Evidence for Auto-Correlation and Symmetry Detection in Primary Visual Cortex

The detectability of patterns in random dot arrays was measured as a function of dot density and compared with the statistical limit set by different methods of detecting the pattern. For filtering, cross-correlation, convolution, or template matching, the limit is expected to be inversely proportional to the square root of dot density. But for auto-correlation, which can detect symmetries of various types, the limit is unaffected by dot density under many conditions. Confirming previous results, we found that the coherence-threshold is often constant for Glass patterns, but the range of constancy depends on details of the display procedure. Coherence-thresholds were found to increase when the average number of dots expected at each location rose towards or exceeded a value of one; we therefore think it results from the non-linear effects of occlusion that occur when a later-programmed dot falls in the same location as an earlier one. To test this, these non-linear effects were prevented by arranging the luminance of each location to be directly proportional to the number of times that location was covered by a dot. Millions of dots can be used for these images, and they retain the streakiness of Glass patterns, while discrete dots disappear. The constant coherence threshold for detecting this streakiness is maintained over a huge range of dot densities, extending right down to the range where discrete dots become visible and up to patterns that are essentially full-tone images with no discrete dots. At threshold, all these patterns have similar auto-correlation functions, as we can see from the way both low dot-number Glass-patterns and these mega-dot, multi-tone, Glass-like images are formed. This startling fact raises the question whether primary visual cortex computes auto-correlations as well as, or even instead of, the local, Fourier-type, wavelet analysis of the currently popular paradigm

Evidence for a neural model to evaluate symmetry in V1

50 years ago Hubel and Wiesel discovered simple and complex cells in V1, but there is still no consensus on their functional roles. It is agreed that complex cells are more often selective for direction of motion than simple cells, that there are differences in the way they combine information within their receptive fields, and that complex cells probably receive most of their input from simple cells, but what this serial hierarchy achieves is not understood. There is another puzzling dichotomy that we think is related, namely that of cross-correlation, which is widely accepted as the operation performed on the input image by simple cells, and auto-correlation, which some think underlies the perception of Glass patterns, and possibly motion. We propose the hypothesis that complex cells signal auto-correlations in the visual image, but to evaluate them they require the preliminary analysis done by simple cells, and also pinwheels - structures intervening between simple cells and complex cells that were quite unknown to Hubel and Wiesel. We shall first present psychophysical evidence, using a new kind of random dot display, which suggests that both cross-correlation and auto-correlation are performed in early vision. We then point to recent evidence on the micro-circuitry of pinwheels, and mappings of their intrinsic activity, which shows how pinwheels might enable complex cells to respond selectively to autocorrelations in the input image that activates the simple cells. Auto-correlation is a powerful tool for detecting symmetry, and many may be surprised by evidence that such an abstract property is detected so early in visual perception

Spectral Statistics and Dynamical Localization: sharp transition in a generalized Sinai billiard

We consider a Sinai billiard where the usual hard disk scatterer is replaced by a repulsive potential with $V(r)\sim\lambda r^{-\alpha}$ close to the origin. Using periodic orbit theory and numerical evidence we show that its spectral statistics tends to Poisson statistics for large energies when $\alpha2$, while for $\alpha=2$ it is independent of energy, but depends on $\lambda$. We apply the approach of Altshuler and Levitov [Phys. Rep. {\bf 288}, 487 (1997)] to show that the transition in the spectral statistics is accompanied by a dynamical localization-delocalization transition. This behaviour is reminiscent of a metal-insulator transition in disordered electronic systems.Comment: 8 pages, 2 figures, accepted for publication in Phys. Rev. Let

