Recurrence plots bridge deterministic systems and stochastic systems topologically and measure-theoretically

We connect a common conventional value to quantify a recurrence plot with its motifs, which have recently been termed "recurrence triangles." The common practical value we focus on is DET, which is the ratio of the points forming diagonal line segments of length 2 or longer within a recurrence plot. As a topological value, we use different recurrence triangles defined previously. As a measure-theoretic value, we define the typical recurrence triangle frequency dimension, which generally fluctuates around 1 when the underlying dynamics are governed by deterministic chaos. By contrast, the dimension becomes higher than 1 for a purely stochastic system. Additionally, the typical recurrence triangle frequency dimension correlates most precisely with DET among the above quantities. Our results show that (i) the common practice of using DET could be partly theoretically supported using recurrence triangles, and (ii) the variety of recurrence triangles behaves more consistently for identifying the strength of stochasticity for the underlying dynamics. The results in this study should be useful in checking basic properties for modeling a given time series.

A review of symbolic dynamics and symbolic reconstruction of dynamical systems

Discretizing a nonlinear time series enables us to calculate its statistics fast and rigorously. Before the turn of the century, the approach using partitions was dominant. In the last two decades, discretization via permutations has been developed to a powerful methodology, while recurrence plots have recently begun to be recognized as a method of discretization. In the meantime, horizontal visibility graphs have also been proposed to discretize time series. In this review, we summarize these methods and compare them from the viewpoint of symbolic dynamics, which is the right framework to study the symbolic representation of nonlinear time series and the inverse process: the symbolic reconstruction of dynamical systems. As we will show, symbolic dynamics is currently a very active research field with interesting applications.

Imputation-free reconstructions of three-dimensional chromosome architectures in human diploid single-cells using allele-specified contacts

Single-cell Hi-C analysis of diploid human cells is difficult because of the lack of dense chromosome contact information and the presence of homologous chromosomes with very similar nucleotide sequences. Thus here, we propose a new algorithm to reconstruct the three-dimensional (3D) chromosomal architectures from the Hi-C dataset of single diploid human cells using allele-specific single-nucleotide variations (SNVs). We modified our recurrence plot-based algorithm, which is suitable for the estimation of the 3D chromosome structure from sparse Hi-C datasets, by newly incorporating a function of discriminating SNVs specific to each homologous chromosome. Here, we eventually regard a contact map as a recurrence plot. Importantly, the proposed method does not require any imputation for ambiguous segment information, but could efficiently reconstruct 3D chromosomal structures in single human diploid cells at a 1-Mb resolution. Datasets of segments without allele-specific SNVs, which were considered to be of little value, can also be used to validate the estimated chromosome structure. Introducing an additional mathematical measure called a refinement further improved the resolution to 40-kb or 100-kb. The reconstruction data supported the notion that human chromosomes form chromosomal territories and take fractal structures where the dimension for the underlying chromosome structure is a non-integer value.

Improving time series prediction accuracy for the maxima of a flow by reconstructions using local cross sections

Despite a long history of time series analysis/prediction, theoretically few is known on how to predict the maxima better. To predict the maxima of a flow more accurately, we propose to use its local cross sections or plates the flow passes through. First, we provide a theoretical underpinning for the observability using local cross sections. Second, we show that we can improve short-term prediction of local maxima by employing a generalized prediction error, which weighs more for the larger values. The proposed approach is demonstrated by rainfalls, where heavier rains may cause casualties.

Solar activity facilitates daily forecasts of large earthquakes

Despite the extensive literature related to earthquakes, an effective method to forecast and avoid occasional seismic hazards that cause substantial damage is lacking. The Sun has recently been identified as a potential precursor to earthquakes, although no causal relationship between its activity and the Earth's seismicity has been established. This study was aimed at investigating whether such a relationship exists and whether it can be used to improve earthquake forecasting. The edit distances between earthquake point processes were combined with delay-coordinate distances for sunspot numbers. The comparison of these two indicated the existence of unidirectional causal coupling from solar activity to seismicity on Earth, and a radial basis function regressor showed accuracy improvements in the largest magnitude prediction of next days by 2.6%-17.9% in the odds ratio when sunspot distances were included.

A preliminary study of the safety and effectiveness of isoproterenol loading transesophageal echocardiography in atrial fibrillation

Funding Acknowledgements

Type of funding sources: None.

