Rosepack Document 1: Guidelines for Writing Semi-portable Fortran

Transferring Fortran subroutines from one manufacturer's machine to another or from one operating system to another puts certain constrains on the construction of the Fortran statements that are used in the subroutines. The reliable performance of this mathematical software should be unaffected by the host environment in which the software is used or by the compiler from which the code is generated. In short, the algorithm is to he independent of the computing environment in which it is run. The subroutines of ROSEPACK (Robust Statistics Estimation Package) are Fortran IV source code designed to be semi-portable where semi-portable is defined to mean transportable with minimum change.*

Synthetic dimensions in ultracold molecules: quantum strings and membranes

Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many - potentially hundreds of - synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a membrane, with an emergent condensate that lives on this string or membrane. All these phases can be detected using measurements of rotational state populations.Comment: 5-page article + 4 figures + references; 7 pages + 4 figures in Supplemen

Induced Subgraphs of Johnson Graphs

The Johnson graph J(n,N) is defined as the graph whose vertices are the n-subsets of the set {1,2,...,N}, where two vertices are adjacent if they share exactly n - 1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before. We give some necessary conditions and some sufficient conditions for a graph to be JIS, including: in a JIS graph, any two maximal cliques share at most two vertices; all trees, cycles, and complete graphs are JIS; disjoint unions and Cartesian products of JIS graphs are JIS; every JIS graph of order n is an induced subgraph of J(m,2n) for some m <= n. This last result gives an algorithm for deciding if a graph is JIS. We also show that all JIS graphs are edge move distance graphs, but not vice versa.Comment: 12 pages, 4 figure

The Singular Value Analysis in Matrix Computation

This paper discusses the robustness and the computational stability of the singular value decomposition algorithm used at the NBER Computer Research Center. The effect of perturbations on input data is explored. Suggestions are made for using the algorithm to get information about the rank of a real square or rectangular matrix. The algorithm can also be used to compute the best approximate solution of linear system of equations in the least squares sense, to solve linear systems of equations with equality constraints, and to determine dependencies or near dependencies among the rows or columns of a matrix. A copy of the subroutine that is used and some examples on which it has been tested are included in the appendixes.

Accessing Rydberg-dressed interactions using many-body Ramsey dynamics

We demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions. In contrast to many prior proposals, our scheme operates comfortably within experimentally measured lifetimes, and accesses a regime where quantum superpositions are crucial. The key idea is to build a spin-1/2 from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, for which we derive an exact solution. Due to the structure of Rydberg interactions, the dynamics differs significantly from that in other spin systems. As one example, spin echo can increase the rate at which coherence decays. The results also apply to bare (undressed) Rydberg states as a special case, for which we quantitatively reproduce recent ultrafast experiments without fitting

Characterizing Release in Electrospun PCL Capsules: Preliminary Findings for Future Model Design

Engineering controlled drug release is a biomedical research interest due to its many clinical applications including: disease targeting, sustained release, and eliminating the need for repeating dosages. For example, in veterinary medicine, there is a need for a long-lasting and reversible contraceptive option for large and small animals. A device made of electrospun material is proposed to provide longer lasting release of Deslorelin, gonadotropin-releasing hormone agonist than current conceptive devices. Engineering this capsule-based device requires an understanding of the polymer components, one of which will be a layer of electrospun polycaprolactone (PCL). The short-term release of a specific fluorescent dye, Rose Bengal, through a single layer of sintered electrospun PCL was quantified in two solutions: distilled water and phosphate buffered saline (PBS). The results showed that the PBS solution significantly (p=0.0006) impacted the release of the dye. PBS induced an average flux of 0.009 ng/mm2-day while the flux in solution without PBS was essentially nil. These results prompted further investigation and a literature review of available drug release models to create a better understanding of the plausible mechanisms of release. The implication of this investigation is that diffusion may not be the only significant contributor to the release through these capsules, as is often assumed.No embargoAcademic Major: Biomedical Engineerin