The Odyssey of Palazzolo: Public Rights Litigation and Coastal Change

The question of whether the state has the right to “take” (in the form of regulation) land in its coastal zones is a much more complex question that the courts, to date, have not been able to manage adequately. The problems faced along the coasts are difficult problems, and will likely not be settled by asking judges to determine the “rightness” of claims made through an adversarial process that tends to oversimplify situations in the process of constructing winnable legal arguments. Nor can we rely simply on administrative agencies or legislatures to protect the rights of individuals or protect them adequately from natural disasters. Clearly, the citizenry needs to be more active in these matters, and the administrative process needs to be both transparent and simplified. Quite frankly, it makes as much sense to have these cases drag out over decades as it does to have them framed in a way that oversimplifies the complex political challenges facing the governments attempting to regulate their coasts. The courts should stand ready to engage in oversight of these processes; but, if we can learn anything from Palazzolo, it may be that litigating with an overly simple goal of increasing private property rights could, in fact, only make matters more difficult because it will force the courts to continue muddling the waters of the takings clause. From a social science perspective, the longer the resolution, the more complicated and difficult the situation becomes. Prolonging the process into decades, then, is the last thing that should happen

Electromagnetic mirror drive system

Oscillatory electromagnetic mirror drive system for horizon scanner

Binary Adaptive Semi-Global Matching Based on Image Edges

Image-based modeling and rendering is currently one of the most challenging topics in Computer Vision and Photogrammetry. The key issue here is building a set of dense correspondence points between two images, namely dense matching or stereo matching. Among all dense matching algorithms, Semi-Global Matching (SGM) is arguably one of the most promising algorithms for real-time stereo vision. Compared with global matching algorithms, SGM aggregates matching cost from several (eight or sixteen) directions rather than only the epipolar line using Dynamic Programming (DP). Thus, SGM eliminates the classical “streaking problem” and greatly improves its accuracy and efficiency. In this paper, we aim at further improvement of SGM accuracy without increasing the computational cost. We propose setting the penalty parameters adaptively according to image edges extracted by edge detectors. We have carried out experiments on the standard Middlebury stereo dataset and evaluated the performance of our modified method with the ground truth. The results have shown a noticeable accuracy improvement compared with the results using fixed penalty parameters while the runtime computational cost was not increased

Euler Integration of Gaussian Random Fields and Persistent Homology

In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to compute the expected Euler integral of a Gaussian random field using the Gaussian kinematic formula and obtain a simple closed form expression. This results in the first explicitly computable mean of a quantitative descriptor for the persistent homology of a Gaussian random field.Comment: 21 pages, 1 figur

Evolutionary rates and gene dispensability associate with replication timing in the Archaeon Sulfolobus islandicus

In bacterial chromosomes, the position of a gene relative to the single origin of replication generally reflects its replication timing, how often it is expressed, and consequently, its rate of evolution. However, because some archaeal genomes contain multiple origins of replication, bias in gene dosage caused by delayed replication should be minimized and hence the substitution rate of genes should associate less with chromosome position. To test this hypothesis, six archaeal genomes from the genus Sulfolobus containing three origins of replication were selected, conserved orthologs were identified, and the evolutionary rates (dN and dS) of these orthologs were quantified. Ortholog families were grouped by their consensus position and designated by their proximity to one of the three origins (O1, O2, O3). Conserved orthologs were concentrated near the origins and most variation in genome content occurred distant from the origins. Linear regressions of both synonymous and nonsynonymous substitution rates on distance from replication origins were significantly positive, the rates being greatest in the region furthest from any of the origins and slowest among genes near the origins. Genes near O1 also evolved faster than those near O2 and O3, which suggest that this origin may fire later in the cell cycle. Increased evolutionary rates and gene dispensability are strongly associated with reduced gene expression caused in part by reduced gene dosage during the cell cycle. Therefore, in this genus of Archaea as well as in many Bacteria, evolutionary rates and variation in genome content associate with replication timing

Homological Product Codes

Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing. However, all families of quantum LDPC codes known to this date suffer from a poor distance scaling limited by the square-root of the code length. This is in a sharp contrast with the classical case where good families of LDPC codes are known that combine constant encoding rate and linear distance. Here we propose the first family of good quantum codes with low-weight stabilizers. The new codes have a constant encoding rate, linear distance, and stabilizers acting on at most $\sqrt{n}$ qubits, where $n$ is the code length. For comparison, all previously known families of good quantum codes have stabilizers of linear weight. Our proof combines two techniques: randomized constructions of good quantum codes and the homological product operation from algebraic topology. We conjecture that similar methods can produce good stabilizer codes with stabilizer weight $n^a$ for any $a>0$. Finally, we apply the homological product to construct new small codes with low-weight stabilizers.Comment: 49 page

Why genes evolve faster on secondary chromosomes in bacteria

In bacterial genomes composed of more than one chromosome, one replicon is typically larger, harbors more essential genes than the others, and is considered primary. The greater variability of secondary chromosomes among related taxa has led to the theory that they serve as an accessory genome for specific niches or conditions. By this rationale, purifying selection should be weaker on genes on secondary chromosomes because of their reduced necessity or usage. To test this hypothesis we selected bacterial genomes composed of multiple chromosomes from two genera, Burkholderia and Vibrio, and quantified the evolutionary rates (dN and dS) of all orthologs within each genus. Both evolutionary rate parameters were faster among orthologs found on secondary chromosomes than those on the primary chromosome. Further, in every bacterial genome with multiple chromosomes that we studied, genes on secondary chromosomes exhibited significantly weaker codon usage bias than those on primary chromosomes. Faster evolution and reduced codon bias could in turn result from global effects of chromosome position, as genes on secondary chromosomes experience reduced dosage and expression due to their delayed replication, or selection on specific gene attributes. These alternatives were evaluated using orthologs common to genomes with multiple chromosomes and genomes with single chromosomes. Analysis of these ortholog sets suggested that inherently fast-evolving genes tend to be sorted to secondary chromosomes when they arise; however, prolonged evolution on a secondary chromosome further accelerated substitution rates. In summary, secondary chromosomes in bacteria are evolutionary test beds where genes are weakly preserved and evolve more rapidly, likely because they are used less frequently

Minimal kernels of Dirac operators along maps

Let $M$ be a closed spin manifold and let $N$ be a closed manifold. For maps $f\colon M\to N$ and Riemannian metrics $g$ on $M$ and $h$ on $N$, we consider the Dirac operator $D^f_{g,h}$ of the twisted Dirac bundle $\Sigma M\otimes_{\mathbb{R}} f^*TN$. To this Dirac operator one can associate an index in $KO^{-dim(M)}(pt)$. If $M$ is $2$-dimensional, one gets a lower bound for the dimension of the kernel of $D^f_{g,h}$ out of this index. We investigate the question whether this lower bound is obtained for generic tupels $(f,g,h)$