Background

In patients with sludge or severe spontaneous echo contrast (SEC) in the left atrial appendage (LAA), isoproterenol loading transesophageal echocardiography (ISP-TEE) has been reported to check the presence of thrombus in the LAA, as the sludge or severe SEC disappears (Figure 1).

Purpose

The aim of this study was to assess the safety of ISP-TEE for the identification of LAA thrombus and the hemodynamic changes in the LAA caused by ISP loading.

Methods

We prospectively enrolled 25 patients with atrial fibrillation (AF) and sludge or SEC in the LAA who underwent ISP-TEE from April 2020 to July 2021. ISP was administered intravenously to achieve the target heart rate (HR) defined as follows: Max HR [beats per minutes: bpm] = 220 – age (years), Target HR [bpm] = Max HR × 0.8. Patients with tachycardia exceeding Max HR before ISP administration, hemodynamic instability, and other contraindications to ISP were excluded from the study. To assess the safety of ISP-TEE, we evaluated patients’ condition, changes in systolic blood pressure (sBP) and HR before and after ISP loading. We also assessed the presence or absence of worsening heart failure, new arrhythmias other than atrial fibrillation, and cerebral infarction or transient ischemic attack during the examination, and after 24 hours. Hemodynamic evaluation was performed using LAA blood flow velocity, LAA tissue Doppler imaging (TDI) velocity, and LAA volume fraction (LAAVF) defined as follows: LAAVF (%) = (Max LAA volume – Min LAA volume) / Max LAA volume × 100. Quantification of LAA volume was performed using the stacked-contour method of a 3-dimensional TEE full-volume acquisition.

Results

Among 25 patients, 13 patients had sludge or grade3 SEC, 7 patients had grade2 SEC, 5 patients had grade1 SEC. HR after ISP loading was significantly higher than before loading, but sBP did not change significantly before and after ISP loading. No complications due to ISP loading were observed during examination and after 24 hours. After ISP loading, there were 18 patients with grade 1 SEC or no SEC (classified as Group1), 7 patients had residual sludge or grade 2 to 3 SEC (classified as Group2). The differences in LAA blood flow velocity between before and after ISP loading was faster in Group1 than in Group2: 13.0 ± 10.5 vs 2.6 ± 4.2. p = 0.019. The differences in TDI velocity was also faster in Group1 than in Group2: 1.46 ± 1.14 vs 0.19 ± 0.50, p = 0.010. The differences in LAAVF was higher in Group1 than in Group2: 13.7 ± 10.3 vs 2.2 ± 2.0, p = 0.009.

Conclusions

In our study, no complications were observed in ISP-TEE for the identification of LAA thrombus. Patients with grade 1 SEC or no SEC, the LAA function was increased by ISP loading. These results may provide insights into the mechanisms of ISP loading on SEC in the LAA. Abstract Figure.

Fast reconstruction of an original continuous series from a recurrence plot

We propose an algorithm to refine the reconstruction of an original time series given a recurrence plot, which is also referred to as a contact map. The refinement process calculates the local distances based on the Jaccard coefficients with the neighbors in the previous resolution for each point and takes their weighted average using local distances. We demonstrate the utility of our method using two examples.

Forecasting wind power ramps with prediction coordinates

To the best of our knowledge, the method of prediction coordinates is the only forecasting method in nonlinear time series analysis that explicitly uses the stochastic characteristics of a system with dynamical noise. Specifically, it generates multiple predictions to jointly infer the current states and dynamical noises. Recent findings based on hypothesis testing show that weather is nonlinear and stochastic and, therefore, so are renewable energy power outputs. This being the case, in this paper, we apply the method of prediction coordinates to forecast wind power ramps, which are rapid transitions in the wind power output that can deteriorate the quality of the electricity supply. First, the method of prediction coordinates is tested using numerical simulations. Then, we present an example of wind power ramp forecasting with empirical data. The results show that the method of prediction coordinates compares favorably with other methods, validating it as a reliable tool for forecasting transitions in nonlinear stochastic dynamics, particularly in the field of renewable energies.

Deep learning for screening of pulmonary hypertension using standard chest X-ray

Background

Early detection of pulmonary hypertension (PH) is crucial to ensure that patients receive timely treatment for the progressive clinical course. The chest X-ray (CXR), a routine method at hospitals, has recommended in order to reveal features supportive of a diagnosis of PH. However, it is well known that the sensitivity and specificity are low.

Purpose

We tested the hypothesis that application of artificial intelligence (AI) to the CXR could identify PH.

