Towards an expanded model of litigation

Introduction: The call for contributions for this workshop describes the important new challenges for the legal search community this domain brings. Rather than just understanding the challenges this domain poses in terms of their technical properties, we would like to suggest that understanding these challenges as socio-technical challenges will be important. That is, as well as calling for research on a technical level to address these challenges we are also calling for work to understand the social practices of those involved in e-discovery (ED) and related legal work. A particularly interesting feature of this field is that it is likely that search technologies will (at least semi-)automate responsiveness review in the relatively near term and this will change the way that the work is organised and done in many ways – offering new possibilities for new ways of organising the work. As well as designing those technologies for automating responsiveness review we need to be envisioning how the work will be done in the future, how these technologies will impact the organisation of the case and so on. In this position paper we therefore outline the importance of understanding the wider social context of ED when designing tools and technologies to support and change the work. We would like to reinforce and expand on Conrad’s call for IR researchers to understand just what ED entails [2], include the stages that come both before and after core retrieval activities. The importance of considering the social aspects of work in the design of the technology has been established for some time. Ushering in this ‘turn to the social,’ and focusing on interface design, Gentner and Grudin [4] described how the GUI has already changed from an interface for engineers, representing the engineering model of the machine to one that supported single ‘everyman’ users (based on ideas from psychology). From then onwards the interface has evolved to support groups of users, taking into account the social and organisational contexts of use. This has particular resonance for the design of ED technologies: during ED in particular and the wider legal process there are often many lawyers involved – reviewing documents, determining issues, etc. Even if the way that their work is organised currently is not seen as collaborative in the traditional sense – with individual lawyers working on individual document sets to review them - their work needs to be coordinated and it seems likely that their work could be enhanced by, for example, knowledge of what their colleagues had found, how the case was shaping up, new key terms and facts turned up and so on. Work is often modelled for the purposes of design using process models, but this misses out on the richness and variety actually found when one examines how the work is carried out [3]. Technologies which strictly enforce the process models can often hinder the work, or end up being worked around as was the case with workflow systems since people interpret processes very flexibly to get the work done ([1], [3]). Other studies in other fields have found similar problems when systems are designed on for example cognitive models of how the work is done; they often do not take into account the situated nature of the work and thus they can be very difficult to use [5]. We believe, like [2], that a clear understanding of the social practices of ED is vital for the creation of high-quality, meaningful tools and technologies. We furthermore propose that work practice studies, to be used in combination with other methods, are a central part of getting the detailed understanding of the work practices central to designing useful and intelligent tools. Work practice studies would involve ethnographies, consisting primarily of observation, undertaken of practitioners engaging in the work of ED

Neural Relax

We present an algorithm for data preprocessing of an associative memory inspired to an electrostatic problem that turns out to have intimate relations with information maximization

Tiling Spaces are Inverse Limits

Let M be an arbitrary Riemannian homogeneous space, and let Omega be a space of tilings of M, with finite local complexity (relative to some symmetry group Gamma) and closed in the natural topology. Then Omega is the inverse limit of a sequence of compact finite-dimensional branched manifolds. The branched manifolds are (finite) unions of cells, constructed from the tiles themselves and the group Gamma. This result extends previous results of Anderson and Putnam, of Ormes, Radin and Sadun, of Bellissard, Benedetti and Gambaudo, and of G\"ahler. In particular, the construction in this paper is a natural generalization of G\"ahler's.Comment: Latex, 6 pages, including one embedded figur

Lattice Glass Models

Motivated by the concept of geometrical frustration, we introduce a class of statistical mechanics lattice models for the glass transition. Monte Carlo simulations in three dimensions show that they display a dynamical glass transition which is very similar to that observed in other off-lattice systems and which does not depend on a specific dynamical rule. Whereas their analytic solution within the Bethe approximation shows that they do have a discontinuous glass transition compatible with the numerical observations.Comment: 4 pages, 2 figures; minor change

