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Emotional support from family members may have an important effect on adolescent health outcomes, and has been identified as a target for policy to protect against the impacts of poverty and other early life adversities. However, few studies have assessed the extent to which poverty and adversity themselves influence the nature of emotional support that parents can provide to adolescents. We, therefore, aimed to investigate the impact of trajectories of income poverty and family adversities, including parental mental ill health, alcohol misuse and domestic violence across childhood developmental stages on young people’s relationships with their families and perceived emotional support received. We analysed longitudinal data on 10,976 children from the nationally representative UK Millennium Cohort study. Exposure trajectories of poverty and family adversities were characterised using group-based multi-trajectory models (age 9 months–14 years). The outcomes were perceived emotional support and quality of family relationships, measured by the three-item Short Social Provisions Scale (SPS-3) and levels of parent–adolescent closeness and conflict, measured at age 14. ORs and 95% CIs were estimated using multivariable logistic regression models, adjusting for potential confounding factors. At age 14, the overall prevalence of low perceived emotional support was 13% (95% CI: 12, 14). Children of mothers with lower socioeconomic status (SES) were more likely to report low emotional support, with a clear social gradient (education—degree plus: 10.3% vs. no qualifications: 15.4%). Compared with children exposed to low levels of poverty and adversity, children in the persistent adversity trajectory groups experienced higher odds of low emotional support and low-quality parent–adolescent relationship; those exposed to both persistent poverty and poor parental mental health were particularly at increased risk of experiencing poor family relationships and low perceived emotional

Introduction: Drawing upon the framework of life course epidemiology, this study aligns with research on the mental health consequences of significant social transitions during early adulthood. The focus is on the variation in initial labour market attachment and the development of depressiveness, assuming that a firm attachment is associated with decreasing depressiveness. Methods: The baseline investigation of the studied cohort (n = 1,001) took place during their final year of compulsory schooling at age 16. Follow-up surveys were conducted at ages 18, 21, 30, and 43. Depressiveness was measured with a five-item score. Multiple trajectory analysis, incorporating five labour market statuses observed over seven half-year periods from ages 18 to 21, was employed to categorize the cohort into six distinct groups. Among these, ‘All-time education,’ ‘From education to employment,’ ‘Education and employment,’ and ‘From employment to education’ were considered to demonstrate firm labour market attachment. Meanwhile, ‘Active labour market policy’ and ‘Unemployment’ represented less firm attachment. Results: The trajectory of depressive symptoms among the total cohort from age 16 to age 43 exhibited a ‘broken stick’ pattern, reaching its lowest point at age 21. This pattern was evident in all groups classified as having a firm attachment. A substantial decrease in depressiveness was also observed in the relatively weakly attached ‘Active labour market policy’ group, whereas no ‘broken stick’ pattern emerged in the ‘Unemployment’ group. The disparities in the levels of depressiveness observed at age 21 remained relatively stable across the measurements at ages 30 and 43. Discussion: The results were as expected, except for the observed improvement in mental health within the ‘Active labour market policy’ group. Supported labour market attachment during emerging adulthood can enhance mental well-being similarly to regular mainstream attachment. In terms of policy recommendat

Breast cancer is the most frequently diagnosed malignancy in women worldwide, with tumour metastasis being the leading cause of death for these patients. We have improved our understanding of metastatic disease by studying the role of plasticity in tumour heterogeneity, dissemination, and therapeutic resistance. Yet, metastatic breast cancer remains a burden. The development of successful targeted therapies has been limited by a lack of mechanistic insight into the regulation of cellular adaptability. Next generation sequencing platforms can comprehensively profile the molecules that orchestrate adaptability, but the remaining challenge lies in our ability to computationally reconstruct these plastic mechanisms. It is not yet clear which computational approaches facilitate the reconstruction of plastic mechanisms or what interpretations can be drawn from current data analysis paradigms. Particularly with the emergence of single-cell RNA-sequencing (scRNA-seq) technologies, it is necessary to assess how computational approaches should be coordinated with experimental strategies. In this thesis, I assess the value of both single-cell and bulk sequencing approaches and explore new analytical paradigms that address the continuous nature of cellular plasticity. In doing so, I propose mechanisms of plasticity in bulk and single- cell transcriptomic datasets that may contribute to breast cancer metastasis. First, I investigated mechanisms of metastatic organotropism using bulk RNA-seq data from an in-house optical-barcoding model of breast cancer progression. In this first chapter, I demonstrate the value of traditional bulk approaches in providing clinically-relevant insights, which I then contrast to a single-cell analysis of phenotypic plasticity in the next chapter. Here, I use scRNA-seq data from malignant pleural effusions (MPEs) to disentangle cell-cell interactions between invading breast cancer cells and resident mesothelial populations in this unique microenviron

Long-term monitoring programs are fundamental to detect changes in ecosystem health and understand ecological processes. In the current context of increasing anthropogenic threats on marine ecosystems, understanding the dynamics and response of communities becomes essential. We used data collected over 14 years in the REBENT benthic coastal invertebrates monitoring program, at a regional scale in the North-East Atlantic, covering a total of 26 sites and 979 taxa. Four distinct habitats were studied: two biogenic habitats associated with foundation species in the intertidal and subtidal zones and two bare sedimentary habitats in the same respective tidal zones. We used community trajectory analysis (CTA), a statistical approach that allows for quantitative measures and comparisons of temporal trajectories of ecosystems. We compared observed community trajectories to trajectories simulated under a non-directional null model in order to better understand the dynamics of the communities, their potential drivers, and the role of the studied habitats in these dynamics. Despite strong differences in the community compositions between sites and habitats, the communities followed non-directional dynamics during the 14 years monitored, which suggested stability at the regional scale. However, the shape, size, and direction of the trajectories of benthic communities were more similar within than among habitats, also suggesting the influence of the nature of the habitat on community dynamics. Results showed a higher variability in community composition the first years of the monitoring in the intertidal bare habitat and confirmed the role of biogenic habitats in maintaining temporal stability. They also highlighted the need to apprehend the role of transient and rare species and the scale of observation in temporal beta diversity analyses. Finally, our study confirmed the usefulness of CTA to link observed trajectory patterns to fundamental ecological processes.

