Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

Removable singularities for p-harmonic maps: The subquadratic case

We prove a removable singularity theorem for p-harmonic maps in the subquadratic case. The theorem states that an isolated singularity of a weakly p-harmonic map is removable if the energy is sufficiently small in a neighbourhood of the singularity.

The development of retinotectal maps: A review of models based on molecular gradients

Information about the world is often represented in the brain in the form of topographic maps. A paradigm example is the topographic representation of the visual world in the optic tectum/superior colliculus. This map initially forms during neural development using activity-independent molecular cues, most notably some type of chemospecific matching between molecular gradients in the retina and corresponding gradients in the tectum/superior colliculus. Exactly how this process might work has been studied both experimentally and theoretically for several decades. This review discusses the experimental data briefly, and then in more detail the theoretical models proposed. The principal conclusions are that (1) theoretical models have helped clarify several important ideas in the field, (2) earlier models were often more sophisticated than more recent models, and (3) substantial revisions to current modelling approaches are probably required to account for more than isolated subsets of the experimental data.

Molecular cloning and characterization of the mouse Na+ sulfate cotransporter gene (Slc13a4): structure and expression

Sulfate is an essential ion required for numerous functions in mammalian physiology. Due to its hydrophilic nature, cells require sulfate transporters on their plasma membranes to allow entry of sulfate into cells. In this study, we identified a new mouse Na+-sulfate cotransporter (mNaS2), characterized its tissue distribution and determined its cDNA and gene (Slc13a4) structures. mNaS2 mRNA was expressed in placenta, brain, lung, eye, heart, testis, thymus and liver. The mouse NaS2 cDNA spans 3384 nucleotides and its open frame encodes a protein of 624 amino acids. Slc13a4 maps to mouse chromosome 6131 and contains 16 exons, spanning over 40 kb in length. Its 5'-flanking region contains CART- and GC-box motifs and a number of putative transcription factor binding sites, including GATA-1, MTF-1, STAT6 and HNF4 consensus sequences. This is the first study to define the tissue distribution of mNaS2 and resolve its cDNA and gene structures, which will allow us to investigate mNaS2 gene expression in vivo and determine its role in mammalian physiology.

Combining influence maps and cellular automata for reactive game agents

Agents make up an important part of game worlds, ranging from the characters and monsters that live in the world to the armies that the player controls. Despite their importance, agents in current games rarely display an awareness of their environment or react appropriately, which severely detracts from the believability of the game. Some games have included agents with a basic awareness of other agents, but they are still unaware of important game events or environmental conditions. This paper presents an agent design we have developed, which combines cellular automata for environmental modeling with influence maps for agent decision-making. The agents were implemented into a 3D game environment we have developed, the EmerGEnT system, and tuned through three experiments. The result is simple, flexible game agents that are able to respond to natural phenomena (e.g. rain or fire), while pursuing a goal.

The tectonically-confined Firenzuola turbidite system (Miocene, Marnoso-arenacea Formation, northern Apennines, Italy): an example of facies variations related to the basin morphology

The Firenzuola turbidite system formed during a paroxysmal phase of thrust propagation, involving the upper Serravallian deposits of the Marnoso-arenacea Formation (MAF). During this phase the coeval growth of two major tectonic structures, the M. Castellaccio thrust and the Verghereto high, played a key role, causing a closure of the inner basin and a coeval shift of the depocentre to the outer basin. This work focuses on this phase of fragmentation of the MAF basin; it is based on a new detailed high-resolution stratigraphic framework, which was used to determine the timing of growth of the involved structures and their direct influence on sediment dispersal and on the lateral and vertical turbidite facies distribution. The Firenzuola turbidite system stratigraphy is characterized by the occurrence of mass-transport complexes (MTCs) and thick sandstone accumulation in the depocentral area, which passes to finer drape over the structural highs; the differentiation between these two zones increases over time and ends with the deposition of marly units over the structural highs and the emplacement of the Visignano MTC. According to the stratigraphic pattern and turbidite facies characteristics, the Firenzuola System has been split into two phases, namely Firenzuola I and Firenzuola II: the former is quite similar to the underlying deposits, while the latter shows the main fragmentation phase, testifying the progressive isolation of the inner basin and a coeval shift of the depocentre to the outer basin. The final stratigraphic and sedimentological dataset has been used to create a quantitative high-resolution 3D facies distribution using the Petrel software platform. This model allows a detailed analysis of lateral and vertical facies variations that can be exported to several reservoirs settings in hydrocarbon exploration and exploitation areas, since facies distributions and geometries of the reservoir bodies of many sub-surface turbidite basins show a significant relationship to the syndepositional structural activity, but are beyond seismic resolution.

Dynamics and topographic organization of recursive self-organizing maps

Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology.