Politics by Other Means: The Battle over the Classification of Asymmetrical Conflicts

Transnational armed conflicts between states and non-state armed groups have emerged as a defining characteristic of twenty-first century warfare. Humanitarian actors tend to classify such conflicts (e.g., between the United States and ISIL) as non-international armed conflicts rather than international armed conflict. This classification is subject to considerable debate; yet both sides present their views as the inevitable result of the interpretation of the relevant International Humanitarian Law (IHL) treaty articles. This Article demonstrates that the classification of transnational armed conflicts as non-international armed conflicts does not merely concern the application of the relevant laws, but represents a fundamental shift in the attitude of humanitarian actors: while IHL has traditionally been considered the most effective legal constraint on the brutality of warfare, the current trend perceives International Human Rights Law as the desirable legal regime for regulating asymmetrical conflicts. Humanitarian actors prefer to classify these conflicts as non-international armed conflicts because the relative lack of IHL norms applicable to that class of conflict enables extensive application of the more protective international human rights law as a complementary mechanism. Nonetheless, the adoption of this classification by the U.S. Supreme Court in Hamdan v. Rumsfeld may have been a Pyrrhic victory for this novel approach due to the United States\u27 reluctance to apply international human rights law norms to extraterritorial conflicts. Thus, instead of the full application of IHL norms, only the vague norms relevant to non-international armed conflicts apply, without the benefit of applying international human rights law as a complementary legal regime

Targeting the \u3cem\u3eTargeted Killings\u3c/em\u3e Case - International Lawmaking in Domestic Contexts

The targeting of non-state armed groups members is perhaps the most debated legal issue in the law of contemporary armed conflicts between states and non-state actors. The 2006 Targeted Killings case of the Israeli Supreme Court (ISC) is a key reference point in this debate. Recently, without much scholarly or public attention, the government of Israel, in its report on the summer 2014 conflict in Gaza (the 2014 Gaza Conflict Report), dramatically diverged from the Targeted Killings case’s definition of legitimate targets in asymmetric conflicts. The Targeted Killings case held a conduct or functional membership-based approach to targeting. This approach allows only the targeting of those individuals who directly participate in the hostilities. The 2014 Gaza Conflict Report, on the other hand, holds a formal membership approach. This approach allows the targeting of all members of the relevant armed group, regardless of their role in the organization or their actual participation in the hostilities. This change widens the scope of legitimate targets in such conflicts. It signals an increasing support for the formal membership approach, which has thus far been explicitly endorsed only by the United States. This Article offers three complementary explanations for the decision of the Israeli administration to deviate from the Targeted Killings case: (1) the decrease in the ISC’s activism with respect to conduct of hostilities cases. The activist role of the ISC in such cases from the late 1990s to 2008 was widely recognized, celebrated, and discussed in the international law literature. This Article suggests that the international law literature has ignored a countertrend in which, since 2009, the ISC has appeared to defer to the executive’s positions in conduct of hostilities cases. The court’s deference enabled the Israeli administration to deviate from the Targeted Killings case without fear of judicial intervention; (2) the open endorsement in recent years of the formal membership approach by the interpretive community of Military lawyers and the U.S. administration, resulting in the “Americanization” of the Israeli targeting position; and (3) the significant rise in the conflict death toll which may have incentivized a broader definition of legitimate targets. The development of the targeting approach in the Israeli context provides an opportunity to look closely at international law-making processes in the domestic context. It offers new theoretical insight into the relationship between international law and domestic institutions and sheds light on the unique role of competing domestic and international interpretive communities in the internalization of international law norms

On the Ergodic Properties of Certain Additive Cellular Automata over ZmZ_{m}

In this paper, we investigate some ergodic properties of $Z^{2}$-actions $T_{p,n}$ generated by an additive cellular automata and shift acting on the space of all doubly -infinitive sequences taking values in $Z_{m}$.Comment: 5 pag

On the ergodic theory of cellular automata and two-dimensional Markov shifts generated by them

