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PubMed1995

Trajectory mapping: a new nonmetric scaling technique.

Trajectory mapping is a new scaling technique designed to recover the parameterizations, axes, and paths used to traverse a feature space. Unlike with multidimensional scaling, there is no assumption that the space is homogeneous or metric. Although some metric ordering information is obtained with trajectory mapping, the main output is the feature parameterizations that partition the given domain of object samples into different categories. After an introductory example, the technique is further illustrated by using first a set of colors and then a collection of textures.

Color Perception↗

PubMed2006

Utilizing the information content in two-state trajectories.

The signal from many single-molecule experiments monitoring molecular processes, such as enzyme turnover by means of fluorescence and opening and closing of ion channel through the flux of ions, consists of a time series of stochastic "on" and "off" (or open and closed) periods, termed a two-state trajectory. This signal reflects the dynamics in the underlying multisubstate on-off kinetic scheme (KS) of the process. The determination of the underlying KS is difficult and sometimes even impossible because of the loss of information in the mapping of the multidimensional KS onto two dimensions. Here we introduce a previously undescribed procedure that efficiently and optimally relates the signal to all equivalent underlying KS. This procedure partitions the space of KS into canonical (unique) forms that can handle any KS and obtains the topology and other details of the canonical form from the data without the need for fitting. Also established are relationships between the data and the topology of the canonical form to the on-off connectivity of a KS. The suggested canonical forms constitute a powerful tool in discriminating between KS. Based on our approach, the upper bound on the information content in two-state trajectories is determined.

Ion Channel Gating↗

PubMed2003

Encephalization and allometric trajectories in the genus Homo: evidence from the Neandertal and modern lineages.

The term "encephalization" is commonly used to describe an enlargement in brain size, considered as either absolute endocranial volumes or relative values in relation to body size. It is widely recognized that a considerable endocranial expansion occurred throughout the evolution of the genus Homo. This article aims to evaluate whether this phenomenon was the outcome of distinct evolutionary lineages, reaching similar brain expansions but through different trajectories. Endocranial morphology was studied in a sample of fossil hominines by multivariate approaches using both traditional metrics and geometric morphometrics. The analysis was focused on the transition from a generalized archaic pattern within the genus Homo to the modern morphology and compared with changes that occurred along the Neandertal lineage. The main result was the identification of two different evolutionary trajectories, in which a similar expansion in endocranial size has been reached by different changes in shape. Along the Neandertal lineage we observed maintenance of an "archaic" endocranial model, in which a large amount of variability is based on a single allometric trend. By contrast, when modern endocasts were compared with nonmodern ones, we found important differences apparently led by a parietal expansion. In this light, the origin of our species may have represented the opportunity to surpass the constraints imposed on encephalization by the ontogenetic pattern shared by nonmodern Homo representatives.

Animals↗

PubMed1979

Float trajectories in simple kinematic flows.

A simple kinematic model has been used to compute Lagrangian trajectories. Although it is certainly too simple to model geophysical flows, it has provided insights into the behavior of Lagrangian tracers. In particular, the existence of trapping regions has been shown to greatly increase the dispersion rate of tracers and to lead to net tracer displacements when the Eulerian mean flow is zero. In general, the spectrum of spatial scales present in the trajectories is wider than the Eulerian spectrum and is biased towards shorter wavelengths; the disparity between the 100-km Eulerian scale and the much shorter length scales experienced by the tracers is demonstrated. The estimation of the Eulerian parameters of the field from Lagranian observations must be done with a great deal of care, particularly if the eddy flow velocities are comparable to or exceed the mean flow. With a limited number of tracers it is extremely difficult to estimate, with any degree of confidence, the properties of either the mean Eulerian flow or the eddy field. Clearly, more effort must be spent to better understand the behavior of tracers in more realistic flows, to devise data analysis techniques, and to relate the Eulerian and Lagrangian spectra.

Journal Article↗

PubMed2001

Characteristics of cursor trajectories controlled by the computer mouse.

An analysis of computer screen cursor trajectories can provide insights into the factors limiting efficient cursor positioning and can assist in the design of human-computer interfaces. Cursor locations as controlled by a Microsoft computer mouse with standard settings were therefore sampled at 5 ms intervals and kinematic analyses addressed the proportions of time spent in the initiation, accelerative and terminal guidance phases of cursor positioning. Twelve participants used a computer mouse to move a cursor over different distances (7.5 cm, 15 cm) from a home location in the lower centre of the screen to targets of different diameters (8 mm, 16 mm), situated to the left, middle or right of the computer screen. Cursor trajectories were irregular, and participants regularly overshot their targets, spending 70% of movement duration in terminal guidance. Participants appeared to use the initial part of their movement to establish mappings between controller and display. Interventions should seek to reduce the terminal guidance phase of cursor positioning.