Methods

We retrospectively enrolled 900 data with paired CXR and right heart catheter (RHC), including the pulmonary artery pressure, from October 2009 to December 2018. We trained a convolutional neural network to identify patients with PH as actual value of pulmonary artery pressure, using the CXR alone (Figure). The diagnosis of PH was performed using hemodynamic measurements according to the most recent World Symposium standards: mean PAP ≥20 mmHg. We have compared the area under the curve (AUC) by human observers, measurements of CXR images, and AI for detection of PH.

Results

Subjects were divided into two groups with PH (439 patients; mean age, 66±14 years; 233 male) and without PH (461 patients; mean age, 68±12 years; 278 male). In an independent set, AI was the highest diagnostic ability for detection of PH (AUC: 0.71). The AUC by the AI algorithm was significantly higher than the AUC by measurements of CXR images and human observers (0.71 vs. 0.60 and vs. 0.63, all compared p<0.05).

Conclusion

Applying AI to the CXR (a classical, universal, low-cost test) permits the CXR images to serve as a powerful tool to screen for PH.

Neural network

Funding Acknowledgement

Type of funding source: None

Topological epidemic model: Theoretical insight into underlying networks

Although there are various models of epidemic diseases, there are a few individual-based models that can guide susceptible individuals on how they should behave in a pandemic without its appropriate treatment. Such a model would be ideal for the current coronavirus disease 2019 (COVID-19) pandemic. Thus, here, we propose a topological model of an epidemic disease, which can take into account various types of interventions through a time-dependent contact network. Based on this model, we show that there is a maximum allowed number of persons one can see each day for each person so that we can suppress the epidemic spread. Reducing the number of persons to see for the hub persons is a key countermeasure for the current COVID-19 pandemic.

Permutations uniquely identify states and unknown external forces in non-autonomous dynamical systems

It has been shown that a permutation can uniquely identify the joint set of an initial condition and a non-autonomous external force realization added to the deterministic system in given time series data. We demonstrate that our results can be applied to time series forecasting as well as the estimation of common external forces. Thus, permutations provide a convenient description for a time series data set generated by non-autonomous dynamical systems.

A mobile ELF4 delivers circadian temperature information from shoots to roots

The circadian clock is synchronized by environmental cues, mostly by light and temperature. Explaining how the plant circadian clock responds to temperature oscillations is crucial to understanding plant responsiveness to the environment. Here, we found a prevalent temperature-dependent function of the Arabidopsis clock component EARLY FLOWERING 4 (ELF4) in the root clock. Although the clocks in roots are able to run in the absence of shoots, micrografting assays and mathematical analyses show that ELF4 moves from shoots to regulate rhythms in roots. ELF4 movement does not convey photoperiodic information, but trafficking is essential for controlling the period of the root clock in a temperature-dependent manner. Low temperatures favour ELF4 mobility, resulting in a slow-paced root clock, whereas high temperatures decrease movement, leading to a faster clock. Hence, the mobile ELF4 delivers temperature information and establishes a shoot-to-root dialogue that sets the pace of the clock in roots.

540 Assessment of left ventricular ejection fraction from echocardiographic images using machine learning algorithm

Background

Precise and reliable echocardiographic assessment of LVEF is needed for clinical decision-making. LVEF is currently determined through an observer dependent process that requires manual tracing. To remove this manual tracing step, which is both time-consuming and user dependent, automatic computer aided diagnosis systems may be useful in the clinical setting.

Purpose

The aim of this study was to evaluate whether a 3-dimensional convolutional neural networks (3DCNN) could estimate left ventricular ejection fraction (LVEF) and differentiate types of heart failure (preserved EF/reduced EF) using conventional 2-dimensional echocardiographic images.

Methods

We developed a deep learning model to automatically estimate LVEF from echocardiographic data. The 3DCNN model was trained on a dataset of 340 patients. The dataset creation consisted of three main steps: firstly, for each exam, cine-loops showing the parasternal and apical views were manually selected; then, 10 sequential frames were extracted from each 1 beat and; finally, each frame was pre-processed to fit the learning model. Each patient has 2 views, resulting in a total of 6,800 images. Reference LVEF measurement was calculated by two highly experienced readers in each case.

Results

A good correlation was found between estimated LVEF based on apical 2 and 4 chamber views and reference LVEF (r =0.88, p <0.001) (Figure). For classification of heart failure types based on LVEF (LVEF ≥50% or <50%), the area under the receiver-operating characteristic curve by the 3DCNN algorithm was over 0.95.