In cloud-edge computing paradigms, the integration of edge servers and task offloading mechanisms has posed new challenges to developing task scheduling strategies. This paper proposes an efficient convergent firefly algorithm (ECFA) for scheduling security-critical tasks onto edge servers and the cloud datacenter. The proposed ECFA uses a probability-based mapping operator to convert an individual firefly into a scheduling solution, in order to associate the firefly space with the solution space. Distinct from the standard FA, ECFA employs a low-complexity position update strategy to enhance computational efficiency in solution exploration. In addition, we provide a rigorous theoretical analysis to justify that ECFA owns the capability of converging to the global best individual in the firefly space. Furthermore, we introduce the concept of boundary traps for analyzing firefly movement trajectories, and investigate whether ECFA would fall into boundary traps during the evolutionary procedure under different parameter settings. We create various testing instances to evaluate the performance of ECFA in solving the cloud-edge scheduling problem, demonstrating its superiority over FA-based and other competing metaheuristics. Evaluation results also validate that the parameter range derived from the theoretical analysis can prevent our algorithm from falling into boundary traps.

This thesis aims to investigate the potential of a transfer orbit using successive aerocaptures at Saturn and Titan to establish a science orbit around Titan. Titan is an Earth-like moon with a dense atmosphere and organic compounds present. It has many similarities with Earth that are useful to study such as superrotation. Superrotation is when the atmosphere rotates faster than the body it surrounds. In order to study Titan, we need to establish an orbit around it. The Saturn system is distant from Earth, 8.5 Astronomical Units (AU) which makes it difficult to reach from a time and velocity point of view. We propose to use an aerocapture at Saturn to intercept Titan with lower relative velocity in order to perform an aerocapture at Titan. The analysis was performed in primarily MATLAB to simulate the orbits. The results of this showed that we can aerocapture a spacecraft at Saturn and arrive at Titan within roughly 4 to 8 km/s relative velocity regardless of the incoming hyperbolic excess velocity at the Saturn system. This can be improve upon by using intermediate transfer orbits, such as bi-elliptics, to arrive with even lower relative velocities to Titan of as low as 1 km/s. The drag acceleration experienced during the Saturn aerocapture had peak values of between 0.2 and 1.4 g's and acceleration over 50% of the peak is experienced between 6.8 and 8 minutes. This capture method has the potential to make Titan more easily accessible and allow for scientific study of a clear target for improving our understanding of Earth-like processes on other bodies in our solar system.

The general understanding of user behaviour has been often overlooked in the field of Virtual Reality (VR) and Extended Reality (XR) at large. In this work, we want to fill this gap by exploring the relationship between the way in which users navigate in immersive content and the predictability of their trajectories. Inspired by works from social science, our key assumption is that there are navigation trajectories that can be accurately predicted, while others exhibit eclectic patterns that are more challenging to anticipate. However, it is not yet clear how to effectively distinguish between these behaviours. In this context, we conduct an extensive data analysis across multiple datasets investigating users' movements in VR. The ultimate goal is to understand if a specific metric from information theory, such as the entropy of trajectory, can be adopted as a discriminating metric between predictable navigation trajectories and unpredictable ones. Our findings reveal that users with highly regular navigation styles tend to exhibit lower entropy, indicating higher predictability of their movements. Conversely, users with more diverse navigation patterns show higher entropy and lower predictability in their trajectories. Answering the question "how can we distinguish users more predictable than others?'' would be crucial for different purposes in future immersive applications such as enabling new modalities for live streaming services but also for the design of more personalised and engaging VR experiences.

Background: Increasing resilience is a priority in modern pig breeding. Recent research shows that general resilience can be quantified via variability in longitudinal data. The collection of such longitudinal data on weight, feed intake and feeding behaviour in pigs has been facilitated by the development of technologies such as automated feeding stations. The goal of this study was to investigate resilience traits, which were estimated as deviations from longitudinal weight, feed intake and feeding behaviour data during the finishing phase. A dataset with 324,207 records between the age of 95 and 155 days on 5,939 Piétrain pigs with known pedigree and genomic information was used. We provided guidelines for a rigid quality control of longitudinal body weight data, as we found that outliers can significantly affect results. Gompertz growth curve analysis, linear modelling and trajectory analyses were used for quantifying resilience traits. Results: To our knowledge, this is the first study comparing resilience traits from longitudinal body weight, feed intake and feeding behaviour data in pigs. We demonstrated that the resilience traits are lowly to moderately heritable for deviations in body weight (h 2 = 2.9%–20.2%), in feed intake (9.4%–23.3%) and in feeding behaviour (16.2%–28.3%). Additionally, these traits have good predictive abilities in cross-validation analyses. Deviations in individual body weight and feed intake trajectories are highly correlated (r g = 0.78) with low to moderate favourable genetic correlations with feed conversion ratio (r g = 0.39–0.49). Lastly, we showed that some resilience traits, such as the natural logarithm of variances of observed versus predicted body weights (lnvarweight), are more robust to lower observation frequencies and are repeatable over three different time periods of the finishing phase. Conclusions: Our results will help future studies investigating resilience traits and resilience-related traits. Moreover, our stud

Immersive reality technologies, such as Virtual and Augmented Reality, have ushered a new era of user-centric systems, in which every aspect of the coding-delivery-rendering chain is tailored to the interaction of the users. Understanding the actual interactivity and behaviour of the users is still an open challenge and a key step to enabling such a user-centric system. Our main goal is to extend the applicability of existing behavioural methodologies for studying user navigation in the case of 6 Degree-of-Freedom (DoF). Specifically, we first compare the navigation in 6-DoF with its 3-DoF counterpart highlighting the main differences and novelties. Then, we define new metrics aimed at better modelling behavioural similarities between users in a 6-DoF system. We validate and test our solutions on real navigation paths of users interacting with dynamic volumetric media in 6-DoF Virtual Reality conditions. Our results show that metrics that consider both user position and viewing direction better perform in detecting user similarity while navigating in a 6-DoF system. Having easy-To-use but robust metrics that underpin multiple tools and answer the question "how do we detect if two users look at the same content?"open the gate to new solutions for a user-centric system., Multimedia Computing

How do we model, structure or quantify geometric information in geometric data? We study the three components of this question through the lens of computational geometry. We review how geometric information and computations on this data can be theoretically modelled. Specifically, we discuss two common ways to model computations in theoretical computer science: the word RAM which fixes a maximal number of bits per variable (the word size) and the real RAM which assumes that a single register may contain an arbitrary real value up to infinite precision. We study the execution of real RAM programs on the word RAM using smoothed analysis, a probabilistic paradigm used to model the day-to-day inaccuracies of algorithmic input. We show that under smoothed analysis, real RAM programs are `correctly’ executed using the common logarithmic word size. That is, both the real RAM program and its word RAM equivalent reach the same conclusion. Next, we discuss to structure geometric data for efficient reuse. This question is studied in three contexts. First, we show how to preprocess a simple polygon of n vertices such that given two query segments (each traversed by an entity at constant speed), we can decide if there is a time where both entities are mutually visible in sublinear time. Next, we show how to preprocess a trajectory P of n vertices such that given a query segment q, we can compute the Fréchet distance between P and q in sublinear time. Finally, we show how to dynamically maintain a smooth quadtree with worst case constant update time. In the third part of this thesis, we reason about how to mathematically quantify the inherent imprecision in geometric measurements. We model this imprecision as follows: the algorithmic input is an imprecise point set. That is, a set of n regions that each contain a unique point. The goal is to preprocess the regions, such that a data structure can be computed on the point set in time faster than would-be possible without the given

