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PubMed2006

Semiparametric approach to characterize unique gene expression trajectories across time.

BACKGROUND: A semiparametric approach was used to identify groups of cDNAs and genes with distinct expression profiles across time and overcome the limitations of clustering to identify groups. The semiparametric approach allows the generalization of mixtures of distributions while making no specific parametric assumptions about the distribution of the hidden heterogeneity of the cDNAs. The semiparametric approach was applied to study gene expression in the brains of Apis mellifera ligustica honey bees raised in two colonies (A. m. mellifera and ligustica) with consistent patterns across five maturation ages. RESULTS: The semiparametric approach provided unambiguous criteria to detect groups of genes, trajectories and probability of gene membership to groups. The semiparametric results were cross-validated in both colony data sets. Gene Ontology analysis enhanced by genome annotation helped to confirm the semiparametric results and revealed that most genes with similar or related neurobiological function were assigned to the same group or groups with similar trajectories. Ten groups of genes were identified and nine groups had highly similar trajectories in both data sets. Differences in the trajectory of the reminder group were consistent with reports of accelerated maturation in ligustica colonies compared to mellifera colonies. CONCLUSION: The combination of microarray technology, genomic information and semiparametric analysis provided insights into the genomic plasticity and gene networks linked to behavioral maturation in the honey bee.

Age Factors↗
PubMed2004

Optimal trajectories from the Earth-Moon L1 and L3 points to deflect hazardous asteroids and comets.

Software code named asteroff was recently created by the author to simulate the deflection of hazardous asteroids off of their collision course with the Earth. This code was both copyrighted and patented to avoid unauthorized use of ideas that could possibly be vital to construct a planetary defense system in the vicinity of the Earth. Having so said, the basic ideas and equations underlying the asteroff simulation code are openly described in this paper. A system of two space bases housing missiles is proposed to achieve the planetary defense of the Earth against dangerous asteroids and comets, collectively called impactors herein. We show that the layout of the Earth-Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L(1) (between the Earth and the Moon) and L(3) (in the direction opposite to the Moon from the Earth). We show that placing missile bases at L(1) and L(3) would enable those missiles to deflect the trajectory of impactors by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement. One additional remark is that the theory developed in this paper is just a beginning for a wider set of future research. In fact, we only develop the Keplerian analytical theory for the optimal planetary defense achievable from the Earth-Moon Lagrangian points L(1) and L(3). Much more sophisticated analytical refinements would be needed to: (1) take into account many perturbation forces of all kinds acting on both the impactors and missiles shot from L(1) and L(3); (2) add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L(4) and L(5) of the Earth-Moon System or from the surface of the Moon itself; and (3) encompass the full range of missiles currently available to the US (and possibly other countries) so as to really see which impactors could be diverted by which missiles, even in the very simplified scheme outlined here. Published for the first time in February 2002, our Keplerian planetary defense theory has proved, in just one year, to be simple enough to catch the attention of scholars, in addition to popular writers, and even of someone from the US Military. These recent developments might possibly mark the beginning of an all embracing vision in planetary defense beyond all learned congressional activities, dramatic movies, and unknown military plans covered by secrecy.

Journal Article↗
PubMed2005

Trajectory analysis for the lunar flyby rescue of AsiaSat-3/HGS-1.

On May 13, 1998, the Hughes Global Services 1 Spacecraft (HGS-1, originally known as AsiaSat 3) became the first commercial spacecraft to fly by the Moon on a trajectory to reposition it into a useful geosynchronous orbit. This was necessary due to the failure of the last stage of the launch vehicle that left it in a high inclination, eccentric, and unusable orbit. The spacecraft did not have enough propellant to perform the maneuvers required to place it into its intended geostationary orbit via a standard transfer trajectory. However, it did have enough propellant to place it on a trajectory that flew by the Moon twice to finally achieve a useful low inclination geosynchronous orbit. In addition to being the first commercial operation in the vicinity of the Moon, it was the last successful lunar mission of the twentieth century. We discuss of the events leading up to the start of the rescue operation that included contributions from external organizations. We also describe the analytic estimates used to construct the trajectory and provide an overview of the details of the actual mission.

Journal Article↗
PubMed2025

Trajectory inference from single-cell genomics data with a process time model.

