Generalised risk-sensitive control with full and partial state observation

This paper generalises the risk-sensitive cost functional by introducing noise dependent penalties on the state and control variables. The optimal control problems for the full and partial state observation are considered. Using a change of probability measure approach, explicit closed-form solutions are found in both cases. This has resulted in a new risk-sensitive regulator and filter, which are generalisations of the well-known classical results

Exceptionally Preserved Cambrian Trilobite Digestive System Revealed in 3D by Synchrotron-Radiation X-Ray Tomographic Microscopy

The Cambrian ‘Orsten’ fauna comprises exceptionally preserved and phosphatised microscopic arthropods. The external morphology of these fossils is well known, but their internal soft-tissue anatomy has remained virtually unknown. Here, we report the first non-biomineralised tissues from a juvenile polymerid trilobite, represented by digestive structures, glands, and connective strands harboured in a hypostome from the Swedish ‘Orsten’ fauna. Synchrotron-radiation X-ray tomographic microscopy enabled three-dimensional internal recordings at sub-micrometre resolution. The specimen provides the first unambiguous evidence for a J-shaped anterior gut and the presence of a crop with a constricted alimentary tract in the Trilobita. Moreover, the gut is Y-shaped in cross section, probably due to a collapsed lumen of that shape, another feature which has not previously been observed in trilobites. The combination of anatomical features suggests that the trilobite hypostome is functionally analogous to the labrum of euarthropods and that it was a sophisticated element closely integrated with the digestive system. This study also briefly addresses the preservational bias of the ‘Orsten’ fauna, particularly the near-absence of polymerid trilobites, and the taphonomy of the soft-tissue-harbouring hypostome

High order structure preserving explicit methods for solving linear-quadratic optimal control problems

