There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10(6) optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.

/pdf/a-global-geometric-framework-for-nonlinear-dimensionality-5brl02iqtj.pdf

A global geometric framework for nonlinear dimensionality reduction.

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The two basic phenomena that define the problem of visual attention can be illustrated in a simple example. Consider the arrays shown in each panel of Figure 1. In a typical experiment, before the arrays were presented, subjects would be asked to report letters appearing in one color (targets, here black letters), and to disregard letters in the other color (nontargets, here white letters). The array would then be briefly flashed, and the subjects, without any opportunity for eye movements, would give their report. The display mimics our. usual cluttered visual environment: It contains one or more objects that are relevant to current behavior, along with others that are irrelevant. The first basic phenomenon is limited capacity for processing information. At any given time, only a small amount of the information available on the retina can be processed and used in the control of behavior. Subjectively, giving attention to any one target leaves less available for others. In Figure 1, the probability of reporting the target letter N is much lower with two accompa­ nying targets (Figure la) than with none (Figure Ib). The second basic phenomenon is selectivity-the ability to filter out un­ wanted information. Subjectively, one is aware of attended stimuli and largely unaware of unattended ones. Correspondingly, accuracy in identifying an attended stimulus may be independent of the number of nontargets in a display (Figure la vs Ie) (see Bundesen 1990, Duncan 1980).

Neural Mechanisms of Selective Visual Attention

Implantation of magnetic search coils for measurement of eye position: an improved method.

Rex (real-time experimentation) is a real-time system that utilizes the multiple process structure of Unix to divide its functions among various cooperating processes. A running Rex system includes a comm process to control keyboard interaction, a scribe process to write data on disk, an int process to respond to interrupts from clocks, analog-to-digital converters, etc., and a display process to generate online graphic displays. A Rex system is not limited to these processes and may include others. This modular architecture is flexible and easy to maintain. Various applications may use the same comm and scribe but different ints or displays. The boundaries imposed by distributing Rex among multiple processes afford some protection against code becoming excessively intertwined and difficult to modify. Rex is written in c, a structured high level language. 7 references.

Unix-based multiple-process system, for real-time data acquisition and control

We seek a general approach to determine what stimulus features visual neurons are sensitive to and how those features are represented by the neuron's responses. Because lesions of inferior temporal (IT) cortex interfere with a monkey's ability to perform pattern discrimination tasks we studied IT neurons. Previous single-unit studies have shown that IT neurons sometimes respond more strongly to complex stimuli (brushes, hands, faces) than to simple stimuli (bars, slits, edges). However, it is not known how specific stimulus parameters are represented by responses. We studied the responses of IT neurons in alert behaving monkeys to a large set of two-dimensional black and white patterns. The stimulus set was based on 64 Walsh functions that can be used to represent any picture with a resolution of one part in eight along each of two dimensions. The responses to these stimuli spanned a continuum from inhibition to strong excitation. A statistical test showed that the spike count was determined by which Walsh stimulus was presented. Hence, these stimuli form an adequate set for testing IT neurons. The responses showed temporal modulation of the spike train that could not be represented by a change in the spike count alone. Examples of this modulation were changes in latency, changes in the duration of the response, and alternating periods of excitation and inhibition. This temporal modulation may be important in representing stimulus parameters. The next paper in this series develops a method for quantifying this temporal modulation and shows that it is dependent on the stimulus. The third paper in this series shows that this temporal modulation contains more information about stimulus parameters than is contained in the spike count alone.

Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. I. Response characteristics.

As monkeys perform schedules containing several trials with a visual cue indicating reward proximity, their error rates decrease as the number of remaining trials decreases, suggesting that their motivation and/or reward expectancy increases as the reward approaches. About one-third of single neurons recorded in the anterior cingulate cortex of monkeys during these reward schedules had responses that progressively changed strength with reward expectancy, an effect that disappeared when the cue was random. Alterations of this progression could be the basis for the changes from normal that are reported in anterior cingulate population activity for obsessive-compulsive disorder and drug abuse, conditions characterized by disturbances in reward expectancy.

https://science.sciencemag.org/content/sci/296/5573/1709.full.pdf

Anterior cingulate: single neuronal signals related to degree of reward expectancy.

Ablation and single-unit studies in primates have shown that inferior temporal (IT) cortex is important for pattern discrimination. The first paper in this series suggested that single units in IT cortex of alert monkeys respond to a set of two-dimensional patterns with complex temporal modulation of their spike trains. The second paper quantified the waveform of the modulated responses of IT neurons with principal components and demonstrated that the coefficients of two to four of the principal components were stimulus dependent. Although the coefficients of the principal components are uncorrelated, it is possible that they are not statistically independent. That is, several coefficients could be determined by the same feature of the stimulus, and thus could be conveying the same information. The final part of this study examined this issue by comparing the amount of information about the stimulus that can be conveyed by two codes: a temporal waveform code derived from the coefficients of the first three principal components and a mean rate code derived from the spike count. We considered the neuron to be an information channel conveying messages about stimulus parameters. Previous applications of information theory to neurophysiology have dealt either with the theoretical capacity of neuronal channels or the temporal distribution of information within the spike train. This previous work usually used a general binary code to represent the spike train of a neuron's response. Such a general approach yields no indication of the nature of the neuron's intrinsic coding scheme because it depends only on the timing of spikes in the response. In particular, it is independent of any statistical properties of the responses. Our approach uses the principal components of the response waveform to derive a code for representing information about the stimuli. We regard this code as an indication of the neuron's intrinsic coding scheme, because it is based on the statistical properties of the neuronal responses. We measured how much information about the stimulus was present in the neuron's responses. This transmitted information was calculated for codes based on either the spike count or on the first three principal components of the response waveform. The information transmitted by each of the first three principal components was largely independent of that transmitted by the others. It was found that the average amount of information transmitted by the principal components was about twice as large as that transmitted by the spike count.(ABSTRACT TRUNCATED AT 400 WORDS)

Barry J. Richmond

Papers

Implantation of magnetic search coils for measurement of eye position: an improved method.

Unix-based multiple-process system, for real-time data acquisition and control

Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. I. Response characteristics.

Anterior cingulate: single neuronal signals related to degree of reward expectancy.

Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. III: Information theoretic analysis