Learning interpretable collective variables for spreading processes on networks.

Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barabási model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.

Large-scale flow in a cubic Rayleigh-Bénard cell: long-term turbulence statistics and Markovianity of macrostate transitions.

We investigate the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number Ra = 106. The numerical studies are conducted for single flow trajectories up to 105 convective free-fall times to obtain a sufficient sampling of the four discrete LSC states, which can be summarized to one macrostate, and the two crossover configurations which are taken by the flow in between for short periods. We find that large-scale dynamics depends strongly on the Prandtl number Pr of the fluid which has values of 0.1, 0.7, and 10. Alternatively, we run an ensemble of 3600 short-term direct numerical simulations to study the transition probabilities between the discrete LSC states. This second approach is also used to probe the Markov property of the dynamics. Our ensemble analysis gave strong indication of Markovianity of the transition process from one LSC state to another, even though the data are still accompanied by considerable noise. It is based on the eigenvalue spectrum of the transition probability matrix, further on the distribution of persistence times and the joint distribution of two successive microstate persistence times. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

Spectral Properties of Effective Dynamics from Conditional Expectations.

The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers-Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.

Sleep surgery in syndromic and neurologically impaired children.

PURPOSE: To examine surgery performed for obstructive sleep apnea (OSA) in children with syndromic or neurologic comorbidities. MATERIAL AND METHODS: Medical records of 375 children with OSA were retrospectively reviewed, including 142 patients with trisomy 21, 105 with cerebral palsy, 53 with muscular dystrophy, 32 with spinal muscular atrophy, 18 with mucopolysaccharidoses, 14 with achondroplasia, and 11 with Prader-Willi. OUTCOME MEASURES: Apnea-hypopnea index (AHI), complications, length of postoperative stay, and endoscopic findings. RESULTS: 228 patients received 297 surgical interventions, with the remainder undergoing observation or positive pressure ventilation. Adenoidectomy was the most common procedure performed (92.1% of patients), followed by tonsillectomy (91.6%). Average AHI decreased following tonsillectomy, from 12.4 to 5.7 (p = 0.002). The most common DISE finding was the tongue base causing epiglottic retroflexion. Lingual tonsillectomy also resulted in an insignificant decrease in the AHI. CONCLUSIONS: Adenotonsillectomy, when there is hypertrophy, remains the mainstay of management of syndromic and neurologically-impaired children with OSA. However, additional interventions are often required, due to incomplete resolution of the OSA. DISE is valuable in identifying remaining sites of obstruction and guiding future management.

Lagrangian coherent sets in turbulent Rayleigh-Bénard convection.

Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh-Bénard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number Ra=10^{6} and at a Prandtl number Pr=10. Three different Lagrangian analysis techniques based on graph Laplacians (distance spectral trajectory clustering, time-averaged diffusion maps, and finite-element based dynamic Laplacian discretization) are used to monitor the turbulent fields along trajectories of massless Lagrangian particles in the evolving turbulent convection flow. The three methods are compared to each other and the obtained coherent sets are related to results from an analysis in the Eulerian frame of reference. We show that the results of these methods agree with each other and that Lagrangian and Eulerian coherent sets form basically a disjoint union of the flow domain. Additionally, a windowed time averaging of variable interval length is performed to study the degree of coherence as a function of this additional coarse graining which removes small-scale fluctuations that cause trajectories to disperse quickly. Finally, the coherent set framework is extended to study heat transport.

Neonatal retropharyngeal abscess with complications: Apnea and cervical osteomyelitis.

OBJECTIVE: To evaluate the clinical presentation and management strategies for neonatal retropharyngeal abscess (RPA). METHODS: Retrospective chart review was performed, and literature reviewed. RESULTS: We report two cases of neonatal RPA, with one complicated by cervical osteomyelitis, and the other presenting with apparent life-threatening events (ALTEs). A 6-week-old female underwent transoral drainage of an RPA, which grew methicillin sensitive Staphylococcus aureus. She had a prolonged recovery course and was found to have developed osteomyelitis of the dens and atlas. She was treated with 14 weeks of IV antibiotics and rigid collar fixation for spinal cord instability. A 2-month-old female was admitted after multiple ALTEs with episodes of apnea and pallor. Direct laryngoscopy revealed a bulging RPA, which was drained transorally. This grew multiple organisms including methicillin resistant Staphylococcus aureus, Streptococcal oralis and Prevotella species. CONCLUSIONS: Uncommon in neonates, RPA can present in this age group without fever, and are is likely to have airway complications than in older children. In cases with prolonged recovery, additional diagnostic intervention is recommended to rule out rare complications such as osteomyelitis. Emphasis in such complex cases is placed on a multidisciplinary approach to patient care, coordinating neonatologists, infectious disease specialists, neurosurgeons, and otolaryngologists.

