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Purpose Mucositis remains a challenging complication of radiotherapy or chemoradiotherapy (CRT) for head and neck cancer (HNC) patients. There is limited data on the safety or effectiveness of cocaine mouthwash (CMW) to treat mucositis. Methods This was single centre, prospective sequential cohort study in HNC patients undergoing CRT. Patients were allocated to the standard of care mucositis management (SOC arm) or SOC + 0.5% CMW (CMW arm). We assessed the benefit of CMW in the management of mucositis on patient reported quality of life (QoL) using the EORTC QLQ-C30 and H&N35 questionnaires at baseline, during CRT, at 1- and 3-months follow-up. Results 64 patients were enrolled in the SOC arm and 65 patients in the CMW arm. Baseline characteristics were similar between the arms. Most patients were male (80-89%) who received 70Gy of radiation (63-78%) with cisplatin (86-94%). Grade 2 and 3 mucositis were experienced in up to 51.7% and 28.8% patients respectively, but no meaningful differences were observed between the arms. Morbidity was high without significant differences observed between arms, with high hospitalisation rates (45.3-53.8%), need for enterostomy feeding (21.9-36.9%) and opioid analgesic prescription (≤56.5%). Weight at 3-month follow-up was significantly lower compared to baseline for both arms but was not significantly different between the arms. No significant differences were observed in patient reported QoL between the arms (adjusted and unadjusted), or when assessed using a 10-point clinically meaningful difference threshold (p>0.05). Conclusion Addition of CMW to SOC management did not demonstrate benefit or harm. CRT associated mucositis has significant morbidity.

Thirty-seven patients with advanced gastroenteropancreatic neuroendocrine tumors (GEPNETs) were treated on a prospective phase II single-center study with four cycles of 7.8 GBq 177Lu-octreotate combined with capecitabine and temozolomide chemotherapy (CAPTEM). Each 8-week cycle combined radiopeptide therapy with 14 days of capecitabine (1500 mg/m2) and 5 days of temozolomide (200 mg/m2). The incidence of grade ≥ 3 hematologic toxicity was analyzed. At a median follow-up of 7-years (range 1–10), six (16%) patients developed persistent hematologic toxicity (PHT) (defined as sustained grade ≥ 3 hematologic toxicity beyond 36-months follow-up) and three (8%) developed MDS/AL with a median time-to-event of 46 and 34 months, respectively. The estimated cumulative incidence of MDS/AL was 11% (95% CI: 3.45–24.01). Development of PHT was the only significant risk factor for secondary MDS/AL (RR, 16; 95% CI: 2.53 to 99.55; P < 0.001). The median PFS was 48 months (95% CI: 40.80–55.20), and the median OS was 86 months (95% CI: 56.90–115.13). Twenty-one deaths were recorded, including 13 (62%) due to progressive disease and all 3 (14%) patients with MDS/AL. 177Lu-octreotate CAPTEM therapy for GEPNETs is associated with a risk of long-term hematologic toxicity. The rising cumulative incidence of MDS/AL > 10% mandates the long-term monitoring of treated patients. However, time to onset is unpredictable, and incidence does not correlate with conventional baseline risk factors. Novel methods are required for the stratification of prospective patients based on genetic risk.

Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence'. Here, we study these phenomena using the framework of Exact Coherent Structures, which has been successful in characterizing the routes to high Reynolds number turbulence of passive fluids. Exact Coherent Structures are stationary, periodic, quasiperiodic, or traveling wave solutions of the hydrodynamic equations that, together with their invariant manifolds, serve as an organizing template of the dynamics. We compute the dominant Exact Coherent Structures and connecting orbits in a pre-turbulent active nematic channel flow, which enables a fully nonlinear but highly reduced order description in terms of a directed graph. Using this reduced representation, we compute instantaneous perturbations that switch the system between disparate spatiotemporal states occupying distant regions of the infinite dimensional phase space. Our results lay the groundwork for a systematic means of understanding and controlling active nematic flows in the moderate to high activity regime.

Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem of designing infinite horizon optimal controls with stability guarantees for \textit{a single agent or large population systems} of identical, non-cooperative and non-networked agents, with multi-dimensional and nonlinear stochastic dynamics excited by multiplicative noise. For agent dynamics belonging to the class of reversible diffusion processes, we provide constraints on the state and control cost functions which guarantee stability of the closed-loop system under the action of the individual optimal controls. A condition relating the state-dependent control cost and volatility is introduced to prove the stability of the equilibrium density. This condition is a special case of the constraint required to use the path integral Feynman-Kac formula for computing the control. We investigate the connection between the stabilizing optimal control and the path integral formalism, leading us to a control law formulation expressed exclusively in terms of the desired equilibrium density., 6 pages, 0 figures, IEEE Conference on Decision and Control 2020 (accepted)

In this work we present the first systematic framework to sculpt active nematics systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (1) applied vorticity and (2) activity strength, to shape the dynamics of an extensile active nematic that is confined to a disk. In the absence of control inputs, the system exhibits two attractors, clockwise and counterclockwise circulating states characterized by two co-rotating topological $+\frac{1}{2}$ defects. We specifically seek spatiotemporal inputs that switch the system from one attractor to the other; we also examine phase-shifting perturbations. We identify control inputs by optimizing a penalty functional with three contributions: total control effort, spatial gradients in the control, and deviations from the desired trajectory. This work demonstrates that optimal control theory can be used to calculate non-trivial inputs capable of restructuring active nematics in a manner that is economical, smooth, and rapid, and therefore will serve as a guide to experimental efforts to control active matter.

We consider the problem of incentivization and optimal control of autonomous vehicles for improving traffic congestion. In our scenario, autonomous vehicles must be incentivized in order to participate in traffic improvement. Using the theory and methods of optimal transport, we propose a constrained optimization framework over dynamics governed by partial differential equations, so that we can optimally select a portion of vehicles to be incentivized and controlled. The goal of the optimization is to obtain a uniform distribution of vehicles over the spatial domain. To achieve this, we consider two types of penalties on vehicle density, one is the $L^2$ cost and the other is a multiscale-norm cost, commonly used in fluid-mixing problems. To solve this non-convex optimization problem, we introduce a novel algorithm, which iterates between solving a convex optimization problem and propagating the flow of uncontrolled vehicles according to the Lighthill-Whitham-Richards model. We perform numerical simulations, which suggest that the optimization of the $L^2$ cost is ineffective while optimization of the multiscale norm is effective. The results also suggest the use of a dedicated lane for this type of control in practice., 6 pages, 10 figures, submitted to the 2020 IEEE Intelligent Vehicles Symposium

This paper addresses the continuous discrete-time nonlinear filtering problem for stochastic dynamical systems using the feedback particle filter (FPF). The FPF updates each particle using feedback from the measurements, where the gain function that controls the particles is the solution of a Poisson equation. The main difficulty in the FPF is to approximate this solution using the particles that approximate the probability distribution. We develop a novel Galerkin-based method inspired by high-dimensional data-analysis techniques. Based on the time evolution of the particle cloud, we determine basis functions for the gain function and compute values of it for each individual particle. Our method is completely adapted to the recorded history of the particles and the update of the particles do not require further intermediate approximations or assumptions. We provide an extensive numerical evaluation of the proposed approach and show that it compares favorably compared to baseline FPF and particle filters based on the importance-sampling paradigm.

