Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Multi-well fungal co-culture for de novo metabolite-induction in time-series studies based on untargeted metabolomics.

The induction of fungal metabolites by fungal co-cultures grown on solid media was explored using multi-well co-cultures in 2 cm diameter Petri dishes. Fungi were grown in 12-well plates to easily and rapidly obtain the large number of replicates necessary for employing metabolomic approaches. Fungal culture using such a format accelerated the production of metabolites by several weeks compared with using the large-format 9 cm Petri dishes. This strategy was applied to a co-culture of a Fusarium and an Aspergillus strain. The metabolite composition of the cultures was assessed using ultra-high pressure liquid chromatography coupled to electrospray ionisation and time-of-flight mass spectrometry, followed by automated data mining. The de novo production of metabolites was dramatically increased by nutriment reduction. A time-series study of the induction of the fungal metabolites of interest over nine days revealed that they exhibited various induction patterns. The concentrations of most of the de novo induced metabolites increased over time. However, interesting patterns were observed, such as with the presence of some compounds only at certain time points. This result indicates the complexity and dynamic nature of fungal metabolism. The large-scale production of the compounds of interest was verified by co-culture in 15 cm Petri dishes; most of the induced metabolites of interest (16/18) were found to be produced as effectively as on a small scale, although not in the same time frames. Large-scale production is a practical solution for the future production, identification and biological evaluation of these metabolites.

Combination of MRI and dynamic FET PET for initial glioma grading.

AIM: MRI and PET with 18F-fluoro-ethyl-tyrosine (FET) have been increasingly used to evaluate patients with gliomas. Our purpose was to assess the additive value of MR spectroscopy (MRS), diffusion imaging and dynamic FET-PET for glioma grading. PATIENTS, METHODS: 38 patients (42 ± 15 aged, F/M: 0.46) with untreated histologically proven brain gliomas were included. All underwent conventional MRI, MRS, diffusion sequences, and FET-PET within 3±4 weeks. Performances of tumour FET time-activity-curve, early-to-middle SUVmax ratio, choline / creatine ratio and ADC histogram distribution pattern for gliomas grading were assessed, as compared to histology. Combination of these parameters and respective odds were also evaluated. RESULTS: Tumour time-activity-curve reached the best accuracy (67%) when taken alone to distinguish between low and high-grade gliomas, followed by ADC histogram analysis (65%). Combination of time-activity-curve and ADC histogram analysis improved the sensitivity from 67% to 86% and the specificity from 63-67% to 100% (p < 0.008). On multivariate logistic regression analysis, negative slope of the tumour FET time-activity-curve however remains the best predictor of high-grade glioma (odds 7.6, SE 6.8, p = 0.022). CONCLUSION: Combination of dynamic FET-PET and diffusion MRI reached good performance for gliomas grading. The use of FET-PET/MR may be highly relevant in the initial assessment of primary brain tumours.

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Reticulocyte dynamic and hemoglobin variability in hemodialysis patients treated with Darbepoetin alfa and C.E.R.A.: a randomized controlled trial.

BACKGROUND: In a simulation based on a pharmacokinetic model we demonstrated that increasing the erythropoiesis stimulating agents (ESAs) half-life or shortening their administration interval decreases hemoglobin variability. The benefit of reducing the administration interval was however lessened by the variability induced by more frequent dosage adjustments. The purpose of this study was to analyze the reticulocyte and hemoglobin kinetics and variability under different ESAs and administration intervals in a collective of chronic hemodialysis patients. METHODS: The study was designed as an open-label, randomized, four-period cross-over investigation, including 30 patients under chronic hemodialysis at the regional hospital of Locarno (Switzerland) in February 2010 and lasting 2 years. Four subcutaneous treatment strategies (C.E.R.A. every 4 weeks Q4W and every 2 weeks Q2W, Darbepoetin alfa Q4W and Q2W) were compared with each other. The mean square successive difference of hemoglobin, reticulocyte count and ESAs dose was used to quantify variability. We distinguished a short- and a long-term variability based respectively on the weekly and monthly successive difference. RESULTS: No difference was found in the mean values of biological parameters (hemoglobin, reticulocytes, and ferritin) between the 4 strategies. ESAs type did not affect hemoglobin and reticulocyte variability, but C.E.R.A induced a more sustained reticulocytes response over time and increased the risk of hemoglobin overshooting (OR 2.7, p = 0.01). Shortening the administration interval lessened the amplitude of reticulocyte count fluctuations but resulted in more frequent ESAs dose adjustments and in amplified reticulocyte and hemoglobin variability. Q2W administration interval was however more favorable in terms of ESAs dose, allowing a 38% C.E.R.A. dose reduction, and no increase of Darbepoetin alfa. CONCLUSIONS: The reticulocyte dynamic was a more sensitive marker of time instability of the hemoglobin response under ESAs therapy. The ESAs administration interval had a greater impact on hemoglobin variability than the ESAs type. The more protracted reticulocyte response induced by C.E.R.A. could explain both, the observed higher risk of overshoot and the significant increase in efficacy when shortening its administration interval.Trial registrationClinicalTrials.gov NCT01666301.