Conclusions

The 3DCNN can be applied to estimate and classify the LVEF in the clinical setting. Furthermore, this work will serve as a driver for future research using million image databases.

Abstract 540 Figure.

Hepatic epithelioid hemangioendothelioma successfully treated with living donor liver transplantation: A case report and literature review

Hepatic epithelioid hemangioendothelioma is a rare neoplasm with a variable malignant potential and a high risk of recurrence. No general treatment guidelines have been established. Fortunately, we were able to minimize immunosuppressant after liver transplantation because of a full HLA-matched case. There was no recurrence 1 year after treatment.

P1526 Updated prevalence of lambls excrescences using the latest three-dimensional transesophageal echocardiography

Background

Lambl’s excrescences (LEs), filiform strands that occur at sites of cardiac valves, have been suggested the cause cryptogenic stroke. The diagnosis is primarily based upon the echocardiographic study, but conventional two-dimensional transthoracic echocardiography has limitation to detect such as small strands. Latest three dimensional-transesophageal echocardiography (3D-TEE) have high-resolution images with many slices, so small structures are able to be clearly visible and detected.

Purpose

The aim of this study was to assess the prevalence of LEs using the latest 3D-TEE images.

Methods

We retrospectively reviewed consecutive 140 patients who underwent 3D-TEE from November 2018 to May 2019. Forty-seven patients were excluded due to unmeasurable, such as mitral valve prolapse, severe aortic stenosis, prosthetic valves and poor-quality images. We carefully evaluated the mitral and aortic valve leaflets in order to find mobile string structure (diameter <1 mm and length 1–20 mm) in each cardiac cycle. Total analyzed images were over 50 slices per one patient.

Results

Among 93 patients, 83 patients (89%) was detected the presence of LEs. No difference in age and gender were found between patients with LEs and patients without LEs. Of the total 83 patients, there were 35 patients with strands on mitral valve, 32 patients with strands on aortic valve, and 16 patients with strands on both valves. Distribution of LEs at each valve leaflet were shown in Figure. Right coronary cusp of aortic valve (42%) and P2 of mitral valve (35%) were high prevalence among leaflets.

Conclusions

3D-TEE provides an update prevalence of LEs. The prevalence of LEs might be potentially high in the real world.

Abstract P1526 Figure.

Two efficient calculations of edit distance between marked point processes

In this paper, we propose to use linear programming methods or a more specialized method, namely, the Hungarian method, for speeding up the exact calculation of an edit distance for marked point processes [Y. Hirata and K. Aihara, Chaos 25, 123117 (2015)]. The key observation is that the problem of calculating the edit distance reduces to a matching problem on a bipartite graph. Our preliminary numerical results show that the proposed implementations are faster than the conventional ones by a factor of 10-1000.

Detecting nonlinear stochastic systems using two independent hypothesis tests

Various systems in the real world can be nonlinear and stochastic, but because nonlinear time series analysis has been developed to distinguish nonlinear deterministic systems from linear stochastic systems, there have been no appropriate methods developed so far for testing the nonlinear stochasticity for a given system. Thus, here we propose a set of two hypothesis tests, one for the nonlinearity and one for the stochasticity, independent of each other. The test for the linearity is based on Fourier-transform-based surrogate data with a nonlinear test statistic, while the test for determinism depends on the theory of ordinal patterns or permutations recently developed intensively. We demonstrate the proposed set of tests with time series generated from toy models. In addition, we show that both a foreign exchange market and a temperature series in Tokyo could be nonlinear and stochastic, as well as sometimes with determinism beyond pseudoperiodicity.

Practically scheduling hormone therapy for prostate cancer using a mathematical model

Hormone therapy is one of the popular therapeutic methods for prostate cancer. Intermittent androgen suppression (IAS) is the method which stops and resumes hormone therapy repeatedly. The efficacy of IAS differs depending on patients; both the cases have been reported where the relapse of cancer happened and did not happen, for the patients who had undergone IAS. For the patients who cannot avoid the relapse of cancer by IAS, we should delay the relapse of cancer as later as possible. Here we compared some practical methods of determining when to stop and restart hormone therapy for IAS using an existing mathematical model of prostate cancer. The method we suggest is to determine the ratio of on-treatment period and off-treatment period sparsely for each cycle, namely the "sparse search." We also compared the performance of the sparse search with the exhaustive search and the model predictive control. We found that the sparse search can find a good treatment schedule without failure, and the computational cost is not so high compared to the exhaustive method. In addition, we focus on the model predictive control (MPC) method which has been applied to the scheduling of IAS in some existing studies. The MPC is computationary efficient, although it does not always find an optimal schedule in the numerical experiments here. We believe that the MPC method might be also promising because of its reasonable computational costs and its possibility of expanding of the model.