Single-cell transcriptomics experiments provide gene expression snapshots of heterogeneous cell populations across cell states. These snapshots have been used to infer trajectories and dynamic information even without intensive, time-series data by ordering cells according to gene expression similarity. However, while single-cell snapshots sometimes offer valuable insights into dynamic processes, current methods for ordering cells are limited by descriptive notions of "pseudotime" that lack intrinsic physical meaning. Instead of pseudotime, we propose inference of "process time" via a principled modeling approach to formulating trajectories and inferring latent variables corresponding to timing of cells subject to a biophysical process. Our implementation of this approach, called Chronocell, provides a biophysical formulation of trajectories built on cell state transitions. The Chronocell model is identifiable, making parameter inference meaningful. Furthermore, Chronocell can interpolate between trajectory inference, when cell states lie on a continuum, and clustering, when cells cluster into discrete states. By using a variety of datasets ranging from cluster-like to continuous, we show that Chronocell enables us to assess the suitability of datasets and reveals distinct cellular distributions along process time that are consistent with biological process times. We also compare our parameter estimates of degradation rates to those derived from metabolic labeling datasets, thereby showcasing the biophysical utility of Chronocell. Nevertheless, based on performance characterization on simulations, we find that process time inference can be challenging, highlighting the importance of dataset quality and careful model assessment.

Single-Cell Analysis↗
PubMed2004

Superlinear population encoding of dynamic hand trajectory in primary motor cortex.

Neural activity in primary motor cortex (MI) is known to correlate with hand position and velocity. Previous descriptions of this tuning have (1) been linear in position or velocity, (2) depended only instantaneously on these signals, and/or (3) not incorporated the effects of interneuronal dependencies on firing rate. We show here that many MI cells encode a superlinear function of the full time-varying hand trajectory. Approximately 20% of MI cells carry information in the hand trajectory beyond just the position, velocity, and acceleration at a single time lag. Moreover, approximately one-third of MI cells encode the trajectory in a significantly superlinear manner; as one consequence, even small position changes can dramatically modulate the gain of the velocity tuning of MI cells, in agreement with recent psychophysical evidence. We introduce a compact nonlinear "preferred trajectory" model that predicts the complex structure of the spatiotemporal tuning functions described in previous work. Finally, observing the activity of neighboring cells in the MI network significantly increases the predictability of the firing rate of a single MI cell; however, we find interneuronal dependencies in MI to be much more locked to external kinematic parameters than those described recently in the hippocampus. Nevertheless, this neighbor activity is approximately as informative as the hand velocity, supporting the view that neural encoding in MI is best understood at a population level.

Action Potentials↗
PubMed1995

Managing an uncertain illness trajectory in old age: patients' and physicians' views of stroke.

Uncertainty is a central feature of a chronic illness trajectory, resulting from questions about the effects of the illness on daily life, what symptoms mean, and what the future holds. When chronic illness occurs late in life, uncertainty is magnified, and serious questions arise about whether the individual will be able to weather the disruption and go on with daily life. This article examines illness trajectories from two vantage points, that of older persons who have had a stroke and that of physicians who care for stroke patients, by means of interviews with 36 persons who had strokes and with 20 physicians. Physicians' views of stroke were informed not only by knowledge of physiological processes but also by biomedical ideologies and cultural meanings associated with their patients' ages and impairments. People who had strokes focused on recovery; they assumed the trajectory was open to manipulation if they worked hard enough. The vague medical response to uncertainty affected patients' interpretations; what they were not told shaped their expectations about recovery as much as what they were told. The uncertain trajectory of stroke in old age is one example of how illness experience is affected by cultural attitudes about age, biomedical ideologies, the provision of health care services, and economically driven health policies. The anticipation of recovery by persons who have had strokes and the letdown when recovery does not occur reflect critical dilemmas in biomedicine and in society itself that have implications for health policy.

Activities of Daily Living↗
PubMed2006

Analysis of single-molecule FRET trajectories using hidden Markov modeling.

The analysis of single-molecule fluorescence resonance energy transfer (FRET) trajectories has become one of significant biophysical interest. In deducing the transition rates between various states of a system for time-binned data, researchers have relied on simple, but often arbitrary methods of extracting rates from FRET trajectories. Although these methods have proven satisfactory in cases of well-separated, low-noise, two- or three-state systems, they become less reliable when applied to a system of greater complexity. We have developed an analysis scheme that casts single-molecule time-binned FRET trajectories as hidden Markov processes, allowing one to determine, based on probability alone, the most likely FRET-value distributions of states and their interconversion rates while simultaneously determining the most likely time sequence of underlying states for each trajectory. Together with a transition density plot and Bayesian information criterion we can also determine the number of different states present in a system in addition to the state-to-state transition probabilities. Here we present the algorithm and test its limitations with various simulated data and previously reported Holliday junction data. The algorithm is then applied to the analysis of the binding and dissociation of three RecA monomers on a DNA construct.

