Structure preserving schemes for mean-field equations of collective behavior

In this paper we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang-Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.Comment: Proceedings of the XVI International Conference on Hyperbolic Problem

The ϕ6 Cystovirus Protein P7 Becomes Accessible to Antibodies in the Transcribing Nucleocapsid: A Probe for Viral Structural Elements

Protein P7 is a component of the cystovirus viral polymerase complex. In the unpackaged procapsid, the protein is situated in close proximity to the viral directed RNA polymerase, P2. Cryo-electron microscopy difference maps from the species ϕ6 procapsid have demonstrated that P7 and P2 likely interact prior to viral RNA packaging. The location of P7 in the post-packaged nucleocapsid (NC) remains unknown. P7 may translocate closer to the five-fold axis of a filled procapsid but this has not been directly visualized. We propose that monoclonal antibodies (Mabs) can be selected that serve as probe- reagents for viral assembly and structure. A set of Mabs have been isolated that recognize and bind to the ϕ6 P7. The antibody set contains five unique Mabs, four of which recognize a linear epitope and one which recognizes a conformational epitope. The four unique Mabs that recognize a linear epitope display restricted utilization of Vκ and VH genes. The restricted genetic range among 4 of the 5 antibodies implies that the antibody repertoire is limited. The limitation could be the consequence of a paucity of exposed antigenic sites on the ϕ6 P7 surface. It is further demonstrated that within ϕ6 nucleocapsids that are primed for early-phase transcription, P7 is partially accessible to the Mabs, indicating that the nucleocapsid shell (protein P8) has undergone partial disassembly exposing the protein’s antigenic sites

Evaluating Retinal Function in Age-Related Maculopathy with the ERG Photostress Test

PURPOSE. To evaluate the diagnostic potential of the electroretinogram (ERG) photostress test and the focal cone ERG in age-related maculopathy (ARM). METHODS. The cohort comprised 31 patients with ARM and 27 age-matched control subjects. The ERG photostress test was used to monitor cone adaptation after intense light adaptation. Focal 41- and 5-Hz cone ERGs were recorded monocularly (central 20°) to assess steady state retinal function. Univariate analysis identified electrophysiological parameters that differed between groups, and receiver operating characteristic (ROC) curves were constructed to assess their diagnostic potential. Logistic regression analysis determined the diagnostic potential of a model incorporating several independent predictors of ARM. RESULTS. The rate of recovery of the ERG photostress test was reduced (recovery was slower) in subjects with ARM. The parameter exhibited good diagnostic potential (P = 0.002, area under ROC curve = 0.74). The implicit times of the 5-Hz (a-wave, P = 0.002; b-wave, P < 0.001) and the 41-Hz (P < 0.001) focal cone ERGs were increased, and the 41-Hz focal cone ERG amplitude (P = 0.003) and focal to full-field amplitude ratio (P = 0.001) were reduced in the ARM group. Logistic regression analysis identified three independent predictors of ARM, including the rate of recovery of the ERG photostress test. CONCLUSIONS. Early ARM has a marked effect on the kinetics of cone adaptation. The clinical application of the ERG photostress test increases the sensitivity and specificity of a model for the diagnosis of ARM. Improved assessment of the functional integrity of the central retina will facilitate early diagnosis and evaluation of therapeutic interventions

Control of interjoint coordination during the swing phase of normal gait at different speeds

BACKGROUND: It has been suggested that the control of unconstrained movements is simplified via the imposition of a kinetic constraint that produces dynamic torques at each moving joint such that they are a linear function of a single motor command. The linear relationship between dynamic torques at each joint has been demonstrated for multijoint upper limb movements. The purpose of the current study was to test the applicability of such a control scheme to the unconstrained portion of the gait cycle – the swing phase. METHODS: Twenty-eight neurologically normal individuals walked along a track at three different speeds. Angular displacements and dynamic torques produced at each of the three lower limb joints (hip, knee and ankle) were calculated from segmental position data recorded during each trial. We employed principal component (PC) analysis to determine (1) the similarity of kinematic and kinetic time series at the ankle, knee and hip during the swing phase of gait, and (2) the effect of walking speed on the range of joint displacement and torque. RESULTS: The angular displacements of the three joints were accounted for by two PCs during the swing phase (Variance accounted for – PC1: 75.1 ± 1.4%, PC2: 23.2 ± 1.3%), whereas the dynamic joint torques were described by a single PC (Variance accounted for – PC1: 93.8 ± 0.9%). Increases in walking speed were associated with increases in the range of motion and magnitude of torque at each joint although the ratio describing the relative magnitude of torque at each joint remained constant. CONCLUSION: Our results support the idea that the control of leg swing during gait is simplified in two ways: (1) the pattern of dynamic torque at each lower limb joint is produced by appropriately scaling a single motor command and (2) the magnitude of dynamic torque at all three joints can be specified with knowledge of the magnitude of torque at a single joint. Walking speed could therefore be altered by modifying a single value related to the magnitude of torque at one joint

