Jean-Marc Steyaert

Patterns and pattern-matching in trees: an analysis

This paper presents general results on the probabilities of occurrences of patterns in trees, which serve to analyze a commonly used pattern matching algorithm on trees. It appears that for a wide class of statistics on trees, pattern-matching has a linear expected time complexity (in contrast to a quadratic worst-case behaviour). The methods used are both combinatorial and analytic and prove useful in the evaluation of a wide class of tree algorithms.

Analytic variations on the common subexpression problem

Any tree can be represented in a maximally compact form as a directed acyclic graph where common subtrees are factored and shared, being represented only once. Such a compaction can be effected in linear time. It is used to save storage in implementations of functional programming languages, as well as in symbolic manipulation and computer algebra systems. In compiling, the compaction problem is known as the “common subexpression problem” and it plays a central role in register allocation, code generation and optimisation. We establish here that, under a variety of probabilistic models, a tree of size n has a compacted form of expected size asymptotically

The metabolic cooperation between cells in solid cancer tumors

C\frac{n}{{\sqrt {\log n} }},

A Branching Process Arising in Dynamic Hashing, Trie Searching and Polynomial Factorization

where the constant C is explicitly related to the type of trees to be compacted and to the statistical model reflecting tree usage. In particular the savings in storage approach 100% on average for large structures, which overperforms the commonly used form of sharing that is restricted to leaves (atoms).

Hyperosmotic stress contributes to mouse colonic inflammation through the methylation of protein phosphatase 2A

Transmembrane β‐barrel (TMB) proteins are embedded in the outer membrane of Gram‐negative bacteria, mitochondria, and chloroplasts. The cellular location and functional diversity of β‐barrel outer membrane proteins (omps) makes them an important protein class. At the present time, very few nonhomologous TMB structures have been determined by X‐ray diffraction because of the experimental difficulty encountered in crystallizing transmembrane proteins. A novel method using pairwise interstrand residue statistical potentials derived from globular (nonouter membrane) proteins is introduced to predict the supersecondary structure of transmembrane β‐barrel proteins. The algorithm transFold employs a generalized hidden Markov model (i.e., multitape S‐attribute grammar) to describe potential β‐barrel supersecondary structures and then computes by dynamic programming the minimum free energy β‐barrel structure. Hence, the approach can be viewed as a “wrapping” component that may capture folding processes with an initiation stage followed by progressive interaction of the sequence with the already‐formed motifs. This approach differs significantly from others, which use traditional machine learning to solve this problem, because it does not require a training phase on known TMB structures and is the first to explicitly capture and predict long‐range interactions. TransFold outperforms previous programs for predicting TMBs on smaller (≤200 residues) proteins and matches their performance for straightforward recognition of longer proteins. An exception is for multimeric porins where the algorithm does perform well when an important functional motif in loops is initially identified. We verify our simulations of the folding process by comparing them with experimental data on the functional folding of TMBs. A Web server running transFold is available and outputs contact predictions and locations for sequences predicted to form TMBs. Proteins 2006.

On Sets Having Only Hard Subsets

Cancer cells cooperate with stromal cells and use their environment to promote tumor growth. Energy production depends on nutrient availability and O₂ concentration. Well-oxygenated cells are highly proliferative and reorient the glucose metabolism towards biosynthesis, whereas glutamine oxidation replenishes the TCA cycle coupled with OXPHOS-ATP production. Glucose, glutamine and alanine transformations sustain nucleotide and fatty acid synthesis. In contrast, hypoxic cells slow down their proliferation, enhance glycolysis to produce ATP and reject lactate which is recycled as fuel by normoxic cells. Thus, glucose is spared for biosynthesis and/or for hypoxic cell function. Environmental cells, such as fibroblasts and adipocytes, serve as food donors for cancer cells, which reject waste products (CO₂ , H⁺, ammoniac, polyamines…) promoting EMT, invasion, angiogenesis and proliferation. This metabolic-coupling can be considered as a form of commensalism whereby non-malignant cells support the growth of cancer cells. Understanding these cellular cooperations within tumors may be a source of inspiration to develop new anti-cancer agents.

A complexity calculus for recursive tree algorithms

Transmembrane β-barrel (TMB) proteins are embedded in the outer membrane of Gram-negative bacteria, mitochondria and chloroplasts. The cellular location and functional diversity of β-barrel outer membrane proteins makes them an important protein class. At the present time, very few non-homologous TMB structures have been determined by X-ray diffraction because of the experimental difficulty encountered in crystallizing transmembrane (TM) proteins. The transFold web server uses pairwise inter-strand residue statistical potentials derived from globular (non-outer-membrane) proteins to predict the supersecondary structure of TMB. Unlike all previous approaches, transFold does not use machine learning methods such as hidden Markov models or neural networks; instead, transFold employs multi-tape S-attribute grammars to describe all potential conformations, and then applies dynamic programming to determine the global minimum energy supersecondary structure. The transFold web server not only predicts secondary structure and TMB topology, but is the only method which additionally predicts the side-chain orientation of transmembrane β-strand residues, inter-strand residue contacts and TM β-strand inclination with respect to the membrane. The program transFold currently outperforms all other methods for accuracy of β-barrel structure prediction. Available at .

Modeling and predicting all-α transmembrane proteins including helix-helix pairing

We obtain average value and distribution estimates for the height of a class of trees that occurs in various contexts in computer algorithms : in trie searching, as index in several dynamic schemes and as an underlying partition structure in polynomial factorization algorithms. In particular, results given here completely solve the problem of analyzing Extendible Hashing for which practical conclusions are given. The treatment relies on the saddle point method of complex analysis which is used here for extracting coefficients of a probability generating function, and on a particular technique that reveals periodic fluctuations in the behaviour of algorithms which are precisely quantified.