Geometric gauge potentials and forces in low-dimensional scattering systems

We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena. The systems are fully solvable and we compare exact solutions of them with those obtained in a Born-Oppenheimer projection approximation. We illustrate how geometric magnetism manifests in them, and explore the relationship between solutions obtained in the diabatic and adiabatic pictures. We provide an example, involving a neutral atom dressed by an external field, in which the system mimics the behavior of a charged particle that interacts with, and is scattered by, a ferromagnetic material. We also introduce a similar system that exhibits Aharonov-Bohm scattering. We propose some practical applications. We provide a theoretical approach that underscores universality in the appearance of geometric gauge forces. We do not insist on degeneracies in the adiabatic Hamiltonian, and we posit that the emergence of geometric gauge forces is a consequence of symmetry breaking in the latter.Comment: (Final version, published in Phy. Rev. A. 86, 042704 (2012

Handling qualities aspects of NASA YF-12 flight experience

The handling qualities of the YF-12 airplane as observed during NASA research flights over the past five years were reviewed. Aircraft behavior during takeoff, acceleration, climb, cruise, descent, and landing are discussed. Pilot comments on the various flight phases and tasks are presented. Handling qualities parameters such as period, damping, amplitude ratios, roll-yaw coupling, and flight path response sensitivity are compared to existing and proposed handling qualities criteria. The influence of the propulsion systems, stability augmentation, autopilot systems, atmospheric gusts, and temperature changes are also discussed. YF-12 experience correlates well with flying qualities criteria, except for longitudinal short period damping, where existing and proposed criteria appear to be more stringent than necessary

Prediction of 24-hour milk yield and composition in dairy cows from a single part-day yield and sample

peer-reviewedTeagasc PublicationIrish Journal of Agricultural and Food Research | Volume 58: Issue 1 Prediction of 24-hour milk yield and composition in dairy cows from a single part-day yield and sample S. McParlandemail , B. Coughlan , B. Enright , M. O’Keeffe , R. O’Connor , L. Feeney and D.P. Berry DOI: https://doi.org/10.2478/ijafr-2019-0007 | Published online: 09 Aug 2019 PDF Abstract Article PDF References Recommendations Abstract The objective was to evaluate the accuracy of predicting 24-hour milk yield and composition from a single morning (AM) or evening (PM) milk weight and composition. A calibration dataset of 37,481 test-day records with both AM and PM yields and composition was used to generate the prediction equations; equations were validated using 4,644 test-day records. Prediction models were developed within stage of lactation and parity while accounting for the inter-milking time interval. The mean correlation between the predicted 24-hour yields and composition of milk, fat and protein and the respective actual values was 0.97 when based on just an AM milk yield and composition with a mean correlation of 0.95 when based on just a PM milk yield and composition. The regression of predicted 24-hour yield and composition on the respective actual values varied from 0.97 to 1.01 with the exception of 24-hour fat percentage predicted from a PM sample (1.06). A single AM sample is useful to predict 24-hour milk yield and composition when the milking interval is known

Correlations of chaotic eigenfunctions: a semiclassical analysis

We derive a semiclassical expression for an energy smoothed autocorrelation function defined on a group of eigenstates of the Schr\"odinger equation. The system we considered is an energy-conserved Hamiltonian system possessing time-invariant symmetry. The energy smoothed autocorrelation function is expressed as a sum of three terms. The first one is analogous to Berry's conjecture, which is a Bessel function of the zeroth order. The second and the third terms are trace formulae made from special trajectories. The second term is found to be direction dependent in the case of spacing averaging, which agrees qualitatively with previous numerical observations in high-lying eigenstates of a chaotic billiard.Comment: Revtex, 13 pages, 1 postscript figur

Semi-classical calculations of the two-point correlation form factor for diffractive systems

The computation of the two-point correlation form factor K(t) is performed for a rectangular billiard with a small size impurity inside for both periodic or Dirichlet boundary conditions. It is demonstrated that all terms of perturbation expansion of this form factor in powers of t can be computed directly by semiclassical trace formula. The main part of the calculation is the summation of non-diagonal terms in the cross product of classical orbits. When the diffraction coefficient is a constant our results coincide with expansion of exact expressions ontained by a different method.Comment: 42 pages, 10 figures, Late

Fluctuations of wave functions about their classical average

Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes. We compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators. The expectation is broadly confirmed, but deviations due to scars are observed.Comment: 9 pages, 6 figures. Sent to J. Phys.