Combining multiple forecasts for multivariate time series via state-dependent weighting

We present a model-free forecast algorithm that dynamically combines multiple forecasts using multivariate time series data. The underlying principle is based on the fact that forecast performance depends on the position in the state space. This property is exploited to weight multiple forecasts via a local loss function. Specifically, additional weights are assigned to appropriate forecasts depending on their positions in a state space reconstructed via delay coordinates. The function evaluates the forecast error discounted by the distance in the space, whereas most existing methods discount the error in relation to time. In addition, forecasts are selected with the function for each time step based on the existing multiview embedding approach; by contrast, the original multiview embedding selects the reconstructions in advance before starting the forecast. The proposed prediction method has the smallest mean squared error among conventional ensemble methods for the Rössler and the Lorenz'96I models. The results of comparison of the proposed method with conventional machine-learning methods using a flood forecast example indicate that the proposed method yields superior accuracy. We also demonstrate that the proposed method might even correctly forecast the maximum water level of rivers without any prior knowledge.

Transition of Spleen Volume Long After Pediatric Living Donor Liver Transplantation for Biliary Atresia

PURPOSE

After undergoing the Kasai procedure for biliary atresia (BA), most patients develop severe splenomegaly that tends to be improved by liver transplantation. However, fluctuations in splenic volume long after transplantation remain to be elucidated.

PATIENTS AND METHODS

Seventy-one consecutive patients who had undergone pediatric living donor liver transplantation (LDLT) for BA were followed up in our outpatient clinic for 5 years. They were classified into 3 groups according to their clinical outcomes: a good course group (GC, n = 41) who were maintained on only 1 or without an immunosuppressant, a liver dysfunction group (LD, n = 18) who were maintained on 2 or 3 types of immunosuppressants, and a vascular complication group (VC, n = 11). Splenic and hepatic volumes were calculated by computed tomography in 464 examinations and the values compared before and after the treatment, especially in the VC group.

RESULTS

Splenic volume decreased exponentially in the GC group, with splenic volume to standard spleen volume ratio (SD) being 1.59 (0.33) 5 years after liver transplantation. Splenic volume to standard spleen volume ratios were greater in the VC and LD groups than in the GC group. Patients in the VC group with portal vein stenosis developed liver atrophy and splenomegaly, whereas those with hepatic vein stenosis developed hepatomegaly and splenomegaly. Interventional radiation therapy tended to improve the associated symptoms.

CONCLUSIONS

Fluctuations in splenic volume long after pediatric LDLT for BA may reflect various clinical conditions. Evaluation of both splenic and hepatic volumes can facilitate understanding clinical conditions following pediatric LDLT.

Simulation training for medical emergencies in the dental setting using an inexpensive software application

INTRODUCTION

Every dental provider needs to be educated about medical emergencies to provide safe dental care. Simulation training is available with simulators such as advanced life support manikins and robot patients. However, the purchase and development costs of these simulators are high. We have developed a simulation training course on medical emergencies using an inexpensive software application. The purpose of this study was to evaluate the educational effectiveness of this course.

MATERIALS AND METHODS

Fifty-one dental providers participated in this study from December 2014 to March 2015. Medical simulation software was used to simulate a patient's vital signs. We evaluated participants' ability to diagnose and treat vasovagal syncope or anaphylaxis with an evaluation sheet and conducted a questionnaire before and after the scenario-based simulation training.

RESULTS

The median evaluation sheet score for vasovagal syncope increased significantly from 7/9 before to 9/9 after simulation training. The median score for anaphylaxis also increased significantly from 8/12 to 12/12 (P < .01). For the item "I can treat vasovagal syncope/anaphylaxis adequately," the percentage responding "Strongly agree" or "Agree" increased from 14% to 56% for vasovagal syncope and from 6% to 42% for anaphylaxis with simulation training.

CONCLUSIONS

This simulation course improved participants' ability to diagnose and treat medical emergencies and improved their confidence. This course can be offered inexpensively using a software application.