[EN] We consider the numerical integration of linear-quadratic optimal control problems. This problem requires the solution of a boundary value problem: a non-autonomous matrix Riccati differential equation (RDE) with final conditions coupled with the state vector equation with initial conditions. The RDE has positive definite matrix solution and to numerically preserve this qualitative property we propose first to integrate this equation backward in time with a sufficiently accurate scheme. Then, this problem turns into an initial value problem, and we analyse splitting and Magnus integrators for the forward time integration which preserve the positive definite matrix solutions for the RDE. Duplicating the time as two new coordinates and using appropriate splitting methods, high order methods preserving the desired property can be obtained. The schemes make sequential computations and do not require the storrage of intermediate results, so the storage requirements are minimal. The proposed methods are also adapted for solving linear-quadratic N-player differential games. The performance of the splitting methods can be considerably improved if the system is a perturbation of an exactly solvable problem and the system is properly split. Some numerical examples illustrate the performance of the proposed methods.The author wishes to thank the University of California San Diego for its hospitality where part of this work was done. He also acknowledges the support of the Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03. The author also acknowledges the suggestions by the referees to improve the presentation of this work.Blanes Zamora, S. (2015). High order structure preserving explicit methods for solving linear-quadratic optimal control problems. Numerical Algorithms. 69:271-290. https://doi.org/10.1007/s11075-014-9894-0S27129069Abou-Kandil, H., Freiling, G., Ionescy, V., Jank, G.: Matrix Riccati equations in control and systems theory. Basel, Burkhäuser Verlag (2003)Al-Mohy, A.H., Higham, N.J.: Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators. SIAM. J. Sci. Comp. 33, 488–511 (2011)Anderson, B.D.O., Moore, J.B.: Optimal control: linear quadratic methods. Dover, New York (1990)Ascher, U.M., Mattheij, R.M., Russell, R.D.: Numerical solutions of boundary value problems for ordinary differential equations. Prentice-Hall, Englewood Cliffs (1988)Bader, P., Blanes, S., Ponsoda, E.: Structure preserving integrators for solving linear quadratic optimal control problems with applications to describe the flight of a quadrotor. J. Comput. Appl. Math. 262, 223–233 (2014)Basar, T., Olsder, G.J.: Dynamic non cooperative game theory, 2nd Ed, SIAM, Philadelphhia (1999)Blanes, S., Casas, F.: On the necessity of negative coefficients for operator splitting schemes of order higher than two. Appl. Num. Math. 54, 23–37 (2005)Blanes, S., Casas, F., Farrés, A., Laskar, J., Makazaga, J., Murua, A.: New families of symplectic splitting methods for numerical integration in dynamical astronomy. Appl. Numer. Math. 68, 58–72 (2013)Blanes, S., Casas, F., Oteo, J.A., Ros, J.: The Magnus expansion and some of its applications. Phys. Rep. 470, 151–238 (2009)Blanes, S., Casas, F., Ros, J.: High order optimized geometric integrators for linear differential equations. BIT 42, 262–284 (2002)Blanes, S., Diele, F., Marangi, C., Ragni, S.: Splitting and composition methods for explicit time dependence in separable dynamical systems. J. Comput. Appl. Math. 235, 646–659 (2010)Blanes, S., Moan, P.C.: Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nystrm methods. J. Comput. Appl. Math. 142, 313–330 (2002)Blanes, S., Ponsoda, E.: Magnus integrators for solving linear-quadratic differential games. J. Comput. Appl. Math. 236, 3394–3408 (2012)Brif, C., Chakrabarti, R., Rabitz, H.: Control of quantum phenomena: past, present and future. New J. Phys. 12, 075008(68pp) (2010)Cruz, J.B., Chen, C.I.: Series Nash solution of two person non zero sum linear quadratic games. J. Optim. Theory Appl. 7, 240–257 (1971)Dieci, L., Eirola, T.: Positive definitness in the numerical solution of Riccati differential quations. Numer. Math. 67, 303–313 (1994)Engwerda, J.: LQ dynamic optimization and differential games. Wiley (2005)Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations (2nd edition). Springer Series in Computational Mathematics, 31. Springer-Verlag (2006)Hochbruck, M., Ostermann, A.: Exponential integrators. Acta Numerica 19, 209–286 (2010)Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, New York (1985)Iserles, A., Munthe-Kaas, H.Z., Nørsett, S.P., Zanna, A.: Lie group methods. Acta Numerica 9, 215–365 (2000)Iserles, A., Nørsett, S.P.: On the solution of linear differential equations in Lie groups. Phil. Trans. R. Soc. Lond. A 357, 983–1019 (1999)Jódar, L., Ponsoda, E.: Non-autonomous Riccati-type matrix differential equations: existence interval, construction of continuous numerical solutions and error bounds. IMA. J. Num. Anal. 15, 61–74 (1995)Jódar, L., Ponsoda, E., Company, R.: Solutions of coupled Riccati equations arising in differential games. Control. Cybern. 24, 117–128 (1995)Kaitala, V, Pohjola, M. In: Carraro, Filar (eds.) : Sustainable international agreement on greenhouse warming. A game theory study. Control and Game Theoretic Models of the Environment, pp 67–87. Birkhauser, Boston (1995)Keller, H.B.: Numerical solution of two point boundary value problems. In: CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 24. SIAM, Philadelphia (1976)McLachlan, R.I.: Composition methods in the presence of small parameters. BIT 35, 258–268 (1995)McLachlan, R.I., Quispel, R.: Splitting Methods. Acta Numer. 11, 341–434 (2002)Moler, C.B., Van Loan, C.F.: Nineteen Dubious Ways to Compute the Exponential of a Matrix, twenty-five years later. SIAM Rev. 45, 3–49 (2003)Na, T.Y.: Computational methods in engineering boundary value problems. In: Mathematics in Science and Engineering, Vol. 145. Accademic Press, New York (1979)Palao, J.P., Kosloff, R.: Quantum computing by an optimal control algorithm for unitry transformations. Phys. Rev. Lett. 28 (2002)Peirce, A.P., Dahleh, M.A., Rabitz, H.: Optimal control of quantum-mechanical systems: existence, numerical approximation, and applications. Phys. Rev. A 37, 4950–4967 (1988)Reid, W.T.: Riccati Differential Equations. Academic, New York (1972)Sanz-Serna, J.M., Calvo, M.P.: Numerical Hamiltonian Problems. Chapman & Hall, London (1994)Sidje, R.B.: Expokit: a software package for computing matrix exponentials. ACM Trans. Math. Software 24, 130–156 (1998)Speyer, J.L., Jacobson, D.H.: Primer on optimal control theory. SIAM, Philadelphia (2010)Starr, A.W., Ho, Y.C.: Non-zero sum differential games. J. Optim. Theory and Appl 3, 179–197 (1969)Zhu, W., Rabitz, H.: A rapid monotonically convergent iteration algorithm for quantum optimal control ever the expectation value of a positive definite operator. J. Chem. Phys. 109, 385–391 (1998

The optimal starting time of postoperative intraperitoneal mitomycin-C therapy with preserved intestinal wound healing

