrate through extensive simulation studies that the proposed numerical and inferential procedures perform well in realistic settings. Finally, we provide an application to a major epidemiologic cohort study.

Measures of fragmentation of rest activity patterns: mathematical properties and interpretability based on accelerometer real life data.

Accelerometers, devices that measure body movements, have become valuable tools for studying the fragmentation of rest-activity patterns, a core circadian rhythm dimension, using metrics such as inter-daily stability (IS), intradaily variability (IV), transition probability (TP), and self-similarity parameter (named α ). However, their use remains mainly empirical. Therefore, we investigated the mathematical properties and interpretability of rest-activity fragmentation metrics by providing mathematical proofs for the ranges of IS and IV, proposing maximum likelihood and Bayesian estimators for TP, introducing the activity balance index (ABI) metric, a transformation of α , and describing distributions of these metrics in real-life setting. Analysis of accelerometer data from 2,859 individuals (age=60-83 years, 21.1% women) from the Whitehall II cohort (UK) shows modest correlations between the metrics, except for ABI and α . Sociodemographic (age, sex, education, employment status) and clinical (body mass index (BMI), and number of morbidities) factors were associated with these metrics, with differences observed according to metrics. For example, a difference of 5 units in BMI was associated with all metrics (differences ranging between -0.261 (95% CI -0.302, -0.220) to 0.228 (0.18, 0.268) for standardised TP rest to activity during the awake period and TP activity to rest during the awake period, respectively). These results reinforce the value of these rest-activity fragmentation metrics in epidemiological and clinical studies to examine their role for health. This paper expands on a set of methods that have previously demonstrated empirical value, improves the theoretical foundation for these methods, and evaluates their empirical use in a large dataset.

Stacked probability plots of the extended illness-death model using constant transition hazards - an easy to use shiny app.

BACKGROUND: Extended illness-death models (a specific class of multistate models) are a useful tool to analyse situations like hospital-acquired infections, ventilation-associated pneumonia, and transfers between hospitals. The main components of these models are hazard rates and transition probabilities. Calculation of different measures and their interpretation can be challenging due to their complexity. METHODS: By assuming time-constant hazards, the complexity of these models becomes manageable and closed mathematical forms for transition probabilities can be derived. Using these forms, we created a tool in R to visualize transition probabilities via stacked probability plots. RESULTS: In this article, we present this tool and give some insights into its theoretical background. Using published examples, we give guidelines on how this tool can be used. Our goal is to provide an instrument that helps obtain a deeper understanding of a complex multistate setting. CONCLUSION: While multistate models (in particular extended illness-death models), can be highly complex, this tool can be used in studies to both understand assumptions, which have been made during planning and as a first step in analysing complex data structures. An online version of this tool can be found at https://eidm.imbi.uni-freiburg.de/ .

Novel Detection and Progression Markers for Diabetes Based on Continuous Glucose Monitoring Data Dynamics.

PURPOSE: Develop a diabetes diagnostic tool based on two markers of continuous glucose monitoring (CGM) dynamics: CGM entropy rate (ER) and Poincaré plot (PP) ellipse area (S). METHODS: 5,754 daily CGM profiles from 843 individuals with type 1, type 2 diabetes, or healthy individuals with or without islet autoantibody status were used to compute two individual dynamic markers: ER (in bits per transition; BPT) of daily probability matrices describing CGM transitions between eight glycemic states, and the area S (mg2/dL2) of individual CGM PP ellipses using standard PP descriptors. The Youden's index was used to determine "optimal" cut-points for ER and S for health vs. diabetes (case 1); type 1 vs. type 2 (case 2); and low vs. high type 1 immunological risk (case 3). The markers' discriminative power was assessed through the area under the receiver operating characteristics curves (AUC). RESULTS: Optimal cut-off points were determined for ER and S for each of the three cases. ER and S discriminated case 1 with AUC = 0.98 (95% CI: 0.97-0.99) and AUC = 0.99 (95% CI: 0.99-1.00), respectively, (cut-offs ERcase1 = 0.76 BPT, Scase1 = 1993.91 mg2/dL2), case 2 with AUC = 0.81 (95% CI, 0.77-0.84) and AUC = 0.76 (95% CI, 0.72-0.81), respectively (ERcase2 = 1.00 BPT, Scase2 = 5112.98 mg2/dL2), and case 3 with AUC = 0.81 (95% CI, 0.77-0.84) and AUC = 0.76 (95% CI, 0.72-0.81), respectively (ERcase3 = 0.52 BPT, Scase3 = 923.65 mg2/dL2). CONCLUSIONS: CGM dynamics markers can be an alternative to fasting plasma glucose or glucose tolerance testing and identifying individuals at higher immunological risk of progressing to type 1 diabetes.