We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems., Comment: With additional numerics. 23 pages, 17 figures. To appear in CNSNS

Naïve estimation of horizontal wind velocity over complex terrain using measurements from a single wind-LiDAR introduces a bias due to the assumption of uniform velocity in any horizontal plane. While Computational Fluid Dynamics (CFD)-based methods have been proposed for bias removal, there are several issues exist in the implantation. For instance, the upstream atmospheric boundary layer thickness or direction are unknown. Conventional CFD-based corrections use trial and error to estimate the bias. Such approaches not only become numerically intractable for complicated flows, e.g. when the number of unknowns is large, but they also suffer from the fact that there is no guarantee for optimality of the obtained results. We propose a direct-adjoint-loop (DAL) optimization based framework to estimate such unknown parameters in a systematic way. For the validation of the method, we performed an experimental study using DIABREZZA LiDAR on a complex terrain for two wind directions of northwesterly (NW) and southeasterly (SE). The slope error associated with linear regression improved from -0.09 to -0.02 for SE and from -0.09 to +0.04 for NW.

We consider the problem of optimally controlling turbulent buoyancy-driven flows in the built environment, focusing on a model test case of displacement ventilation with a time-varying heat source. The flow is modeled using the unsteady Reynolds-averaged equations (URANS). A direct-adjoint-looping implementation of the nonlinear optimal control problem yields time-varying values of temperature and velocity of the inlet flow that lead to ‘optimal’ time-averaged temperature relative to appropriate objective functionals in a region of interest. The resulting dynamics of both ‘filling’ and ‘intruding’ added layers due to a time-varying source and inlet flow are discussed. The robustness of the optimal solution is demonstrated. It is found that for large enough values of time horizon the optimal steady solution is recovered, while for intermediate values a non-trivial deviation from this optimal steady state design is achieved. The computational framework is flexible, and can be applied to several problems of interest in optimal design and control of indoor airflow.

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game model whose behavior mimics an empirically derived non-local homogeneous flocking model for agents with gradient self-propulsion dynamics. The mean-field game framework provides a non-cooperative optimal control description of the behavior of a population of agents in a distributed setting. In this description, each agent's state is driven by optimally controlled dynamics that result in a Nash equilibrium between itself and the population. The optimal control is computed by minimizing a cost that depends only on its own state, and a mean-field term. The agent distribution in phase space evolves under the optimal feedback control policy. We exploit the low-rank perturbative nature of the non-local term in the forward-backward system of equations governing the state and control distributions, and provide a linear stability analysis demonstrating that our model exhibits bifurcations similar to those found in the empirical model. The present work is a step towards developing a set of tools for systematic analysis, and eventually design, of collective behavior of non-cooperative dynamic agents via an inverse modeling approach., Comment: Revised to incorporate reviewers' suggestions. Accepted to Chaos journal

This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability measure under the action of the closed-loop system. To make the problem analytically tractable, we consider control laws that are stochastic, i.e., the control laws are maps from the state space of the control system to the space of probability measures on the set of admissible control inputs. Under some controllability assumptions on the control system as defined on the state space, we show that the transport problem, considered as a controllability problem for the lifted control system on the space of probability measures, is well-posed for a large class of initial and target measures. We use this to prove the well-posedness of a fixed-endpoint optimal control problem defined on the space of probability measures, where along with the terminal constraints, the goal is to optimize an objective functional along the trajectory of the control system. This optimization problem can be posed as an infinite-dimensional linear programming problem. This formulation facilitates numerical solutions of the transport problem for low-dimensional control systems, as we show in two numerical examples., Final version