Algorithms↗
PubMed2003

Obesity and psychiatric disorder: developmental trajectories.

OBJECTIVES: To identify age-related trajectories of obesity from childhood into adolescence, and to test the association of these trajectories with the development of psychiatric disorders (conduct disorder, oppositional defiant disorder, attention-deficit/hyperactivity disorder, substance abuse, depression, and anxiety). METHODS: White children (N = 991) 9 to 16 years old from the Great Smoky Mountains Study, a representative sample of rural youth, were evaluated annually over an 8-year period for height, weight, psychiatric disorder, and vulnerabilities for psychiatric disorder. Longitudinal analyses on the repeated measures data were conducted using developmental trajectory models and generalized estimating equation models. RESULTS: Obesity was 3 to 4 times more common than expected from national rates using Centers for Disease Control and Prevention 2000 criteria. Four developmental trajectories of obesity were found: no obesity (73%), chronic obesity (15%), childhood obesity (5%), and adolescent obesity (7%). Only chronic obesity was associated with psychiatric disorder: oppositional defiant disorder in boys and girls and depressive disorders in boys. CONCLUSIONS: In a general population sample studied longitudinally, chronic obesity was associated with psychopathology.

Adolescent↗
PubMed1999

Anomalous origin of the left coronary artery from the right pulmonary artery with intramural aortic trajectory. Clinicosurgical diagnostic implications.

OBJECTIVE: Anomalous origin of the left coronary artery from the right pulmonary artery (AOLCARPA), is a rare entity that is usually associated with other defects. Of the 20 cases of AOLCARPA reported in the literature, 14 (70%) had associations. We describe four patients with AOLCARPA without associated defects, but with a peculiar intramural aortic trajectory. METHODS: Fifty-five patients with anomalous origin of the left coronary artery were operated upon at INCORFMUSP. Four of the patients had the anomalous origin from the right pulmonary artery (RPA) without associated defects but with intramural aortic trajectory. Clinical and laboratory examinations were analyzed, as well as surgical findings. RESULTS: All patients had congestive heart failure (CHF) and 3 also had angina pectoris. Two patients had a murmur of mitral regurgitation, signs of myocardial infarction on the ECG and cardiomegaly. The shortening fraction varied from 9% to 23%. The hemodynamic study confirmed the diagnosis of anomalous origin of the coronary artery, but the intramural trajectory and the origin from the RPA were established only at surgery. In 3 patients, the technique of side-to-side anastomosis was performed with a good outcome. One patient, who underwent end-to-side anastomosis, died 6 months after the surgery. CONCLUSION: Association with other defects usually occurs in the AOLCARPA, and the intramural aortic trajectory is difficult to clinically diagnose but easy to surgically correct.

Adolescent↗
PubMed2003

Development and first patient trial of a surgical robot for complex trajectory milling.

OBJECTIVE: Today's surgical robots normally perform "simple" trajectories, e.g., assisting as tool-holding devices in neurosurgery, or milling linear paths for cavities in total hip replacement. From a clinical point of view, it is still a complex undertaking to implement robots in the operating room. Until now, robot systems have not been used in patient trials to mill "complex" trajectories, which involve many positional and orientation changes and are often necessary in cranio-maxillofacial (CMF) surgery. This paper presents the RobaCKa surgical robot system, which allows more precise execution of surgical interventions and milling of "complex" trajectories. MATERIALS AND METHODS: The main components of the RobaCKa system are a (former) CASPAR robot system, a POLARIS system, and a force-torque sensor. RESULTS: In the first patient trial (April 2003) the planned trajectory was executed with an error of 0.66 +/- 0.2 mm. CONCLUSIONS: The use of former industrial robots for surgical applications is possible but complex. The advantages are improved precision and quality and the possibility of documentation. The use of such systems is normally limited to research institutions or large clinics, because it is hardly possible to implement the necessary technical and logistic efforts in routine surgical work.

Craniotomy↗
PubMed2004

The application accuracy of a skull-mounted trajectory guide system for image-guided functional neurosurgery.

