Permutation patterns and statistics

Let S_n denote the symmetric group of all permutations of the set {1, 2, ...,n} and let S = \cup_{n\ge0} S_n. If Pi is a set of permutations, then we let Av_n(Pi) be the set of permutations in S_n which avoid every permutation of Pi in the sense of pattern avoidance. One of the celebrated notions in pattern theory is that of Wilf-equivalence, where Pi and Pi' are Wilf equivalent if #Av_n(Pi)=#Av_n(Pi') for all n\ge0. In a recent paper, Sagan and Savage proposed studying a q-analogue of this concept defined as follows. Suppose st:S->N is a permutation statistic where N represents the nonnegative integers. Consider the corresponding generating function, F_n^{st}(Pi;q) = sum_{sigma in Av_n(Pi)} q^{st sigma}, and call Pi,Pi' st-Wilf equivalent if F_n^{st}(Pi;q)=F_n^{st}(Pi';q) for all n\ge0. We present the first in-depth study of this concept for the inv and maj statistics. In particular, we determine all inv- and maj-Wilf equivalences for any Pi containd in S_3. This leads us to consider various q-analogues of the Catalan numbers, Fibonacci numbers, triangular numbers, and powers of two. Our proof techniques use lattice paths, integer partitions, and Foata's fundamental bijection. We also answer a question about Mahonian pairs raised in the Sagan-Savage article.Comment: 28 pages, 5 figures, tightened up the exposition, noted that some of the conjectures have been prove

In vivo nuclear magnetic resonance imaging

A number of physiological changes have been demonstrated in bone, muscle and blood after exposure of humans and animals to microgravity. Determining mechanisms and the development of effective countermeasures for long duration space missions is an important NASA goal. The advent of tomographic nuclear magnetic resonance imaging (NMR or MRI) gives NASA a way to greatly extend early studies of this phenomena in ways not previously possible; NMR is also noninvasive and safe. NMR provides both superb anatomical images for volume assessments of individual organs and quantification of chemical/physical changes induced in the examined tissues. The feasibility of NMR as a tool for human physiological research as it is affected by microgravity is demonstrated. The animal studies employed the rear limb suspended rat as a model of mucle atrophy that results from microgravity. And bedrest of normal male subjects was used to simulate the effects of microgravity on bone and muscle

Nonlinear Outcome of Gravitational Instability in Disks with Realistic Cooling

We consider the nonlinear outcome of gravitational instability in optically thick disks with a realistic cooling function. We use a numerical model that is local, razor-thin, and unmagnetized. External illumination is ignored. Cooling is calculated from a one-zone model using analytic fits to low temperature Rosseland mean opacities. The model has two parameters: the initial surface density Sigma_0 and the rotation frequency Omega. We survey the parameter space and find: (1) The disk fragments when t_c,eff Omega = 1, where t_c,eff is an effective cooling time defined as the average internal energy of the model divided by the average cooling rate. This is consistent with earlier results that used a simplified cooling function. (2) The initial cooling time t_c0 or a uniform disk with Q = 1 can differ by orders of magnitude from t_c,eff in the nonlinear outcome. The difference is caused by sharp variations in the opacity with temperature. The condition t_c0 Omega = 1 therefore does not necessarily indicate where fragmentation will occur. (3) The largest difference between t_c,eff and t_c0 is near the opacity gap, where dust is absent and hydrogen is largely molecular. (4) In the limit of strong illumination the disk is isothermal; we find that an isothermal version of our model fragments for Q < 1.4. Finally, we discuss some physical processes not included in our model, and find that most are likely to make disks more susceptible to fragmentation. We conclude that disks with t_c,eff Omega < 1 do not exist.Comment: 30 pages, 12 figure

Vortices in Thin, Compressible, Unmagnetized Disks

We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set of long-lived vortices, each of which has a radial extent comparable to the local scale height. But we also find that the resulting velocity field has a positive shear stress, . This effect appears only at high resolution. The transport, which decays with time as t^-1/2, arises primarily because the vortices drive compressive motions. This result suggests a possible mechanism for angular momentum transport in low-ionization disks, with two important caveats: a mechanism must be found to inject vorticity into the disk, and the vortices must not decay rapidly due to three-dimensional instabilities.Comment: 8 pages, 10 figures (high resolution figures available in ApJ electronic edition

