Energy Minimization Strategy Research Articles

Multiscale molecular modeling of chromatin with MultiMM: From nucleosomes to the whole genome

Motivation: We present a user-friendly 3D chromatin simulation model for the human genome based on OpenMM, addressing the challenges posed by existing models with use-specific implementations. Our approach employs a multi-scale energy minimization strategy, capturing chromatin's hierarchical structure. Initiating with a Hilbert curve-based structure, users can input files specifying nucleosome positioning, loops, compartments, or subcompartments.Results: The model utilizes an energy minimization approach with a large choice of numerical integrators, providing the entire genome's structure within minutes. Output files include the generated structures for each chromosome, offering a versatile and accessible tool for chromatin simulation in bioinformatics studies. Furthermore, MultiMM is capable of producing nucleosome-resolution structures by making simplistic geometric assumptions about the structure and the density of nucleosomes on the DNA.Code availability: Open-source software and the manual are freely available on https://github.com/SFGLab/MultiMM or via pip https://pypi.org/project/MultiMM/.

Model-guided navigation of magnetic soft guidewire for safe endovascular surgery

The emergent magnetic soft guidewires (MSGs) that can be remotely navigated by magnetic fields hold great promise in minimally invasive endovascular surgery. However, existing models of MSGs have been limited in practical applications, largely due to insufficient consideration of contacts within actual endovascular settings. In this work, we present a theoretical model incorporating the magneto-mechanical behavior of MSGs with these critical contacts, allowing for a detailed evaluation of their navigation capability in various vascular configurations. Specifically, we categorize blood vessels into two main types: curved vessels and bifurcated vessels and identify a critical contact angle between the MSG tip and the vessel wall, beyond which the vascular damage may occur. By applying the principles of hard-magnetic elastica to account for the large deflection of MSGs, we develop a numerical framework that employs polynomial approximations and an energy minimization strategy. Through parametric analysis of different vessel types, we propose a method for adjusting magnetic fields for the safe navigation of MSGs through them. Our theoretical predictions have been substantiated by finite element modeling and experimental validation. The results of this paper offer a solid foundation for establishing practical guidelines for remote MSG navigation with minimal risk of vascular damage.

Population level behavioural responses to variation in habitat quality across multiple locations in a fragmented landscape

Population level behavioural responses to variation in habitat quality across multiple locations in a fragmented landscape

An energy minimization strategy based on transmission time and re‐clustering (TTRC) for wireless sensor network

AbstractThe Wireless Sensor Network (WSN) is an emerging technology with diverse applications, ranging from industrial settings to environmental monitoring, healthcare, and remote surveillance. In this paper, the focus lies on the minimization of energy consumption during packet transmission, achieved through two primary strategies: (1) Reduction of the transmission distance for packets through the implementation of re‐clustering. (2) Allocation of increased time to those child nodes which necessitate less energy for transmission. Simulation outcomes demonstrate that the proposed transmission time and re‐clustering (TTRC) algorithm effectively harnesses in excess of 99% of the total network energy, marking an improvement of 14.05% to 15.57% over existing approaches. Furthermore, the TTRC algorithm achieves a substantial enhancement in packet delivery, ranging from 32.31% to 58.54%, coupled with a latency reduction spanning from 21.47% to 32.00%. Moreover, the network's lifestime is prolonged by 28.57% to 28.99% through the application of this algorithm.

Divergent migration routes reveal contrasting energy-minimization strategies to deal with differing resource predictability