Benefits and risks of clofarabine in adult acute lymphoblastic leukemia investigated in depth by multi-state modeling.

BACKGROUND: We recently reported results of the prospective, open-label HOVON-100 trial in 334 adult patients with acute lymphoblastic leukemia (ALL) randomized to first-line treatment with or without clofarabine (CLO). No improvement of event-free survival (EFS) was observed, while a higher proportion of patients receiving CLO obtained minimal residual disease (MRD) negativity. AIM: In order to investigate the effects of CLO in more depth, two multi-state models were developed to identify why CLO did not show a long-term survival benefit despite more MRD-negativity. METHODS: The first model evaluated the effect of CLO on going off-protocol (not due to refractory disease/relapse, completion or death) as a proxy of severe treatment-related toxicity, while the second model evaluated the effect of CLO on obtaining MRD negativity. The subsequent impact of these intermediate events on death or relapsed/refractory disease was assessed in both models. RESULTS: Overall, patients receiving CLO went off-protocol more frequently than control patients (35/168 [21%] vs. 18/166 [11%], p = 0.019; HR 2.00 [1.13-3.52], p = 0.02), especially during maintenance (13/44 [30%] vs. 6/56 [11%]; HR 2.85 [95%CI 1.08-7.50], p = 0.035). Going off-protocol was, however, not associated with more relapse or death. Patients in the CLO arm showed a trend towards an increased rate of MRD-negativity compared with control patients (HR MRD-negativity: 1.35 [0.95-1.91], p = 0.10), which did not translate into a significant survival benefit. CONCLUSION: We conclude that the intermediate states, i.e., going off-protocol and MRD-negativity, were affected by adding CLO, but these transitions were not associated with subsequent survival estimates, suggesting relatively modest antileukemic activity in ALL.

Aberrant dynamic properties of whole-brain functional connectivity in acute mild traumatic brain injury revealed by hidden Markov models.

OBJECTIVES: This study aimed to investigate the temporal dynamics of brain activity and characterize the spatiotemporal specificity of transitions and large-scale networks on short timescales in acute mild traumatic brain injury (mTBI) patients and those with cognitive impairment in detail. METHODS: Resting-state functional magnetic resonance imaging (rs-fMRI) was acquired for 71 acute mTBI patients and 57 age-, sex-, and education-matched healthy controls (HCs). A hidden Markov model (HMM) analysis of rs-fMRI data was conducted to identify brain states that recurred over time and to assess the dynamic patterns of activation states that characterized acute mTBI patients and those with cognitive impairment. The dynamic parameters (fractional occupancy, lifetime, interval time, switching rate, and probability) between groups and their correlation with cognitive performance were analyzed. RESULTS: Twelve HMM states were identified in this study. Compared with HCs, acute mTBI patients and those with cognitive impairment exhibited distinct changes in dynamics, including fractional occupancy, lifetime, and interval time. Furthermore, the switching rate and probability across HMM states were significantly different between acute mTBI patients and patients with cognitive impairment (all p < 0.05). The temporal reconfiguration of states in acute mTBI patients and those with cognitive impairment was associated with several brain networks (including the high-order cognition network [DMN], subcortical network [SUB], and sensory and motor network [SMN]). CONCLUSIONS: Hidden Markov models provide additional information on the dynamic activity of brain networks in patients with acute mTBI and those with cognitive impairment. Our results suggest that brain network dynamics determined by the HMM could reinforce the understanding of the neuropathological mechanisms of acute mTBI patients and those with cognitive impairment.

An investigation into the abnormal dynamic connection mechanism of generalized anxiety disorders based on non-homogeneous Markov models.

BACKGROUND: The dynamic and hierarchical nature of the functional brain network. The neural dynamical systems tend to converge to multiple attractors (stable fixed points or dynamical states) in long run. Little is known about how the changes in this brain dynamic "long-term" behavior of the connectivity flow of brain network in generalized anxiety disorder (GAD). METHODS: This study recruited 92 patients with GAD and 77 healthy controls (HC). We applied a reachable probability approach combining a Non-homogeneous Markov model with transition probability to quantify all possible connectivity flows and the hierarchical structure of brain functional systems at the dynamic level and the stationary probability vector (10-step transition probabilities) to describe the steady state of the system in the long run. A random forest algorithm was conducted to predict the severity of anxiety. RESULTS: The dynamic functional patterns in distributed brain networks had larger possibility to converge in bilateral thalamus, posterior cingulate cortex (PCC), right superior occipital gyrus (SOG) and smaller possibility to converge in bilateral superior temporal gyrus (STG) and right parahippocampal gyrus (PHG) in patients with GAD compared to HC. The abnormal transition probability pattern could predict anxiety severity in patients with GAD. LIMITATIONS: Small samples and subjects taking medications may have influenced our results. Future studies are expected to rule out the potential confounding effects. CONCLUSION: Our results have revealed abnormal dynamic neural communication and integration in emotion regulation in patients with GAD, which give new insights to understand the dynamics of brain function of patients with GAD.

Comparison between the theoretical and experimental values of transition rate B(E2), deformation parameters and intrinsic quadrupole moments for some Ti isotopes.

In this study, electric quadrupole transition properties in some even-even Ti nuclei have been investigated by using different effective charges and interactions. In this respect, B(E2) transition rates, deformation parameters and intrinsic quadrupole moments have been calculated. In calculations, NuShellX code has been used to calculated one body matrix elements (OBDM). Theoretical calculations on these quantities have been compared with the experimental results, and it has been seen that theoretical values obtained by using the kb3 and vpnp interactions and Bohr Mottelson (B-M) and Standard (S-T) effective charges are close to the corresponding experimental results.

Measures of fragmentation of rest activity patterns: mathematical properties and interpretability based on accelerometer real life data.

Accelerometers, devices that measure body movements, have become valuable tools for studying the fragmentation of rest-activity patterns, a core circadian rhythm dimension, using metrics such as inter-daily stability (IS), intradaily variability (IV), transition probability (TP), and self-similarity parameter (named α). However, their use remains mainly empirical. Therefore, we investigated the mathematical properties and interpretability of rest-activity fragmentation metrics by providing mathematical proofs for the ranges of IS and IV, proposing maximum likelihood and Bayesian estimators for TP, introducing the activity balance index metric, an adaptation of α, and describing distributions of these metrics in real-life setting. Analysis of accelerometer data from 2,859 individuals (age=60-83 years, 21.1% women) from the Whitehall II cohort (UK) shows modest correlations between the metrics, except for ABI and α. Sociodemographic (age, sex, education, employment status) and clinical (body mass index (BMI), and number of morbidities) factors were associated with these metrics, with differences observed according to metrics. For example, a difference of 5 units in BMI was associated with all metrics (differences ranging between -0.261 (95% CI -0.302, -0.220) to 0.228 (0.18, 0.268) for standardised TP rest to activity during the awake period and TP activity to rest during the awake period, respectively). These results reinforce the value of these rest-activity fragmentation metrics in epidemiological and clinical studies to examine their role for health. This paper expands on a set of methods that have previously demonstrated empirical value, improves the theoretical foundation for these methods, and evaluates their empirical worth in a large dataset.

Evaluation Factors Affecting on Recurrence, Metastasis, and Survival of Breast Cancer in Iranian Women by Multi-State Model Approach.

Background: We used the multistate model to investigate how prognostic factors of breast cancer are seen to affect the disease process. Methods: This cohort study was conducted at Motamed Cancer Institute of Tehran, Iran on 2363 breast cancer patients admitted from 1978 to 2017, and they were followed up until 2018. We applied the multistate models, including four states: diagnosis, recurrence, metastasis, and final absorbing mortality state. Results: Age over 50 years, positive lymph nodes and tumor size intensified the hazard of transition from diagnosis to metastasis (P=0.002, P<0.001 and P=0.001 respectively) and they also intensified the hazard of transition from diagnosis to mortality (P=0.010, P<0.001 and P<0.001 respectively). At the same time, the educational level decreased the hazard of mentioned transitions (P<0.001). Positive estrogen receptors reduced the hazard of transition from diagnosis to metastasis (P=0.007) and positive lymph nodes also intensified the hazard of transition from metastasis to mortality (P=0.040). Tumor size had an increasing role in the transitions from diagnosis to recurrence, recurrence to metastasis, and metastasis to mortality (P=0.014, P=0.018 and P=0.002 respectively). Conclusion: Multistate model presented the detailed effects of prognostic factors on progression of breast cancer. Implementing early diagnosis strategies and providing informational programs, especially in younger ages and lower educational level patients may be helpful in reducing the hazard of transition to higher states of breast cancer and increasing the survival of Iranian women with breast cancer by controlling tumor size growth, lymph nodes involvements and estrogen receptor status.

