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The recovery of long-term climate proxy records with seasonal resolution is rare because of natural smoothing processes, discontinuities and limitations in measurement resolution. Yet insolation forcing, a primary driver of multimillennial-scale climate change, acts through seasonal variations with direct impacts on seasonal climate1. Whether the sensitivity of seasonal climate to insolation matches theoretical predictions has not been assessed over long timescales. Here, we analyse a continuous record of water-isotope ratios from the West Antarctic Ice Sheet Divide ice core to reveal summer and winter temperature changes through the last 11,000 years. Summer temperatures in West Antarctica increased through the early-to-mid-Holocene, reached a peak 4,100 years ago and then decreased to the present. Climate model simulations show that these variations primarily reflect changes in maximum summer insolation, confirming the general connection between seasonal insolation and warming and demonstrating the importance of insolation intensity rather than seasonally integrated insolation or season duration2,3. Winter temperatures varied less overall, consistent with predictions from insolation forcing, but also fluctuated in the early Holocene, probably owing to changes in meridional heat transport. The magnitudes of summer and winter temperature changes constrain the lowering of the West Antarctic Ice Sheet surface since the early Holocene to less than 162 m and probably less than 58 m, consistent with geological constraints elsewhere in West Antarctica4–7.

Reconstructing state-space dynamics from scalar data using time-delay embedding requires choosing values for the delay $\tau$ and the dimension $m$. Both parameters are critical to the success of the procedure and neither is easy to formally validate. While embedding theorems do offer formal guidance for these choices, in practice one has to resort to heuristics, such as the average mutual information (AMI) method of Fraser & Swinney for $\tau$ or the false near neighbor (FNN) method of Kennel et al. for $m$. Best practice suggests an iterative approach: one of these heuristics is used to make a good first guess for the corresponding free parameter and then an "asymptotic invariant" approach is then used to firm up its value by, e.g., computing the correlation dimension or Lyapunov exponent for a range of values and looking for convergence. This process can be subjective, as these computations often involve finding, and fitting a line to, a scaling region in a plot: a process that is generally done by eye and is not immune to confirmation bias. Moreover, most of these heuristics do not provide confidence intervals, making it difficult to say what "convergence" is. Here, we propose an approach that automates the first step, removing the subjectivity, and formalizes the second, offering a statistical test for convergence. Our approach rests upon a recently developed method for automated scaling-region selection that includes confidence intervals on the results. We demonstrate this methodology by selecting values for the embedding dimension for several real and simulated dynamical systems. We compare these results to those produced by FNN and validate them against known results -- e.g., of the correlation dimension -- where these are available. We note that this method extends to any free parameter in the theory or practice of delay reconstruction.

Disentangling the drivers of mean annual temperature change in Antarctica requires an understanding of seasonal temperature change. A high-resolution climate record capable of resolving summer and winter seasons could address long-standing questions about the role of orbitally-driven insolation in driving Antarctic mean-annual temperature change. Here, we present a continuous record of water isotope ratios from the West Antarctic Ice Sheet (WAIS) Divide ice core that reveals both summer and winter temperature change though the last 11,000 years. This novel record shows that summer temperatures increased through the early-to-mid Holocene, reached a plateau at 4 to 2 ka, and then decreased to the present. The observed changes are explained primarily by changes in maximum summer insolation. In the early to mid-Holocene, additional summer warming results from the retreat and thinning of the WAIS. The magnitude of summer temperature change constrains the lowering of the WAIS surface to less than 100 m since the early Holocene, consistent with geologic records. Importantly, annual mean temperatures cannot be fully explained by orbital forcing and ice sheet elevation change alone; in the early Holocene, large wintertime temperature excursions overwhelm the summer signal. These winter excursions indicate that regional heat transport anomalies, rather than local thermodynamics, can dominate the annual mean.