Adult↗

PubMed2002

Generation of bimanual trajectories of disparate eccentricity: levels of interference and spontaneous changes over practice.

The authors examined intermanual interactions of 2 hands that were required to concurrently follow trajectories that differed in eccentricity. Ten healthy participants attempted to learn to trace 2 figures, a circle and an ellipse, with bilaterally isochronous (1:1) timing demands. Initial unimanual trials were followed by bilateral practice comprising 750 movement cycles. Two objectives were addressed: The authors' primary aim was to determine if kinematic interlimb interference is evident independent of spatial and temporal interference and to observe the potential practice-related changes in the nature of that interference. That test was afforded by participants' natural tendency to draw a circle with a relatively constant tangential velocity and an ellipse with a systematically varying velocity. A second aim was to observe the nature of spontaneous changes in the performance of each individual effector, and in the relationship between effectors, across practice. Those objectives were specifically addressed in a context in which augmented feedback was not available to direct the learners' attention to a particular feature of performance. The results suggested that interlimb assimilation of spatial features is the primary source of interference for that task and that apparent effects at the kinematic level are the secondary, indirect product of spatial coupling. Those results were found across blocks of practice. With respect to nondirected performance changes, substantially less improvement was evident in the performance of each individual effector than in the reduction of interlimb interference. Specifically, no practice-related changes in temporal variability or velocity bias, and minimal changes in trajectory smoothness, were evident in individual limbs. Conversely, significant reductions were observed in the variability of relative phase between limbs and in the magnitude of interlimb phase lag.

Adolescent↗

PubMed2004

Movement trajectories in the presence of a distracting stimulus: evidence for a response activation model of selective reaching.

Consistent with action-based theories of attention, the presence of a nontarget stimulus in the environment has been shown to alter the characteristics of goal-directed movements. Specifically, it has been reported that movement trajectories veer away from (Howard & Tipper, 1997) or towards (Welsh, Elliott, & Weeks, 1999) the location of a nontarget stimulus. The purpose of the experiments reported in this paper was to test a response activation model of selective reaching conceived to account for these variable results. In agreement with the model, the trajectory changes in the movements appear to be determined by the activation levels of each competing response at the moment of response initiation. The results of the present work, as well as those of previous studies, are discussed within the framework of the model of response activation.

Adult↗

PubMed2006

Data mining of molecular dynamics trajectories of nucleic acids.

Analysis, storage, and transfer of molecular dynamic trajectories are becoming the bottleneck of computer simulations. In this paper we discuss different approaches for data mining and data processing of huge trajectory files generated from molecular dynamic simulations of nucleic acids.

Computer Simulation↗

PubMed2026

Integrated multi-omics profiling of amniotic fluid identifies predictive biomarkers for fetal growth restriction trajectories.

BACKGROUND: Fetal growth restriction (FGR) is a complex condition with highly heterogeneous clinical outcomes, making prenatal distinction between transient and persistent growth failure challenging. This study aims to identify amniotic fluid (AF) biomarkers capable of differentiating distinct FGR trajectories and characterizing persistent growth failure mechanisms. METHODS: Integrated proteomic and metabolomic profiling was performed on AF samples from transient FGR (n = 11), persistent FGR (n = 9), and healthy controls (n = 13). Diagnostic and prognostic models were developed using multivariate analysis. Selected protein candidates were validated via ELISA in an independent cohort (n = 69). RESULTS: Multi-omics analysis revealed distinct molecular signatures for FGR stratification. A two-protein diagnostic panel (PDGFA and phospho-STAT5A) achieved an AUC of 1.000 in the discovery stage and 0.780 in the external validation cohort. For prognostic assessment, a molecular signature including IREB2, HLA-C, and PLXNB2 accurately predicted persistent growth failure from transient recovery (AUC = 0.966). Cross-platform integration highlighted the mass spectrometry-derived WASHC2C as a central hub protein with a significant progressive increase across the control, transient, and persistent groups (p < 0.001). CONCLUSIONS: This study establishes a multi-omics framework for prenatal FGR stratification. Our findings identify distinct molecular signatures reflecting the intrauterine environment and provide high-performance molecular tools for predicting divergent fetal growth trajectories to guide personalized clinical decision-making.