Outdoor physical activities can promote public health and they are largely influenced by the built environment in different urban settings. Understanding the association between outdoor physical activities and the built environment is important for promoting a high quality of life. Existing studies typically focus on one type of outdoor activity using interview-based small samples and are often lack of systematic understanding of the activities' intensity and frequency. In this study, we intend to gain deeper insight into how the built environment influences physical activities using the data extracted from individual's wearables and other open data sources for integrated analysis. Multi-linear regression with logarithm transformation is applied to perform the analysis using the data from Changsha, China. We found that built environment impacts on outdoor physical activities in Changsha are not always consistent with similar studies' results in other cities. The most effective measures to promote outdoor physical activities are the provision of good arterial and secondary road networks, community parks, among others in Changsha. The results shed light on future urban planning practices in terms of promoting public health, Design & Construction Management

Outdoor physical activities can promote public health and they are largely influenced by the built environment in different urban settings. Understanding the association between outdoor physical activities and the built environment is important for promoting a high quality of life. Existing studies typically focus on one type of outdoor activity using interview-based small samples and are often lack of systematic understanding of the activities' intensity and frequency. In this study, we intend to gain deeper insight into how the built environment influences physical activities using the data extracted from individual's wearables and other open data sources for integrated analysis. Multi-linear regression with logarithm transformation is applied to perform the analysis using the data from Changsha, China. We found that built environment impacts on outdoor physical activities in Changsha are not always consistent with similar studies' results in other cities. The most effective measures to promote outdoor physical activities are the provision of good arterial and secondary road networks, community parks, among others in Changsha. The results shed light on future urban planning practices in terms of promoting public health.

Alcoholic hepatitis (AH) is the most severe form of alcoholic liver disease for which there is no efficacious treatment aiding most patients. AH manifests differently in individuals, with some patients showing debilitating symptoms more so than others. Previous studies showed significant metabolic dysregulation associated with AH. Therefore, we sought to analyze how the activity of metabolic pathways differed in the liver of patients with varying degrees of AH severity. We utilized a genome-scale metabolic modeling approach that allowed for integration of a generic human cellular metabolic model with specific RNA-seq data corresponding to healthy and multiple liver disease states to predict the metabolic fluxes within each disease state. Additionally, we performed a systems-level analysis of the transcriptomic data and predicted metabolic flux data to identify the regulatory and functional differences in liver metabolism with increasing severity of AH. Our results provide unique insights into the sequential dysregulation of the solute transport mechanisms underlying the glutathione metabolic pathway with increasing AH disease severity. We propose targeting of the solute transporters in the glutathione pathway to mimic the flux activity of the healthy liver state as a potential therapeutic intervention for AH.

The aim of our study was to investigate adherence to lifestyle recommendations and lifestyle changes after diagnosis in patients with non-muscle invasive bladder cancer (NMIBC). Second, we aimed to identify distinct trajectories of lifestyle change and their correlates. We analysed data of 935 patients with NMIBC from a prospective cohort study at six weeks (evaluating pre-diagnostic lifestyle), three months, and fifteen months after diagnosis. An overall lifestyle score (range 0–7) was calculated based on the 2018 World Cancer Research Fund/American Institute for Cancer Research (WCRF/AICR) recommendations focusing on diet, body mass index, and physical activity. Linear mixed models were used to analyse absolute lifestyle changes over time. Distinct trajectories of change were identified with latent class trajectory models. We found an overall lifestyle score of 3.3 which remained constant over time. The largest lifestyle changes were observed for the consumption of red and processed meat (−96 g/week) and fruit and vegetables (−38 g/day). Two to four trajectory groups were identified for each single lifestyle behaviour. Correlates differed per trajectory group. In conclusion, adherence to the WCRF/AICR recommendations was low. Small to moderate changes in and different trajectories of single lifestyle behaviours were observed. Effective strategies for lifestyle improvement are warranted.

Objective To examine the hypothesis that PTSD with delayed expression in some cases occurs without subthreshold PTSD symptoms above background levels bridging the gap between the traumatic exposure(s) and the clinical diagnosis. Methods We performed systematic searches of peer-reviewed papers in English referenced in Pubmed, Embase, or PsycINFO and ascertained 34 prospective studies of PTSD symptom trajectories identified by latent class growth statistical modeling. Studies with delayed and low-stable trajectories provided appropriate data for this study. We computed the difference between the delayed trajectory PTSD symptom sumscore and the low-stable PTSD sumscore at the observed points in time after the traumatic event(s). Results In 29 study populations, the latent class growth analyses displayed delayed trajectories, and in these, we identified 110 data points (% PTSD sumscore difference/months since traumatic exposure). The median PTSD symptom sumscore was 25% higher during the initial 6 months among individuals in the delayed trajectory compared to those in low-stable trajectory. From this level, the difference widened and reached a plateau of 40-50% higher. The variation was large, and the baseline participation rate and loss to follow-up were exceeding 25% in the majority of the studies. Heterogeneity of populations, measures, and analyses precluded formal meta-analysis. Conclusion Delayed PTSD is preceded by PTSD symptoms during the first year in most cases. Still, few individuals may experience an asymptomatic delay. The results underpin the rationale for monitoring PTSD symptoms and may inform forensic assessments in that delayed PTSD without symptoms bridging the traumatic event is rare.