Detecting directional couplings from multivariate flows by the joint distance distribution

The identification of directional couplings (or drive-response relationships) in the analysis of interacting nonlinear systems is an important piece of information to understand their dynamics. This task is especially challenging when the analyst's knowledge of the systems reduces virtually to time series of observations. Spurred by the success of Granger causality in econometrics, the study of cause-effect relationships (not to be confounded with statistical correlations) was extended to other fields, thus favoring the introduction of further tools such as transfer entropy. Currently, the research on old and new causality tools along with their pitfalls and applications in ever more general situations is going through a time of much activity. In this paper, we re-examine the method of the joint distance distribution to detect directional couplings between two multivariate flows. This method is based on the forced Takens theorem, and, more specifically, it exploits the existence of a continuous mapping from the reconstructed attractor of the response system to the reconstructed attractor of the driving system, an approach that is increasingly drawing the attention of the data analysts. The numerical results with Lorenz and Rössler oscillators in three different interaction networks (including hidden common drivers) are quite satisfactory, except when phase synchronization sets in. They also show that the method of the joint distance distribution outperforms the lowest dimensional transfer entropy in the cases considered. The robustness of the results to the sampling interval, time series length, observational noise, and metric is analyzed too.

Electronic Structure of Ce-Doped and -Undoped Nd_{2}CuO_{4} Superconducting Thin Films Studied by Hard X-Ray Photoemission and Soft X-Ray Absorption Spectroscopy

In order to realize superconductivity in cuprates with the T^{'}-type structure, not only chemical substitution (Ce doping) but also postgrowth reduction annealing is necessary. In the case of thin films, however, well-designed reduction annealing alone without Ce doping can induce superconductivity in the T^{'}-type cuprates. In order to unveil the origin of superconductivity in the Ce-undoped T^{'}-type cuprates, we have performed bulk-sensitive hard x-ray photoemission and soft x-ray absorption spectroscopy on superconducting and nonsuperconducting Nd_{2-x}Ce_{x}CuO_{4} (x=0, 0.15, and 0.19) thin films. By postgrowth annealing, core-level spectra exhibited dramatic changes, which we attributed to the enhancement of core-hole screening in the CuO_{2} plane and the shift of chemical potential along with changes in the band filling. The result suggests that the superconducting Nd_{2}CuO_{4} film is doped with electrons despite the absence of the Ce substitution.

Element Selectivity in Second-Harmonic Generation of GaFeO_{3} by a Soft-X-Ray Free-Electron Laser

Nonlinear optical frequency conversion has been challenged to move down to the extreme ultraviolet and x-ray region. However, the extremely low signals have allowed researchers to only perform transmission experiments of the gas phase or ultrathin films. Here, we report second harmonic generation (SHG) of the reflected beam of a soft x-ray free-electron laser from a solid, which is enhanced by the resonant effect. The observation revealed that the double resonance condition can be met by absorption edges for transition metal oxides in the soft x-ray range, and this suggests that the resonant SHG technique can be applicable to a wide range of materials. We discuss the possibility of element-selective SHG spectroscopy measurements in the soft x-ray range.

Tensile-Strain-Dependent Spin States in Epitaxial LaCoO_{3} Thin Films

The spin states of Co^{3+} ions in perovskite-type LaCoO_{3}, governed by the complex interplay between the electron-lattice interactions and the strong electron correlations, still remain controversial due to the lack of experimental techniques which can directly detect them. In this Letter, we revealed the tensile-strain dependence of spin states, i.e., the ratio of the high- and low-spin states, in epitaxial thin films and a bulk crystal of LaCoO_{3} via resonant inelastic soft x-ray scattering. A tensile strain as small as 1.0% was found to realize different spin states from that in the bulk.

Endotoxin Metabolism Reflects Hepatic Functional Reserve in End-Stage Liver Disease

BACKGROUND

The hepatic clearance of endotoxin (Et) may reflect hepatic functional reserve and ischemic injury to hepatocytes. Therefore, we examined the relationships between Et activity (EA) and the metrics Pediatric End-Stage Liver Disease (PELD)/Model of End-Stage Liver Disease (MELD) score and alanine transaminase (ALT) levels in the postoperative period.

METHODS

We performed 8 living-donor liver transplantations (LDLTs) for biliary atresia at our center from April 2012 to December 2012. EA was measured by means of an Et activity assay (EAA) in samples collected from a vein 1 day before LDLT, from the portal vein during the intraoperative anhepatic phase, from an artery 1 hour after reperfusion, from an artery on postoperative day (POD) 1, and from an artery or vein at PODs 7 and 14.