Explaining how and why some species evolved to have more complex social structures than others has been a long-term goal for many researchers in animal behaviour because it would provide important insight into the links between evolution and ecology, sociality and cognition. However, despite long-standing interest, the evolution of social complexity is still poorly understood. This may be due in part to researchers focusing on the feasibility of quantifying aspects of sociality, rather than what features are characteristic of animal social complexity in the first place. Any given approach to studying complexity can tell us some things about animal sociality, but may miss others, so it is critical to decide first how to conceptualize complexity before jumping in to quantifying it. Here, we briefly summarize five existing approaches to measuring social complexity. Then, we highlight three fundamental concepts that are commonly used in the field of complex systems: (1) scales of organization, (2) compression and (3) emergence. All of these concepts are applicable to the study of animal social systems, but are not often explicitly addressed in existing social complexity measures. We discuss how these concepts can provide a rigorous foundation for conceptualizing social complexity, the potential benefits of incorporating them and how existing measures do (or do not) include them. Ultimately, researchers need to critically evaluate any measure of animal social complexity in order to balance the biological relevance of the aspect of sociality they are quantifying with the feasibility of obtaining enough data.

With the rise of the South–South Development Cooperation (SSDC), the international development community has entered into a new paradigm of development cooperation. The Organisation for Economic Co...

While it is tempting in experimental practice to seek as high a data rate as possible, oversampling can become an issue if one takes measurements too densely. These effects can take many forms, some of which are easy to detect: e.g., when the data sequence contains multiple copies of the same measured value. In other situations, as when there is mixing$-$in the measurement apparatus and/or the system itself$-$oversampling effects can be harder to detect. We propose a novel, model-free technique to detect local mixing in time series using an information-theoretic technique called permutation entropy. By varying the temporal resolution of the calculation and analyzing the patterns in the results, we can determine whether the data are mixed locally, and on what scale. This can be used by practitioners to choose appropriate lower bounds on scales at which to measure or report data. After validating this technique on several synthetic examples, we demonstrate its effectiveness on data from a chemistry experiment, methane records from Mauna Loa, and an Antarctic ice core., Comment: Submission for Physical Review E

We propose a curvature-based approach for choosing a good value for the time-delay parameter τ in delay reconstructions. The idea is based on the effects of the delay on the geometry of the reconstructions. If the delay is too small, the reconstructed dynamics are flattened along the main diagonal of the embedding space; too-large delays, on the other hand, can overfold the dynamics. Calculating the curvature of a two-dimensional delay reconstruction is an effective way to identify these extremes and to find a middle ground between them: both the sharp reversals at the extremes of an insufficiently unfolded reconstruction and the bends in an overfolded one create spikes in the curvature. We operationalize this observation by computing the mean Menger curvature of a trajectory segment on 2D reconstructions as a function of time delay. We show that the minimum of these values gives an effective heuristic for choosing the time delay. In addition, we show that this curvature-based heuristic is useful even in cases where the customary approach, which uses average mutual information, fails-e.g., noisy or filtered data.

From biofilms to whale pods, organisms have repeatedly converged on sociality as a strategy to improve individual fitness. Yet, it remains challenging to identify the most important drivers—and by extension, the evolutionary mechanisms—of sociality for particular species. Here, we present a conceptual framework, literature review, and model demonstrating that the direction and magnitude of the response of group size to sudden resource shifts provides a strong indication of the underlying drivers of sociality. We catalog six functionally distinct mechanisms related to the acquisition of resources, and we model these mechanisms’ effects on the survival of individuals foraging in groups. We find that whether, and to what degree, optimal group size increases, decreases, or remains constant when resource abundance declines depends strongly on the dominant mechanism. Existing empirical data support our model predictions, and we demonstrate how our framework can be used to predict the dominant social benefit for particular species. Together, our framework and results show that a single easily measurable characteristic, namely, group size under different resource abundances, can illuminate the potential drivers of sociality across the tree of life.

