Splitting an Uncertain (Natural) Capital

Most natural commons are subject to discontinuities and threshold effects, so their gradual depletion may result in a sudden irreversible loss of the associated ecological services. Yet, it is often impossible to locate these thresholds with certainty. We analyze this context using a variant of the divide-the-dollar game, in which the amount to be split among players follows a discrete or multimodal probability distribution. “Cautions equilibria” – where agents collectively behave as if the worst-case scenario were certain – are found to coexist with “dangerous equilibria” – where overall demand for ecological services might lead to their collapse – and “dreadful equilibria” – where agents collectively request so much natural capital that a collapse of ecological services is certain, even if all agents are risk averse. Communication/cooperation among agents, however, which raises the possibility of coordinated group deviations, would eliminate dreadful equilibria and reduce the occurrence of dangerous equilibria, while cautions equilibria are robust to such deviations. A direct corollary is that dangerous equilibria are Pareto-dominated by any cautions equilibrium in which all agents claim less natural capital. These results shed light on the management of common-pool resources, international climate change negotiations, and the implementation of precautionary policies.Common-pool resources, ecological thresholds, divide-the-dollar game, coalition-proof Nash equilibrium

Splitting an Uncertain (Natural) Capital

Most natural commons are subject to discontinuities and threshold effects, so their gradual depletion may result in a sudden irreversible loss of the associated ecological services. Yet, it is often impossible to locate these thresholds with certainty. We analyze this context using a variant of the divide-the-dollar game, in which the amount to be split among players follows a discrete or multimodal probability distribution. ‘Cautious equilibria’ – where agents collectively behave as if the worst-case scenario were certain - are found to coexist with ‘dangerous equilibria’ - where overall demand for ecological services might lead to their collapse - and ‘dreadful equilibria’ - where agents collectively request so much natural capital that a collapse of ecological services is certain, even if all agents are risk averse. Communication/cooperation among agents, however, which raises the possibility of coordinated group deviations, would eliminate dreadful equilibria and reduce the occurrence of dangerous equilibria, while cautious equilibria are robust to such deviations. A direct corollary is that dangerous equilibria are Pareto-dominated by any cautious equilibrium in which all agents claim less natural capital. These results shed light on the management of common-pool resources, international climate change negotiations, and the implementation of precautionary policies.Common-pool resources, Ecological thresholds, Divide-the-dollar game, Coalition-proof Nash equilibrium

Optimal control theory and the efficiency of the swimming mechanism of the Copepod Zooplankton

International audienceIn this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the motion occurs minimizing the energy dissipated by the fluid drag forces in relation with the concept of efficiency of a stroke. The maximum principle is used to compute periodic controls candidates as minimizing controls and is a decisive tool combined with appropriate numerical simulations using indirect optimal control schemes to determine the most efficient stroke compared with standard computations using Stokes theorem and curvature control. Also the concept of graded approximations in SR-geometry is used to evaluate strokes with small amplitudes providing a fixed displacement and minimizing the dissipated energy

Evaluation of tandem repeats for MLVA typing of Streptococcus uberis isolated from bovine mastitis

BACKGROUND: Streptococcus uberis is a common cause of bovine mastitis and recommended control measures, based on improved milking practice, teat dipping and antibiotic treatment at drying-off, are poorly efficient against this environmental pathogen. A simple and efficient typing method would be helpful in identifying S.uberis sources, virulent strains and cow to cow transmission. The potential of MLVA (Multiple Loci VNTR Analysis; VNTR, Variable Number of Tandem Repeats) for S. uberis mastitis isolates genotyping was investigated. RESULTS: The genomic sequence of Streptococcus uberis (strain 0104J) was analyzed for potential variable number tandem repeats (VNTRs). Twenty-five tandem repeats were identified and amplified by PCR with DNA samples from 24 S. uberis strains. A set of seven TRs were found to be polymorphic and used for MLVA typing of 88 S. uberis isolates. A total of 82 MLVA types were obtained with 22 types among 26 strains isolated from the milk of mastitic cows belonging to our experimental herd, and 61 types for 62 epidemiologically unrelated strains, i.e. collected in different herds and areas. CONCLUSION: The MLVA method can be applied to S. uberis genotyping and constitutes an interesting complement to existing typing methods. This method, which is easy to perform, low cost and can be used in routine, could facilitate investigations of the epidemiology of S. uberis mastitis in dairy cows

