Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1843 (T9).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1861 (SER2).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1923 (VOL82).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1862 (SER3,T8 = VOL28).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1834 (T1).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1875 (SER5,T3 = VOL41).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1884 (SER5,T12 = VOL50).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1867 (SER4,T3 = VOL33).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1921 (VOL80).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1913 (VOL77).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1872 (SER4,T8 = VOL38).

Bulletin monumental / publié sous les auspices de la Société française pour la conservation et la description des monuments historiques ; et dirigé par M. de Caumont

1877 (SER5,T5,N5 = VOL43).

Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.

Research Priorities for seabirds: Improving seabird conservation and management in the 21st century

Seabirds are facing a growing number of threats in both terrestrial and marine habitats, and many populations have experienced dramatic changes over past decades. Years of seabird research have improved our understanding of seabird populations and provided a broader understanding of marine ecological processes. In an effort to encourage future research and guide seabird conservation science, seabird researchers from 9 nations identified the 20 highest priority research questions and organized these into 6 general categories: (1) population dynamics, (2) spatial ecology, (3) tropho-dynamics, (4) fisheries interactions, (5) response to global change, and (6) management of anthropogenic impacts (focusing on invasive species, contaminants and protected areas). For each category, we provide an assessment of the current approaches, challenges and future directions. While this is not an exhaustive list of all research needed to address the myriad conservation challenges seabirds face, the results of this effort represent an important synthesis of current expert opinion across sub-disciplines within seabird ecology. As this synthesis highlights, research, in conjunction with direct management, education, and community engagement, can play an important role in facilitating the conservation and management of seabird populations and of the ocean ecosystems on which they and we depend.

Concluding Remarks on River Conservation

We have pragmatic and ethical obligations to conserve rivers and their biodiversity. This chapter outlines how and why river conservation is important. To make a difference, we must act as individuals and groups, using water wisely and protecting vulnerable assets such as water quality, riparian zones and aquatic biodiversity