BackgroundSeasonal long-distance movements are a common feature in many taxa allowing animals to deal with seasonal habitats and life-history demands. Many species use different strategies to prioritize time- or energy-minimization, sometimes employing stop-over behaviours to offset the physiological burden of the directed movement associated with migratory behaviour. Migratory strategies are often limited by life-history and environmental constraints, but can also be modulated by the predictability of resources en route. While theory on population-wide strategies (e.g. energy-minimization) are well studied, there are increasing evidence for individual-level variation in movement patterns indicative of finer scale differences in migration strategies.MethodsWe aimed to explore sources of individual variation in migration strategies for long-distance migrators using satellite telemetry location data from 41 narwhal spanning a 21-year period. Specifically, we aimed to determine and define the long-distance movement strategies adopted and how environmental variables may modulate these movements. Fine-scale movement behaviours were characterized using move-persistence models, where changes in move-persistence, highlighting autocorrelation in a movement trajectory, were evaluated against potential modulating environmental covariates. Areas of low move-persistence, indicative of area-restricted search-type behaviours, were deemed to indicate evidence of stop-overs along the migratory route.ResultsHere, we demonstrate two divergent migratory tactics to maintain a similar overall energy-minimization strategy within a single population of narwhal. Narwhal migrating offshore exhibited more tortuous movement trajectories overall with no evidence of spatially-consistent stop-over locations across individuals. Nearshore migrating narwhal undertook more directed routes, contrasted by spatially-explicit stop-over behaviour in highly-productive fjord and canyon systems along the coast of Baffin Island for periods of several days to several weeks.ConclusionsWithin a single population, divergent migratory tactics can achieve a similar overall energy-minimizing strategy within a species as a response to differing trade-offs between predictable and unpredictable resources. Our methodological approach, which revealed the modulators of fine-scale migratory movements and predicted regional stop-over sites, is widely applicable to a variety of other aquatic and terrestrial species. Quantifying marine migration strategies will be key for adaptive conservation in the face of climate change and ever increasing human pressures.

New approach to improve power consumption associated with blockchain in WSNs.

Nowadays, Wireless Sensor Networks (WSNs) are widely used for collecting, communicating, and sharing information in various applications. Due to its limited resources in terms of computation, power, battery lifetime, and memory storage for sensor nodes, it is difficult to add confidentiality and integrity security features. It is worth noting that blockchain (BC) technology is one of the most promising technologies, because it provides security, avoids centralization, and a trusted third party. However, to apply BCs in WSNs is not an easy task because BC is typically resource-hungry for energy, computation, and memory. In this paper, the additional complication of adding BC in WSNs is compensated by an energy minimization strategy, which basically depends on minimizing the processing load of generating the blockchain hash value, and encrypting and compressing the data that travel from the cluster-heads to the base station to reduce the overall traffic, leading to reduced energy per node. A specific (dedicated) circuit is designed to implement the compression technique, generate the blockchain hash values and data encryption. The compression algorithm is based on chaotic theory. A comparison of the power consumed by a WSN using a blockchain implementation with and without the dedicated circuit, illustrates that the hardware design contributes considerably to reduce the consumption of power. When simulating both approaches, the energy consumed when replacing functions by hardware decreases up to 63%.

Research on identification of server energy consumption characteristics via dirichlet max-margin factor analysis similarity preservation model

Growing server energy consumption is a significant environmental issue, and mitigating it is a key technological challenge. Application-level energy minimization strategies depend on accurate modeling of energy consumption during an application’s execution. This paper presents a theoretical and experimental study of the dpMMSPFA model in the field of server energy consumption identification. The dpMMSPFA for classification of hidden spaces uses latent variable support vector machines (LVSVM) to learn discriminative subspaces with maximal marginal constraints. The factor analysis (FA) model, the similarity preservation (SP) item, the Dirichlet process mixture (DPM) model, and the maximal marginal classifier are jointly learned beneath a unified Bayesian architecture to advance classification of predictive power. The parameters of the proposed model can be inferred by the simple and efficient Gibbs sampling in terms of the conditional conjugate property. Empirical results on various datasets demonstrate that 1) max-margin joint learning can significantly improve the prediction performance of the model implemented by feature extraction and classification separately and meanwhile retain the generative ability; 2) dpMMSPFA is superior to MMFA when employing SP item and Dirichlet process mixture as prior knowledge; 3) the classification of dpMMSPFA model can often achieve better results on benchmark and measured energy server consumption datasets; 4) and the recognition rate can reach as high as 95.79% at 10 components, far better than other models on measured energy server consumption datasets.

An energy minimization strategy based on an improved nonlinear conjugate gradient method for accelerating the charged polymer dynamics simulation.