Scaling regions -- intervals on a graph where the dependent variable depends linearly on the independent variable -- abound in dynamical systems, notably in calculations of invariants like the correlation dimension or a Lyapunov exponent. In these applications, scaling regions are generally selected by hand, a process that is subjective and often challenging due to noise, algorithmic effects, and confirmation bias. In this paper, we propose an automated technique for extracting and characterizing such regions. Starting with a two-dimensional plot -- e.g., the values of the correlation integral, calculated using the Grassberger-Procaccia algorithm over a range of scales -- we create an ensemble of intervals by considering all possible combinations of endpoints, generating a distribution of slopes from least-squares fits weighted by the length of the fitting line and the inverse square of the fit error. The mode of this distribution gives an estimate of the slope of the scaling region (if it exists). The endpoints of the intervals that correspond to the mode provide an estimate for the extent of that region. When there is no scaling region, the distributions will be wide and the resulting error estimates for the slope will be large. We demonstrate this method for computations of dimension and Lyapunov exponent for several dynamical systems, and show that it can be useful in selecting values for the parameters in time-delay reconstructions.

Permutation entropy techniques can be useful in identifying anomalies in paleoclimate data records, including noise, outliers, and post-processing issues. We demonstrate this using weighted and unweighted permutation entropy of water-isotope records in a deep polar ice core. In one region of these isotope records, our previous calculations revealed an abrupt change in the complexity of the traces: specifically, in the amount of new information that appeared at every time step. We conjectured that this effect was due to noise introduced by an older laboratory instrument. In this paper, we validate that conjecture by re-analyzing a section of the ice core using a more-advanced version of the laboratory instrument. The anomalous noise levels are absent from the permutation entropy traces of the new data. In other sections of the core, we show that permutation entropy techniques can be used to identify anomalies in the raw data that are not associated with climatic or glaciological processes, but rather effects occurring during field work, laboratory analysis, or data post-processing. These examples make it clear that permutation entropy is a useful forensic tool for identifying sections of data that require targeted re-analysis---and can even be useful in guiding that analysis., 15 pages, 7 figures

Understanding the mechanics behind the coordinated movement of mobile animal groups (collective motion) provides key insights into their biology and ecology, while also yielding algorithms for bio-inspired technologies and autonomous systems. It is becoming increasingly clear that many mobile animal groups are composed of heterogeneous individuals with differential levels and types of influence over group behaviors. The ability to infer this differential influence, or leadership, is critical to understanding group functioning in these collective animal systems. Due to the broad interpretation of leadership, many different measures and mathematical tools are used to describe and infer "leadership", e.g., position, causality, influence, information flow. But a key question remains: which, if any, of these concepts actually describes leadership? We argue that instead of asserting a single definition or notion of leadership, the complex interaction rules and dynamics typical of a group implies that leadership itself is not merely a binary classification (leader or follower), but rather, a complex combination of many different components. In this paper we develop an anatomy of leadership, identify several principle components and provide a general mathematical framework for discussing leadership. With the intricacies of this taxonomy in mind we present a set of leadership-oriented toy models that should be used as a proving ground for leadership inference methods going forward. We believe this multifaceted approach to leadership will enable a broader understanding of leadership and its inference from data in mobile animal groups and beyond., 13 pages, 3 figures

Successfully predicting the future states of systems that are complex, stochastic, and potentially chaotic is a major challenge. Model forecasting error (FE) is the usual measure of success; however model predictions provide no insights into the potential for improvement. In short, the realized predictability of a specific model is uninformative about whether the system is inherently predictable or whether the chosen model is a poor match for the system and our observations thereof. Ideally, model proficiency would be judged with respect to the systems’ intrinsic predictability, the highest achievable predictability given the degree to which system dynamics are the result of deterministic vs. stochastic processes. Intrinsic predictability may be quantified with permutation entropy (PE), a model‐free, information‐theoretic measure of the complexity of a time series. By means of simulations, we show that a correlation exists between estimated PE and FE and show how stochasticity, process error, and chaotic dynamics affect the relationship. This relationship is verified for a data set of 461 empirical ecological time series. We show how deviations from the expected PE–FE relationship are related to covariates of data quality and the nonlinearity of ecological dynamics. These results demonstrate a theoretically grounded basis for a model‐free evaluation of a system's intrinsic predictability. Identifying the gap between the intrinsic and realized predictability of time series will enable researchers to understand whether forecasting proficiency is limited by the quality and quantity of their data or the ability of the chosen forecasting model to explain the data. Intrinsic predictability also provides a model‐free baseline of forecasting proficiency against which modeling efforts can be evaluated., Ecological Monographs, 89 (2), ISSN:0012-9615, ISSN:1557-7015, ISSN:1741-7015

