Receptive fields and the representation of visual information.

Receptive fields in the retina indicate the first measurements taken over the (discrete) visual image. Why are they circular surround with an excitatory/inhibitory structure? We hypothesize that this provides a representation of the visual information in a form suitable for transmission over the optic nerve, a rather limited channel, that can then be extended into a variety of representations at the cortex. These cortical representations span a range of sizes and functionally separate positive and negative contrast data, precisely as is required for further processing. Our scheme is both physiologically and psychophysically plausible. In particular, we derive an explicit formula for constructing large receptive fields from small ones, and introduce the notion of de-blurring to derive interpolation filters for hyperacuity. A mathematical requirement of our scheme is a form of separation between positive and negative contrast data, a nonlinearity that we predict will agree with observations. Furthermore, the mathematics that we utilize are more naturally applicable to physiological models based on Gaussian than are (Fourier) spatial frequencies.

On the foundations of relaxation labeling processes.

A large class of problems can be formulated in terms of the assignment of labels to objects. Frequently, processes are needed which reduce ambiguity and noise, and select the best label among several possible choices. Relaxation labeling processes are just such a class of algorithms. They are based on the parallel use of local constraints between labels. This paper develops a theory to characterize the goal of relaxation labeling. The theory is founded on a definition of con-sistency in labelings, extending the notion of constraint satisfaction. In certain restricted circumstances, an explicit functional exists that can be maximized to guide the search for consistent labelings. This functional is used to derive a new relaxation labeling operator. When the restrictions are not satisfied, the theory relies on variational cal-culus. It is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality. A procedure nearly identical to the relaxation operator derived under restricted circum-stances serves in the more general setting. Further, a local convergence result is established for this operator. The standard relaxation labeling formulas are shown to approximate our new operator, which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here. Observations about con-vergence and generalizations to higher order compatibility relations are described.

A gradient projection algorithm for relaxation methods.

We consider a particular problem which arises when apply-ing the method of gradient projection for solving constrained optimiza-tion and finite dimensional variational inequalities on the convex set formed by the convex hull of the standard basis unit vectors. The method is especially important for relaxation labeling techniques applied to problems in artificial intelligence. Zoutendijk's method for finding feasible directions, which is relatively complicated in general situations, yields a very simple finite algorithm for this problem. We present an extremely simple algorithm for performing the gradient projection and an independent verification of its correctness.

A three-dimensional edge operator.

Modern scanning techniques, such as computed tomography, have begun to produce true three-dimensional imagery of internal structures. The first stage in finding structure in these images, like that for standard two-dimensional images, is to evaluate a local edge operator over the image. If an edge segment in two dimensions is modeled as an oriented unit line segment that separates unit squares (i.e., pixels) of different intensities, then a three-dimensional edge segment is an oriented unit plane that separates unit volumes (i.e., voxels) of different intensities. In this correspondence we derive an operator that finds the best oriented plane at each point in the image. This operator, which is based directly on the 3-D problem, complements other approaches that are either interactive or heuristic extensions of 2-D techniques.

A search for the presence of 2,3,7,8 tetrachlorodibenzo-p-dioxin in beef fat.

Specimens of fat taken from steers which had grazed on rangeland previously treated with 2,4,5-T herbicides were analyzed for the presence of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). A cleanup procedure resulting in a 500-fold concentration was followed by a gas chromatography-mass spectrometry detection technique. The limit of detection of TCDD (2.5 times peak to peak noise) was found to be in the 30-60 picogram range (3-6 ppt in beef fat using 10 gram samples). None of the sixteen samples comprising two of the three studies showed any response for TCDD. In the third study, in which the animals were confined to a fenced pasture sprayed in its entirety with a 2,4,5-T herbicide, samples from three of the seven animals gave a positive response at the extremely low level of 3 to 4 ppt TCDD, which is at the detection limit.

The determination of 2,3,7,8-tetrachlorodibenzo-p-dioxin in biological extracts by gas chromatography mass spectrometry.

Using both gas chromatography low resolution mass spectrometry and gas chromatography high resolution mass spectrometry, 2,3,7,8-tetrachlorodibenzo-p-dioxin at the part per trillion level may be determined in pre-concentrated extracts of bovine fat, liver and milk; human milk; rats; rice; grass; soil and water. Criteria are set forth for the objective determination of detection limit, signal and noise as applied to these determinations.

A search for 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) in an environment exposed annually to 2,4,5-trichlorophenoxyacetic acid ester (2,4,5-T) herbicides.

As part of a broad study to determine whether 2,3,7,8-tetrachlorodibenzo-P-dioxin (TCDD) is accumulating in the environment due to approved uses of 2,4,5-trichlorophenoxyacetic acid (2,4,5-T) based herbicides, samples of fish, water, mud and human milk were collected from areas in Arkansas and Texas where 2,4,5-T herbicides are used and were analyzed for TCDD. No TCDD was detected by a GC-MS procedure with a detection limit which averaged less than 10 ppt.

Determination of purity of compounds by extraction-solubility.

Thirty-three organic compounds prepared for use as analytical standards were examined for purity by the extraction-solubility method. Of these, twenty-one gave satisfactory results, seven behaved non-ideally, and five were not soluble in the useful range. Results on the twenty-one satisfactory samples compared favourably with those obtained by differential scanning calorimetry and other analytical methods. The method was found to be useful for following the improvement of compounds undergoing purification.