Exact solutions and asymptotic behaviors for the reflected Wiener, Ornstein-Uhlenbeck and Feller diffusion processes.

We analyze the transition probability density functions in the presence of a zero-flux condition in the zero-state and their asymptotic behaviors for the Wiener, Ornstein Uhlenbeck and Feller diffusion processes. Particular attention is paid to the time-inhomogeneous proportional cases and to the time-homogeneous cases. A detailed study of the moments of first-passage time and of their asymptotic behaviors is carried out for the time-homogeneous cases. Some relationships between the transition probability density functions for the restricted Wiener, Ornstein-Uhlenbeck and Feller processes are proved. Specific applications of the results to queueing systems are provided.

Quantum AI and hybrid simulators for a Universal Quantum Field Computation Model.

Quantum field theory (QFTh) simulators simulate physical systems using quantum circuits that process quantum information (qubits) via single field (SF) and/or quantum double field (QDF) transformation. This review presents models that classify states against pairwise particle states |ij〉, given their state transition (ST) probability P|ij〉. A quantum AI (QAI) program, weighs and compares the field's distance between entangled states as qubits from their scalar field of radius R≥|rij|. These states distribute across 〈R〉 with expected probability 〈Pdistribute〉 and measurement outcome 〈M(Pdistribute)〉=P|ij〉. A quantum-classical hybrid model of processors via QAI, classifies and predicts states by decoding qubits into classical bits. For example, a QDF as a quantum field computation model (QFCM) in IBM-QE, performs the doubling of P|ij〉 for a strong state prediction outcome. QFCMs are compared to achieve a universal QFCM (UQFCM). This model is novel in making strong event predictions by simulating systems on any scale using QAI. Its expected measurement fidelity is 〈M(F)〉≥7/5 in classifying states to select 7 optimal QFCMs to predict 〈M〉's on QFTh observables. This includes QFCMs' commonality of 〈M〉 against QFCMs limitations in predicting system events. Common measurement results of QFCMs include their expected success probability 〈Psuccess〉 over STs occurring in the system. Consistent results with high F's, are averaged over STs as 〈Pdistribute〉yielding 〈Psuccess〉≥2/3 performed by an SF or QDF of certain QFCMs. A combination of QFCMs with this fidelity level predicts error rates (uncertainties) in measurements, by which a P|ij〉=〈Psuccess〉<∼1 is weighed as a QAI output to a QFCM user. The user then decides which QFCMs perform a more efficient system simulation as a reliable solution. A UQFCM is useful in predicting system states by preserving and recovering information for intelligent decision support systems in applied, physical, legal and decision sciences, including industry 4.0 systems.

Individual Differences in Holistic and Compositional Language Processing.

Individual differences in cognitive abilities are ubiquitous across the spectrum of proficient language users. Although speakers differ with regard to their memory capacity, ability for inhibiting distraction, and ability to shift between different processing levels, comprehension is generally successful. However, this does not mean it is identical across individuals; listeners and readers may rely on different processing strategies to exploit distributional information in the service of efficient understanding. In the following psycholinguistic reading experiment, we investigate potential sources of individual differences in the processing of co-occurring words. Participants read modifier-noun bigrams like absolute silence in a self-paced reading task. Backward transition probability (BTP) between the two lexemes was used to quantify the prominence of the bigram as a whole in comparison to the frequency of its parts. Of five individual difference measures (processing speed, verbal working memory, cognitive inhibition, global-local scope shifting, and personality), two proved to be significantly associated with the effect of BTP on reading times. Participants who could inhibit a distracting global environment in order to more efficiently retrieve a single part and those that preferred the local level in the shifting task showed greater effects of the co-occurrence probability of the parts. We conclude that some participants are more likely to retrieve bigrams via their parts and their co-occurrence statistics whereas others more readily retrieve the two words together as a single chunked unit.

Evaluation of transitions from early hypertension to hypertensive chronic kidney disease, coronary artery disease, stroke and mortality: a Thai real-world data cohort.

