This paper presents our working notes for FIRE 2017, Information Retrieval from Legal documents -Task 2 (Precedence retrieval). Common Law Systems around the world recognize the importance of precedence in Law. In making decisions, Judges are obliged to consult prior cases that had already been decided to ensure that there is no divergence in treatment of similar situations in different cases. ...

We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a nonmean field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin glass condensation transition similar to the one occurring in the usual m...

Selection of some of the numerous series expansion involving the famous constant π.

Query expansion is a well known method to improve the performance of information retrieval systems. In this work we have tested different approaches to extract the candidate query terms from the top ranked documents returned by the first-pass retrieval. One of them is the cooccurrence approach, based on measures of cooccurrence of the candidate and the query terms in the retrieved documents. Th...

We give some sufficient and necessary conditions for an analytic function f on the unit ball B with Hadamard gaps, that is, for f (z)=∑k=1Pnk (z) (the homogeneous polynomial expansion of f ) satisfying nk+1/nk ≥ λ > 1 for all k ∈N, to belong to the space p(B)= { f |sup0<r<1(1− r2)‖R fr‖p <∞, f ∈H(B)}, p = 1,2,∞ as well as to the corresponding little space. A remark on analytic functions with Ha...

We show how to find series expansions for π of the form π = ∞ n=0 S(n) mn pn a n , where S(n) is some polynomial in n (depending on m, p, a). We prove that there exist such expansions for m = 8k, p = 4k, a = (−4) k , for any k, and give explicit examples for such expansions for small values of m, p and a.

The purpose of this paper is to initiate the study of a new kind of asymptotic series expansion for solutions of differential equations containing a parameter. We obtain uniform asymptotic solutions for certain equations of the form ê»y" = ait, e)y , ( )' = d/dt, where n is a positive integer, t and e are real variables ranging over \t\ S U, 0 < e ^ €o, and a is a function infinitely differenti...

In this report we discuss the experiments we conducted at the University of Wolverhampton for the Microblog Track at TREC-2011. As this was the first time we participated in TREC and the particular task presents some unique challenges we initially focused on properly analyzing and indexing the new Tweets2011 Corpus. We experimented with the effects that some standard IR techniques, such as quer...

This paper presents a simple two-branch transmit diversity scheme. Using two transmit antennas and one receive antenna the scheme provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas. It is also shown that the scheme may easily be generalized to two transmit antennas and M receive antennas to provide a diversity order o...