Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

Single Synapse Information Coding in Intraburst Spike Patterns of Central Pattern Generator Motor Neurons

Burst firing is ubiquitous in nervous systems and has been intensively studied in central pattern generators (CPGs). Previous works have described subtle intraburst spike patterns (IBSPs) that, despite being traditionally neglected for their lack of relation to CPG motor function, were shown to be cell-type specific and sensitive to CPG connectivity. Here we address this matter by investigating how a bursting motor neuron expresses information about other neurons in the network. We performed experiments on the crustacean stomatogastric pyloric CPG, both in control conditions and interacting in real-time with computer model neurons. The sensitivity of postsynaptic to presynaptic IBSPs was inferred by computing their average mutual information along each neuron burst. We found that details of input patterns are nonlinearly and inhomogeneously coded through a single synapse into the fine IBSPs structure of the postsynaptic neuron following burst. In this way, motor neurons are able to use different time scales to convey two types of information simultaneously: muscle contraction (related to bursting rhythm) and the behavior of other CPG neurons (at a much shorter timescale by using IBSPs as information carriers). Moreover, the analysis revealed that the coding mechanism described takes part in a previously unsuspected information pathway from a CPG motor neuron to a nerve that projects to sensory brain areas, thus providing evidence of the general physiological role of information coding through IBSPs in the regulation of neuronal firing patterns in remote circuits by the CNS.

Bioluminescent sensor for naphthalene in air: Cell immobilization and evaluation with a dynamic standard atmosphere generator

A dynamic atmosphere generator with a naphthalene emission source has been constructed and used for the development and evaluation of a bioluminescence sensor based on the bacteria Pseudomonas fluorescens HK44 immobilized in 2% agar gel (101 cell mL(-1)) placed in sampling tubes. A steady naphthalene emission rate (around 7.3 nmol min(-1) at 27 degrees C and 7.4 mLmin(-1) of purified air) was obtained by covering the diffusion unit containing solid naphthalene with a PTFE filter membrane. The time elapsed from gelation of the agar matrix to analyte exposure (""maturation time"") was found relevant for the bioluminescence assays, being most favorable between 1.5 and 3 h. The maximum light emission, observed after 80 min, is dependent on the analyte concentration and the exposure time (evaluated between 5 and 20 min), but not on the flow rate of naphthalene in the sampling tube, over the range of 1.8-7.4 nmol min(-1). A good linear response was obtained between 50 and 260 nmol L-1 with a limit of detection estimated in 20 nmol L-1 far below the recommended threshold limit value for naphthalene in air. (c) 2008 Elsevier B.V. All rights reserved.