Due to society aging, age-related issues such as mild cognitive impairments (MCI) and dementia are attracting the attention of health professionals, scientists and governments. Seniors suffering from such impairments notice a slight deterioration in their cognitive abilities, which may lead to memory loss and behavioural disorders. In consequence, such seniors refrain from doing their everyday outdoor activities. Technology, e.g. smartphones, wearables and artificial intelligence, can provide seniors and their relatives with a variety of monitoring tools. In a nutshell, locations are analysed and, under specific situations, alarms are raised so that caregivers urgently informed. In this context, the discovery and prediction of trajectories and behaviours play a key role in deploying effective monitoring solutions. In this paper, we present a real-time smartphone-based monitoring system, called SafeMove, to discover and predict elderly people behaviours by analyzing outdoor trajectories. This is achieved by firstly analysing the elder's mobility data previously collected using the proposed model called SpaceTime-Convolutional Neural Network (ST-CNN) in order to predict the most popular locations he/she might visit in the next time. Based on the predicted locations, the elder can be monitored in bounded region. Time and space-related variables, such as the distance traversed, the direction of the movements and the time spent, are analyzed in our abnormal behaviour detection (ABD) model that takes advantage of recurrent neural networks (RNNs). The effectiveness and the efficiency of our system for predicting the next location and detection the abnormal behaviors are evaluated using different datasets comprising real-world GPS trajectories.

We study three covering problems in the plane. Our original motivation for these problems come from trajectory analysis. The first is to decide whether a given set of line segments can be covered by up to four unit-sized, axis-parallel squares. The second is to build a data structure on a trajectory to efficiently answer whether any query subtrajectory is coverable by up to three unit-sized axis-parallel squares. The third problem is to compute a longest subtrajectory of a given trajectory that can be covered by up to two unit-sized axis-parallel squares.

High levels of early emotionality (of either negative or positive valence) are hypothesized to be important precursors to early psychopathology, with attention-deficit/hyperactivity disorder (ADHD) a prime early target. The positive and negative affect domains are prime examples of Research Domain Criteria (RDoC) concepts that may enrich a multilevel mechanistic map of psychopathology risk. Utilizing both variable-centered and person-centered approaches, the current study examined whether levels and trajectories of infant negative and positive emotionality, considered either in isolation or together, predicted children's ADHD symptoms at 4 to 8 years of age. In variable-centered analyses, higher levels of infant negative affect (at as early as 3 months of age) were associated with childhood ADHD symptoms. Findings for positive affect failed to reach statistical threshold. Results from person-centered trajectory analyses suggest that additional information is gained by simultaneously considering the trajectories of positive and negative emotionality. Specifically, only when exhibiting moderate, stable or low levels of positive affect did negative affect and its trajectory relate to child ADHD symptoms. These findings add to a growing literature that suggests that infant negative emotionality is a promising early life marker of future ADHD risk and suggest secondarily that moderation by positive affectivity warrants more consideration.

Ecological research focuses on the spatio-temporal patterns of ecosystems and communities. The recently proposed framework of Community Trajectory Analysis considers community dynamics as trajectories in a chosen space of community resemblance and utilizes geometrical properties of trajectories to compare and analyse temporal changes. Here, we extend the initial framework, which focused on consecutive trajectory segments, by considering additional metrics with respect to initial or baseline states. Addressing questions about community dynamics and more generally temporal and spatial ecological variability requires synthetic and efficient modes of representation. Hence, we propose a set of innovative maps, charts and trajectory roses to represent trajectory properties and complement the panel of traditional modes of representation used in community ecology. We use four case studies to highlight the complementarity and the ability of the new metrics and innovative figures to illustrate ecological trajectories and to facilitate their interpretation. Finally, we encourage ecologists skilled in multivariate analysis to integrate CTA into their toolbox in order to quantitatively evaluate spatio-temporal changes.

A case study of a foehn event in the Inn Valley near Innsbruck, Austria, is in- vestigated that occurred on 29 October 2017 in the framework of the first Inten- sive Observation Period (IOP) of the Penetration and Interruption of Alpine Foehn (PIANO) field campaign. Accompanied with northwesterly crest-level flow, foehn broke through at the valley floor as strong westerly winds in the moring and was terminated in the afternoon by a cold front arriving from the north. The differ- ence between local and large-scale wind direction rises the question of whether the event should be classified as north or west foehn – a question that has not been convincingly answered in the past for similar events based on Eulerian approaches. Hence, the goal of this study is to assess the air mass origin and the mechanisms of foehn penetration to the valley floor based on a Lagrangian perspective. For this purpose a mesoscale simulation with WRF and backward trajectory analysis with LAGRANTO are conducted. The trajectory analysis shows that the major part of the air mass arriving at Innsbruck originates six hours earlier over eastern France, crosses the two mountain ranges of the Vosges and the Black Forest and finally impinges on the Alps near Lake Constance and the Rhine Valley. Orographic precipitation over the mountains leads to a net diabatic heating of about 2.5 K and to a moisture loss of about 1 g kg −1 along the trajectories. A secondary air stream originates further south over the Swiss Plateau and contributes with about 10 to 25 % to the foehn air in Innsbruck. Corresponding trajectories are initially nearly parallel to the northern Alpine rim and get lifted above crest level in the same region as the main trajectory branch. Air parcels within this branch experience a net diabatic heating of about 2 K, and, in contrast to the ones of the main branch, an overall moisture uptake due to evaporation of precipitation formed above this air mass. Penetration into the Inn Valley main, by Manuel Saigger, Masterarbeit University of Innsbruck 2021

The wide usage of GPS-equipped devices enables the mass recording of vehicle movement trajectories describing the movement behavior of the traffic participants. An important aspect of the road traffic is the impact of anomalies, like accidents, on traffic flow. Accidents are especially important as they contribute to the the aspects of safety and also influence travel time estimations. In this paper, the impact of accidents is determined based on a massive GPS trajectory and accident dataset. Due to the missing precise date of the accidents in the data set used, first, the date of the accident is estimated based on the speed profile at the accident time. Further, the temporal impact of the accident is estimated using the speed profile of the whole day. The approach is applied in an experiment on a one month subset of the datasets. The results show that more than 72% of the accident dates are identified and the impact on the temporal dimension is approximated. Moreover, it can be seen that accidents during the rush hours and on high frequency road types (e.g. motorways, trunks or primaries) have an increasing effect on the impact duration on the traffic flow.

Data prediction and imputation are important parts of marine animal movement trajectory analysis as they can help researchers understand animal movement patterns and address missing data issues. Compared with traditional methods, deep learning methods can usually provide enhanced pattern extraction capabilities, but their applications in marine data analysis are still limited. In this research, we propose a composite deep learning model to improve the accuracy of marine animal trajectory prediction and imputation. The model extracts patterns from the trajectories with an encoder network and reconstructs the trajectories using these patterns with a decoder network. We use attention mechanisms to highlight certain extracted patterns as well for the decoder. We also feed these patterns into a second decoder for prediction and imputation. Therefore, our approach is a coupling of unsupervised learning with the encoder and the first decoder and supervised learning with the encoder and the second decoder. Experimental results demonstrate that our approach can reduce errors by at least 10% on average comparing with other methods.