Using a hybrid simulation method that combines a non-linear conjugate gradient (NCG) method for solving large-scale unconstrained optimization problems with a Brownian dynamics (BD) model for polymer chains, we investigate the pre-equilibrium simulation of charged polymers in different dielectric systems from an energy minimization perspective. We propose an improved NCG coefficient (βLPRPk) that satisfies a sufficient descent condition with a greater parameter under a strong Wolfe line search and converges globally for nonconvex minimization. Furthermore, preliminary numerical results show that the βLPRPk coefficient is more efficient than many existing NCG coefficients for a large number of practical test problems from our model. We further compare the performance of the improved NCG method with that of other mainstream numerical methods in energy minimization, and the simulation results suggest that the NCG method is more competitive in terms of cost-effectiveness. Importantly, we apply the geometrically optimized configuration obtained by performing the NCG method to the pre-equilibrium simulation, and the numerical results show that it increases the computational efficiency of a pure solvent and biomolecule-solution systems at most by about 32 and 70 times, respectively, with the relative energy errors being controlled below 1 × 10-2 and 4.5 × 10-3, respectively. More importantly, the final pre-equilibrium configuration of the BD simulation that performs energy minimization and the traditional BD simulation matched closely.

Second-order flows for computing the ground states of rotating Bose-Einstein condensates

Second-order flows in this paper refer to some artificial evolutionary differential equations involving second-order time derivatives distinguished from gradient flows which are considered to be first-order flows. This is a popular topic due to the recent advances of inertial dynamics with damping in convex optimization. Mathematically, the ground state of a rotating Bose-Einstein condensate (BEC) can be modeled as a minimizer of the Gross-Pitaevskii energy functional with angular momentum rotational term under the normalization constraint. We introduce two types of second-order flows as energy minimization strategies for this constrained non-convex optimization problem, in order to approach the ground state. The proposed artificial dynamics are novel second-order nonlinear hyperbolic partial differential equations with dissipation. Several numerical discretization schemes are discussed, including explicit and semi-implicit methods for temporal discretization, combined with a Fourier pseudospectral method for spatial discretization. These provide us a series of efficient and robust algorithms for computing the ground states of rotating BECs. Particularly, the newly developed algorithms turn out to be superior to the state-of-the-art numerical methods based on the gradient flow. In comparison with the gradient flow type approaches: When explicit temporal discretization strategies are adopted, the proposed methods allow for larger stable time step sizes; While for semi-implicit discretization, using the same step size, a much smaller number of iterations are needed for the proposed methods to reach the stopping criterion, and every time step encounters almost the same computational complexity. Rich and detailed numerical examples are documented for verification and comparison.

A neuro evolutionary scheme for improved IoT energy efficiency in smart cities

With the emergence of Internet of Things (IoT) and allied applications for smart cities, sustainability goals have seen a prominent emphasis. This paper focuses on the energy efficiency aspect of such sustainable smart city goals. Although energy efficiency has been studied at different levels of a smart city’s Information and Communication Technology (ICT) infrastructure, this paper specially focuses on device level energy minimization strategy by means of modelling the energy consumption while accounting for the Clusterheads (CluH) and duty cycling and thereby using evolutionary algorithms. In this paper, a Genetic Algorithm (GA) and a hybrid Artificial Neural Network based Particle Swarm Optimization (PSO), namely Feed Forward Neural Network based PSO(FFNN-PSO) has been used to solve the energy minimization problem. Simulation experiments carried out for different scenarios with varying configuration demonstrate the efficacy of the hybrid neuro evolutionary scheme.

Hierarchical energy management strategy for fuel cell/ultracapacitor/battery hybrid vehicle with life balance control

Fuel cell (FC) is an ideal power source for electric vehicles with high efficiency and little pollution. However, with its weak dynamic reaction, it needs to be used in combination with other energy storage devices, and the coupling of multiple energy sources makes it difficult to fully utilize the system performance. Meanwhile, the cost and durability of FC hinder its commercialization. This paper takes the composite energy storage system composed of FC, battery (BAT) and ultracapacitor (UC) as the research object. In order to improve the system performance, a hierarchical energy management strategy is proposed based on the analysis of the relationship between UC output power and vehicle demand power under dynamic programming (DP) strategy, taking into account the vehicle energy consumption and energy source lifetime. A fuzzy control based on speed prediction and a dynamic state-of-charge (SOC) threshold control optimization algorithm of UC based on working condition recognition are designed to optimize the hierarchical control strategy. In the upper layer strategy, for realizing the online real-time distribution of UC output power, the generalized regression neural network is used to learn the relationship between UC output power and demand power under DP strategy; in the lower layer strategy, the power of the FC and BAT is distributed using an equivalent energy minimization strategy. Based on above strategy, this paper proposes a life balance control strategy for energy sources to maximize the lifetime of the composite energy storage system. Simulation and experimental results show that the proposed strategy has a comparable life-cycle average operating cost to the DP strategy with better life mileage.