Network measures of mixing.

Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as those obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches, where trajectories serve as nodes and some similarity or distance measure between them is employed to build a (possibly weighted) network, which is then analyzed using spectral methods. Here, we consider the simplest case of an unweighted, undirected network and analytically relate local network measures such as node degree or clustering coefficient to flow structures. In particular, we use these local measures to divide the family of trajectories into groups of similar dynamical behavior via manifold learning methods.

From metastable to coherent sets- Time-discretization schemes.

Given a time-dependent stochastic process with trajectories x(t) in a space Ω, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable setsM are defined in space M⊂Ω, and coherent setsM(t)âŠ‚Ω are defined in space and time. Hence, if we extend the space Ω by the time-variable t, coherent sets are metastable sets in Ω×[0,∞) of an appropriate space-time process. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.

From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian Data.

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time-and-space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance-in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.

Utility of concurrent direct laryngoscopy and bronchoscopy with drug induced sleep endoscopy in pediatric patients with obstructive sleep apnea.

OBJECTIVES: The goal of this report was to find the frequency of synchronous airway lesions (SAL) identified during microdirect laryngoscopy and bronchoscopy (MDLB) that influenced treatment decisions beyond the information provided by drug induced sleep endoscopy (DISE) alone in children with obstructive sleep apnea (OSA) at a tertiary care pediatric hospital. METHODS: This was a retrospective chart review of all pediatric patients who underwent drug induced sleep endoscopy in conjunction with direct laryngoscopy and bronchoscopy as part of a comprehensive airway evaluation for obstructive sleep apnea at a tertiary care pediatric hospital. RESULTS: Three hundred thirty-five patients with obstructive sleep apnea were evaluated with both sleep endoscopy and direct laryngoscopy with bronchoscopy. Five percent of patients had SAL identified on MDLB contributing to airway obstruction. Three patients (0.9%) who underwent MDLB for OSA required surgical correction of SAL that was identified. CONCLUSION: In a limited subset of patients, direct laryngoscopy with bronchoscopy provides additional positive findings to aid with treatment planning for obstructive sleep apnea.

Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics.

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.

Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations.

Markov state models (MSMs) and master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variational approach conformation dynamics/molecular kinetics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters. While it is known how to estimate MSMs from trajectories whose starting points are not sampled from an equilibrium ensemble, this has not yet been the case for TICA and the VAC. Previous estimates from short trajectories have been strongly biased and thus not variationally optimal. Here, we employ the Koopman operator theory and the ideas from dynamic mode decomposition to extend the VAC and TICA to non-equilibrium data. The main insight is that the VAC and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to compute a stationary vector to reweight the data to equilibrium. From such a Koopman-reweighted sample, equilibrium expectation values and variationally optimal reversible Koopman models can be constructed even with short simulations. The Koopman model can be used to propagate densities, and its eigenvalue decomposition provides estimates of relaxation time scales and slow collective variables for dimension reduction. Koopman models are generalizations of Markov state models, TICA, and the linear VAC and allow molecular kinetics to be described without a cluster discretization.

Understanding the geometry of transport: Diffusion maps for Lagrangian trajectory data unravel coherent sets.

Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a method for extracting coherent sets from possibly sparse Lagrangian trajectory data. Our method can be seen as an extension of diffusion maps to trajectory space, and it allows us to construct "dynamical coordinates," which reveal the intrinsic low-dimensional organization of the data with respect to transport. The only a priori knowledge about the dynamics that we require is a locally valid notion of distance, which renders our method highly suitable for automated data analysis. We show convergence of our method to the analytic transfer operator framework of coherence in the infinite data limit and illustrate its potential on several two- and three-dimensional examples as well as real world data.

Lingual Tonsillectomy for Treatment of Pediatric Obstructive Sleep Apnea: A Meta-analysis.