The ARC pilot plant conceptual design study has been extended beyond its initial scope [B. N. Sorbom et al., FED 100 (2015) 378] to explore options for managing ∼525 MW of fusion power generated in a compact, high field (B0 = 9.2 T) tokamak that is approximately the size of JET (R0 = 3.3 m). Taking advantage of ARC's novel design – demountable high temperature superconductor toroidal field (TF) magnets, poloidal magnetic field coils located inside the TF, and vacuum vessel (VV) immersed in molten salt FLiBe blanket – this follow-on study has identified innovative and potentially robust power exhaust management solutions. The superconducting poloidal field coil set has been reconfigured to produce double-null plasma equilibria with a long-leg X-point target divertor geometry. This design choice is motivated by recent modeling which indicates that such configurations enhance power handling and may attain a passively-stable detachment front that stays in the divertor leg over a wide power exhaust window. A modified VV accommodates the divertor legs while retaining the original core plasma volume and TF magnet size. The molten salt FLiBe blanket adequately shields all superconductors, functions as an efficient tritium breeder, and, with augmented forced flow loops, serves as an effective single-phase, low-pressure coolant for the divertor, VV, and breeding blanket. Advanced neutron transport calculations (MCNP) indicate a tritium breeding ratio of ∼1.08. The neutron damage rate (DPA/year) of the remote divertor targets is ∼3–30 times lower than that of the first wall. The entire VV (including divertor and first wall) can tolerate high damage rates since the demountable TF magnets allow the VV to be replaced every 1–2 years as a single unit, employing a vertical maintenance scheme. A tungsten swirl tube FLiBe coolant channel design, similar in geometry to that used by ITER, is considered for the divertor heat removal and shown capable of exhausting divertor heat flux levels of up to 12 MW/m2. Several novel, neutron tolerant diagnostics are explored for sensing power exhaust and for providing feedback control of divertor conditions over long time scales. These include measurement of Cherenkov radiation emitted in FLiBe to infer DT fusion reaction rate, measurement of divertor detachment front locations in the divertor legs with microwave interferometry, and monitoring “hotspots” on the divertor chamber walls via IR imaging through the FLiBe blanket. ©2018, DOE NNSA Stewardship Science Graduate Fellowship (No. DE-NA0002135), National Science Foundation Graduate Research Fellowship (Grant No. DGE1122374)

This work considers the assignment of vehicle traffic consisting of both individual, opportunistic vehicles and a cooperative fleet of vehicles. The first set of vehicles seek a user-optimal policy and the second set seeks a fleet-optimal policy. We provide explicit sufficient conditions for the existence and uniqueness of a Nash equilibrium at which both policies are satisfied. We also propose two different algorithms to determine the equilibrium, one centralized and one decentralized. Furthermore, we present a control scheme to attain such an equilibrium in a dynamical network flow. An example is considered showing the workings of our scheme and numerical results are presented.

A One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D Rayleigh-B\'enard convection system in the turbulent regime with Rayleigh number $\mathrm{Ra}=10^6$. The state vector of the 1D ROM is horizontally averaged temperature. Using the Green's Function (GRF) method, which involves applying many localized, weak forcings to the system one at a time and calculating the responses using long-time averaged Direct Numerical Simulations (DNS), the system's Linear Response Function (LRF) has been computed. Another matrix, called the Eddy Flux Matrix (EFM), that relates changes in the divergence of vertical eddy heat fluxes to changes in the state vector, has also been calculated. Using various tests, it is shown that the LRF and EFM can accurately predict the time-mean responses of temperature and eddy heat flux to external forcings, and that the LRF can well predict the forcing needed to change the mean flow in a specified way (inverse problem). The non-normality of the LRF is discussed and its eigen/singular vectors are compared with the leading Proper Orthogonal Decomposition (POD) modes of the DNS data. Furthermore, it is shown that if the LRF and EFM are simply scaled by the square-root of Rayleigh number, they perform equally well for flows at other $\mathrm{Ra}$, at least in the investigated range of $ 5 \times 10^5 \le \mathrm{Ra} \le 1.25 \times 10^6$. The GRF method can be applied to develop 1D or 3D ROMs for any turbulent flow, and the calculated LRF and EFM can help with better analyzing and controlling the nonlinear system., Comment: Accepted for publication in Physical Review Fluids

We demonstrate the use of the ‘Direct-Adjoint-Looping method’ for the identification of optimal buoyancy-driven ventilation flows governed by Boussinesq equations. We use the incompressible Reynolds-averaged Navier-Stokes (RANS) equations, derive the corresponding adjoint equations and solve the resulting sensitivity equations with respect to inlet conditions. We focus on a displacement ventilation scenario with a steady plume due to a line source. Subject to an enthalpy flux constraint on the incoming flow, we identify boundary conditions leading to ‘optimal’ temperature distributions in the occupied zone. Our results show that depending on the scaled volume and momentum flux of the inlet flow, qualitatively different flow regimes may be obtained. The numerical optimal results agree with analytically obtained optimal inlet conditions available from classical plume theory in an ‘intermediate’ regime of strong stratification and two-layer flow.