Forest degradation is widespread around the world, due to multiple factors such as unsustainable logging, agriculture, invasive species, fire, fuelwood gathering, and livestock grazing. In the Brazilian Amazon forest degradation from August 2006 to July 2016 reached 1,1 869 800 ha. The processes of forest degradation are still poorly understood, being a missing component in anthropogenic CO2 emission estimates in tropical forests. In this work, we analyzed temporal trajectories of forest degradation from August 2006 to July 2016 in the Brazilian Amazon and assessed their impact on the regional carbon balance. We combined the degradation process with deforestation-related processes (clear-cut deforestation and secondary vegetation dynamics), using the spatially-explicit INPE-EM carbon emission model. The trajectory analysis showed that 13% of the degraded area ended up being cleared and converted in the period and 61% of the total degraded area experienced only one event of degradation throughout the whole period. Net emissions added up to 5.4 GtCO2, considering the emissions from forest degradation and deforestation, absorption from degraded forest recovery, and secondary vegetation dynamics. The results show an increase in the contribution of forest degradation to net emissions towards the end of the period, related to the decrease in clear-cut deforestation rates, decoupled from the forest degradation rates. The analysis also indicates that the regeneration of degraded forests absorbed 1.8 GtCO2 from August 2006 and July 2016—a component typically overlooked in the regional carbon balance.

The flight planning process is an extensive and long process to direct and maintain a high level of operations within the airspace. As air traffic demand grows year after year, it's worthwhile to optimise the European air traffic system further. One way of optimising the system, is by creating optimal flight schedules that solve for demand-capacity imbalances. These schedules require an evaluation with respect to punctuality and fuel consumption in the tactical phase. For this article, an air traffic model has been developed in BlueSky to simulate air traffic while taking the variance of wind and delay into account. Subsequently, the performance of several optimised schedules will be assessed and compared with respect to wind, speed changes, punctuality and fuel consumption., Aerospace Engineering

Within the aviation framework, determining an optimal flight path or having up-to-date information on the status of the aircraft's internal system are key factors for improving efficiency and ensuring incident free flights. Given the current rise of unmanned aerial vehicles, this project entails the development of an algorithm, by Excel-VBA, to monitor the navigation parameters and internal system elements. Specifically, we aim to monitor the performance of a hex-copter and the phases of flight, in order to be able to put into context the other parameters to be analyzed. This information is essentially provided with tables and graphics. This study has been carried out by collecting sets of navigation data for several flights in a model airfield. It has been considered that the conditions for each flight were practically the same. Finally, after processing and monitoring the data gathered, it is verified that the algorithm is capable to identify the phases and flight maneuvers adequately.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10707-019-00386-7, We study five existing map construction algorithms, designed and tested with urban vehicle data in mind, and apply them to hiking trajectories with different terrain characteristics. Our main goal is to better understand the existing strategies and their limitations, in order to shed new light into the current challenges for map construction algorithms. We carefully analyze the results obtained by each algorithm focusing on the local details of the generated maps. Our analysis includes the characterization of 10 types of common artifacts, which occur in the results of more than one algorithm, and 7 algorithmic-specific artifacts, which are consequences of different algorithmic strategies. This allows us to extract systematic conclusions about the main challenges to fully automatize the construction of maps from trajectory data, to detect the strengths and weaknesses of the potential different strategies, and to suggest possible ways to design higher-quality map construction methods. We consider that this analysis will be of help for designing new and better methods that perform well in wider and more realistic contexts, not only for road map or hiking reconstruction, but also for other types of trajectory data., Departament de Matem`atiques, Universitat Polit`ecnica de Catalunya, and BGSMath, Spain. {vera.sacristan,rodrigo.silveira}@upc.edu. Partially supported by projects MTM2015-63791-R (MINECO/FEDER), Gen. Cat. 2017SGR1640. R.I. S. was also supported by MINECO through the Ram´on y Cajal program., Peer Reviewed, Postprint (author's final draft)

We introduce a computational toolset, named GROmaρs, to obtain and compare time-averaged density maps from molecular dynamics simulations. GROmaρs efficiently computes density maps by fast multi-Gaussian spreading of atomic densities onto a three-dimensional grid. It complements existing map-based tools by enabling spatial inspection of atomic average localization during the simulations. Most importantly, it allows the comparison between computed and reference maps (e.g., experimental) through calculation of difference maps and local and time-resolved global correlation. These comparison operations proved useful to quantitatively contrast perturbed and control simulation data sets and to examine how much biomolecular systems resemble both synthetic and experimental density maps. This was especially advantageous for multimolecule systems in which standard comparisons like RMSDs are difficult to compute. In addition, GROmaρs incorporates absolute and relative spatial free-energy estimates to provide an energetic picture of atomistic localization. This is an open-source GROMACS-based toolset, thus allowing for static or dynamic selection of atoms or even coarse-grained beads for the density calculation. Furthermore, masking of regions was implemented to speed up calculations and to facilitate the comparison with experimental maps. Beyond map comparison, GROmaρs provides a straightforward method to detect solvent cavities and average charge distribution in biomolecular systems. We employed all these functionalities to inspect the localization of lipid and water molecules in aquaporin systems, the binding of cholesterol to the G protein coupled chemokine receptor type 4, and the identification of permeation pathways through the dermicidin antimicrobial channel. Based on these examples, we anticipate a high applicability of GROmaρs for the analysis of molecular dynamics simulations and their comparison with experimentally determined densities., QCR 20190513

A work environment characterized by poor psychosocial working conditions may lead to stress and mental health problems such as depression, a common and burdensome public health problem with significant consequences for individuals and for society at large. A number of psychosocial working characteristics have been found to be associated with increased depressive symptoms or clinical depression. This thesis aims to further examine how certain psychosocial working conditions predict depressive symptoms over time, in working life and across retirement. This was done by using several repeated measures from the Swedish Longitudinal Occupational Survey of Health (SLOSH) in 2006–2018. In study I, we investigated how long-term patterns of exposure to job demands and job control were associated with major depressive symptoms. Those with high strain (high demands, low control) and active (high demands, high control) jobs were more likely to have subsequent major depressive symptoms compared to those with low strain jobs (low demands, high control). However, after adjusting for baseline depressive symptoms and various demographic factors, the associations did not remain statistically significant. In study II, we assessed how job demands, job control and workplace social support were related to long-term development of depressive symptoms. A perception of high job demands and low social support predicted higher or increasing depressive symptom trajectories. In addition, negative changes in job demands, job control and social support were associated with increased symptoms, indicating that the onset of poor working conditions could negatively impact depressive symptoms. In study III, we investigated simultaneous and lagged bidirectional associations between job demands, job control, balance between demands and control, social support, procedural justice, effort, reward, balance between efforts and rewards, and depressive symptoms, while controlling for individual time-stable cha, At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.

