My Brigade suffered severely & behaved well - Longstreet’s Attack of July 2nd and its Greater Memory

An analytical study of the July 2nd, 1863 Confederate assault at Gettysburg both during and after the fighting

Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization

We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in $d$ spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality "oracles,'"so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubit costs and entangling gate counts involved with the protocols. The LSH basis could save or cost more qubits than a Kogut-Susskind-type representation basis, depending on how the bases are digitized as well as the spatial dimension. The numerous other clear benefits encourage future studies into applying this framework.Comment: 10 pages, 9 figures. v3: Journal version. A few added remarks and plots regarding qubit cost

Reserve Size And Fragmentation Alter Community Assembly, Diversity, And Dynamics

Researchers have disputed whether a single large habitat reserve will support more species than many small reserves. However, relatively little is known from a theoretical perspective about how reserve size affects competitive communities structured by spatial abiotic gradients. We investigate how reserve size affects theoretical communities whose assembly is governed by dispersal limitation, abiotic niche differentiation, and source-sink dynamics. Simulations were conducted with varying scales of dispersal across landscapes with variable environmental spatial autocorrelation. Landscapes were inhabited by simulated trees with seedling and adult stages. For a fixed total area in reserves, we found that small reserve systems increased the distance between environments dominated by different species, diminishing the effects of source-sink dynamics. As reserve size decreased, environmental limitations to community assembly became stronger, species richness decreased, and richness increased. When dispersal occurred across short distances, a large reserve strategy caused greater stochastic community variation, greater richness, and lower richness than in small reserve systems. We found that reserve size variation trades off between preserving different aspects of natural communities, including diversity versus diversity. Optimal reserve size will depend on the importance of source-sink dynamics and the value placed on different characteristics of natural communities. Anthropogenic changes to the size and separation of remnant habitats can have far-reaching effects on community structure and assembly.Integrative Biolog

On the Use of a Magnetometer to Determine the Angular Motion of a Spinning Body in Regular Precession

Magnetometer for determination of angular motion of spinning body in regular precessio