Humans↗

PubMed2002

The unfolding illness trajectory of stroke.

PURPOSE: To describe the characteristics of the illness trajectory of stroke during the first year. METHOD: A qualitative, prospective case study design; repeated in-depth semi-structured interviews with nine mild to moderately affected stroke patients during the course of the first year. A total of 63 interviews were conducted. The interview data were transcribed verbatim and analysed as a text, using a hermeneutic approach. RESULTS: A stroke is not necessarily experienced as an abrupt psychosocial crisis by the stroke patient. The adjustment process seems to be gradually evolving and prolonged over most of the first year following the cerebro-vascular accident (CVA). The illness trajectory may be divided into four phases, each with characteristic tasks and focal points. The adjustment process involves hard physical and psychosocial work on the part of patient. A necessary pre-requisite for adjustment is a realistic conception of the illness and its implications. This takes time and experience to achieve. CONCLUSIONS: The adjustment process following stroke is gradual and prolonged. In order to move away from the predominant functional rehabilitation approach towards a more comprehensive and better targeted service, increased understanding of the complexities of the adjustment process is necessary.

Aged↗

PubMed2006

Prenatal stress affects the developmental trajectory of the rat amygdala.

The amygdala plays a critical role in generating the emotion of fear, and alterations in amygdala fear processing are thought to underlie the acquisition and maintenance of anxiety disorders. The prenatally stressed (PS) rat displays hormonal, behavioral and brain anatomical similarities to anxious humans and is useful to study the neurobiological underpinnings of pathological anxiety. We studied PS and control male rats at postnatal days 7 (P7), P25, P45 and P60. Using unbiased stereological analyses we examined the volumes, anterior-posterior lengths and total numbers of neurons and glia of the basolateral (BL), central (Ce) and lateral (La) amygdalar nuclei. We found prenatal stress-associated differences in the developmental trajectories of each nucleus. These were apparent in some measures as early as P7, most extensive at P25 and resolved by P45, at least as seen by Nissl staining. These changes were not a result of differential brain growth. This early divergence in developmental trajectories seen here may be the harbinger of PS rat amygdalas that ultimately function very differently in adulthood.

Amygdala↗

PubMed2005

The return to smoking: 1-year relapse trajectories among female smokers.

Research has demonstrated that a lapse in cigarette abstinence often leads smokers to fully relapse (i.e., return to daily smoking). However, patterns of smoking resumption beyond the point at which relapse occurs have not been examined in systematic follow-up studies. Daily cigarette intake data for 108 female adult smokers who participated in a smoking cessation trial were recorded at several points during the 365 days following the participants' quit date. SAS Proc Traj, a group-based mixture modeling procedure, was used to determine cigarette-use trajectories over time (i.e., patterns of smoking resumption). Over the 365 days, 27% of the sample maintained abstinence. Among the 73% who relapsed, four distinct trajectories emerged: low-level users (8% of the overall sample), moderate users (17%), slow-returners (15%), and quick-returners (33%). A few individual characteristics differentiated these groups. Overall, the findings illustrate that, after relapsing, smokers do not follow a unitary course of smoking resumption; rather, they exhibit more variable resumption patterns than previously assumed.

Adult↗

PubMed2026

Parallel evolutionary trajectories rewire enteropathogenic Escherichia coli adhesion to restore host attachment.

Enteropathogenic Escherichia coli (EPEC) causes disease in children, presenting as chronic diarrhea that can impair physical and cognitive development. The attachment of typical EPEC (tEPEC) to the gut epithelium via bundle-forming pili (BFP) is a key factor in its virulence. Yet, infections by atypical EPEC (aEPEC), which lack BFP, have become increasingly common. To investigate how aEPEC recover host-attachment in the absence of BFP, we performed experimental evolution using a non-adherent E. coli, constructed to mimic the ancestor of aEPEC, and selected adherent progeny. Highly adherent variants evolved through phase-variable activation of type I fimbriae (T1F), followed by two alternative trajectories: bacterial filamentation, which increases T1F avidity, or point mutations in the T1F adhesin FimH that enhance ligand affinity. Extending our analysis to the genomes of 327 aEPEC strains isolated from infected patients revealed that similar FimH mutations are common. We further demonstrated experimentally that these naturally occurring variants often increase epithelial-attachment. Our findings implicate T1F in aEPEC pathogenesis and suggest it may be clinically relevant for anti-adhesion therapy. More broadly, these results indicate that impaired host-attachment can be rapidly compensated by upregulating and optimizing an alternative adhesin, and that combining experimental evolution with comparative genomics can reveal evolutionary trajectories occurring in nature.