In this thesis we study measurable and topological dynamics of certain classes of cellular automata and multi-dimensional subshifts. In Chapter 1 we consider one-dimensional cellular automata, i.e. the maps T: PZ -> PZ (P is a finite set with more than one element) which are given by (Tx)i==F(xi+1, ..., xi+r), x=(xi)iEZ E PZ for some integers 1≤r and a mapping F: Pr-1+1 -> P. We prove that if F is right- (left-) permutative (in Hedlund's terminology) and 0≤1<r (resp. 1<r≤0), then the natural extension of the dynamical system (PZ,B,μ,T) is a Bernoulli automorphism (μ stands for the (1/p, ..., 1/p )-Bernoulli measure on the full shift PZ). If r0 and T is surjective, then the natural extension of the system (PZ, B, μ, T) is a Kautomorphism. We also prove that the shift Z2-action on a two-dimensional subshift of finite type canonically associated with the cellular automaton T is mixing, if F is both right and left permutative. Some more results about ergodic properties of surjective cellular automata are obtained Let X be a closed translationally invariant subset of the d-dimensional full shift PZd, where P is a finite set, and suppose that the Zd-action on X by translations has positive topological entropy. Let G be a finitely generated group of polynomial growth. In Chapter 2 we prove that if growth(G)<d, then any G-action on X by homeomorphisms commuting with translations is not expansive. On the other hand, if growth(G) = d, then any G-action on X by homeomorphisms commuting with translations has positive topological entropy. Analogous results hold for semigroups. For a finite abelian group G define the two-dimensional Markov shift XG ={xEGZ2 : x(i,j) + x(i+1,j) + x(i,j+1) = 0 for all (i, j) E Z2 }. Let μG be the Haar measure on the subgroup XG C GZ2. The group Z2 acts on the measure space (XG, μG) by shifts. In Chapter 3 we prove that if G1 and G2 are p-groups and E(G1)≠E(G2), where E(G) is the least common multiple of the orders of the elements of G, then the shift actions on (XG1, μG1) and (XG2, μG2) are not measure-theoretically isomorphic. We also prove that the shift actions on XG1 and XG2 are topologically conjugate if and only if G1 and G2 are isomorphic. In Chapter 4 we consider the closed shift-invariant subgroups X = = ⊥c (Zp)Z2 defined by the principal ideals c Zp [u±1, v±t] ≃ ((Zp)Z2)^ with f(u, v) = cf(0,0) + cf(1,0)u + cf(0,1)v, cf(i, j) E Zp\{0}, on which Z2 acts by shifts. We give the complete topological classification of these subshifts with respect to measurable isomorphism

Space-time directional Lyapunov exponents for cellular automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved

Topological properties of cellular automata on trees

We prove that there do not exist positively expansive cellular automata defined on the full k-ary tree shift (for k>=2). Moreover, we investigate some topological properties of these automata and their relationships, namely permutivity, surjectivity, preinjectivity, right-closingness and openness.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Cellular automata and Lyapunov exponents

In this article we give a new definition of some analog of Lyapunov exponents for cellular automata . Then for a shift ergodic and cellular automaton invariant probability measure we establish an inequality between the entropy of the automaton, the entropy of the shift and the Lyapunov exponent

Lyapunov Exponents in Random Boolean Networks

A new order parameter approximation to Random Boolean Networks (RBN) is introduced, based on the concept of Boolean derivative. A statistical argument involving an annealed approximation is used, allowing to measure the order parameter in terms of the statistical properties of a random matrix. Using the same formalism, a Lyapunov exponent is calculated, allowing to provide the onset of damage spreading through the network and how sensitive it is to minimal perturbations. Finally, the Lyapunov exponents are obtained by means of different approximations: through distance method and a discrete variant of the Wolf's method for continuous systems.Comment: 16 pages, 5 eps-figures included, article submitted to Physica

Mesoscopic cross-film cryotrons: Vortex trapping and dc-Josephson-like oscillations of the critical current

We investigate theoretically and experimentally the transport properties of a plain Al superconducting strip in the presence of a single straight current-carrying wire, oriented perpendicular to the superconducting strip. It is well known that the critical current of the superconducting strip, Ic, in such cryotron--like system can be tuned by changing the current in the control wire, Iw. We demonstrated that the discrete change in the number of the pinned vortices/antivortices inside the narrow and long strip nearby the current-carrying wire results in a peculiar oscillatory dependence of Ic on Iw.Comment: 8 pages, 8 figure

Whispering Vortices

Experiments indicating the excitation of whispering gallery type electromagnetic modes by a vortex moving in an annular Josephson junction are reported. At relativistic velocities the Josephson vortex interacts with the modes of the superconducting stripline resonator giving rise to novel resonances on the current-voltage characteristic of the junction. The experimental data are in good agreement with analysis and numerical calculations based on the two-dimensional sine--Gordon model.Comment: 5 pages, 5 figures, text shortened to fit 4 pages, correction of typo