Hybrid Power Management Strategy with Fuel Cell, Battery, and Supercapacitor for Fuel Economy in Hybrid Electric Vehicle Application

The power management strategy (PMS) is intimately linked to the fuel economy in the hybrid electric vehicle (HEV). In this paper, a hybrid power management scheme is proposed; it consists of an adaptive neuro-fuzzy inference method (ANFIS) and the equivalent consumption minimization technique (ECMS). Artificial intelligence (AI) is a key development for managing power among various energy sources. The hybrid power supply is an eco-acceptable system that includes a proton exchange membrane fuel cell (PEMFC) as a primary source and a battery bank and ultracapacitor as electric storage systems. The Haar wavelet transform method is used to calculate the stress σ on each energy source. The proposed model is developed in MATLAB/Simulink software. The simulation results show that the proposed scheme meets the power demand of a typical driving cycle, i.e., Highway Fuel Economy Test Cycle (HWFET) and Worldwide Harmonized Light Vehicles Test Procedures (WLTP—Class 3), for testing the vehicle performance, and assessment has been carried out for various PMS based on the consumption of hydrogen, overall efficiency, state of charge of ultracapacitors and batteries, stress on hybrid sources and stability of the DC bus. By combining ANFIS and ECMS, the consumption of hydrogen is minimized by 8.7% compared to the proportional integral (PI), state machine control (SMC), frequency decoupling fuzzy logic control (FDFLC), equivalent consumption minimization strategy (ECMS) and external energy minimization strategy (EEMS).

Time and energy minimization strategy codetermine the loop migration of demoiselle cranes around the Himalayas.

Tens of thousands of demoiselle cranes' crossing the Himalayas to the Indian subcontinent have been reported for decades, but their exact spring migration route remained a mystery until our previous study found they made a detour in spring along the western edge of the Himalayas and crossed the Mongolian Plateau to their breeding areas based on satellite telemetry of 3 birds. To corroborate the loop migration pattern and explore whether demoiselle crane's loop migration route is shaped by time- and energy-minimization strategies in spring and autumn and how the temporal and spatial variation of environmental conditions contribute to crane's selection of migration routes, we tracked 11 satellite-tagged demoiselle cranes from their breeding area in China and Russia, simulated 2 pseudo migration routes, and then compared the environmental conditions, time, and energy cost between true and pseudo routes in the same season. Results show that demoiselles' spring migration obeyed time-minimization hypothesis, avoiding the colder Qinghai-Tibet Plateau, benefited by abundant food and higher thermal and orographic uplift along the route; autumn migration follows energy-minimization hypothesis with the shorter route. Our research will contribute to uncover the mechanical reasons why demoiselle crane avoids crossing the giant barrier of the Himalayas in spring, and shapes a loop migration route.

Second-Order Flows for Computing the Ground States of Rotating Bose-Einstein Condensates

Second-order flows in this paper refer to some artificial evolutionary differential equations involving second-order time derivatives distinguished from gradient flows which are considered to be first-order flows. This is a popular topic due to the recent advances of inertial dynamics with damping in convex optimization. Mathematically, the ground state of a rotating Bose-Einstein condensate (BEC) can be modelled as a minimizer of the Gross-Pitaevskii energy functional with angular momentum rotational term under the normalization constraint. We introduce two types of second-order flows as energy minimization strategies for this constrained non-convex optimization problem, in order to approach the ground state. The proposed artificial dynamics are novel second-order nonlinear hyperbolic partial differential equations with dissipation. Several numerical discretization schemes are discussed, including explicit and semi-implicit methods for temporal discretization, combined with a Fourier pseudospectral method for spatial discretization. These provide us a series of efficient and robust algorithms for computing the ground states of rotating BECs. Particularly, the newly developed algorithms turn out to be superior to the state-of-the-art numerical methods based on the gradient flow. This is judged by the fact that larger size of time steps can be applied in explicit methods, and much smaller number of time steps are needed in both explicit and semi-implicit discretizations, while every time step encounters almost the same computational complexity in comparison with the respective gradient flow type approaches. Rich and detailed numerical examples are documented for verification and comparison.