Bacterial Adhesion↗

PubMed1998

Leaf trajectory calculation for dynamic multileaf collimation to realize optimized fluence profiles.

An algorithm for the calculation of the required leaf trajectories to generate optimized intensity modulated beam profiles by means of dynamic multileaf collimation is presented. This algorithm iteratively accounts for leaf transmission and collimator scatter and fully avoids tongue-and-groove underdosage effects. Tests on a large number of intensity modulated fields show that only a limited number of iterations, generally less than 10, are necessary to minimize the differences between optimized and realized fluence profiles. To assess the accuracy of the algorithm in combination with the dose calculation algorithm of the Cadplan 3D treatment planning system, predicted absolute dose distributions for optimized fluence profiles were compared with dose distributions measured on the MM50 Racetrack Microtron and resulting from the calculated leaf trajectories. Both theoretical and clinical cases yield an agreement within 2%, or within 2 mm in regions with a high dose gradient, showing that the accuracy is adequate for clinical application.

Algorithms↗

PubMed2000

3D cone-beam CT reconstruction for circular trajectories.

3D reconstruction from 2D projections obtained along a single circular source trajectory is most commonly done using an algorithm due to Feldkamp, Davis and Kress. In this paper we propose an alternative approach based on a cone-beam to parallel-beam rebinning step, a corresponding rebinning step into a rectangular virtual detector plane and a filtered backprojection. This approach yields an improved image quality reflected by a decreased low-intensity drop which is well known for 3D reconstruction from projection data obtained along circular trajectories. At the same time the computational complexity is lower than in Feldkamp's original approach. Based on this idea, a hybrid 3D cone-beam reconstruction method is formulated that enlarges the reconstruction volume in its dimension along the rotation axis of the cone-beam CT system. This enlargement is achieved by applying different reconstruction conditions for each voxel. An optimal ratio between the reconstructible and irradiated volume of the scanned object is achieved.

Algorithms↗

PubMed2004

Image reconstruction for the circle and line trajectory.

We propose an exact shift-invariant filtered backprojection algorithm for inversion of the cone beam data in the case when the source trajectory consists of an incomplete circle and a line segment. The algorithm allows for axial truncation of the cone beam data. The length of the line scan is determined only by the region of interest and is independent of the size of the entire object. The algorithm is quite flexible and can also be used for more general trajectories consisting of several (complete or incomplete) circles and line segments. Results of numerical experiments demonstrate good image quality.

Algorithms↗

PubMed2004

Three-dimensional seed reconstruction for prostate brachytherapy using Hough trajectories.

In order to perform intra-operative or post-implant dosimetry in prostate brachytherapy, the 3D coordinates of the implanted radioactive seeds must be determined. Film or fluoroscopy based seed reconstruction techniques use back projection of x-ray data obtained at two or three x-ray positions. These methods, however, do not perform well when some of the seed images are undetected. To overcome this problem we have developed an alternate technique for 3D seed localization using the principle of Hough transform. The Hough method utilizes the fact that, for each seed coordinate in three dimensions, there exists a unique trajectory in Hough feature space. In this paper we present the Hough transform parametric equations to describe the path of the seed projections from one view to the next and a method to reconstruct the 3D seed coordinates. The results of simulation and phantom studies indicate that the Hough trajectory method can accurately determine the 3D seed positions even from an incomplete dataset.

Algorithms↗

PubMed2005

Image reconstruction for the circle-and-arc trajectory.

Proposed is an exact shift-invariant filtered backprojection algorithm for the circle-and-arc trajectory. The algorithm has several important features. First, it allows for the circle to be incomplete. Second, axial truncation of the cone beam data is allowed. Third, the length of the arc is determined only by the region of interest and is independent of the size of the entire object. The algorithm is quite flexible and can be used for even more general trajectories that consist of several circular segments and arcs. The algorithm applies also in the case when the circle (or, circles) is complete. A numerical experiment with the clock phantom demonstrated good image quality.

Algorithms↗