In space mission trajectory planning in dynamic environments, such as at asteroids, scenarios leading to failure must be discovered. Given an initial state of a spacecraft about an asteroid, failure can be simply quantified as impact of the vehicle with the asteroid or escape of the vehicle from the asteroid. For mission planning and execution purposes it is necessary to perform maneuvers to avoid such outcomes, however the overall set of possible maneuvers that either avoid impact or escape can be a complex set that cannot be analytically characterized. This paper introduces a reachable set explorer (RSE) for exploring the reachable set of a spacecraft—the set of trajectories under a range of ΔV expenditures. This approach is applied to the circular restricted 3-body problem (CR3BP) where a brute-force approach is intractable. RSE focuses on the boundaries between impact, escape, and in-system regions, known as the end-result regions.

Paleoclimate records are rich sources of information about the past history of the Earth system. Information theory provides a new means for studying these records. We demonstrate that weighted permutation entropy of water-isotope data from the West Antarctica Ice Sheet (WAIS) Divide ice core reveals meaningful climate signals in this record. We find that this measure correlates with accumulation (meters of ice equivalent per year) and may record the influence of geothermal heating effects in the deepest parts of the core. Dansgaard-Oeschger and Antarctic Isotope Maxima events, however, do not appear to leave strong signatures in the information record, suggesting that these abrupt warming events may actually be predictable features of the climate's dynamics. While the potential power of information theory in paleoclimatology is significant, the associated methods require well-dated and high-resolution data. The WAIS Divide core is the first paleoclimate record that can support this kind of analysis. As more high-resolution records become available, information theory could become a powerful forensic tool in paleoclimate science.

Delay-coordinate reconstruction is a proven modeling strategy for building effective forecasts of nonlinear time series. The first step in this process is the estimation of good values for two parameters, the time delay and the embedding dimension. Many heuristics and strategies have been proposed in the literature for estimating these values. Few, if any, of these methods were developed with forecasting in mind, however, and their results are not optimal for that purpose. Even so, these heuristics-intended for other applications-are routinely used when building delay coordinate reconstruction-based forecast models. In this paper, we propose an alternate strategy for choosing optimal parameter values for forecast methods that are based on delay-coordinate reconstructions. The basic calculation involves maximizing the shared information between each delay vector and the future state of the system. We illustrate the effectiveness of this method on several synthetic and experimental systems, showing that this metric can be calculated quickly and reliably from a relatively short time series, and that it provides a direct indication of how well a near-neighbor based forecasting method will work on a given delay reconstruction of that time series. This allows a practitioner to choose reconstruction parameters that avoid any pathologies, regardless of the underlying mechanism, and maximize the predictive information contained in the reconstruction.

Paleoclimate records are extremely rich sources of information about the past history of the Earth system. We take an information-theoretic approach to analyzing data from the WAIS Divide ice core, the longest continuous and highest-resolution water isotope record yet recovered from Antarctica. We use weighted permutation entropy to calculate the Shannon entropy rate from these isotope measurements, which are proxies for a number of different climate variables, including the temperature at the time of deposition of the corresponding layer of the core. We find that the rate of information production in these measurements reveals issues with analysis instruments, even when those issues leave no visible traces in the raw data. These entropy calculations also allow us to identify a number of intervals in the data that may be of direct relevance to paleoclimate interpretation, and to form new conjectures about what is happening in those intervals—including periods of abrupt climate change.