Spatial structures and dynamics of kinetically constrained models for glasses

Kob and Andersen's simple lattice models for the dynamics of structural glasses are analyzed. Although the particles have only hard core interactions, the imposed constraint that they cannot move if surrounded by too many others causes slow dynamics. On Bethe lattices a dynamical transition to a partially frozen phase occurs. In finite dimensions there exist rare mobile elements that destroy the transition. At low vacancy density, $v$, the spacing, $\Xi$, between mobile elements diverges exponentially or faster in $1/v$. Within the mobile elements, the dynamics is intrinsically cooperative and the characteristic time scale diverges faster than any power of $1/v$ (although slower than $\Xi$). The tagged-particle diffusion coefficient vanishes roughly as $\Xi^{-d}$.Comment: 4 pages. Accepted for pub. in Phys. Rev. Let

Alexander quandle lower bounds for link genera

We denote by Q_F the family of the Alexander quandle structures supported by finite fields. For every k-component oriented link L, every partition P of L into h:=|P| sublinks, and every labelling z of such a partition by the natural numbers z_1,...,z_n, the number of X-colorings of any diagram of (L,z) is a well-defined invariant of (L,P), of the form q^(a_X(L,P,z)+1) for some natural number a_X(L,P,z). Letting X and z vary in Q_F and among the labellings of P, we define a derived invariant A_Q(L,P)=sup a_X(L,P,z). If P_M is such that |P_M|=k, we show that A_Q(L,P_M) is a lower bound for t(L), where t(L) is the tunnel number of L. If P is a "boundary partition" of L and g(L,P) denotes the infimum among the sums of the genera of a system of disjoint Seifert surfaces for the L_j's, then we show that A_Q(L,P) is at most 2g(L,P)+2k-|P|-1. We set A_Q(L):=A_Q(L,P_m), where |P_m|=1. By elaborating on a suitable version of a result by Inoue, we show that when L=K is a knot then A_Q(K) is bounded above by A(K), where A(K) is the breadth of the Alexander polynomial of K. However, for every g we exhibit examples of genus-g knots having the same Alexander polynomial but different quandle invariants A_Q. Moreover, in such examples A_Q provides sharp lower bounds for the genera of the knots. On the other hand, A_Q(L) can give better lower bounds on the genus than A(L), when L has at least two components. We show that in order to compute A_Q(L) it is enough to consider only colorings with respect to the constant labelling z=1. In the case when L=K is a knot, if either A_Q(K)=A(K) or A_Q(K) provides a sharp lower bound for the knot genus, or if A_Q(K)=1, then A_Q(K) can be realized by means of the proper subfamily of quandles X=(F_p,*), where p varies among the odd prime numbers.Comment: 36 pages; 16 figure

Effects of supercoiling on enhancer-promoter contacts.

Using Brownian dynamics simulations, we investigate here one of possible roles of supercoiling within topological domains constituting interphase chromosomes of higher eukaryotes. We analysed how supercoiling affects the interaction between enhancers and promoters that are located in the same or in neighbouring topological domains. We show here that enhancer-promoter affinity and supercoiling act synergistically in increasing the fraction of time during which enhancer and promoter stay in contact. This stabilizing effect of supercoiling only acts on enhancers and promoters located in the same topological domain. We propose that the primary role of recently observed supercoiling of topological domains in interphase chromosomes of higher eukaryotes is to assure that enhancers contact almost exclusively their cognate promoters located in the same topological domain and avoid contacts with very similar promoters but located in neighbouring topological domains

Spectral geometry as a probe of quantum spacetime

Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the expectation value of the spectral dimension on the ensemble of geometries defined by these models, and comparing its large scale behaviour to that of a sphere (Euclidean de Sitter). From the same measurement we are also able to confirm the phenomenon of dynamical dimensional reduction observed in this and other approaches to quantum gravity -- the first time this has been done for three-dimensional causal dynamical triangulations. In this case, the value for the short-scale limit of the spectral dimension that we find is approximately 2. We comment on the relevance of these results for the comparison to asymptotic safety and Horava-Lifshitz gravity, among other approaches to quantum gravity.Comment: 25 pages, 6 figures. Version 2: references to figures added, acknowledgment added