We present a set-oriented graph-based computational framework for continuous-time optimal transport over nonlinear dynamical systems. We recover provably optimal control laws for steering a given initial distribution in phase space to a final distribution in prescribed finite time for the case of non-autonomous nonlinear control-affine systems, while minimizing a quadratic control cost. The resulting control law can be used to obtain approximate feedback laws for individual agents in a swarm control application. Using infinitesimal generators, the optimal control problem is reduced to a modified Monge-Kantorovich optimal transport problem, resulting in a convex Benamou-Brenier type fluid dynamics formulation on a graph. The well-posedness of this problem is shown to be a consequence of the graph being strongly-connected, which in turn is shown to result from controllability of the underlying dynamical system. Using our computational framework, we study optimal transport of distributions where the underlying dynamical systems are chaotic, and non-holonomic. The solutions to the optimal transport problem elucidate the role played by invariant manifolds, lobe-dynamics and almost-invariant sets in efficient transport of distributions in finite time. Our work connects set-oriented operator-theoretic methods in dynamical systems with optimal mass transportation theory, and opens up new directions in design of efficient feedback control strategies for nonlinear multi-agent and swarm systems operating in nonlinear ambient flow fields., 34 pages, 12 figures. Incorporated reviewers' suggestions

We present results on stabilization for reduced order models (ROM) of partial differential equations using learning. Stabilization is achieved via closure models for ROMs, where we use a model-free extremum seeking (ES) dither-based algorithm to learn the best closure models' parameters, for optimal ROM stabilization. We first propose to auto-tune linear closure models using ES, and then extend the results to a closure model combining linear and nonlinear terms, for better stabilization performance. The coupled Burgers' equation is employed as a test-bed for the proposed tuning method.

We study the problem of optimizing the performance of a nonlinear spring-mass-damper attached to a class of multiple-degree-of-freedom systems. We aim to maximize the rate of one-way energy transfer from primary system to the attachment, and focus on impulsive excitation of a two-degree-of-freedom primary system with an essentially nonlinear attachment. The nonlinear attachment is shown to be able to perform as a `nonlinear energy sink' (NES) by taking away energy from the primary system irreversibly for some types of impulsive excitations. Using perturbation analysis and exploiting separation of time scales, we perform dimensionality reduction of this strongly nonlinear system. Our analysis shows that efficient energy transfer to nonlinear attachment in this system occurs for initial conditions close to homoclinic orbit of the slow time-scale undamped system, a phenomenon that has been previously observed for the case of single-degree-of-freedom primary systems. Analytical formulae for optimal parameters for given impulsive excitation input are derived. Generalization of this framework to systems with arbitrary number of degrees-of-freedom of the primary system is also discussed. The performance of both linear and nonlinear optimally tuned attachments is compared. While NES performance is sensitive to magnitude of the initial impulse, our results show that NES performance is more robust than linear tuned-mass-damper to several parametric perturbations. Hence, our work provides evidence that homoclinic orbits of the underlying Hamiltonian system play a crucial role in efficient nonlinear energy transfers, even in high dimensional systems, and gives new insight into robustness of systems with essential nonlinearity., Comment: Updated results. 34 pages, 29 figures