RESULTS

EAs generally remained at low levels. EA at the reperfusion period was significantly lowest. The correlation coefficient for the preoperative MELD/PELD score and the EAA was 0.837, and the corresponding P value was .009; thus, there was a significant relationship between the preoperative MELD/PELD score and the EAA. The correlation coefficients for ALT at POD 1 and EA during the anhepatic phase, at 1 hour after reperfusion, and at POD 1 were 0.64, 0.43, and 0.38, respectively, and the P values for these correlations were .08, .67, and .34. Thus, we observed that ALT and EA generally tended to be somewhat directly correlated, but no significant relationships between these 2 metrics were observed.

CONCLUSIONS

Endotoxin metabolism reflects the hepatic functional reserve capacity of end-stage liver disease.

Reconstructing latent dynamical noise for better forecasting observables

I propose a method for reconstructing multi-dimensional dynamical noise inspired by the embedding theorem of Muldoon et al. [Dyn. Stab. Syst. 13, 175 (1998)] by regarding multiple predictions as different observables. Then, applying the embedding theorem by Stark et al. [J. Nonlinear Sci. 13, 519 (2003)] for a forced system, I produce time series forecast by supplying the reconstructed past dynamical noise as auxiliary information. I demonstrate the proposed method on toy models driven by auto-regressive models or independent Gaussian noise.

Personalizing Androgen Suppression for Prostate Cancer Using Mathematical Modeling

Using a dataset of 150 patients treated with intermittent androgen suppression (IAS) through a fixed treatment schedule, we retrospectively designed a personalized treatment schedule mathematically for each patient. We estimated 100 sets of parameter values for each patient by randomly resampling each patient’s time points to take into account the uncertainty for observations of prostate specific antigen (PSA). Then, we identified 3 types and classified patients accordingly: in type (i), the relapse, namely the divergence of PSA, can be prevented by IAS; in type (ii), the relapse can be delayed by IAS later than by continuous androgen suppression (CAS); in type (iii) IAS was not beneficial and therefore CAS would have been more appropriate in the long run. Moreover, we obtained a treatment schedule of hormone therapy by minimizing the PSA of 3 years later in the worst case scenario among the 100 parameter sets by searching exhaustively all over the possible treatment schedules. If the most frequent type among 100 sets was type (i), the maximal PSA tended to be kept less than 100 ng/ml longer in IAS than in CAS, while there was no statistical difference for the other cases. Thus, mathematically personalized IAS should be studied prospectively.

Antibody Drug Treatment for Steroid-Resistant Rejection After Pediatric Living Donor Liver Transplantation: A Single-Center Experience

BACKGROUND

Antibody drugs have been used to treat steroid-resistant rejection (SRR) after liver transplantation. Although anti-thymocyte globulin has been used for SRR after liver transplantation in place of muromonab-CD3 since 2011 in Japan, the effectiveness of anti-thymocyte globulin after pediatric living-donor liver transplantation (LDLT) has not yet been reported. The aim of this study was to evaluate the effectiveness of antibody drug treatment for SRR after pediatric LDLT in our single center.

METHODS

Between May 2001 and December 2013, 220 pediatric LDLTs were performed. Initial immunosuppression after LDLT included tacrolimus and methylprednisolone therapy. Acute rejection was diagnosed by use of a liver biopsy and the administration of steroid pulse treatment, and SRR was defined as acute rejection refractory to the steroid pulse treatment.

RESULTS

Acute rejection and SRR occurred in 74 (33.6%) and 16 patients (7.3%), respectively. The graft survival rates of non-SRR and SRR were 92.4% and 87.5%, respectively (P = .464). The median concentration of alanine aminotransferase before and after the administration of antibody drug was 193.5 mU/mL (range, 8-508) and 78 mU/mL (range, 9-655), respectively (P = .012). The median rejection activity index before and after the administration of antibody drugs was 5 (range, 2-9) and 1 (range, 0-9), respectively (P = .004). After antibody drug treatment, 12 patients had cytomegalovirus infections, 2 patients had Epstein-Barr virus infections, 3 patients had respiratory infections, and 1 patient had encephalitis. The cause of death in 1 patient with SRR was recurrence of infant fulminant hepatic failure.

CONCLUSIONS

Antibody drug treatment for SRR after pediatric LDLT is safe and effective.