Dynamic Pavement Deflection Measurements, Progress Report, HR-178, 1977

The Road Rater is a dynamic deflection measuring appa-ratus for flexible base pavements. The basic operating principle of the Road Rater is to impart a dynamic loading and measure the resultant movement of the pavement with velocity sensors. This data, when properly adjusted for temperature by use of a nomograph included in this report, can be used to determine pavement life expectancy and estimate overlay thickness required. Road Rater testing will be conducted in the spring, when pave-ments are in their weakest condition, until seasonal correction factors can be developed. The Road Rater does not have sufficient ram weight to effectively evaluate load carrying capacity of rigid pavements. All rigid pavements react similarly to Road Rater testing and generally deflect from 0.65 to 1.30 mils. Research will be continued to evaluate rigid pavements with the Road Rater, however. The Road Rater has proven to be a reliable, trouble free pavement evaluation machine. The deflection apparatus was originally front-mounted, but was rear-mounted during the winter of 1977-78. Since that time, van handling has greatly improved, and front suspension parts are no longer overstressed due to improper weight distribution. The Road Rater provides a fast, economical, nondestructive test method to evaluate flexible pavements. Road Rater test data can be used to predict pavement life, set priorities for asphaltic concrete resurfacing, and design asphaltic concrete overlays. Temperature and seasonal variations significantly affect Road Rater deflection readings and must be considered. A nomograph included in this report adjusts for temperature, but does not correct for seasonal effect. Road Rater testing will be conducted in the spring until seasonal correction factors can be developed. The Road Rater has not successfully evaluated rigid pavements, but research will continue in this area. 1. Recommendations for continuing Road Rater research, evaluation and application are as follows:A computer program should be established to reduce Road Rater raw data (Range and Sensor reading) to HR-178 Road Rater Dynamic Deflections For Determining Structural Rating Of Flexible Pavements mean deflection (mils) and/or structural rating. This computer printout would be similar to present friction testing printouts, and would greatly reduce Road Rater data reduction manpower needs and costs. 2. Seasonal variation study should continue to develop seasonal correction factors. Seasonal test roads will be studied concurrently with routine testing during 1979 to develop this relationship. All Road Rater testing will be conducted in the spring until the seasonal relationship is established. 3. An asphaltic concrete overlay design method should be established based on Road Rater de-flection readings. The AASHTO Interim Guide for Design of Pavement Structures 1972 will be used as a base document for this study. 4. AASHTO Structural numbers should be compared to Road Rater Structural Ratings during 1979 on asphaltic concrete overlay projects. This analysis will enable us to refine Road Rater evaluation of flexible pavements. Roads will be tested before resurfacing and several months

Is it the grain size or the characteristic pore size that controls the induced polarization relaxation time of clean sands and sandstones?

There is a wide range of evidence to suggest that permeability can be constrained through of induced polarization measurements. For clean sands and sandstones, current mechanistic models of induced polarization predict a relationship between the low-frequency time constant inferred from induced polarization measurements and the grain diameter. A number of observations do, however, disagree with this and indicate that the observed relaxation behavior is rather governed by the so-called dynamic pore radius L. To test this hypothesis, we have developed a set of new scaling relationships, which allow the relaxation time to be computed from the pore size and the permeability to be computed from both the Cole-Cole time constant and the formation factor. Moreover, these new scaling relationships can be also used to predict the dependence of the Cole-Cole time constant as a function of the water saturation under unsaturated conditions. Comparative tests of the proposed new relationships with regard to various published experimental results for saturated clean sands and sandstones as well as for partially saturated clean sandstones, do indeed confirm that the dynamic pore radius L is a much more reliable indicator of the observed relaxation behavior than grain-size-based models.

Dynamic Deflections for Determining Structural Rating of Flexible Pavements, HR-178, 1979

The Road Rater is a dynamic deflection measuring apparatus for flexible base pavements. The Road Rater replaces the Benkelman Beam which was last used by the Iowa DOT in 1977. Road Rater test results correlate reasonably well (correlation coefficient = 0.83) with Benkelman Beam test data. The basic differences between the Road Rater and Benkelman Beam are as follows: 1. The Benkelman Beam uses a static 18,000 lb. load while the Road Rater uses a dynamic 800 to 2,000 lb. loading. 2. The Road Rater tests much faster and more economically than the Benkelman Beam. 3. The Road Rater better simulates a moving truck than the Benkelman Beam. The basic operating principle of the Road Rater is to impart a dynamic loading and measure the resultant movement of the pavement with velocity sensors. This data, when properly adjusted for temperature by use of a nomograph included in this report, can be used to determine pavement life expectancy and estimate overlay thickness required. Road Rater testing will be conducted in the spring, when pavements are in their weakest condition, until seasonal correction factors can be developed. The Road Rater does not have sufficient ram weight to effectively evaluate load carrying capacity of rigid pavements. All rigid pavements react similarly to Road Rater testing and generally deflect from 0.65 to 1.30 mils. Research will be contined to evaluate rigid pavements with the Road Rater, however. The Road Rater has proven to be a reliable, troublefree pavement evaluation machine. The deflection apparatus was originally front-mounted,but was rear-mounted during the winter of 1977-78. Since that time, van handling has greatly improved, and front suspension parts are no longer overstressed due to improper weight distribution.