We present a sparse sensing framework based on Dynamic Mode Decomposition (DMD) to identify flow regimes and bifurcations in large-scale thermo-fluid systems. Motivated by real-time sensing and control of thermal-fluid flows in buildings and equipment, we apply this method to a Direct Numerical Simulation (DNS) data set of a 2D laterally heated cavity. The resulting flow solutions can be divided into several regimes, ranging from steady to chaotic flow. The DMD modes and eigenvalues capture the main temporal and spatial scales in the dynamics belonging to different regimes. Our proposed classification method is data-driven, robust w.r.t measurement noise, and exploits the dynamics extracted from the DMD method. Namely, we construct an augmented DMD basis, with "built-in" dynamics, given by the DMD eigenvalues. This allows us to employ a short time-series of data from sensors, to more robustly classify flow regimes, particularly in the presence of measurement noise. We also exploit the incoherence exhibited among the data generated by different regimes, which persists even if the number of measurements is small compared to the dimension of the DNS data. The data-driven regime identification algorithm can enable robust low-order modeling of flows for state estimation and control., Expanded discussion. Fixed some typos and figures

The deformable and continuum nature of soft robots promises versatility and adaptability. However, control of modular, multi-limbed soft robots for terrestrial locomotion is challenging due to the complex robot structure, actuator mechanics and robot-environment interaction. Traditionally, soft robot control is performed by modeling kinematics using exact geometric equations and finite element analysis. The research presents an alternative, model-free, data-driven, reinforcement learning inspired approach, for controlling multi-limbed soft material robots. This control approach can be summarized as a four-step process of discretization, visualization, learning and optimization. The first step involves identification and subsequent discretization of key factors that dominate robot-environment, in turn, the robot control. Graph theory is used to visualize relationships and transitions between the discretized states. The graph representation facilitates mathematical definition of periodic control patterns (simple cycles) and locomotion gaits. Rewards corresponding to individual arcs of the graph are weighted displacement and orientation change for robot state-to-state transitions. These rewards are specific to surface of locomotion and are learned. Finally, the control patterns result from optimization of reward dependent locomotion task (e.g. translation) cost function. The optimization problem is an Integer Linear Programming problem which can be quickly solved using standard solvers. The framework is generic and independent of type of actuator, soft material properties or the type of friction mechanism, as the control exists in the robot's task space. Furthermore, the data-driven nature of the framework imparts adaptability to the framework toward different locomotion surfaces by re-learning rewards., Comment: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2015

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler, Ross, Grover, Kumar, Topological chaos and periodic braiding of almost-cyclic sets. Physical Review Letters 106 (2011), 114101]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or `ghost rods' around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems., Comment: Submitted to Chaos

Objective The objective of this study was to evaluate general practitioners' (GPs) perceptions regarding access to medicines in New Zealand. Design Qualitative. Setting Primary care. Participants GPs. Main outcome measures GPs' views and perceptions. Results GPs were of the view that the current range of medicines available in New Zealand was reasonable; however, it was acknowledged that there were some drugs that patients were missing out on. When considering the range of subsidised medicines available in New Zealand, some GPs felt that there had been an improvement over recent years. It was highlighted that unexpected funding changes could create financial barriers for some patients and that administrative procedures and other complexities created barriers in receiving a subsidy for restricted medicines. GPs also reported problems with the availability and sole supply of certain medicines and claimed that switching from a branded medicine to its generic counterpart could be disruptive for patients. Conclusions The research concluded that although there were some issues with the availability of certain drugs, most GPs were satisfied with the broader access to medicines situation in New Zealand. This view is to contrary to the situation presented by the pharmaceutical industry. The issues around sole supply, the use of generic medicines and the administrative barriers regarding funding of medicines could be improved with better systems. The current work provides a solid account of what GPs see as the advantages and disadvantages of the current system and how they balance these demands in practice., Article summary Article focus To evaluate GPs' perceptions regarding access to medicines in New Zealand. To identify GPs' views and perceptions regarding the role of PHARMAC within the New Zealand healthcare system. Key messages GPs were of the view that the current range of medicines available in New Zealand was reasonable; however, it was acknowledged that there were some drugs that patients were missing out on. When considering the range of subsidised medicines available in New Zealand, some GPs felt that there had been an improvement over recent years. It was highlighted that unexpected funding changes could create financial barriers for some patients and that administrative procedures and other complexities created barriers in receiving a subsidy for restricted medicines. Strengths and limitations of this study This is the first independent objective study covering GPs' perceptions regarding access to medicines issues in New Zealand. Findings from this study will form an essential component of any future research, which reviews New Zealand's current medicines policy. It will also help in developing strategies to better inform patients' access to medicines, with GPs being a large group of health professionals likely to positively affect patient knowledge and views. All GPs were working in a large metropolitan city in New Zealand—it is not known whether their views and experiences differ from colleagues working and living in small towns and rural locales. Also, only 19 of 150 contacted were interested in participating so this could be another source of bias in the study.