Prediction of flow dynamics using point processes

Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one. But, for a time-continuous system, such a compact description does not have a solid basis. Here, we propose to describe a time-continuous time series using a local cross section and the times when the orbit crosses the local cross section. We show that if such a series of crossing times and some past observations are given, we can predict the system's dynamics with fine accuracy. This reconstructability neither depends strongly on the size nor the placement of the local cross section if we have a sufficiently long database. We demonstrate the proposed method using the Lorenz model as well as the actual measurement of wind speed.

Dimensionless embedding for nonlinear time series analysis

Recently, infinite-dimensional delay coordinates (InDDeCs) have been proposed for predicting high-dimensional dynamics instead of conventional delay coordinates. Although InDDeCs can realize faster computation and more accurate short-term prediction, it is still not well-known whether InDDeCs can be used in other applications of nonlinear time series analysis in which reconstruction is needed for the underlying dynamics from a scalar time series generated from a dynamical system. Here, we give theoretical support for justifying the use of InDDeCs and provide numerical examples to show that InDDeCs can be used for various applications for obtaining the recurrence plots, correlation dimensions, and maximal Lyapunov exponents, as well as testing directional couplings and extracting slow-driving forces. We demonstrate performance of the InDDeCs using the weather data. Thus, InDDeCs can eventually realize "dimensionless embedding" while we enjoy faster and more reliable computations.

On the limits of probabilistic forecasting in nonlinear time series analysis II: Differential entropy

In a previous paper, the authors studied the limits of probabilistic prediction in nonlinear time series analysis in a perfect model scenario, i.e., in the ideal case that the uncertainty of an otherwise deterministic model is due to only the finite precision of the observations. The model consisted of the symbolic dynamics of a measure-preserving transformation with respect to a finite partition of the state space, and the quality of the predictions was measured by the so-called ignorance score, which is a conditional entropy. In practice, though, partitions are dispensed with by considering numerical and experimental data to be continuous, which prompts us to trade off in this paper the Shannon entropy for the differential entropy. Despite technical differences, we show that the core of the previous results also hold in this extended scenario for sufficiently high precision. The corresponding imperfect model scenario will be revisited too because it is relevant for the applications. The theoretical part and its application to probabilistic forecasting are illustrated with numerical simulations and a new prediction algorithm.

Hawkes process model with a time-dependent background rate and its application to high-frequency financial data

A Hawkes process model with a time-varying background rate is developed for analyzing the high-frequency financial data. In our model, the logarithm of the background rate is modeled by a linear model with a relatively large number of variable-width basis functions, and the parameters are estimated by a Bayesian method. Our model can capture not only the slow time variation, such as in the intraday seasonality, but also the rapid one, which follows a macroeconomic news announcement. By analyzing the tick data of the Nikkei 225 mini, we find that (i) our model is better fitted to the data than the Hawkes models with a constant background rate or a slowly varying background rate, which have been commonly used in the field of quantitative finance; (ii) the improvement in the goodness-of-fit to the data by our model is significant especially for sessions where considerable fluctuation of the background rate is present; and (iii) our model is statistically consistent with the data. The branching ratio, which quantifies the level of the endogeneity of markets, estimated by our model is 0.41, suggesting the relative importance of exogenous factors in the market dynamics. We also demonstrate that it is critically important to appropriately model the time-dependent background rate for the branching ratio estimation.

Computational design of treatment strategies for proactive therapy on atopic dermatitis using optimal control theory

Atopic dermatitis (AD) is a common chronic skin disease characterized by recurrent skin inflammation and a weak skin barrier, and is known to be a precursor to other allergic diseases such as asthma. AD affects up to 25% of children worldwide and the incidence continues to rise. There is still uncertainty about the optimal treatment strategy in terms of choice of treatment, potency, duration and frequency. This study aims to develop a computational method to design optimal treatment strategies for the clinically recommended 'proactive therapy' for AD. Proactive therapy aims to prevent recurrent flares once the disease has been brought under initial control. Typically, this is done by using an anti-inflammatory treatment such as a potent topical corticosteroid intensively for a few weeks to 'get control', followed by intermittent weekly treatment to suppress subclinical inflammation to 'keep control'. Using a hybrid mathematical model of AD pathogenesis that we recently proposed, we computationally derived the optimal treatment strategies for individual virtual patient cohorts, by recursively solving optimal control problems using a differential evolution algorithm. Our simulation results suggest that such an approach can inform the design of optimal individualized treatment schedules that include application of topical corticosteroids and emollients, based on the disease status of patients observed on their weekly hospital visits. We demonstrate the potential and the gaps of our approach to be applied to clinical settings.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.