Recent evidence suggests that pulmonary vein isolation (PVI) may perturb the electrophysiological substrate for maintenance of atrial fibrillation (AF). Our previous work indicates that information theory metrics can quantify electrical communications during arrhythmia. We hypothesized that PVI ‘rewires’ the electrical communication network during AF such that the topology exhibits higher levels of small-world network properties, with higher clustering coefficient and lower path length, than would be expected by chance. Thirteen consecutive patients (n=6 with prior PVI and n=7 without) underwent AF ablation using a 64-electrode basket catheter in the left atrium. Multielectrode recording was performed during AF for 60 seconds, followed by PVI. Mutual information was calculated from the time series between each pair of electrodes using the Kraskov-Stögbauer-Grassberger estimator. The all-to-all mutual information matrix (64x64; Figure, upper panels) was thresholded by the median and standard deviations of mutual information to build a binary adjacency matrix for electrical communication networks. The properties of small-world network ( swn ; ‘small-world-ness’) were quantified by the ratio of the observed average clustering coefficient to that of a random network over the ratio of the observed average path length to that of a random network. swn was expressed in normal Z standard deviation units. As the binarizing threshold increased, the Z-score of swn decreased (Figure, lower panel). However, the Z-score at each threshold value was consistently higher with prior PVI than those without (pswn of electrical communication network may be a promising metric to quantify substrate modification.

Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a number of free parameters and the computation of homology for a large number of simplices can be expensive. This paper is a study of how to avoid a full (diffeomorphic) reconstruction and how to decrease the computational burden. Using trajectories from the classic Lorenz system, we reconstruct the dynamics using the method of delays, then build a parsimonious simplicial complex---the "witness complex"---to compute its homology. Surprisingly, we find that the witness complex correctly resolves the homology of the underlying invariant set from noisy samples of that set even if the reconstruction dimension is well below the thresholds specified in the embedding theorems for assuring topological conjugacy between the true and reconstructed dynamics. We conjecture that this is because the requirements for reconstructing homology, are less stringent than those in the embedding theorems. In particular, to faithfully reconstruct the homology, a homeomorphism is sufficient---as opposed to a diffeomorphism, as is necessary for the full dynamics. We provide preliminary evidence that a homeomorphism, in the form of a delay-coordinate reconstruction map, may manifest at a lower dimension than that required to achieve an embedding., 21 pages, 10 figures

Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical communication using information theory metrics in 2-dimensional cell lattice models of cardiac excitation propagation. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell was calculated from the time series during four clinically important heart rhythms: normal heartbeat, anatomical reentry, spiral reentry, and multiple reentry. We also used mutual information to perform spatial profiling of communication during these cardiac arrhythmias. We found that information sharing between cells was spatially heterogeneous. In addition, cardiac arrhythmia significantly impacted information sharing within the heart. Entropy localized the path of the drifting core of spiral reentry, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques., 26 pages (including Appendix), 6 figures, 8 videos (not uploaded due to size limitation)

Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from scalar time-series data---e.g., via delay-coordinate embedding---can be a real challenge. In this paper, we show that forecast models that employ incomplete embeddings of the dynamics can produce surprisingly accurate predictions of the state of a dynamical system. In particular, we demonstrate the effectiveness of a simple near-neighbor forecast technique that works with a two-dimensional embedding. Even though correctness of the topology is not guaranteed for incomplete reconstructions like this, the dynamical structure that they capture allows for accurate predictions---in many cases, even more accurate than predictions generated using a full embedding. This could be very useful in the context of real-time forecasting, where the human effort required to produce a correct delay-coordinate embedding is prohibitive., Comment: 13 pages, 7 figures, 3 tables

