Baby-Step Giant-Step Algorithms for the Symmetric Group

We study discrete logarithms in the setting of group actions. Suppose that $G$ is a group that acts on a set $S$. When $r,s \in S$, a solution $g \in G$ to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study the case where $G = S_n$, and develop analogs to the Shanks baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets $A, B \subseteq S_n$ such that every permutation of $S_n$ can be written as a product $ab$ of elements $a \in A$ and $b \in B$. Our deterministic procedure is optimal up to constant factors, in the sense that $A$ and $B$ can be computed in optimal asymptotic complexity, and $|A|$ and $|B|$ are a small constant from $\sqrt{n!}$ in size. We also analyze randomized "collision" algorithms for the same problem

Energy efficient engine sector combustor rig test program

Under the NASA-sponsored Energy Efficient Engine program, Pratt & Whitney Aircraft has successfully completed a comprehensive combustor rig test using a 90-degree sector of an advanced two-stage combustor with a segmented liner. Initial testing utilized a combustor with a conventional louvered liner and demonstrated that the Energy Efficient Engine two-stage combustor configuration is a viable system for controlling exhaust emissions, with the capability to meet all aerothermal performance goals. Goals for both carbon monoxide and unburned hydrocarbons were surpassed and the goal for oxides of nitrogen was closely approached. In another series of tests, an advanced segmented liner configuration with a unique counter-parallel FINWALL cooling system was evaluated at engine sea level takeoff pressure and temperature levels. These tests verified the structural integrity of this liner design. Overall, the results from the program have provided a high level of confidence to proceed with the scheduled Combustor Component Rig Test Program

Exact results for the Barabasi model of human dynamics

Human activity patterns display a bursty dynamics, with interevent times following a heavy tailed distribution. This behavior has been recently shown to be rooted in the fact that humans assign their active tasks different priorities, a process that can be modeled as a priority queueing system [A.-L. Barabasi, Nature 435, 207 (2005)]. In this work we obtain exact results for the Barabasi model with two tasks, calculating the priority and waiting time distribution of active tasks. We demonstrate that the model has a singular behavior in the extremal dynamics limit, when the highest priority task is selected first. We find that independently of the selection protocol, the average waiting time is smaller or equal to the number of active tasks, and discuss the asymptotic behavior of the waiting time distribution. These results have important implications for understanding complex systems with extremal dynamics.Comment: 4 pages, 4 figures, revte

Raising the unification scale in supersymmetry

In the minimal supersymmetric standard model, the three gauge couplings appear to unify at a mass scale near $2 \times 10^{16}$ GeV. We investigate the possibility that intermediate scale particle thresholds modify the running couplings so as to increase the unification scale. By requiring consistency of this scenario, we derive some constraints on the particle content and locations of the intermediate thresholds. There are remarkably few acceptable solutions with a single cleanly defined intermediate scale far below the unification scale.Comment: 22 pages, macros included. One figure, available at ftp://ftp.phys.ufl.edu/incoming/rais.ep

Double Charge Exchange And Configuration Mixing

The energy dependence of forward pion double charge exchange reactions on light nuclei is studied for both the Ground State transition and the Double-Isobaric-Analog-State transitions. A common characteristic of these double reactions is a resonance-like peak around 50 MeV pion lab energy. This peak arises naturally in a two-step process in the conventional pion-nucleon system with proper handling of nuclear structure and pion distortion. A comparison among the results of different nuclear structure models demonstrates the effects of configuration mixing. The angular distribution is used to fix the single particle wave function.Comment: Added 1 figure (now 8) corrected references and various other change

SDSS J143030.22-001115.1: A misclassified narrow-line Seyfert 1 galaxy with flat X-ray spectrum

We used multi-component profiles to model H$\beta$ and [O III]$\lambda \lambda$4959,5007 lines for SDSS J143030.22-001115.1, a narrow-line Seyfert 1 galaxy (NLS1) in a sample of 150 NLS1s candidates selected from the Sloan Digital Sky Survey (SDSS) Early Data Release (EDR). After subtracting the H$\beta$ contribution from narrow line regions (NLRs), we found that its full width half maximum (FWHM) of broad H$\beta$ line is nearly 2900 \kms, significantly larger than the customarily adopted criterion of 2000 \kms. With its weak Fe II multiples, we think that SDSS J143030.22-001115.1 can't be classified as a genuine NLS1. When we calculate the virial black hole masses of NLS1s, we should use the H$\beta$ linewidth after subtracting the H$\beta$ contribution from NLRs.Comment: 7 pages, 1 table, accepted by ChJA

Glycine decarboxylase deficiency causes neural tube defects and features of non-ketotic hyperglycinemia in mice.

Glycine decarboxylase (GLDC) acts in the glycine cleavage system to decarboxylate glycine and transfer a one-carbon unit into folate one-carbon metabolism. GLDC mutations cause a rare recessive disease non-ketotic hyperglycinemia (NKH). Mutations have also been identified in patients with neural tube defects (NTDs); however, the relationship between NKH and NTDs is unclear. We show that reduced expression of Gldc in mice suppresses glycine cleavage system activity and causes two distinct disease phenotypes. Mutant embryos develop partially penetrant NTDs while surviving mice exhibit post-natal features of NKH including glycine accumulation, early lethality and hydrocephalus. In addition to elevated glycine, Gldc disruption also results in abnormal tissue folate profiles, with depletion of one-carbon-carrying folates, as well as growth retardation and reduced cellular proliferation. Formate treatment normalizes the folate profile, restores embryonic growth and prevents NTDs, suggesting that Gldc deficiency causes NTDs through limiting supply of one-carbon units from mitochondrial folate metabolism

Hall effect in cobalt-doped TiO2−δ_{2-\delta}

We report Hall effect measurements on thin films of cobalt-doped TiO$_{2-\delta}$. Films with low carrier concentrations (10$^{18}$ - 10$^{19}$) yield a linear behavior in the Hall data while those having higher carrier concentrations (10$^{21}$ - 10$^{22}$) display anomalous behavior near zero field. In the entire range of carrier concentration, n-type conduction is observed. The appearance of the anomalous behavior is accompanied by a possible structural change from rutile TiO$_{2}$ to Ti_[n}O$_{2n-1}$ Magneli phase(s)

Refining tree recruitment models

We used a micrometeorological dispersal model to simulate seed and seedling distributions derived from subcanopy balsam fir (Abies balsamea (L.) Mill.) source trees in a trembling aspen (Populus tremuloides Michx.) dominated forest. Our first objective was to determine the effect of substituting basal area for cone production as a proxy for seed output. The results showed that the r2 from the regression of predicted versus observed densities increased by ∼5% for seeds and ∼15% for seedling simulations. Our second objective was to determine the effects of changing the median horizontal wind speed. The median speed in this forest environment varies according to the proportion of leaves abscised. For values of the median expected wind speed between the extremes of leafless and full-canopy forests, the r2 of predicted versus observed varied between 0.35 and 0.49 for seeds and between 0.33 and 0.62 for seedling simulations. We demonstrated that the simple one-dimensional model can have added precision if the dispersal parameters are chosen so as to allow more fine-scale variation