BACKGROUND: There is controversy about the effect of the timing of intraperitoneal administration of chemotherapeutic agents on the healing of intestinal anastomosis. We have investigated the effect on intestinal wound healing of mitomycin-C administered at different times post-operatively. METHODS: Eighty-four Wistar-Albino female rats underwent ileal resection and end-to-end anastomosis. The rats were randomly selected for intraperitoneal administration of mitomycin-C or saline as follows: mitomycin-C group (n = 65), 2 mg/kg mitomycin-C; control group (n = 13), 10 ml saline. The former was sub-divided into 5 equal groups (A 1–5) and mitomycin-C was administered postoperatively as follows: day 0 (A1), day 3 (A2), day 5 (A3), day 7 (A4) and day 10 (A5). All the rats were sacrificed on the 14th postoperative day and anastomotic bursting pressures and tissue hydroxyproline levels were determined. RESULTS: Five of the animals died postoperatively: 2 (15.4%) in group A1, 2 (15.4%) in group A2 and 1(7.7%) in group A3. Non-lethal anastomotic leakage was observed in a further five animals: 1 in group A1, 2 in group A2, 1 in group A5 and 1 in the control group. Groups A1 and A2 had significantly lower anastomotic bursting pressures than the other groups (P was <0.05 for each comparison). The anastomotic bursting pressures of group A3, A4 and A5 were comparable with those of the controls (P was >0.05 for each comparison). Tissue hydroxyproline levels in group A1 and A2 were significantly lower than in the controls (P values were <0.05 for each comparison) or the other mitomycin-C sub-groups (P was <0.05 for each comparison). CONCLUSIONS: Intraperitoneal chemotherapy impairs intestinal wound healing when applied before the 5th postoperative day. Additional therapeutic approaches are needed to prevent this potentially lethal side effect of early intraperitoneal mitomycin-C administration

A phase I study of intravenous liposomal daunorubicin (DaunoXome) in paediatric patients with relapsed or resistant solid tumours

Anthracyclines are widely used in paediatric oncology, but their use is limited by the risk of cumulative cardiac toxicity. Encapsulating anthracyclines in liposomes may reduce cardiac toxicity and possibly increase drug availability to tumours. A phase I study in paediatric patients was designed to establish the dose limiting toxicity (DLT) and maximum tolerated dose (MTD) after a single course of liposomal daunorubicin, ‘DaunoXome', as a 1 h infusion on day 1 of a 21 day cycle. Patients were stratified into two groups according to prior treatment: Group A (conventional) and group B (heavily pretreated patients). Dose limiting toxicity was expected to be haematological, and a two-step escalation was planned, with and without G-CSF support. Pharmacokinetic studies were carried out in parallel. In all, 48 patients aged from 1 to 18 years were treated. Dose limiting toxicity was neutropenia for both groups. Maximum tolerated dose was defined as 155 mg m−2 for Group A and 100 mg m−2 for Group B. The second phase with G-CSF was interrupted because of evidence of cumulative cardiac toxicity. Cardiac toxicity was reported in a total of 15 patients in this study. DaunoXome shares the early cardiotoxicity of conventional anthracyclines in paediatric oncology. This study has successfully defined a haematological MTD for DaunoXome, but the significance of this is limited given the concerns of delayed cardiac toxicity. The importance of longer-term follow-up in patients enrolled into phase I studies has been underestimated previously, and may lead to an under-recognition of important adverse events

Surrogate markers and survival in women receiving first-line combination anthracycline chemotherapy for advanced breast cancer

Surrogate markers may help predict the effects of first-line treatment on survival. This metaregression analysis examines the relationship between several surrogate markers and survival in women with advanced breast cancer after receiving first-line combination anthracycline chemotherapy 5-fluorouracil, adriamycin and cyclophosphamide (FAC) or 5-fluorouracil, epirubicin and cyclophosphamide (FEC) . From a systematic literature review, we identified 42 randomised trials. The surrogate markers were complete or partial tumour response, progressive disease and time to progression. The treatment effect on survival was quantified by the hazard ratio. The treatment effect on each surrogate marker was quantified by the odds ratio (or ratio of median time to progression). The relationship between survival and each surrogate marker was assessed by a weighted linear regression of the hazard ratio against the odds ratio. There was a significant linear association between survival and complete or partial tumour response (P<0.001, R2=34%), complete tumour response (P=0.02, R2=12%), progressive disease (P<0.001, R2=38%) and time to progression (P<0.0001, R2=56%); R2 is the proportion of the variability in the treatment effect on survival that is explained by the treatment effect on the surrogate marker. Time to progression may be a useful surrogate marker for predicting survival in women receiving first-line anthracycline chemotherapy and could be used to estimate the survival benefit in future trials of first-line chemotherapy compared to FAC or FEC. The other markers, tumour response and progressive disease, were less good

