Revisiting the Random Subset Sum Problem

International audienceThe average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we seek a subset of the $X_i$'s whose sum approximates $z$ up to error $\varepsilon$.In this setup, it has been shown that, under mild assumptions on the distribution of the random variables, a sample of size $\mathcal{O}\left(\log (1/\varepsilon)\right)$ suffices to obtain, with high probability, approximations for all values in $[-1/2, 1/2]$. Recently, this result has been rediscovered outside the algorithms community, enabling meaningful progress in other fields. In this work we present an alternative proof for this theorem, with a more direct approach and resourcing to more elementary tools, in the hope of disseminating it even further

Clinical implication of genome-wide profiling in diffuse large B-cell lymphoma and other subtypes of B-cell lymphoma.

The differentiation of lymphoid cells is tightly regulated by transcription factors at various stages during their development. During the maturation processes, different genomic alterations or aberrations such as chromosomal translocation, mutation and deletions may occur that can eventually result in distinct biological and clinical tumors. The different differentiation stages create heterogeneity in lymphoid malignancies, which can complicate the diagnosis. The initial diagnostic scheme for lymphoid diseases was coined by Rappaport followed by Revised European and American Classification of Lymphoid Neoplasms (REAL) and World Health Organization (WHO) classifications. These classification methods were based on histological, immunophenotypic and cytogenetic markers and widely accepted by pathologists and oncologists worldwide. During last several decades, great progress has been made in understanding the etiology, pathogenesis and molecular biology of malignant lymphoma. However, detailed knowledge in the molecular mechanism of lymphomagenesis is largely unknown. New therapeutic protocols based on the new classification have been on clinical trials, but with little success. Therefore, it is imperative to understand the basic biology of the tumor at molecular level. One important approach will be to measure the activity of the tumor genome and this can partly be achieved by the measurement of whole cellular mRNA. One of the key technologies to perform a high-throughput analysis is DNA microarray technology. The genome-wide transcriptional measurement, also called gene expression profile (GEP) can accurately define the biological phenotype of the tumor. In this review, important discoveries made by genome-wide GEP in understanding the biology of lymphoma and additionally the diagnostic and prognostic value of microarrays are discussed

Predicting Meningioma Consistency on Preoperative Neuroimaging Studies

This article provides an overview of the neuroimaging literature focused on preoperative prediction of meningioma consistency. A validated, noninvasive neuroimaging method to predict tumor consistency can provide valuable information regarding neurosurgical planning and patient counseling. Most of the neuroimaging literature indicates conventional MRI using T2-weighted imaging may be helpful to predict meningioma consistency; however, further rigorous validation is necessary. Much less is known about advanced MRI techniques, such as diffusion MRI, MR elastography (MRE), and MR spectroscopy. Of these methods, MRE and diffusion tensor imaging appear particularly promising