Dynamic Shannon Coding

We present a new algorithm for dynamic prefix-free coding, based on Shannon coding. We give a simple analysis and prove a better upper bound on the length of the encoding produced than the corresponding bound for dynamic Huffman coding. We show how our algorithm can be modified for efficient length-restricted coding, alphabetic coding and coding with unequal letter costs.Comment: 6 pages; conference version presented at ESA 2004; journal version submitted to IEEE Transactions on Information Theor

Minimax Trees in Linear Time with Applications

A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves\u27 depths, it minimizes the maximum of any leaf\u27s weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffman-like, $O (n log n)$-time algorithm for building them. Drmota and Szpankowski (2002) gave another $O (n log n)$-time algorithm, which takes linear time when the weights are already sorted by their fractional parts. In this paper we give the first linear-time algorithm for building minimax trees for unsorted real weights

Structural investigation of nucleophosmin interaction with the tumor suppressor Fbw7γ

Nucleophosmin (NPM1) is a multifunctional nucleolar protein implicated in ribogenesis, centrosome duplication, cell cycle control, regulation of DNA repair and apoptotic response to stress stimuli. The majority of these functions are played through the interactions with a variety of protein partners. NPM1 is frequently overexpressed in solid tumors of different histological origin. Furthermore NPM1 is the most frequently mutated protein in acute myeloid leukemia (AML) patients. Mutations map to the C-terminal domain and lead to the aberrant and stable localization of the protein in the cytoplasm of leukemic blasts. Among NPM1 protein partners, a pivotal role is played by the tumor suppressor Fbw7γ, an E3-ubiquitin ligase that degrades oncoproteins like c-MYC, cyclin E, Notch and c-jun. In AML with NPM1 mutations, Fbw7γ is degraded following its abnormal cytosolic delocalization by mutated NPM1. This mechanism also applies to other tumor suppressors and it has been suggested that it may play a key role in leukemogenesis. Here we analyse the interaction between NPM1 and Fbw7γ, by identifying the protein surfaces implicated in recognition and key aminoacids involved. Based on the results of computational methods, we propose a structural model for the interaction, which is substantiated by experimental findings on several site-directed mutants. We also extend the analysis to two other NPM1 partners (HIV Tat and CENP-W) and conclude that NPM1 uses the same molecular surface as a platform for recognizing different protein partners. We suggest that this region of NPM1 may be targeted for cancer treatment

Optimal Prefix Codes for Infinite Alphabets with Nonlinear Costs

Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a source code that is optimal in the sense of minimizing expected codeword length. For some applications, however, a source code should instead minimize one of a family of nonlinear objective functions, $\beta$-exponential means, those of the form $\log_a \sum_i p(i) a^{n(i)}$, where $n(i)$ is the length of the $i$th codeword and $a$ is a positive constant. Applications of such minimizations include a novel problem of maximizing the chance of message receipt in single-shot communications ($a<1$) and a previously known problem of minimizing the chance of buffer overflow in a queueing system ($a>1$). This paper introduces methods for finding codes optimal for such exponential means. One method applies to geometric distributions, while another applies to distributions with lighter tails. The latter algorithm is applied to Poisson distributions and both are extended to alphabetic codes, as well as to minimizing maximum pointwise redundancy. The aforementioned application of minimizing the chance of buffer overflow is also considered.Comment: 14 pages, 6 figures, accepted to IEEE Trans. Inform. Theor

Multiscale combinatorial grouping

We propose a unified approach for bottom-up hierarchical image segmentation and object candidate generation for recognition, called Multiscale Combinatorial Grouping (MCG). For this purpose, we first develop a fast normalized cuts algorithm. We then propose a high-performance hierarchical segmenter that makes effective use of multiscale information. Finally, we propose a grouping strategy that combines our multiscale regions into highly-accurate object candidates by exploring efficiently their combinatorial space. We conduct extensive experiments on both the BSDS500 and on the PASCAL 2012 segmentation datasets, showing that MCG produces state-of-the-art contours, hierarchical regions and object candidates. 1