While traditional accounts characterize speech planning as serial, discrete, and walled off from behavior, newer proposals describe it as parallel, continuous, and delicately interweaved with execution. This dissertation evaluates the claim that speakers under time pressure produce articulatory trajectories that are graded fits to continually evolving partial, parallel constraints. In three form preparation experiments, motion-tracked digital video captured oral postures over time. Participants were sometimes primed with the nuclear vowels of CVC words. All words contained either /i/ (spread lips; e.g., “seed”) or /u/ (rounded lips, e.g., “soup”). In the first two experiments, initial consonants were highly uncertain. In Experiment 1, articulatory postures produced before stimulus presentation anticipated the upcoming vowel when it was primed. Experiment 2 included two pairs of vowel-primed blocks. The words of one /i/-block began with the rounded consonants /w/ or /r/ (e.g., “weak”). Primed vowels influenced anticipatory articulation except when superseded by conflicting demands from likely initial consonants. In Experiment 3, initial consonants were always bilabial, but words were blocked such that either vowel (/i/ versus /u/) or coda type (alveolar/lateral versus bilabial/labiodental) was initially uncertain. For example, a participant might know that an upcoming word would use an /i/ sound but not know whether the final consonant left the mouth relatively open (e.g., “meal”) or closed (e.g., “peep”). Analysis emphasized words ending in alveolar/lateral codas, and followed the evolution of articulatory trajectories over the acoustic phase of the utterance, in both horizontal and vertical lip aperture dimensions. Contrary to expectations, priming did not appreciably impact the shape of these two-dimensional trajectories.

© 2019 The Author(s). Background: Understanding the early roots of physical activity and sedentary behaviors is critical to developing intervention programs that promote healthy lifestyle habits in infants and children. There is, however, no evidence on how these behaviors cluster and develop together during early childhood. The aim of this study was to identify single and joint longitudinal trajectories in physical activity and screen time amongst children aged 0 to 9 years, their social-demographic predictors and their prospective health-related quality-of-life and socio-emotional outcomes. Methods: Three waves of data from The Longitudinal Study of Australian Children, a national study tracking two cohorts every 2 years (B-cohort, 0-5 years, n = 4,164; K-cohort, 4-9 years, n = 3,974) were analysed. Growth mixture modelling was applied to longitudinal time-use diary data to identify joint trajectories in children's physical activity and screen time over Waves 1-3. Key socio-demographic variables measured at Wave 1 were used to predict membership in different trajectories. The prospective consequences (at Wave 3) of time-use trajectories on health-related quality-of-life and socio-emotional outcomes were assessed. Results: Three physical-activity/screen-time trajectories were identified for both cohorts: Cluster-A - children who maintained low levels of physical activity and screen time (50% of the sample), Cluster-B - children who progressively increased physical activity and maintained low screen-time levels (25%), and Cluster-C - children who maintained low physical-activity levels and increased screen time (25%). Children in Cluster-B experienced the best health-related quality-of-life and socio-emotional outcomes, while those in Cluster-C experienced the worst. Children who were female, Indigenous, from non-English-speaking backgrounds, not living with two biological parents, in more affluent households and neighbourhoods, without siblings and with parent

The environment of the vehicle can significantly influence the driving situation. Which conditions lead to unsafe driving behaviour is not always clear, also not to a human driver, as the causes might be unconscious, and thus cannot be revealed by expert interviews. Therefore, it is important to investigate how such situations can be reliably detected, and then search for their triggers. It is conceivable that such insecure situations (e.g. near-accidents, U-turns, avoiding obstacles) are reflected, for example, as anomalies in the movement trajectories of road users. Collecting real world traffic data in driving studies is very time consuming and expensive. However, a lot of roads or public areas are already monitored with video cameras. In addition, nowadays more and more of such video data is made publicly available over the internet so that the amount of free video data is increasing. This research will exploit the use of such kind of opportunistic VGI. In the paper the first step of an automatic analysis are presented, namely: to introduce a real time processing pipeline to extract road user trajectories from surveillance video data.

Depression and musculoskeletal pain are associated, but long-term follow-up studies are rare. We aimed to examine the relationship of early depressive symptoms with developmental patterns of musculoskeletal pain from adolescence to middle age. Adolescents ending compulsory school (age 16) in Lulea, Northern Sweden, in 1981 (n = 1083) were studied and followed up in 1986, 1995, and 2008 (age 43) for musculoskeletal pain. Attrition was very low. Indicators for any and severe pain were based on pain in the neck-shoulders, low back, and the extremities. Latent class growth analyses were performed on 563 men and 503 women. Associations of a depressive symptoms score (DSS, range 0.0-2.0) at age 16 with pain trajectory membership were assessed by logistic and multinomial regression, adjusting for parental socioeconomic status, social adversities, smoking, exercise, body mass index, and alcohol consumption at age 16. For any pain, 3 trajectories emerged: high-stable (women 71%, men 61%), moderate (11%, 17%), and low-increasing (18%, 22%). With the low-increasing trajectory as reference, for each 0.1-point increase in the DSS, the odds ratio of belonging to the high-stable trajectory was 1.25 (95% confidence interval 1.11-1.41) in women and 1.23 (1.10-1.37) in men. For severe pain, 2 trajectories were found: moderate-increasing (women 19%, men 9%) and low-stable. For each 0.1-point increase in the DSS, the odds ratio of membership in the moderate-increasing trajectory was 1.14 (1.04-1.25) in women and 1.17 (1.04-1.31) in men in the fully adjusted model. Thus, depressive symptoms at baseline are strongly associated with pain trajectory membership.

We present efficient algorithms for segmenting and classifying trajectories based on a movement model parameterised by a single parameter, like the Brownian bridge movement model. Segmentation is the problem of subdividing a trajectory into interior-disjoint parts such that each part is homogeneous in its movement characteristics. We formalise this using the likelihood of the model parameter, and propose a new algorithm for trajectory segmentation based on this. We consider the case where a discrete set of m parameter values is given and present an algorithm to compute an optimal segmentation with respect to an information criterion in O(nm) time for a trajectory with n sampling points. We also present an algorithm that efficiently computes the optimal segmentation if we allow the parameter values to be drawn from a continuous domain. Classification is the problem of assigning trajectories to classes of similar movement characteristics. The set of trajectories might for instance be the subtrajectories resulting from segmenting a trajectory, thus identifying movement phases. We give an algorithm to compute the optimal classification with respect to an information criterion in O(m2+ kmlog m) time for m parameter values and k trajectories, assuming bitonic likelihood functions. We also show that classification is NP-hard if the parameter values are allowed to vary continuously and present an algorithm that solves the problem in polynomial time under mild assumptions on the input.