Importance: Evidence indicates correlations between lingual tonsil hypertrophy and pediatric obstructive sleep apnea (OSA). However, to our knowledge, a meta-analysis of surgical outcomes for lingual tonsillectomy in children with OSA has not been conducted. Objective: To evaluate the therapeutic outcomes of lingual tonsillectomy for treatment of pediatric OSA. Data Sources: The study protocol was registered on PROSPERO (CRD42015027053). PubMed, MEDLINE, EMBASE, and the Cochrane Reviews databases were searched independently by 2 authors for relevant articles published by September 2016. Study Selection: The literature search identified English-language studies that used polysomnography to evaluate children with lingual tonsil hypertrophy and OSA after lingual tonsillectomy alone. The search keywords were lingual tonsil, lingual tonsillectomy, sleep endoscopy, sleep apnea, and child. Data Extraction and Synthesis: Polysomnographic data from each study were extracted. A random-effects model pooled postoperative sleep variable changes and success rates for lingual tonsillectomy in treating pediatric OSA. Main Outcomes and Measures: Four outcomes for lingual tonsillectomy were analyzed. These included net postoperative changes in the apnea-hypopnea index (AHI), net postoperative changes in the minimum oxygen saturation, the overall success rate for a postoperative AHI less than 1, and the overall success rate for a postoperative AHI less than 5. Results: This meta-analysis consisted of 4 studies (mean sample size, 18.25 patients), with a total of 73 unique patients (mean [SD] age, 8.3 [1.1] years). Fifty-nine percent (27 of 46) of the patients were male, and 1 of the 4 studies did not specify number of males. Lingual tonsillectomy was indicated for persistent OSA after adenotonsillectomy in all cases. Lingual tonsil hypertrophy was evaluated using computed tomography or magnetic resonance imaging in 1 study, sleep endoscopy in 2 studies, and cine magnetic resonance imaging in 1 study. The mean change in the AHI after lingual tonsillectomy was a reduction of 8.9 (95% CI, -12.6 to -5.2) events per hour. The mean change in the minimum oxygen saturation after lingual tonsillectomy was an increase of 6.0% (95% CI, 2.7%-9.2%). The overall success rate was 17% (95% CI, 7%-35%) for a postoperative AHI less than 1 and 51% (95% CI, 25%-76%) for a postoperative AHI less than 5. Postoperative complications that developed included airway obstruction, bleeding, and pneumonia. Conclusions and Relevance: Lingual tonsillectomy is an effective surgical management for children with OSA caused by lingual tonsil hypertrophy, and it achieves significant improvement in the AHI and the minimum oxygen saturation. However, children frequently have residual OSA after lingual tonsillectomy, and postoperative complications must be carefully managed.

It Is Just Attention-Deficit Hyperactivity Disorder or Is It?

CASE: Carly is a 5-year-old girl who presents for an interdisciplinary evaluation due to behaviors at school and home suggestive of attention-deficit hyperactivity disorder (ADHD). Parent report of preschool teacher concerns was consistent with ADHD. Psychological testing showed verbal, visual-spatial, and fluid reasoning IQ scores in the average range; processing speed and working memory were below average. Carly's behavior improved when her mother left the room, and she was attentive during testing with a psychologist. Tests of executive function (EF) skills showed mixed results. Working memory was in the borderline range, although scores for response inhibition and verbal fluency were average. Parent ratings of ADHD symptoms and EF difficulties were elevated.Carly's parents recently separated; she now lives with her mother and sees her father on weekends. Multiple caregivers with inconsistent approaches to discipline assist with child care while her mother works at night as a medical assistant. Family history is positive for ADHD and learning problems in her father. Medical history is unremarkable. Review of systems is significant for nightly mouth breathing and snoring, but no night waking, bruxism, or daytime sleepiness. She has enlarged tonsils and a high-arched palate on physical examination.At a follow-up visit, parent rating scales are consistent with ADHD-combined type; teacher rating scales support ADHD hyperactive-impulsive type. Snoring has persisted. A sleep study indicated obstructive sleep apnea. After adenotonsillectomy, Carly had significant improvement in ADHD symptoms. She developed recurrence of behavior problems 1 year after the surgery.

The current state of pediatric drug-induced sleep endoscopy.

OBJECTIVES/HYPOTHESIS: The purpose of this investigation was to assess current drug-induced sleep endoscopy (DISE) practice patterns at centers that have published on the technique, to identify areas of agreement, and to identify areas of disagreement that may represent opportunities for improvement and standardization. STUDY DESIGN: Multi-institutional survey. METHODS: A survey was designed in two phases to evaluate preoperative assessment, intraoperative performance, and postoperative management of patients undergoing DISE. The survey was constructed iteratively in consultation with the all of the coauthors, each selected as an expert owing to their previous publication of one or more articles pertaining to pediatric DISE. In the first phase of survey creation, each expert was asked to provide narrative answers to questions pertaining to DISE. These responses served as the basis for a second survey. This second survey was then administered to all pediatric otolaryngologists at each respective institution. RESULTS: Overall, there was a low rate of agreement (33%) among the respondents; however, there was substantial agreement within institution, particularly for the use of anesthetic medications, the use of cine magnetic resonance imaging, and performance of bronchoscopy along with DISE. There was strong agreement among all respondents for performing DISE in a child with severe obstructive sleep apnea following adenotonsillectomy, regardless of comorbidities. CONCLUSION: This multi-institutional survey demonstrated a lack of consensus between experts and multiple opportunities for improvement. In general, there was agreement regarding the workup prior to DISE performance and the endoscopic protocol but disagreement regarding anesthetic protocol and management decisions. LEVEL OF EVIDENCE: 4. Laryngoscope, 127:266-272, 2017.