In certain (2 + 1)-dimensional dynamical systems, the braiding of periodic orbits provides a framework for analyzing chaos in the system through application of the Thurston-Nielsen classification theorem. Periodic orbits generated by the dynamics can behave as physical obstructions that "stir" the surrounding domain and serve as the basis for this topological analysis. We provide evidence that, even in the absence of periodic orbits, almost-cyclic regions identified using a transfer operator approach can reveal an underlying structure that enables topological analysis of chaos in the domain. National Science Foundation DMS-0701126, DEB-0919088

The functional consequences of missense variants in disease genes are difficult to predict. We assessed if gene expression profiles could distinguish between BRCA1 or BRCA2 pathogenic truncating and missense mutation carriers and familial breast cancer cases whose disease was not attributable to BRCA1 or BRCA2 mutations (BRCAX cases). 72 cell lines from affected women in high-risk breast ovarian families were assayed after exposure to ionising irradiation, including 23 BRCA1 carriers, 22 BRCA2 carriers, and 27 BRCAX individuals. A subset of 10 BRCAX individuals carried rare BRCA1/2 sequence variants considered to be of low clinical significance (LCS). BRCA1 and BRCA2 mutation carriers had similar expression profiles, with some subclustering of missense mutation carriers. The majority of BRCAX individuals formed a distinct cluster, but BRCAX individuals with LCS variants had expression profiles similar to BRCA1/2 mutation carriers. Gaussian Process Classifier predicted BRCA1, BRCA2 and BRCAX status, with a maximum of 62% accuracy, and prediction accuracy decreased with inclusion of BRCAX samples carrying an LCS variant, and inclusion of pathogenic missense carriers. Similarly, prediction of mutation status with gene lists derived using Support Vector Machines was good for BRCAX samples without an LCS variant (82–94%), poor for BRCAX with an LCS (40–50%), and improved for pathogenic BRCA1/2 mutation carriers when the gene list used for prediction was appropriate to mutation effect being tested (71–100%). This study indicates that mutation effect, and presence of rare variants possibly associated with a low risk of cancer, must be considered in the development of array-based assays of variant pathogenicity., Author Summary Inherited mutations in the genes BRCA1 and BRCA2 increase risk of breast cancer and contribute to a proportion of breast cancer families. However, more than half of the reported sequence alterations in BRCA1 and BRCA2 are currently of unknown clinical significance. We analysed gene expression in lymphoblastoid cell lines derived from blood of patients with sequence alterations in BRCA1 and BRCA2 and compared these to lymphoblastoid cells from familial breast cancer patients without such alterations. We then classified these lymphoblastoid cells based on their gene profiles. We found that BRCA1 and BRCA2 samples were more similar to each other than to familial breast cancer patients without BRCA1/2 mutations, and that the type of sequence change in BRCA1 and BRCA2 (missense or truncating) influenced gene expression. We included in the study ten familial breast cancer samples, which carried sequence changes in BRCA1 or BRCA2, that are believed to be of little clinical significance. Interestingly these samples were distinct from other familial breast cancer cases without any sequence alteration in BRCA1 or BRCA2, indicating that further work needs to be performed to determine the possible association of these “low clinical significance” sequence changes with a low to moderate risk of cancer.