Toward Geometric Time Minimal Control without Legendre Condition and with Multiple Singular Extremals for Chemical Networks. An Extended Version

This article deals with the problem of maximizing the production of a species for a chemical network by controlling the temperature. Under the socalled mass kinetics assumption the system can be modeled as a single-input control system using the Feinberg-Horn-Jackson graph associated to the reactions network. Thanks to Pontryagin's Maximum Principle, the candidates as minimizers can be found among extremal curves, solutions of a (non smooth) Hamiltonian dynamics and the problem can be stated as a time minimal control problem with a terminal target of codimension one. Using geometric control and singularity theory the time minimal syntheses (closed loop optimal control) can be classified near the terminal manifold under generic conditions. In this article, we focus to the case where the generalized Legendre-Clebsch condition is not satisfied, which paves the road to complicated syntheses with several singular arcs. In particular, it is related to the situation for a weakly reversible network like the McKeithan scheme

Geometric Optimal Control of the Generalized Lotka-Volterra Model with Applications Controlled Stability of Microbiota

International audienceIn this talk we present the Generalized Lotka–Volterra dynamics associated to themodel of C-difficile infection of the intestine microbiote and aiming to transfer the systemfrom an infected state to an healthy state. The control inputs are of two types : fecalinjection or bactericides which act as Dirac pulses and prebiotics or antibiotics which act ascontinuous controls. An uniform frame can be introduced using the tools from geometriccontrol to analyze the accessibility set as the orbit of a pseudo-semi group. Optimalcontrol can be considered in the frame of permanent control or sampled-data control. Thelater being adapted to the practical constraints of a finite set of medical interventions. Inboth case the optimal control problems can be analyzed using direct and indirect schemesaiming to reach an healthy state. Such methods are tested on toys models in dimension 2and 3 related to the construction of reduced dynamics. Even those simple situations leadto interesting questions of accessibility and integrability issues in relation with the studyof dynamical systems

Bacillus licheniformis BlaR1 L3 Loop Is a Zinc Metalloprotease Activated by Self-Proteolysis

In Bacillus licheniformis 749/I, BlaP β-lactamase is induced by the presence of a β-lactam antibiotic outside the cell. The first step in the induction mechanism is the detection of the antibiotic by the membrane-bound penicillin receptor BlaR1 that is composed of two functional domains: a carboxy-terminal domain exposed outside the cell, which acts as a penicillin sensor, and an amino-terminal domain anchored to the cytoplasmic membrane, which works as a transducer-transmitter. The acylation of BlaR1 sensor domain by the antibiotic generates an intramolecular signal that leads to the activation of the L3 cytoplasmic loop of the transmitter by a single-point cleavage. The exact mechanism of L3 activation and the nature of the secondary cytoplasmic signal launched by the activated transmitter remain unknown. However, these two events seem to be linked to the presence of a HEXXH zinc binding motif of neutral zinc metallopeptidases. By different experimental approaches, we demonstrated that the L3 loop binds zinc ion, belongs to Gluzincin metallopeptidase superfamily and is activated by self-proteolysis

Feedback Classification and Optimal Control with Applications to the Controlled Lotka-Volterra Model

Let M be a σ-compact C^∞ manifold of dimension n ≥ 2 and consider a single-input control system: ẋ(t) = X (x(t)) + u(t) Y (x(t)), where X , Y are C^∞ vector fields on M. We prove that there exist an open set of pairs (X , Y ) for the C^∞ –Whitney topology such that they admit singular abnormal rays so that the spectrum of the projective singular Hamiltonian dynamics is feedback invariant. It is applied to controlled Lotka–Volterra dynamics where such rays are related to shifted equilibria of the free dynamics