Development of Asphalt Dynamic Modulus Master Curve Using Falling Weight Deflectometer Measurements, TR-659

The asphalt concrete (AC) dynamic modulus (|E*|) is a key design parameter in mechanistic-based pavement design methodologies such as the American Association of State Highway and Transportation Officials (AASHTO) MEPDG/Pavement-ME Design. The objective of this feasibility study was to develop frameworks for predicting the AC |E*| master curve from falling weight deflectometer (FWD) deflection-time history data collected by the Iowa Department of Transportation (Iowa DOT). A neural networks (NN) methodology was developed based on a synthetically generated viscoelastic forward solutions database to predict AC relaxation modulus (E(t)) master curve coefficients from FWD deflection-time history data. According to the theory of viscoelasticity, if AC relaxation modulus, E(t), is known, |E*| can be calculated (and vice versa) through numerical inter-conversion procedures. Several case studies focusing on full-depth AC pavements were conducted to isolate potential backcalculation issues that are only related to the modulus master curve of the AC layer. For the proof-of-concept demonstration, a comprehensive full-depth AC analysis was carried out through 10,000 batch simulations using a viscoelastic forward analysis program. Anomalies were detected in the comprehensive raw synthetic database and were eliminated through imposition of certain constraints involving the sigmoid master curve coefficients. The surrogate forward modeling results showed that NNs are able to predict deflection-time histories from E(t) master curve coefficients and other layer properties very well. The NN inverse modeling results demonstrated the potential of NNs to backcalculate the E(t) master curve coefficients from single-drop FWD deflection-time history data, although the current prediction accuracies are not sufficient to recommend these models for practical implementation. Considering the complex nature of the problem investigated with many uncertainties involved, including the possible presence of dynamics during FWD testing (related to the presence and depth of stiff layer, inertial and wave propagation effects, etc.), the limitations of current FWD technology (integration errors, truncation issues, etc.), and the need for a rapid and simplified approach for routine implementation, future research recommendations have been provided making a strong case for an expanded research study.

A new conservative-dynamic treatment for the acute ruptured Achilles tendon.

INTRODUCTION: There is a trend towards surgical treatment of acute ruptured Achilles tendon. While classical open surgical procedures have been shown to restore good functional capacity, they are potentially associated with significant complications like wound infection and paresthesia. Modern mini-invasive surgical techniques significantly reduce these complications and are also associated with good functional results so that they can be considered as the surgical treatment of choice. Nevertheless, there is still a need for conservative alternative and recent studies report good results with conservative treatment in rigid casts or braces. PATIENTS/METHOD: We report the use of a dynamic ankle brace in the conservative treatment of Achilles tendon rupture in a prospective non-randomised study of 57 consecutive patients. Patients were evaluated at an average follow-up time of 5 years using the modified Leppilahti Ankle Score, and the first 30 patients additionally underwent a clinical examination and muscular testing with a Cybex isokinetic dynamometer at 6 and 12 months. RESULTS: We found good and excellent results in most cases. We observed five complete re-ruptures, almost exclusively in case of poor patient's compliance, two partial re-ruptures and one deep venous thrombosis complicated by pulmonary embolism. CONCLUSION: Although prospective comparison with other modern treatment options is still required, the functional outcome after early ankle mobilisation in a dynamic cast is good enough to ethically propose this method as an alternative to surgical treatment.

Navigator-gated and real-time motion corrected free-breathing MR Imaging of myocardial late enhancement.

PURPOSE: A new magnetic resonance imaging approach for detection of myocardial late enhancement during free-breathing was developed. METHODS AND RESULTS: For suppression of respiratory motion artifacts, a prospective navigator technology including real-time motion correction and a local navigator restore was implemented. Subject specific inversion times were defined from images with incrementally increased inversion times acquired during a single dynamic scout navigator-gated and real-time motion corrected free-breathing scan. Subsequently, MR-imaging of myocardial late enhancement was performed with navigator-gated and real-time motion corrected adjacent short axis and long axis (two, three and four chamber) views. This alternative approach was investigated in 7 patients with history of myocardial infarction 12 min after i. v. administration of 0.2 mmol/kg body weight gadolinium-DTPA. CONCLUSION: With the presented navigator-gated and real-time motion corrected sequence for MR-imaging of myocardial late enhancement data can be completely acquired during free-breathing. Time constraints of a breath-hold technique are abolished and optimized patient specific inversion time is ensured.