Persistent atrial fibrillation (AF) can be viewed as disintegrated patterns of information transmission by action potential across the communication network consisting of nodes linked by functional connectivity. To test the hypothesis that ablation of persistent AF is associated with improvement in both local and global connectivity within the communication networks, we analyzed multi-electrode basket catheter electrograms of 22 consecutive patients (63.5 ± 9.7 years, 78% male) during persistent AF before and after the focal impulse and rotor modulation-guided ablation. Eight patients (36%) developed recurrence within 6 months after ablation. We defined communication networks of AF by nodes (cardiac tissue adjacent to each electrode) and edges (mutual information between pairs of nodes). To evaluate patient-specific parameters of communication, thresholds of mutual information were applied to preserve 10% to 30% of the strongest edges. There was no significant difference in network parameters between both atria at baseline. Ablation effectively rewired the communication network of persistent AF to improve the overall connectivity. In addition, successful ablation improved local connectivity by increasing the average clustering coefficient, and also improved global connectivity by decreasing the characteristic path length. As a result, successful ablation improved the efficiency and robustness of the communication network by increasing the small-world index. These changes were not observed in patients with AF recurrence. Furthermore, a significant increase in the small-world index after ablation was associated with synchronization of the rhythm by acute AF termination. In conclusion, successful ablation rewires communication networks during persistent AF, making it more robust, efficient, and easier to synchronize. Quantitative analysis of communication networks provides not only a mechanistic insight that AF may be sustained by spatially localized sources and global connectivity, but also patient-specific metrics that could serve as a valid endpoint for therapeutic interventions.

This paper provides insight into when, why, and how forecast strategies fail when they are applied to complicated time series. We conjecture that the inherent complexity of real-world time-series data---which results from the dimension, nonlinearity, and non-stationarity of the generating process, as well as from measurement issues like noise, aggregation, and finite data length---is both empirically quantifiable and directly correlated with predictability. In particular, we argue that redundancy is an effective way to measure complexity and predictive structure in an experimental time series and that weighted permutation entropy is an effective way to estimate that redundancy. To validate these conjectures, we study 120 different time-series data sets. For each time series, we construct predictions using a wide variety of forecast models, then compare the accuracy of the predictions with the permutation entropy of that time series. We use the results to develop a model-free heuristic that can help practitioners recognize when a particular prediction method is not well matched to the task at hand: that is, when the time series has more predictive structure than that method can capture and exploit., Comment: 23 pages, 8 figures, 1 table

Community detection in online social networks is typically based on the analysis of the explicit connections between users, such as "friends" on Facebook and "followers" on Twitter. But online users often have hundreds or even thousands of such connections, and many of these connections do not correspond to real friendships or more generally to accounts that users interact with. We claim that community detection in online social networks should be question-oriented and rely on additional information beyond the simple structure of the network. The concept of 'community' is very general, and different questions such as "whom do we interact with?" and "with whom do we share similar interests?" can lead to the discovery of different social groups. In this paper we focus on three types of communities beyond structural communities: activity-based, topic-based, and interaction-based. We analyze a Twitter dataset using three different weightings of the structural network meant to highlight these three community types, and then infer the communities associated with these weightings. We show that the communities obtained in the three weighted cases are highly different from each other, and from the communities obtained by considering only the unweighted structural network. Our results confirm that asking a precise question is an unavoidable first step in community detection in online social networks, and that different questions can lead to different insights about the network under study., Comment: 22 pages, 4 figures, 1 tables

The purpose of this study was to determine differences in insertional articular trauma in infrapatellar tibial portal and suprapatellar portal intramedullary tibial nail insertion techniques. A cadaveric study was performed on 10 matched pairs of fresh-frozen adult cadaver lower extremities with intact extensor mechanisms. Two study groups with 10 limbs each were created: left lower limbs were treated with a standard medial parapatellar nailing portal and right lower limbs were treated with a suprapatellar tibial nailing portal. Start points were created under fluoroscopic guidance in anteroposterior and mediolateral planes. A start wire was placed and opening reaming was performed on the specimens using instrumentation specific to the nailing portal. Specimens were then dissected by medial parapatellar arthrotomy, revealing the intra-articular condition of the knee structures. The border of the tibial entry reamer hole was measured to the anterior horns of the menisci, anterior cruciate ligament root, and intermeniscal ligament using a digital caliper accurate to 0.02 mm. The structure was considered damaged if the structure was obviously damaged on visual inspection or if a measurement was less than 1 mm. Impact to intra-articular structures was numerically lower in the suprapatellar group (2/10) compared with the infrapatellar group (4/10), but the difference was not statistically significant between the 2 groups ( P =.629). The suprapatellar portal approach to the tibial start point demonstrated a lower overall incidence of damage to intra-articular structures, but no significant statistical difference existed between the 2 treatment groups.

