# Verboseness

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## verboseness

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where c is a collection of documents, d is a document, and t is a term. We claim that there are other properties of documents and terms that are important but under-represented, namely verboseness and the previously introduced burstiness (Roelleke 2013). In this paper we will focus primarily on verboseness, but we will also make some observations on burstiness and its relation with IDF. However, before starting, we introduce the notation used.

In this work, it is heuristically shown that the parameter b is inversely proportional to a statistic of the collection, the average collection verboseness ED[vd], and that it can be predicted without statistically damaging the performance of the trained BM25.

PL(d) is the location based probability of a document. Dividing this by the term based probability of d, PT(d)=Td/T yields the pivoted verboseness. Dividing by the document based probability of d, PD(d)=Dd/D=1/D, yields the pivoted document length.

However, the components of this formulation for λq are generally not very informative (queries tend to be significantly shorter than documents, and therefore we cannot really talk about the verboseness of a query). Instead, at this place we can exploit the duality of document verboseness and length with term length and burstiness (see Sect. 3.3):

Distribution of verboseness in the x-axis and document length in the y-axis of the relevant documents (in gold) and all the documents (in black). Left plot shows the non-elite pivotization case of verboseness (vd) and length (ld) and the right plot shows the elite pivotization case of verboseness (v^d) and length (l^d)

Difference on a per topic based between the AP of the trained TFBM25-IDF with verboseness combined in conjunction with elite pivots, and the trained classic TFBM25-IDF. When the difference is positive the variant with verboseness performs better than the classic version

Go to the source code of this file.Defines#define CUT_ITER 1 Boolean to stop iteration if MLE function starts to decrease by some very small amount. #define DATA "/home/max/Desktop/2/" Output location for the matrices produced by the program. #define DO_MLE 1 Boolean to specify whether MLE should be performed. #define EPS 0.05 Experimental State Error value. #define KEEP_GOING 1 Boolean to cutoff MLE based on MAX_FIDELITY. #define MAX_FIDELITY 0.90 Max fidelity cutoff point. If fidelity is over this value, simulations stops. #define MAXCHAR 512 Defines the numerical value of a character - do not alter. #define MAXITER 100 Maximum number of iterations of MLE function, an integer. #define MILLION 1000000 Defines the numerical value of one million - do not alter. #define NQ 2 Number of Qubits. #define NUMTRIALS 1 Number of times tomography is repeated. #define STATE 5 Main control which selects what kind of tomography will be perfomred. #define VERBOSE 1 Boolean extra verboseness level toggle. #define WRITE_DENSITY 1 Boolean toggle for density matrices to be written to disc. Functionsdouble abs_val (gsl_vector *vec) Returns absolute value (length) of vector vec. void base_4_rep_inc (int counter[], int n) Input array has base-4 rep of n-1, it's incremented to n. double concurrence (gsl_matrix_complex *matrix) Returns concurrence of the input density matrix. void display_matrix (gsl_matrix_complex *data) Prints complex matrix to screen. void display_matrix_real (gsl_matrix *data) Prints real matrix to screen. void display_vector_real (gsl_vector *data) Prints real-valued vector to screen. double entropy_linear (gsl_matrix_complex *matrix) Returns entropy of the input complex-valued density matrix. double fidelity (gsl_matrix_complex *m1, gsl_matrix_complex *m2) Returns fidelity between two density matrices m1 and m2. int Fwrite (const void *ptr, size_t size, size_t nmemb, FILE *stream) Wrapper function for fwrite to handle return codes. void gsl_vector_add_element (gsl_vector *vector, double element) Adds element as last element in vector, after re-allocating size of vector. void kron (gsl_matrix_complex *a, gsl_matrix_complex *b, gsl_matrix_complex *c) Performs tensor product on matrices A and B storing the output into pre-allocated matrix C. void make_T (const gsl_vector *t, gsl_matrix_complex *T) Seeds in values from vector t into Cholesky lower-diagonal matrix T, like described in the paper. void matrix_complex_random_init (gsl_matrix_complex *random) Fills a pre-allocated matrix with random values sampled from U(-1,1). void mu_tensor (gsl_matrix_complex *mu_cell[], gsl_matrix_complex *mu_array[], int mu_counter[], int counter[]) Shortcut algorithm for tensoring on additional mu matrices to save computation time. void outer_product (gsl_vector_complex *a, gsl_matrix_complex *outp) Performs outer product a>void void int void void void gsl_complex void int int int gsl_matrix_complex * gsl_matrix_complex * 1 qubits, as described in the paper. double N Specifies the simulated number of times an experiment is performed. gsl_complex one Computational constant. gsl_matrix_complex * ones Matrix full of ones. gsl_matrix_complex * sig_array [4] Stores the 4 Pauli matrices. gsl_matrix_complex * sigma_cell [NQ] Stores tensored sigma matrices to compute the Pauli operators for >1 qubits, as described in the paper. double theta_handle Used to adjust the tangle value. double Werner_handle State handle used to adjust the Werner state. gsl_complex zero Computational constant. Detailed DescriptionMain header file which specifies arguments for the program. Numerical State Tomography Using GSL -> www.gnu.org/software/gsl Copyright (C) 2007 Max S KaznadyThis program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation;AUTHOR Max S Kaznady, [EMAIL PROTECTED] max.kaznady@gmail.com Summer, 2007This header file is used to specify all the parameters for the program instead of using command line arguments. This is not a very good software practice but saved a lot of time while developing the code. Definition in file header.h. 041b061a72