On metastability and Markov state models for non-stationary molecular dynamics.

Unlike for systems in equilibrium, a straightforward definition of a metastable set in the non-stationary, non-equilibrium case may only be given case-by-case-and therefore it is not directly useful any more, in particular in cases where the slowest relaxation time scales are comparable to the time scales at which the external field driving the system varies. We generalize the concept of metastability by relying on the theory of coherent sets. A pair of sets A and B is called coherent with respect to the time interval [t1, t2] if (a) most of the trajectories starting in A at t1 end up in B at t2 and (b) most of the trajectories arriving in B at t2 actually started from A at t1. Based on this definition, we can show how to compute coherent sets and then derive finite-time non-stationary Markov state models. We illustrate this concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples.

Comparison of treatment outcomes between intracapsular and total tonsillectomy for pediatric obstructive sleep apnea.

BACKGROUND: Intracapsular tonsillectomy (IT) has been advocated as a treatment for pediatric obstructive sleep apnea (OSA). However, evidence in the literature utilizing polysomnography (PSG) is limited. OBJECTIVE: To examine the experience at a tertiary children's hospital to evaluate the effectiveness and risks of intracapsular tonsillectomy compared to total tonsillectomy (TT) for treating pediatric OSA. METHODS: A retrospective study was undertaken of pediatric tonsillectomy cases performed for OSA at a tertiary children's hospital from 2005 to 2010. Patients with recurrent tonsillitis, craniofacial abnormalities, chromosomal abnormalities, neuromuscular disease, and congenital malformations were excluded. Main outcome measures were apnea-hypopnea index (AHI), minimum oxygen saturation (minO2), and surgical complications. RESULTS: Of the 1583 patients reviewed in this study, there were 75 IT and 93 TT patients with pre- and post-operative PSG results. The IT patients were younger, had lower BMI, larger tonsil size, lower pre-operative (AHI) and lower post-operative AHI (p < 0.05). There was a similar percentage of patients that showed improvement in AHI and minimum oxygen saturation between the IT and TT groups. There were statistically similar average change in AHI and minimum oxygen saturation between the IT and TT groups at 5.6 ± 8.6 and 8.6 ± 12.9, respectively (p = 0.8) as well as similar improvement in minimum oxygen saturation between the two groups at 3.3% ± 4.3% and 3.0% ± 5.2%, respectively (p = 0.66). Of TT patients, 2.9% experienced post-operative bleeding with 1.6% requiring OR for control of hemorrhage. Of IT patients, 2.2% were found to have tonsillar regrowth with 2.0% returning to the OR for secondary tonsillectomy. CONCLUSIONS: Intracapsular tonsillectomy, like total tonsillectomy, is effective in improving polysomnogram results in appropriately selected children. Intracapsular tonsillectomy is a suitable option for the surgical treatment of pediatric OSA consequent to its demonstrated efficacy in relieving OSA and its favorable safety profile.

Gizmo is a mean word!

The editorial titled "Gizmos" in the April issue of Otolaryngology-Head and Neck Surgery was unfortunate. Intracapsular tonsillectomy is a rational surgical option for managing tonsillar hypertrophy causing obstructive sleep apnea in selected children. It is performed routinely by surgeons across the globe and has become the standard of care across northern Europe due to the high safety profile of the operation. The semirigid, dartlike design of the sinuplasty devices suggested the idea for an airway-specific set of high-pressure balloons. We began working on these in 2007 and had FDA approval in 2009. They are in wide use by many airway surgeons. Lingual tonsils are a frequent cause of obstructive sleep apnea, and there is no tool that manages this as effectively as endoscopic plasma ablation. We are all engaged in an honorable effort to improve care; surgical and creative skills are as important as analytical skills. Both are necessary for the continuous improvement of our work. Both are worthy of respect.