Plaster has been used for centuries as a stiffening agent to treat fractures and other musculoskeletal conditions that require rest, immobilization, or correction of a deformity. Despite modern metallurgy and internal stabilization, plaster casts and splints remain an important means of external stabilization. Casting is a dying art as modern internal and external fixation replace external immobilization. Proper casting technique is paramount. This manuscript outlines the history and chemistry of immobilization materials and techniques as well as the differences among them and the advantages and disadvantages of each.Historical references, peer-reviewed journals, textbooks, and primary sources were reviewed to provide data for this review.The history of immobilization reveals a progressive development and refinement of materials that culminated in Mathijsen's plaster bandage in 1851. In 1798, calcium sulfate (plaster of Paris) was introduced. By 1927, crinoline rolls dipped in plaster treated with binding agents facilitated application. Synthetic casting "tapes" (45% polyurethane resin and 55% fiberglass) were introduced in the 1970s. Splinting techniques are ancient, with development spurred by treatment of war wounds. Plaster relies on soft-tissue contact to maintain rigidity. There are well-known advantages, disadvantages, and complications of plaster management. Casting materials all create an exothermic reaction. Burns are associated with water temperatures ofgt;24°C, more than eight layers (ply), and inadequate ventilation. The maximum water temperature must be lower with fiberglass casts. Plaster was the definitive management for most fractures for over 100 years until it was replaced by modern surgical techniques involving internal fixation in the latter part of the twentieth century.Plaster casts and splints remain an important treatment method for acute and chronic orthopaedic conditions.

We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete-time dynamical system in which each time step corresponds to the application of one of the finite collection of maps. The maps, which represent distinct dynamical regimes, may be selected deterministically or stochastically. Given a time series from an IFS, our algorithm detects the sequence of regime switches under the assumption that each map is continuous. This method is tested on a simple example and an experimental computer performance data set. This methodology has a wide range of potential uses: from change-point detection in time-series data to the field of digital communications.

Background: Plaster has been used for centuries as a stiffening agent to treat fractures and other musculoskeletal conditions that require rest, immobilization, or correction of a deformity. Despite modern metallurgy and internal stabilization, plaster casts and splints remain an important means of external stabilization. Casting is a dying art as modern internal and external fixation replace external immobilization. Proper casting technique is paramount. This manuscript outlines the history and chemistry of immobilization materials and techniques as well as the differences among them and the advantages and disadvantages of each. Methods: Historical references, peer-reviewed journals, textbooks, and primary sources were reviewed to provide data for this review. Results: The history of immobilization reveals a progressive development and refinement of materials that culminated in Mathijsen’s plaster bandage in 1851. In 1798, calcium sulfate (plaster of Paris) was introduced. By 1927, crinoline rolls dipped in plaster treated with binding agents facilitated application. Synthetic casting “tapes” (45% polyurethane resin and 55% fiberglass) were introduced in the 1970s. Splinting techniques are ancient, with development spurred by treatment of war wounds. Plaster relies on soft-tissue contact to maintain rigidity. There are well-known advantages, disadvantages, and complications of plaster management. Casting materials all create an exothermic reaction. Burns are associated with water temperatures of >24°C, more than eight layers (ply), and inadequate ventilation. The maximum water temperature must be lower with fiberglass casts. Plaster was the definitive management for most fractures for over 100 years until it was replaced by modern surgical techniques involving internal fixation in the latter part of the twentieth century. Conclusions: Plaster casts and splints remain an important treatment method for acute and chronic orthopaedic conditions.