Objective: Systemic arterial hypertension (HT) is a major modifiable risk factor for cardiovascular disease (CVDs), associated with all-cause death (ACD). Understanding its progression from the early state to late complications should lead to more timely intensification of treatment. This study aimed to construct a real-world cohort profile of HT and to estimate transition probabilities from the uncomplicated state to any of these long-term complications; chronic kidney disease (CKD), coronary artery disease (CAD), stroke, and ACD. Methods: This real-world cohort study used routine clinical practice data for all adult patients diagnosed with HT in the Ramathibodi Hospital, Thailand from 2010 to 2022. A multi-state model was developed based on the following: state 1-uncomplicated HT, 2-CKD, 3-CAD, 4-stroke, and 5-ACD. Transition probabilities were estimated using Kaplan-Meier method. Results: A total of 144,149 patients were initially classified as having uncomplicated HT. The transition probabilities (95% CI) from the initial state to CKD, CAD, stroke, and ACD at 10-years were 19.6% (19.3%, 20.0%), 18.2% (17.9%, 18.6%), 7.4% (7.1%, 7.6%), and 1.7% (1.5%, 1.8%), respectively. Once in the intermediate-states of CKD, CAD, and stroke, 10-year transition probabilities to death were 7.5% (6.8%, 8.4%), 9.0% (8.2%, 9.9%), and 10.8% (9.3%, 12.5%). Conclusions: In this 13-year cohort, CKD was observed as the most common complication, followed by CAD and stroke. Among these, stroke carried the highest risk of ACD, followed by CAD and CKD. These findings provide improved understanding of disease progression to guide appropriate prevention measures. Further investigations of prognostic factors and treatment effectiveness are warranted.

Pseudo-Qutrit Formed by Two Interacting Identical Spins (s = 1/2) in a Variable External Magnetic Field.

An analytical solution is obtained for the problem of two interacting, identical but separated spin 1/2 particles in a time-dependent external magnetic field, in a general case. The solution involves isolating the pseudo-qutrit subsystem from a two-qubit system. It is shown that the quantum dynamics of a pseudo-qutrit system with a magnetic dipole-dipole interaction can be described clearly and accurately in an adiabatic representation, using a time-dependent basis set. The transition probabilities between the energy levels for an adiabatically varying magnetic field, which follows the Landau-Majorana-Stuckelberg-Zener (LMSZ) model within a short time interval, are illustrated in the appropriate graphs. It is shown that for close energy levels and entangled states, the transition probabilities are not small and strongly depend on the time. These results provide insight into the degree of entanglement of two spins (qubits) over time. Furthermore, the results are applicable to more complex systems with a time-dependent Hamiltonian.

Estimating Transition Probabilities Across the Alzheimer's Disease Continuum Using a Nationally Representative Real-World Database in the United States.

INTRODUCTION: Clinical Alzheimer's disease (AD) begins with mild cognitive impairment (MCI) and progresses to mild, moderate, or severe dementia, constituting a disease continuum that eventually leads to death. This study aimed to estimate the probabilities of transitions across those disease states. METHODS: We developed a mixed-effects multi-state Markov model to estimate the transition probabilities, adjusted for 5 baseline covariates, using the Health and Retirement Study (HRS) database. HRS surveys older adults in the United States bi-annually. Alzheimer states were defined using the modified Telephone Interview of Cognitive Status (TICS-m). RESULTS: A total of 11,292 AD patients were analyzed. Patients were 70.8 ± 9.0 years old, 54.9% female, and with 12.0 ± 3.3 years of education. Within 1 year from the initial state, the model estimated a higher probability of transition to the next AD state in earlier disease: 12.8% from MCI to mild AD and 5.0% from mild to moderate AD, but < 1% from moderate to severe AD. After 10 years, the probability of transition to the next state was markedly higher for all states, but still higher in earlier disease: 29.8% from MCI to mild AD, 23.5% from mild to moderate AD, and 5.7% from moderate to severe AD. Across all AD states, the probability of transition to death was < 5% after 1 year and > 15% after 10 years. Older age, fewer years of education, unemployment, and nursing home stay were associated with a higher risk of disease progression (p < 0.01). CONCLUSIONS: This analysis shows that the risk of progression is greater in earlier AD states, increases over time, and is higher in patients who are older, with fewer years of education, unemployed, or in a nursing home at baseline. The estimated transition probabilities can provide guidance for future disease management and clinical trial design optimization, and can be used to refine existing cost-effectiveness frameworks.