Evaluating the Psychometric Quality of Social Skills Measures: A Systematic Review

Introduction - Impairments in social functioning are associated with an array of adverse outcomes. Social skills measures are commonly used by health professionals to assess and plan the treatment of social skills difficulties. There is a need to comprehensively evaluate the quality of psychometric properties reported across these measures to guide assessment and treatment planning. Objective - To conduct a systematic review of the literature on the psychometric properties of social skills and behaviours measures for both children and adults. Methods - A systematic search was performed using four electronic databases: CINAHL, PsycINFO, Embase and Pubmed; the Health and Psychosocial Instruments database; and grey literature using PsycExtra and Google Scholar. The psychometric properties of the social skills measures were evaluated against the COSMIN taxonomy of measurement properties using pre-set psychometric criteria. Results - Thirty-Six studies and nine manuals were included to assess the psychometric properties of thirteen social skills measures that met the inclusion criteria. Most measures obtained excellent overall methodological quality scores for internal consistency and reliability. However, eight measures did not report measurement error, nine measures did not report cross-cultural validity and eleven measures did not report criterion validity. Conclusions - The overall quality of the psychometric properties of most measures was satisfactory. The SSBS-2, HCSBS and PKBS-2 were the three measures with the most robust evidence of sound psychometric quality in at least seven of the eight psychometric properties that were appraised. A universal working definition of social functioning as an overarching construct is recommended. There is a need for ongoing research in the area of the psychometric properties of social skills and behaviours instruments

The Formation of Collective Silk Balls in the Spider Mite Tetranychus urticae Koch

Tetranychus urticae is a phytophagous mite that forms colonies of several thousand individuals. These mites construct a common web to protect the colony. When plants become overcrowded and food resources become scarce, individuals gather at the plant apex to form a ball composed of mites and their silk threads. This ball is a structure facilitating group dispersal by wind or animal transport. Until now, no quantitative study had been done on this collective form of migration. This is the first attempt to understand the mechanisms that underlie the emergence and growth of the ball. We studied this collective behaviour under laboratory conditions on standardized infested plants. Our results show that the collective displacement and the formation of balls result from a recruitment process: by depositing silk threads on their way up to the plant apex, mites favour and amplify the recruitment toward the balls. A critical threshold (quorum response) in the cumulative flow of mites must be reached to observe the emergence of a ball. At the beginning of the balls formation, mites form an aggregate. After 24 hours, the aggregated mites are trapped inside the silk balls by the complex network of silk threads and finally die, except for recently arrived individuals. The balls are mainly composed of immature stages. Our study reconstructs the key events that lead to the formation of silk balls. They suggest that the interplay between mites' density, plant morphology and plant density lead to different modes of dispersions (individual or collective) and under what conditions populations might adopt a collective strategy rather than one that is individually oriented. Moreover, our results lead to discuss two aspects of the cooperation and altruism: the importance of Allee effects during colonization of new plants and the importance of the size of a founding group

Role of the Chemokine Receptors CCR1, CCR2 and CCR4 in the Pathogenesis of Experimental Dengue Infection in Mice

Dengue virus (DENV), a mosquito-borne flavivirus, is a public health problem in many tropical countries. Recent clinical data have shown an association between levels of different chemokines in plasma and severity of dengue. We evaluated the role of CC chemokine receptors CCR1, CCR2 and CCR4 in an experimental model of DENV-2 infection in mice. Infection of mice induced evident clinical disease and tissue damage, including thrombocytopenia, hemoconcentration, lymphopenia, increased levels of transaminases and pro-inflammatory cytokines, and lethality in WT mice. Importantly, infected WT mice presented increased levels of chemokines CCL2/JE, CCL3/MIP-1α and CCL5/RANTES in spleen and liver. CCR1-/- mice had a mild phenotype with disease presentation and lethality similar to those of WT mice. In CCR2-/- mice, lethality, liver damage, levels of IL-6 and IFN-γ, and leukocyte activation were attenuated. However, thrombocytopenia, hemoconcentration and systemic TNF-α levels were similar to infected WT mice. Infection enhanced levels of CCL17/TARC, a CCR4 ligand. In CCR4-/- mice, lethality, tissue injury and systemic inflammation were markedly decreased. Despite differences in disease presentation in CCR-deficient mice, there was no significant difference in viral load. In conclusion, activation of chemokine receptors has discrete roles in the pathogenesis of dengue infection. These studies suggest that the chemokine storm that follows severe primary dengue infection associates mostly to development of disease rather than protection