On the controllability of distributed systems

To “control” a system is to make it behave (hopefully) according to our “wishes,” in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed—i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our “wish” is to drive the system in a given time, by an adequate choice of the controls, from a given initial state to a final given state, which is the target. If this can be achieved (respectively, if we can reach any “neighborhood” of the target) the system, with the controls at our disposal, is exactly (respectively, approximately) controllable. A very general (and fuzzy) idea is that the more a system is “unstable” (chaotic, turbulent) the “simplest,” or the “cheapest,” it is to achieve exact or approximate controllability. When the PDEs are the Navier–Stokes equations, it leads to conjectures, which are presented and explained. Recent results, reported in this expository paper, essentially prove the conjectures in two space dimensions. In three space dimensions, a large number of new questions arise, some new results support (without proving) the conjectures, such as generic controllability and cases of decrease of cost of control when the instability increases. Short comments are made on models arising in climatology, thermoelasticity, non-Newtonian fluids, and molecular chemistry. The Introduction of the paper and the first part of all sections are not technical. Many open questions are mentioned in the text.

Gene2EST: a BLAST2 server for searching expressed sequence tag (EST) databases with eukaryotic gene-sized queries

Expressed sequence tags (ESTs) are randomly sequenced cDNA clones. Currently, nearly 3 million human and 2 million mouse ESTs provide valuable resources that enable researchers to investigate the products of gene expression. The EST databases have proven to be useful tools for detecting homologous genes, for exon mapping, revealing differential splicing, etc. With the increasing availability of large amounts of poorly characterised eukaryotic (notably human) genomic sequence, ESTs have now become a vital tool for gene identification, sometimes yielding the only unambiguous evidence for the existence of a gene expression product. However, BLAST-based Web servers available to the general user have not kept pace with these developments and do not provide appropriate tools for querying EST databases with large highly spliced genes, often spanning 50 000–100 000 bases or more. Here we describe Gene2EST (http://woody.embl-heidelberg.de/gene2est/), a server that brings together a set of tools enabling efficient retrieval of ESTs matching large DNA queries and their subsequent analysis. RepeatMasker is used to mask dispersed repetitive sequences (such as Alu elements) in the query, BLAST2 for searching EST databases and Artemis for graphical display of the findings. Gene2EST combines these components into a Web resource targeted at the researcher who wishes to study one or a few genes to a high level of detail.

Training and search methods for speech recognition.

Speech recognition involves three processes: extraction of acoustic indices from the speech signal, estimation of the probability that the observed index string was caused by a hypothesized utterance segment, and determination of the recognized utterance via a search among hypothesized alternatives. This paper is not concerned with the first process. Estimation of the probability of an index string involves a model of index production by any given utterance segment (e.g., a word). Hidden Markov models (HMMs) are used for this purpose [Makhoul, J. & Schwartz, R. (1995) Proc. Natl. Acad. Sci. USA 92, 9956-9963]. Their parameters are state transition probabilities and output probability distributions associated with the transitions. The Baum algorithm that obtains the values of these parameters from speech data via their successive reestimation will be described in this paper. The recognizer wishes to find the most probable utterance that could have caused the observed acoustic index string. That probability is the product of two factors: the probability that the utterance will produce the string and the probability that the speaker will wish to produce the utterance (the language model probability). Even if the vocabulary size is moderate, it is impossible to search for the utterance exhaustively. One practical algorithm is described [Viterbi, A. J. (1967) IEEE Trans. Inf. Theory IT-13, 260-267] that, given the index string, has a high likelihood of finding the most probable utterance.