Examining annual transitions in healthcare spending among U.S. medicare beneficiaries using multistate Markov models: Analysis of medicare current beneficiary survey data, 2003-2019.

Many studies have examined factors associated with individuals of high or low healthcare spending in a given year. However, few have studied how healthcare spending changes over multiple years and which factors are associated with the changes. In this study, we examined the dynamic patterns of healthcare spending over a three-year period, among a nationally representative cohort of Medicare beneficiaries in the U.S. and identified factors associated with these patterns. We extracted data for 30,729 participants from the national Medicare Current Beneficiary Survey (MCBS), for the period 2003-2019. Using multistate Markov (MSM) models, we estimated the probabilities of year-to-year transitions in healthcare spending categorized as three states (low (L), medium (M) and high (H)), or to the terminal state, death. The participants, 13,554 (44.1%), 13,715 (44.6%) and 3,460 (11.3%) were in the low, medium and high spending states at baseline, respectively. The majority of participants remained in the same spending category from one year to the next (L-to-L: 76.8%; M-to-M: 71.7%; H-to-H: 56.6 %). Transitions from the low to high spending state were significantly associated with older age (75-84, ≥85 years), residing in a long-term care facility, greater assistance with activities of daily living, enrollment in fee-for-service Medicare, not receiving a flu shot, and presence of specific medical conditions, including cancer, dementia, and heart disease. Using data from a large population-based longitudinal survey, we have demonstrated that MSM modelling is a flexible framework and useful tool for examining changes in healthcare spending over time.

Two Features of the GINAR(1) Process and Their Impact on the Run-Length Performance of Geometric Control Charts.

The geometric first-order integer-valued autoregressive process (GINAR(1)) can be particularly useful to model relevant discrete-valued time series, namely in statistical process control. We resort to stochastic ordering to prove that the GINAR(1) process is a discrete-time Markov chain governed by a totally positive order 2 (TP2) transition matrix.Stochastic ordering is also used to compare transition matrices referring to pairs of GINAR(1) processes with different values of the marginal mean. We assess and illustrate the implications of these two stochastic ordering results, namely on the properties of the run length of geometric charts for monitoring GINAR(1) counts.

Order of statistical learning depends on perceptive uncertainty.

Statistical learning (SL) is an innate mechanism by which the brain automatically encodes the n-th order transition probability (TP) of a sequence and grasps the uncertainty of the TP distribution. Through SL, the brain predicts a subsequent event (e n+1 ) based on the preceding events (e n ) that have a length of "n". It is now known that uncertainty modulates prediction in top-down processing by the human predictive brain. However, the manner in which the human brain modulates the order of SL strategies based on the degree of uncertainty remains an open question. The present study examined how uncertainty modulates the neural effects of SL and whether differences in uncertainty alter the order of SL strategies. It used auditory sequences in which the uncertainty of sequential information is manipulated based on the conditional entropy. Three sequences with different TP ratios of 90:10, 80:20, and 67:33 were prepared as low-, intermediate, and high-uncertainty sequences, respectively (conditional entropy: 0.47, 0.72, and 0.92 bit, respectively). Neural responses were recorded when the participants listened to the three sequences. The results showed that stimuli with lower TPs elicited a stronger neural response than those with higher TPs, as demonstrated by a number of previous studies. Furthermore, we found that participants adopted higher-order SL strategies in the high uncertainty sequence. These results may indicate that the human brain has an ability to flexibly alter the order based on the uncertainty. This uncertainty may be an important factor that determines the order of SL strategies. Particularly, considering that a higher-order SL strategy mathematically allows the reduction of uncertainty in information, we assumed that the brain may take higher-order SL strategies when encountering high uncertain information in order to reduce the uncertainty. The present study may shed new light on understanding individual differences in SL performance across different uncertain situations.

A Physical Measure for Characterizing Crossover from Integrable to Chaotic Quantum Systems.

In this paper, a quantity that describes a response of a system's eigenstates to a very small perturbation of physical relevance is studied as a measure for characterizing crossover from integrable to chaotic quantum systems. It is computed from the distribution of very small, rescaled components of perturbed eigenfunctions on the unperturbed basis. Physically, it gives a relative measure to prohibition of level transitions induced by the perturbation. Making use of this measure, numerical simulations in the so-called Lipkin-Meshkov-Glick model show in a clear way that the whole integrability-chaos transition region is divided into three subregions: a nearly integrable regime, a nearly chaotic regime, and a crossover regime.