ICIC: A Dual Mode Intra-Cluster and Inter-Cluster Energy Minimization Approach for Multihop WSN

Energy minimization is one of the paramount issues in designing of the wireless sensor network and becomes more complex for multi-hop transmission. Furthermore, selection of multi hop route for the packets transmission is also a tedious task. In this paper, we propose an intra-cluster and inter-cluster (ICIC) energy minimization strategy for multihop wireless sensor network (WSN). In the proposed strategy, in intra cluster communication, a dynamic duty cycle allocation based on the cluster head (CH) node distance from the child nodes for the energy minimization is presented. In the inter cluster communication, minimum energy consumption route is chosen for the transmission of packets to base station (BS). The proposed strategy is compared with four state of the art techniques i.e., HEEMP, LEACH, MLEACH, and SEP protocols of clustering. The evaluation of the proposed and existing strategies is done in two different scenarios i.e., number of round and number of nodes. Results of the simulation show that the proposed strategy transmits more packets and has lower number of dead nodes than other strategies. Furthermore, proposed strategy utilizes more network energy and more energy for relaying.

The Indo‐European flyway: Opportunities and constraints reflected by Common Rosefinches breeding across Europe

AbstractAimThe configuration of the earth's landmasses influences global weather systems and spatiotemporal resource availability, thereby shaping biogeographical patterns and migratory routes of animals. Here, we aim to identify potential migratory barriers and corridors, as well as general migration strategies within the understudied Indo‐European flyway.LocationEurope, Central Asia.Major taxon studiedCommon rosefinches.MethodsWe used a combination of theoretical optimization modelling and empirical tracking of Common Rosefinches (Carpodacus erythrinus) breeding across a large latitudinal gradient in Europe. First, we identified optimal migration routes driven by wind and resource availability along the Indo‐European flyway. Second, we tracked rosefinches from five breeding populations using light‐level geolocators. Finally, we compared to what extent empirical tracks overlapped with the modelled optimal routes.ResultsIn autumn, theoretical wind driven migration routes formed a broad‐front corridor connecting Europe and the Indian Subcontinent while the theoretical resource driven routes formed a distinct north‐south divide. The latter pattern also reflected the rosefinch tracks with all but the most southerly breeding birds making a northern detour towards non‐breeding sites in Pakistan and India. In spring, the resource availability model predicted a similar migratory divide, however, the southern route seemed relatively more favourable and closely matched with the optimal wind driven migration routes. Spring tracking data showed larger overlap with the modelled wind driven migration routes compared to the resource driven routes.Main conclusionsOptimal wind and resource driven migration routes along the Indo‐European flyway are seasonally specific and to a large extend do not overlap with one another. Under these conditions, migratory birds adopt seasonally distinct migration strategies following energy minimization strategy in autumn, driven by resource availability, and time minimizing strategy in spring, driven by wind conditions. Our optimal migration models can be applied worldwide and used to validate against empirical data to explain large‐scale biogeographic pattern of migratory animals.

Diet and Activity Budget in Colobus angolensis ruwenzorii at Nabugabo, Uganda: Are They Energy Maximizers?

Introduction: Colobine monkeys are specialized folivores that use foregut fermentation to digest leaves. The slow process of fermentation forces them to spend a lot of time resting and to minimize their energy expenditure to subsist on a lower-quality diet. Methods: We recorded the diet and activity budget of Colobus angolensis ruwenzorii, which form a three-tiered multi-level society, at Lake Nabugabo, Uganda, over 12 months using scan sampling on adults and subadults, to determine whether they utilize the energy minimization strategy typical of colobines. Results: We found that the annual diet was primarily comprised of high-quality food resources (young leaves 65% and fruit 31%), and fruits were the only plant part the monkeysselected when available. Both the fruits and young leaves of some species were preferred food items in some months, and mature leaf consumption correlated negatively with preferred food availability. Mature leaves appear to be a fallback food for this population but are rarely relied upon (3%). The C. a. ruwenzoriiat Nabugabo spent less time resting (40%) and more time moving (25%) than is typical for other species of black-and-white colobus. Discussion/Conclusion: The high-quality diet of this population appears to allow them to utilize an energy maximization strategy. Their reliance on food items that tend to be clumped in space and time likely explains the frequent fission-fusion behaviour that we observe between core units. Our findings demonstrate that the foraging strategies of colobines may be more flexible than was previously thought and illustrate how food availability and distribution can impact primate social organization.

