Low-level processing for real-time image analysis

A system that detects object outlines in television images in real time is described. A high-speed pipeline processor transforms the raw image into an edge map and a microprocessor, which is integrated into the system, clusters the edges, and represents them as chain codes. Image statistics, useful for higher level tasks such as pattern recognition, are computed by the microprocessor. Peak intensity and peak gradient values are extracted within a programmable window and are used for iris and focus control. The algorithms implemented in hardware and the pipeline processor architecture are described. The strategy for partitioning functions in the pipeline was chosen to make the implementation modular. The microprocessor interface allows flexible and adaptive control of the feature extraction process. The software algorithms for clustering edge segments, creating chain codes, and computing image statistics are also discussed. A strategy for real time image analysis that uses this system is given

Computing region moments from boundary representations

The class of all possible formulas for computing arbitrary moments of a region from the region's boundary is derived. The selection of a particular formula depends on the choice of an independent parameter. Several choices of this parameter are explored for region boundaries approximated by polygons. The parameter choice that minimizes computation time for boundaries represented by chain code is derived. Algorithms are presented for computing arbitrary moments for a region from a polygonal approximation of its boundary and for computing low order moments from chain encoded boundaries

Absence of pre-classical solutions in Bianchi I loop quantum cosmology

Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this paper, we consider the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and show using generating function techniques that only the zero solution satisfies these constraints. This implies either that there are technical difficulties with the current method of quantizing the evolution equation, or else loop quantum gravity imposes strong restrictions on the physically allowed solutions.Comment: 4 pages, no figures, version to appear in PR

Predicting the size and probability of epidemics in a population with heterogeneous infectiousness and susceptibility

We analytically address disease outbreaks in large, random networks with heterogeneous infectivity and susceptibility. The transmissibility $T_{uv}$ (the probability that infection of $u$ causes infection of $v$) depends on the infectivity of $u$ and the susceptibility of $v$. Initially a single node is infected, following which a large-scale epidemic may or may not occur. We use a generating function approach to study how heterogeneity affects the probability that an epidemic occurs and, if one occurs, its attack rate (the fraction infected). For fixed average transmissibility, we find upper and lower bounds on these. An epidemic is most likely if infectivity is homogeneous and least likely if the variance of infectivity is maximized. Similarly, the attack rate is largest if susceptibility is homogeneous and smallest if the variance is maximized. We further show that heterogeneity in infectious period is important, contrary to assumptions of previous studies. We confirm our theoretical predictions by simulation. Our results have implications for control strategy design and identification of populations at higher risk from an epidemic.Comment: 5 pages, 3 figures. Submitted to Physical Review Letter

Subclasses of Presburger Arithmetic and the Weak EXP Hierarchy

It is shown that for any fixed $i>0$, the $\Sigma_{i+1}$-fragment of Presburger arithmetic, i.e., its restriction to $i+1$ quantifier alternations beginning with an existential quantifier, is complete for $\mathsf{\Sigma}^{\mathsf{EXP}}_{i}$, the $i$-th level of the weak EXP hierarchy, an analogue to the polynomial-time hierarchy residing between $\mathsf{NEXP}$ and $\mathsf{EXPSPACE}$. This result completes the computational complexity landscape for Presburger arithmetic, a line of research which dates back to the seminal work by Fischer & Rabin in 1974. Moreover, we apply some of the techniques developed in the proof of the lower bound in order to establish bounds on sets of naturals definable in the $\Sigma_1$-fragment of Presburger arithmetic: given a $\Sigma_1$-formula $\Phi(x)$, it is shown that the set of non-negative solutions is an ultimately periodic set whose period is at most doubly-exponential and that this bound is tight.Comment: 10 pages, 2 figure

How do the blind ‘see’? The role of spontaneous brain activity in self-generated perception

Spontaneous activity of the human brain has been well documented, but little is known about the functional role of this ubiquitous neural phenomenon. It has previously been hypothesized that spontaneous brain activity underlies unprompted (internally generated) behaviour. We tested whether spontaneous brain activity might underlie internally-generated vision by studying the cortical visual system of five blind/visually-impaired individuals who experience vivid visual hallucinations (Charles Bonnet syndrome). Neural populations in the visual system of these individuals are deprived of external input, which may lead to their hyper-sensitization to spontaneous activity fluctuations. To test whether these spontaneous fluctuations can subserve visual hallucinations, the functional MRI brain activity of participants with Charles Bonnet syndrome obtained while they reported their hallucinations (spontaneous internally-generated vision) was compared to the: (i) brain activity evoked by veridical vision (externally-triggered vision) in sighted controls who were presented with a visual simulation of the hallucinatory streams; and (ii) brain activity of non-hallucinating blind controls during visual imagery (cued internally-generated vision). All conditions showed activity spanning large portions of the visual system. However, only the hallucination condition in the Charles Bonnet syndrome participants demonstrated unique temporal dynamics, characterized by a slow build-up of neural activity prior to the reported onset of hallucinations. This build-up was most pronounced in early visual cortex and then decayed along the visual hierarchy. These results suggest that, in the absence of external visual input, a build-up of spontaneous fluctuations in early visual cortex may activate the visual hierarchy, thereby triggering the experience of vision

Hidden structure in the randomness of the prime number sequence?

We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes, that would eventually appear in applications. Finally, our theory allows us to link with three different but important topics: the Hardy-Littlewood conjecture, the statistical mechanics of spin systems, and the celebrated Sierpinski fractal.Comment: 13 pages, 5 figures. New section establishing connection with the Hardy-Littlewood theory. Published in the journal where the solved problem was first describe

First Evidence for Wollemi Pine-type Pollen (Dilwynites: Araucariaceae) in South America

We report the first fossil pollen from South America of the lineage that includes the recently discovered, extremely rare Australian Wollemi Pine, Wollemia nobilis (Araucariaceae). The grains are from the late Paleocene to early middle Eocene Ligorio Márquez Formation of Santa Cruz, Patagonia, Argentina, and are assigned to Dilwynites, the fossil pollen type that closely resembles the pollen of modern Wollemia and some species of its Australasian sister genus, Agathis. Dilwynites was formerly known only from Australia, New Zealand, and East Antarctica. The Patagonian Dilwynites occurs with several taxa of Podocarpaceae and a diverse range of cryptogams and angiosperms, but not Nothofagus. The fossils greatly extend the known geographic range of Dilwynites and provide important new evidence for the Antarctic region as an early Paleogene portal for biotic interchange between Australasia and South America.Facultad de Ciencias Naturales y Muse