On Fragments and Geometry: The International Legal Order as Metaphor and How it Matters

This article engages the narrative of fragmentation in international law by asserting that legal academics and professionals have failed to probe more deeply into ‘fragmentation’ as a concept and, more specifically, as a spatial metaphor. The contention here is that however central fragmentation has been to analyses of contemporary international law, this notion has been conceptually assumed, ahistorically accepted and philosophically under-examined. The ‘fragment’ metaphor is tied historically to a cartographic rationality – and thus ‘reality’ – of all social space being reducible to a geometric object and, correspondingly, a planimetric map. The purpose of this article is to generate an appreciation among international lawyers that the problem of ‘fragmentation’ is more deeply rooted in epistemology and conceptual history. This requires an explanation of how the conflation of social space with planimetric reduction came to be constructed historically and used politically, and how that model informs representations of legal practices and perceptions of ‘international legal order’ as an inherently absolute and geometric. This implies the need to dig up and expose background assumptions that have been working to precondition a ‘fragmented’ characterization of worldly space. With the metaphor of ‘digging’ in mind, I draw upon Michel Foucault’s ‘archaeology of knowledge’ and, specifically, his assertion that epochal ideas are grounded by layers of ‘obscure knowledge’ that initially seem unrelated to a discourse. In the case of the fragmentation narrative, I argue obscure but key layers can be found in the Cartesian paradigm of space as a geometric object and the modern States’ imperative to assert (geographic) jurisdiction. To support this claim, I attempt to excavate the fragment metaphor by discussing key developments that led to the production and projection of geometric and planimetric reality since the 16th century

Performing Legality in the Theatre of Hostilities: Asymmetric Conflict, Lawfare and the Rise of Vicarious Litigation

This Article explores the extent of the change by looking at the ways in which asymmetric conflict and legalization have reshaped the theatre of hostilities and the implications for the institution of war itself. The shift from one literal battlefield to multiple and disaggregated battlespaces has led to a reconfigured theatre of hostilities, which now involves a complex mix of local and global spaces as well as kinetic and narrative forms of combat. This re-making of armed hostilities in geographical, material, and social terms has increased access to the drama, stage, and audience of military theatres. Further, the more globalized and publicized character of hostilities has allowed a higher number of actors, and actors of higher quality, to participate in and observe hostilities, whether kinetic, narrative, or both. This has given a powerful platform for law to mediate the conduct of warfare, and it is thus unsurprising that the notion of legality regularly occupies center stage in a reconstructed theatre of hostilities. Accordingly, military actors, whether state or non-state, are producing performances of legality in combat to influence not only their adversaries but also, crucially, formal and informal judgments across the theatre’s more expansive and global audience. The term “performances” does not imply cynical theatrics, but rather concerted actions to display legality or illegality as an integral part of warfare. In this way, such performances of legality have become a crucial strategic asset for interacting kinetic and narrative confrontations. This has led to a distinctive struggle between adversaries over appearances of legality and illegality, which has produced an institutional and narrative battlespace of growing importance that this Article conceptualizes as vicarious litigation. The Article is organized in five sections. Section I introduces and elaborates on the related notions of legal performances and vicarious litigation by bridging sociological theorizing on social performances with noted developments in asymmetric warfare. This conceptual effort draws insight from Performative Sociology and the so-called “practice turn” in international relations theory. Section II describes the origin of vicarious litigation as flowing from the asymmetric warfare’s disruption of the institutional bargain behind modern war and, consequently, International Humanitarian Law (IHL). To understand that institutional disruption, Section II discusses Andrew Mack’s under-examined inquiry into and conceptualization of “asymmetric conflict.” Sections III and IV look at how international lawyers, and specifically IHL scholars, have struggled to grasp the rise of asymmetric conflict and how the dominant “lawfare” literature has suffered from conceptual straining and the incapacity to theorize institutional change precipitated by the prevalence of asymmetric conflict. Section V focuses on the novel notions of legal performances and vicarious litigation and examines how these novel notions provide alternatives to the hobbled semantics of lawfare by offering greater insight into institutional mutations that now define the legalization of contemporary warfare

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants

MSC 2010: 11B83, 05A19, 33C45This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the generalized Somos-4 property. Here, we recognize well known number sequences such as: the Fibonacci, Catalan, Motzkin and SchrÄoder sequences, like special cases

Hormad1 mutation disrupts synaptonemal complex formation, recombination, and chromosome segregation in mammalian meiosis

Meiosis is unique to germ cells and essential for reproduction. During the first meiotic division, homologous chromosomes pair, recombine, and form chiasmata. The homologues connect via axial elements and numerous transverse filaments to form the synaptonemal complex. The synaptonemal complex is a critical component for chromosome pairing, segregation, and recombination. We previously identified a novel germ cell-specific HORMA domain encoding gene, Hormad1, a member of the synaptonemal complex and a mammalian counterpart to the yeast meiotic HORMA domain protein Hop1. Hormad1 is essential for mammalian gametogenesis as knockout male and female mice are infertile. Hormad1 deficient (Hormad1-/-) testes exhibit meiotic arrest in the early pachytene stage, and synaptonemal complexes cannot be visualized by electron microscopy. Hormad1 deficiency does not affect localization of other synaptonemal complex proteins, SYCP2 and SYCP3, but disrupts homologous chromosome pairing. Double stranded break formation and early recombination events are disrupted in Hormad1-/- testes and ovaries as shown by the drastic decrease in the γH2AX, DMC1, RAD51, and RPA foci. HORMAD1 co-localizes with cH2AX to the sex body during pachytene. BRCA1, ATR, and γH2AX co-localize to the sex body and participate in meiotic sex chromosome inactivation and transcriptional silencing. Hormad1 deficiency abolishes γH2AX, ATR, and BRCA1 localization to the sex chromosomes and causes transcriptional de-repression on the X chromosome. Unlike testes, Hormad1-/- ovaries have seemingly normal ovarian folliculogenesis after puberty. However, embryos generated from Hormad1-/- oocytes are hyper- and hypodiploid at the 2 cell and 8 cell stage, and they arrest at the blastocyst stage. HORMAD1 is therefore a critical component of the synaptonemal complex that affects synapsis, recombination, and meiotic sex chromosome inactivation and transcriptional silencing. © 2010 Shin et al

q-Analogue of Shock Soliton Solution

By using Jackson's q-exponential function we introduce the generating function, the recursive formulas and the second order q-differential equation for the q-Hermite polynomials. This allows us to solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary N moving zeroes, and to find operator solution for the Initial Value Problem for the q-heat equation. By the q-analog of the Cole-Hopf transformation we construct the q-Burgers type nonlinear heat equation with quadratic dispersion and the cubic nonlinearity. In q -> 1 limit it reduces to the standard Burgers equation. Exact solutions for the q-Burgers equation in the form of moving poles, singular and regular q-shock soliton solutions are found.Comment: 13 pages, 5 figure

Power series determined by an experiment on the unit interval

We consider the linear combinations of elements of two sequences: the first one a priory given nonnegative sequence and the second random sequence from the unit interval. We investigate the expected value of the smallest natural number such that the value of these linear combinations exceed a positive number. After very clear geometrical conclusions, we find the function which expresses the expected value. Here, we recognize a few known results like the special cases.Comment: 9 pages, 5 figure