The detection of unusual behavior plays a crucial role in the prevention of illegal and harmful activities such as smuggling, piracy, arms trading, human trafficking and illegal immigration. Also for military applications, it is useful to detect anomalous behavior to provide an alert for potential threats, especially with the more recent widespread use of drones for warfare and terrorist activities. In order to provide a solution for these emerging needs, in this work, a novel method for target dynamic behavior classification by analyzing trajectories using data gathered from multiple heterogeneous sensors is presented. The aim is to develop a context-free (i.e., sensor indifferent) method to robustly classify a selected set of anomalous trajectories and present those results to a human operator in remote sensing applications. In order to track maneuvering targets, it is typically required to use multiple (dynamic) model approach to make dynamic state inferences accurately. In practice, system parameters are typically tuned manually. The approach taken here is to estimate the parameters of a set of these so-called hybrid systems, also known as jump-Markov systems (JMS). This task will be carried out using a maximum likelihood (ML) approach, via the expectation-maximization (EM) algorithm. To handle highly nonlinear measurement models, such as those typically present in remote sensing applications, sequential Monte Carlo (SMC) or particle filters will be used to make accurate state estimations. These methods are also capable of dealing with non-Gaussian measurement or process noise. The central question explored in this work is if jump-Markov systems are a suitable class of models for trajectory classification by learning their parameters from multi-sensor measurement data., Electrical Engineering

The feasibility of improving the Earth collision uncertainty knowledge of a potentially Earth impacting asteroid by means of a multi-flyby mission has been researched in this thesis. The feasibility is assessed both from an astrodynamics point of view and from a systems engineering point of view. The astrodynamics part provides knowledge evolution results from a covariance analysis, which combines radiometric measurements of the spacecraft from Earth and optical measurements of the asteroid from the spacecraft. The systems engineering aspect on the other hand identifies all mission and subsystem requirements and provides possible subsystem design options. From the 1906 potentially hazardous asteroids known at the time of writing, Apophis has been selected as the main research target due to its extremely close expected Earth encounter on April 13th, 2029: the expected miss distance is just 38440 km. Asteroids 2012 UE34 and 2001 WN5 have been selected as secondary targets. High-fidelity resonant trajectories have been generated using a multiple shooting method implemented in NASA's General Mission Analysis Tool. As a robust initial guess for these simulations, results from porkchop plots have been used, which combine the solution of Lambert's problem and resonance data. Only 1:1 resonance has been researched for this thesis. All trajectories target the asteroid B-plane at 600 km distance. Data from JPL's HORIZONS has been used, alongside the generated high-fidelity trajectories, as input for a covariance analysis to produce the asteroid position knowledge evolution and the knowledge evolution of the asteroid in Earth's B-plane at the expected close-approach date. It has been found that, for Apophis, two flybys are sufficient to ensure mission success. After the second set of optical measurements, the orbital period of the asteroid is accurately known, which improves the asteroid position knowledge by roughly two orders of magnitude while improving t, Aerospace Engineering

Depressive symptoms vary in severity and chronicity. We used group-based trajectory models to describe trajectories of depressive symptoms (measured using the Patient Health Questionnaire-9) and predictors of trajectory group membership among 1493 HIV-infected men (84%) and 292 HIV-infected women (16%). At baseline, 29% of women and 26% of men had depressive symptoms. Over a median of 30 months of follow-up, we identified four depressive symptom trajectories for women (labeled "low" [experienced by 56% of women], "mild/moderate" [24%], "improving" [14%], and "severe" [6%]) and five for men ("low" [61%], "mild/moderate" [14%], "rebounding" [5%], "improving" [13%], and "severe" [7%]). Baseline antidepressant prescription, panic symptoms, and prior mental health diagnoses were associated with more severe or dynamic depressive symptom trajectories. Nearly a quarter of participants experienced some depressive symptoms, highlighting the need for improved depression management. Addressing more severe or dynamic depressive symptom trajectories may require interventions that additionally address mental health comorbidities.

The white blood cell count (WBC) at admission correlates with prognosis in septic shock. It is not known if the WBC trajectory impacts survival. We used trajectory analysis to study the WBC over 7 days of ICU admission. We developed a multinomial logistic regression model to evaluate the patient and illness factors with WBC trajectories. We constructed a multivariable Cox proportional hazard models to evaluate the association of WBC trajectory on 30-day mortality. The favored model identified seven WBC trajectories. We found that platelet count and sex were associated with WBC trajectory. In a multivariable Cox proportional hazard model, group 5 (rising WBC) was associated with increased hazard of death (HR 3.41 (95% CI 1.86 to 6.26), p<0.01). We found seven unique and clinically relevant groups of patients. Routine baseline characteristics are poor predictors of trajectory group assignment. The rising WBC trajectory is associated with an increased risk of death.

This report documents the program and the outcomes of Dagstuhl Seminar 17282 "From Observations to Prediction of Movement". This seminar brought together researchers from Animal Behaviour, GIS, Computational Geometry, Data Science and other fields to exchange insights from these diverse fields. Presentations focused both on outstanding practical questions, as well as on fundamental mathematical and computational tools.

In this work, we focus on two fundamental questions that are unprecedentedly important to urban planners to understand the functional characteristics of various urban regions throughout a city, namely, (i) how to identify regional weather-traffic sensitivity index throughout a city, that indicates the degree to which the region traffic in a city is impacted by weather changes; (ii) among complex regional features, such as road structure and population density, how to dissect the most influential regional features that drive the urban region traffic to be more vulnerable to weather changes. However, these two questions are nontrivial to answer, because urban traffic changes dynamically over time and is essentially affected by many other factors, which may dominate the overall impact. We make the first study on these questions, by developing a weather-traffic index (WTI) system. The system includes two main components: weather-traffic index establishment and key factor analysis. Using the proposed system, we conducted comprehensive empirical study in Shanghai, and the weather-traffic indices extracted have been validated to be surprisingly consistent with real world observations. Further regional key factor analysis yields interesting results. For example, house age has significant impact on the weather-traffic index, which sheds light on future urban planning and reconstruction.