Clonal selection algorithm for energy minimization in software defined networks

With the advancements of Information and Communication Technologies (ICT), large scale distributed computing and massive data center infrastructures are becoming more common these days. Such trends have drastically put a lot of load on the volumes of data transferred over networks, thus necessitating close to capacity link utilizations flexible forwarding decision-making. Software-defined networking (SDN), with its inherent segregation of control and data planes, provides flexible decision making that can leverage the global network information available to the SDN controller for dynamic and accurate solutions. However, contemporary researchers have focused on the flexibility and security aspects of SDN, widely ignoring energy consumption strategies in next-generation IP networks, which otherwise is a crucial driver in any research field. The scanty existing energy minimization strategies are mostly based on aggregate traffic, which leads to imbalanced utilization of links and affects the quality of service (QoS) adversely. In this paper, we leverage SDN’s key benefits for reducing energy network consumption while realizing dynamic load balance with a few QoS constraints. To this end, a multiobjective optimization problem (MOOP) is formulated that attempts to minimize power consumption and link utilization. With different capacities of switches and links, finding optimal configurations and deciding best paths, even for relatively small networks, become computationally challenging and is, in fact, an NP-hard problem. In this paper, we propose to employ the Clonal Selection Algorithm (CSA), a discrete, metaheuristic solution to find out optimal solutions for this MOOP, namely a Clonal Selection based Energy Minimization (CSEM). Simulations have been carried out for testing the efficacy of the proposed CSEM using real-life network topologies and link-traffic data. The results obtained by the proposed CSEM prove to be efficacious, and the same have also been validated with three different benchmark functions to test the suitability of SDN for CSA.

Satellite tracking reveals age and origin differences in migration ecology of two populations of Broad-winged Hawks (Buteo platypterus)

Recent conservation plans for long-distance Neotropical migrant birds have emphasized the importance of understanding the ecology and threats facing a species throughout its life cycle, including migration and overwintering periods. To better understand the ecology of Broad-winged Hawks (Buteo platypterus) during the nonbreeding period, we followed the movements of 14 hawks from 2 breeding populations during July 2014–April 2019 to their overwintering sites. Three juvenile and 8 adult female Broad-winged Hawks were satellite-tracked from Pennsylvania, USA, and 3 adults (2 females and 1 male) were tracked from Alberta, Canada. We documented pre-migratory movements (post-breeding) of 4 of the 14 individuals. Adults initiated fall migration on x = 25 August ± 16.38 d and 2 of the 3 juveniles began fall migration on x = 20 August ± 2 d. Adults had 1–12 (x = 5.0 ± 3.5) stopovers in autumn that lasted for 1–24 d and juveniles had 2–5 (x = 3.0 ± 1.7) stopovers that lasted 2–51 d. Adults from Pennsylvania spent the overwintering period in Nicaragua, Brazil, Peru, and Colombia (n = 8) whereas those from Alberta wintered in Suriname, Venezuela, and Bolivia (n = 3). The distance traveled on autumn migration was greater for Alberta birds (x = 10,021 ± 866 km, n = 3) than for Pennsylvania birds (x = 7,925 ± 1,631 km, n = 8). Migration distance and overwintering region varied by geographic origin with age but with some overlap between the 2 distinct geographic breeding populations. Broad-winged Hawks appear to follow a hybrid time–energy minimization strategy during fall and spring migrations with (1) energy minimization in North America, and (2) time minimization in Mexico and Central America. Stopover frequency, duration, and migration rate support this hypothesis.

Moving with the flow: an automatic tour of unsteady flow fields

We present a novel framework that creates an automatic tour of unsteady flow fields for exploring internal flow features. Our solution first identifies critical flow regions for time steps and computes their temporal correspondence. We then extract skeletons from critical regions for feature orientation and pathline placement. The key part of our algorithm determines which critical region to focus on at each time step and derives the region traversal order over time using a combination of energy minimization and dynamic programming strategies. After that, we create candidate viewpoints based on the construction of a simplified mesh enclosing each focal region and select the best viewpoints using a viewpoint quality measure. Finally, we design a spatiotemporal tour that efficiently traverses focal regions over time. We demonstrate our algorithm with several unsteady flow data sets and perform a user study and an expert evaluation to confirm the benefits of including internal viewpoints in the design.