Uncertainty quantification for kinetic models in socio-economic and life sciences

Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic. The construction of kinetic models describing the above processes, however, has to face the difficulty of the lack of fundamental principles since physical forces are replaced by empirical social forces. These empirical forces are typically constructed with the aim to reproduce qualitatively the observed system behaviors, like the emergence of social structures, and are at best known in terms of statistical information of the modeling parameters. For this reason the presence of random inputs characterizing the parameters uncertainty should be considered as an essential feature in the modeling process. In this survey we introduce several examples of such kinetic models, that are mathematically described by nonlinear Vlasov and Fokker--Planck equations, and present different numerical approaches for uncertainty quantification which preserve the main features of the kinetic solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic Equations

Unconstrained three-dimensional reaching in Rhesus monkeys

To better understand normative behavior for quantitative evaluation of motor recovery after injury, we studied arm movements by non-injured Rhesus monkeys during a food-retrieval task. While seated, monkeys reached, grasped, and retrieved food items. We recorded three-dimensional kinematics and muscle activity, and used inverse dynamics to calculate joint moments due to gravity, segmental interactions, and to the muscles and tissues of the arm. Endpoint paths showed curvature in three dimensions, suggesting that maintaining straight paths was not an important constraint. Joint moments were dominated by gravity. Generalized muscle and interaction moments were less than half of the gravitational moments. The relationships between shoulder and elbow resultant moments were linear during both reach and retrieval. Although both reach and retrieval required elbow flexor moments, an elbow extensor (triceps brachii) was active during both phases. Antagonistic muscles of both the elbow and hand were co-activated during reach and retrieval. Joint behavior could be described by lumped-parameter models analogous to torsional springs at the joints. Minor alterations to joint quasi-stiffness properties, aided by interaction moments, result in reciprocal movements that evolve under the influence of gravity. The strategies identified in monkeys to reach, grasp, and retrieve items will allow the quantification of prehension during recovery after a spinal cord injury and the effectiveness of therapeutic interventions

Short-term variability of biomarkers of proteinase activity in patients with emphysema associated with type Z alpha-1-antitrypsin deficiency

BACKGROUND: The burden of proteinases from inflammatory cells in the lung of subjects with type Pi ZZ of alpha-1-antitrypsin deficiency is higher than in those without the deficiency. Cross-sectional studies have shown increased levels of biomarkers of extracellular matrix degradation in vivo. Longitudinal variability of these biomarkers is unknown but desirable for clinical studies with proteinase inhibitors. METHODS: We measured three different types of biomarkers, including desmosines, elastase-formed fibrinogen fragments and heparan sulfate epitope JM403, in plasma and urine for a period of 7 weeks in a group of 12 patients who participated in a placebo-controlled study to assess the safety of a single inhalation of hyaluronic acid. RESULTS: Effect of study medication on any of the biomarkers was not seen. Baseline desmosines in plasma and urine correlated with baseline CO diffusion capacity (R = 0.81, p = 0.01 and R = 0.65, p = 0.05). Mean coefficient of variation within patients (CVi) for plasma and urine desmosines was 18.7 to 13.5%, respectively. Change in urinary desmosine levels correlated significantly with change in plasma desmosine levels (R = 0.84, p < 0.01). Mean CVi for fibrinogen fragments in plasma was 20.5% and for JM403 in urine was 27.8%. No correlations were found between fibrinogen fragments or JM403 epitope and desmosines. CONCLUSION: We found acceptable variability in our study parameters, indicating the feasibility of their use in an evaluation of biochemical efficacy of alpha-1-antitrypsin augmentation therapy in Pi Z subjects

A model study of quark number susceptibility at finite temperature beyond rainbow-ladder approximation

In this paper we calculate the quark number susceptibility (QNS) of QCD at finite temperature under the rainbow-ladder and Ball-Chiu type truncation schemes of the Dyson-Schwinger approach. It is found that the difference between the result of the rainbow-ladder truncation and that of Ball-Chiu type truncation is small, which shows that the dressing effect of the quark-gluon vertex on the QNS at finite temperature is small. It is also found that at low temperature the quark number susceptibility is nearly zero and it increases sharply when the temperature approaches the chiral phase transition point. A comparison between the result in the present paper with those in the literature is made.Comment: 17 pages, 6 figure