This thesis is set in the context of solving the problem of user’s cognitive workload in real-time, which is a complex multifaceted problem. Attempts have been made to measure cognitive workload with single and multimodal input with some success - but no comprehensive framework has existed earlier in this regard. The investigation begins by comprehensively reviewing efforts to measure cognitive workload in both human factors and psychology of learning domains. Human factors domain is relevant to the real-time dimension and application of this problem while psychology of learning provides the comprehensive cognitive load theory framework for experimental research. With this background, the thesis explores user mouse input modality and develops temporal and spatial features that can index user’s cognitive workload under experimental conditions. These features are then further explored for (a) generalizability using three subject groups and (b) viability in real-time environment using modified adaptive windowing and concept drift detection techniques. A pause/hesitation analysis is developed to link user mouse interactivity features to changing cognitive workload levels. Considering these empirical explorations and other prior attempts, a framework is proposed for real-time cognitive workload measures. User’s Load-Effort Homeostasis (LEH) is an important discovery while putting together the framework and is then explored using Big-Five personality traits. Another contribution is explaining and interpreting LEH using both Baddeley’s working memory model and Cowen’s embedded process model. Framework applicability is then demonstrated by applying it to the problem of making machine learning usable (in the context of decision support systems). Finally, interactive machine learning is presented and argued as the best application context for the real-time cognitive workload framework. Future work would include developing and extending the multimodal aspect of this framework

This paper presents a methodology that aims at the incremental representation of areas inside environments in terms of attractive forces. It is proposed a parametric representation of velocity fields ruling the dynamics of moving agents. It is assumed that attractive spots in the environment are responsible for modifying the motion of agents. A switching model is used to describe near and far velocity fields, which in turn are used to learn attractive characteristics of environments. The effect of such areas is considered radial over all the scene. Based on the estimation of attractive areas, a map that describes their effects in terms of their localizations, ranges of action, and intensities is derived in an online way. Information of static attractive areas is added dynamically into a set of filters that describes possible interactions between moving agents and an environment. The proposed approach is first evaluated on synthetic data; posteriorly, the method is applied on real trajectories coming from moving pedestrians in an indoor environment.

The human behaviour analysis has been a subject of study in various fields of science (e.g. sociology, psychology, computer science). Specifically, the automated understanding of the behaviour of both individuals and groups remains a very challenging problem from the sensor systems to artificial intelligence techniques. Being aware of the extent of the topic, the objective of this paper is to review the state of the art focusing on machine learning techniques and computer vision as sensor system to the artificial intelligence techniques. Moreover, a lack of review comparing the level of abstraction in terms of activities duration is found in the literature. In this paper, a review of the methods and techniques based on machine learning to classify group behaviour in sequence of images is presented. The review takes into account the different levels of understanding and the number of people in the group.

© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., Classical Pre-Post Intervention Studies are often analyzed using traditional statistics. Nevertheless, the nutritional interventions have small effects on the metabolism and traditional statistics are not enough to detect these subtle nutrient effects. Generally, this kind of studies assumes that the participants are adhered to the assigned dietary intervention and directly analyzes its effects over the target parameters. Thus, the evaluation of adherence is generally omitted. Although, sometimes, participants do not effectively adhere to the assigned dietary guidelines. For this reason, the Trajectory Map is proposed as a visual tool where dietary patterns of individuals can be followed during the intervention and can also be related with nutritional prescriptions. The Trajectory Analysis is also proposed allowing both analysis: 1) adherence to the intervention and 2) intervention effects. The analysis is made by projecting the differences of the target parameters over the resulting trajectories between states of different time-stamps which might be considered either individually or by groups. The proposal has been applied over a real nutritional study showing that some individuals adhere better than others and some individuals of the control group modify their habits during the intervention. In addition, the intervention effects are different depending on the type of individuals, even some subgroups have opposite response to the same intervention., Peer Reviewed, Postprint (author's final draft)

The study of intracellular dynamic processes is of fundamental importance for understanding a wide variety of diseases and developing effective drugs and therapies. Advanced fluorescence microscopy imaging systems nowadays allow the recording of virtually any type of process in space and time with super-resolved detail and with high sensitivity and specificity. The large volume and high information content of the resulting image data, and the desire to obtain objective, quantitative descriptions and biophysical models of the processes of interest, require a high level of automation in data analysis. Two key tasks in extracting biologically meaningful information about intracellular dynamics from image data are particle tracking and particle trajectory analysis. Here we present state-of-the-art software tools for these tasks and describe how to use them., info:eu-repo/semantics/published

An important task in trajectory analysis is defining a meaningful representative for a cluster of similar trajectories. Formally defining and computing such a representative r is a challenging problem. We propose and discuss two new definitions, both of which use only the geometry of the input trajectories. The definitions are based on the homotopy area as a measure of similarity between two curves, which is a minimum area swept by all possible deformations of one curve into the other. In the first definition we wish to minimize the maximum homotopy area between r and any input trajectory, whereas in the second definition we wish to minimize the sum of the homotopy areas between r and the input trajectories. For both definitions computing an optimal representative is NP-hard. However, for the case of minimizing the sum of the homotopy areas, an optimal representative can be found efficiently in a natural class of restricted inputs, namely, when the arrangement of trajectories forms a directed acyclic graph.

Objectives The unemployed are assumed to adopt unhealthy behaviours, including harmful use of alcohol. This study sought to elucidate the relations between unemployment before age 21years and consumption of alcohol from 21 to 42years. The design was based on the conception of youth as a sensitive period for obtaining drinking scars' that are visible up to middle age. Setting The Northern Swedish Cohort Study has followed up a population sample from 1981 to 2007 with five surveys. Participants All pupils (n=1083) attending the last year of compulsory school in Lulea participated in the baseline survey in classrooms, and 1010 of them (522 men and 488 women) participated in the last follow-up survey that was conducted at classmate reunions or by post or by phone. Outcome measure The trajectory of alcohol consumption from 21 to 43years, obtained with latent class growth analyses, was scaled. Results Men were assigned to five and women to three consumption trajectories. The trajectory membership was regressed on accumulation of unemployment from 16 to 21years, with multinomial logistic regression analyses. The trajectory of moderate consumption was preceded by lowest exposure to unemployment in men and in women. With reference to this, the relative risk ratios for high-level trajectory groups were 3.49 (1.25 to 9.79) in men and 1.41 (0.74 to 2.72) in women, but also the trajectories of low-level consumption were more probable (relative risk ratio 3.18 (1.12 to 9.02) in men and 2.41 (1.24 to 4.67) in women). Conclusions High-level alcohol consumption throughout adulthood is, particularly among men, partly due to scars' from youth unemployment, particularly in men, but there are also groups of men and women where unemployment in the teens predicts a trajectory of low consumption.