OBJECTIVE: Frameless image guided systems have traditionally been perceived as being less accurate than stereotactic frames, limiting their adoption for trajectory-based procedures such as deep brain stimulator placement which require submillimetric accuracy. However, some studies have suggested that high degrees of accuracy are attainable with optical localization systems. We evaluated the application accuracy of a skull-mounted trajectory guide coupled to an optical image-guided surgery system in a laboratory setting. MATERIALS AND METHODS: A plastic skull phantom was fitted with five fiducial markers rigidly attached via self-drilling bone screws. Varying MRI and CT imaging protocols were obtained at 25 different centers. A metal disc marked in 1-mm increments was placed at the expected target point. Following registration and alignment of the trajectory guide, radial and depth localization errors were measured. A total of 560 measurements were obtained and detailed statistical analyses were performed. RESULTS: Mean localization error was 1.25 mm with a 95% confidence interval of 2.7 mm and a 99.9% confidence interval of 4.0 mm. These values were significantly lower than those published for the two most widely used frame systems (p<0.001). CONCLUSIONS: Accuracy of image-guided localization using a rigid trajectory guide can meet or exceed that achievable with a stereotactic frame.

Humans↗
PubMed2006

The control of saccade trajectories: direction of curvature depends on prior knowledge of target location and saccade latency.

Recent reports have shown that saccades can deviate either toward or away from distractors. However, the specific conditions responsible for the change in initial saccade direction are not known. One possibility, examined here, is that the direction of curvature (toward or away from distractors) reflects preparatory tuning of the oculomotor system when the location of the target and distractor are known in advance. This was investigated by examining saccade trajectories under predictable and unpredictable target conditions. In Experiment 1, the targets and the distractors appeared unpredictably, whereas in Experiment 2 an arrow cue presented at fixation indicated the location of the forthcoming target prior to stimulus onset. Saccades were made to targets on the horizontal, vertical, and principal oblique axis, and distractors appeared simultaneously at an adjacent location (a separation of +/- 45 degrees of visual angle). On average, saccade trajectories curved toward distractors when target locations were unpredictable and curved away from distractors when target locations were known in advance. There was no overall difference in mean saccade latencies between the two experiments. The magnitude of the distractor modulation of saccade trajectory (either toward or away from) was comparable across the different saccade directions (horizontal, vertical, and oblique). These results are interpreted in terms of the time course of competitive interactions operating in the neural structures involved in the suppression of distractors and the selection of a saccade target. A relatively slow mechanism that inhibits movements to distractors produces curvature away from the distractor. This mechanism has more time to operate when target location is predictable, increasing the likelihood that the saccade trajectory will deviate away from the distractor.

Adolescent↗
PubMed2000

The natural history of cigarette smoking from adolescence to adulthood in a midwestern community sample: multiple trajectories and their psychosocial correlates.

Previous research on the natural history of smoking has focused on overall group trajectories without considering the possibility of risk subgroup variation. To address this limitation, the authors of the present study aimed to identify subgroups with varying trajectories of smoking behavior. The authors accomplished this within a cohort-sequential study of a large community sample (N = 8,556) with measurements spanning ages 11-31. After removing 2 a priori groups (abstainers and erratics), the authors empirically identified 4 trajectory groups--early stable smokers, late stable smokers, experimenters, and quitters--and psychosocial variables from adolescence and young adulthood were significantly distinguished among them. Given recent advances in quantitative methods, it is now feasible to consider subgroups of trajectories within an overall longitudinal design.

Adolescent↗
PubMed2001

Outcome trajectories for assisted living and nursing facility residents in Oregon.

OBJECTIVE: To compare assisted living residents and nursing home residents on outcome trajectories for three outcomes: ability to perform activities of daily living (ADLs), psychological well-being, and pain and discomfort. DATA SOURCES/STUDY SETTING: A representative sample of one-third of the census from 38 participating assisted living facilities (N = 605) and two-fifths of the census from 31 participating nursing facilities (N = 610). STUDY DESIGN: A longitudinal design using hierarchical linear models to examine how setting (being in an assisted living setting or in a nursing home) affected growth trajectories for each outcome studied when adjusting for other resident characteristics. DATA COLLECTION: Residents or their proxies were interviewed and chart reviews done at baseline, six months, and one year. All baseline data were collected between August 1995 and May 1996. PRINCIPAL FINDINGS: We found differences in case mix between assisted living and nursing facility residents but no differences in outcome trajectories for ADLs, psychological well-being, and pain and discomfort. For ADLs and pain and discomfort on average, residents in both settings experienced change over the study period. For psychological well-being, residents experienced no change on average. CONCLUSIONS: The lack of difference in growth trajectories for ADLs, pain and discomfort, and psychological well-being between the two settings was noteworthy.

Activities of Daily Living↗
PubMed2001

Infant sensitivity to trajectory forms.

The authors investigated whether infants are sensitive to visual event trajectory forms, and whether they are sensitive to the underlying dynamics of trajectory forms. The authors habituated 8-month-old infants to a videotaped event run either forward or reversed in time and then switched them to the same event run in the opposite direction. Infants dishabituated when switched to the event with the novel direction in time, indicating sensitivity to the form of the trajectory. Infants exhibited equivalent habituation rates and looking times for forward and reversed events, thus failing to provide evidence that infants are sensitive to the underlying dynamics. In a partial replication of this first experiment, the same pattern of results was found. Both experiments revealed infant sensitivity to the trajectory forms, but not the underlying dynamics of events. The authors discuss implications for methods used in infant event perception studies.

Child Development↗
PubMed2002

Congruent qualitative behavior of complete and reconstructed phase space trajectories from biomolecular dynamics simulation.

Central to the study of a complex dynamical system is knowledge of its phase space behavior. Experimentally, it is rarely possible to record a system's (multidimensional) phase space variables. Rather, the system is observed via one (or few) scalar-valued signal(s) of emission or response. In dynamical systems analysis, the multidimensional phase space of a system can be reconstructed by manipulation of a one-dimensional signal. The trick is in the construction of a (higher-dimensional) space through the use of a time lag (or delay) on the signal time series. The trajectory in this embedding space can then be examined using phase portraits generated in selected subspaces. By contrast, in computer simulation, one has an embarrassment of riches: direct access to the complete multidimensional phase space variables, at arbitrary time resolution and precision. Here, the problem is one of reducing the dimensionality to make analysis tractable. This can be achieved through linear or nonlinear projection of the trajectory into subspaces containing high information content. This study considers trajectories of the small protein crambin from molecular dynamics simulations. The phase space behavior is examined using principal component analysis on the Cartesian coordinate covariance matrix of 138 dimensions. In addition, the phase space is reconstructed from a one dimensional signal, representing the radius of gyration of the structure along the trajectory. Comparison of low-dimensional phase portraits obtained from the two methods shows that the complete phase space distribution is well represented by the reconstruction. The study suggests that it may be possible to develop a deeper connection between the experimental and simulated dynamics of biomolecules via phase space reconstruction using data emerging from recent advances in single-molecule time-resolved biophysical techniques.

Animals↗
PubMed2005

Palliative trajectory markers for end-stage heart failure. Or "oh Toto. This doesn't look like kancerous!".

Heart failure is a complex syndrome with a high morbidity and mortality rate. The Canadian mortality rate is between 25% and 40% annually. End-stage heart failure patients suffer from many debilitating symptoms. Palliative symptom management and funding programs can assist many of these patients. Unfortunately, designating a heart failure patient as palliative with a trajectory of six months or less is not an easy task. This is difficult to determine due to the lack of tangible trajectory markers and the roller-coaster nature of the trajectory itself. These circumstances were the impetus for a review of the current literature and a clinical experience in a cardiac clinic within a major teaching hospital in Vancouver. The objective was to determine if clear palliative trajectory markers for heart failure existed and, if so, could they be used to produce a tool to assist health care professionals to accurately determine a timeline of six months or less.

Aged↗
PubMed1991

The trajectory of cancer recovery.

In response to the Corbin and Strauss illness trajectory framework, this paper offers a recovery model as a more relevant trajectory for cancer as a specific chronic disease and as a general framework for clinical science. As counterpoint, the course of recovery is considered as a separate but influential continuum vis-à-vis the course of illness. The text presents an overview of the nature and meaning of cancer as a chronic disease, an operational definition of the recovery model, and a comparison and contrast of the illness and recovery trajectory frameworks in terms of their philosophic nature, therapeutic approach and research and educational and health policy-making emphases with regard to the cancer experience. When fully grounded in recovery science, the recovery trajectory model is predicted to be the more therapeutically effective clinical approach for professionals who care for patients diagnosed with cancer and their families.

Adaptation, Psychological↗