A Titanium Nitride Absorber for Controlling Optical Crosstalk in Horn-Coupled Aluminum LEKID Arrays for Millimeter Wavelengths

We discuss the design and measured performance of a titanium nitride (TiN) mesh absorber we are developing for controlling optical crosstalk in horn-coupled lumped-element kinetic inductance detector arrays for millimeter-wavelengths. This absorber was added to the fused silica anti-reflection coating attached to previously-characterized, 20-element prototype arrays of LEKIDs fabricated from thin-film aluminum on silicon substrates. To test the TiN crosstalk absorber, we compared the measured response and noise properties of LEKID arrays with and without the TiN mesh. For this test, the LEKIDs were illuminated with an adjustable, incoherent electronic millimeter-wave source. Our measurements show that the optical crosstalk in the LEKID array with the TiN absorber is reduced by 66\% on average, so the approach is effective and a viable candidate for future kilo-pixel arrays.Comment: 7 pages, 5 figures, accepted for publication in the Journal of Low Temperature Physic

MaxEnt power spectrum estimation using the Fourier transform for irregularly sampled data applied to a record of stellar luminosity

The principle of maximum entropy is applied to the spectral analysis of a data signal with general variance matrix and containing gaps in the record. The role of the entropic regularizer is to prevent one from overestimating structure in the spectrum when faced with imperfect data. Several arguments are presented suggesting that the arbitrary prefactor should not be introduced to the entropy term. The introduction of that factor is not required when a continuous Poisson distribution is used for the amplitude coefficients. We compare the formalism for when the variance of the data is known explicitly to that for when the variance is known only to lie in some finite range. The result of including the entropic measure factor is to suggest a spectrum consistent with the variance of the data which has less structure than that given by the forward transform. An application of the methodology to example data is demonstrated.Comment: 15 pages, 13 figures, 1 table, major revision, final version, Accepted for publication in Astrophysics & Space Scienc

Gender & Sport Related Differences in Electrocardiogram & Pre-Participation Exams (PPE) in College Age Athletes

Background and Purpose: The NCAA requires all college level athletes receive a pre-participation physical exam. However, the pre-participation exams occasionally do not require electrocardiogram screening to help detect cardiac abnormalities. Though electrocardiograms may not be available at all testing’s, using specific markers and finding differences between gender and sport abnormalities could help detect cardiac abnormalities. The purpose of this study was to determine if there were significant differences in resting 12-Lead ECG markers in a group NCAA Div. II collegiate level athletes. Methods: Four hundred fifty-one college level athlete’s ages 18 to 25 participated in this study. Age, gender, height, weight, BMI, blood pressure and heart rate were measured during a pre-participation exam. Electrocardiogram measurements were gathered by using Mortara X-Scribe™ , Vacumed Turbo Fit 5™, Welch Allyn CardioPerfect™. Twelve-Lead ECGs were categorized by sport and analyzed by the lab director and the attending physician. One-way ANOVA was used to analyze differences in ECG findings in sports. Independent t-test and linear regression were used to analyze differences between male and female outcomes. Significance was set at the 0.05 level. Results: No significant differences in wave durations were found between male and female athletes. However, P wave amplitude was higher in males (1.50 ± 0.61 mm) than females (1.44 ± .55 mm) (P=0.01). Males had higher resting blood pressures (SBP=123.1 ± 10.9 mmHg) (DBP=73.6 ± 8.1 mmHg) than females (SBP=112.6 ± 9.6 mmHg) (DBP=69.9 ± 7.9 mmHg) (P\u3c0.001). Males also had a higher frequency of arrhythmias, T wave inversions, and 1st degree atrioventricular blocks when compared to females. Similarly, SBP was significantly higher in football compared to all other sports. Relative to ECG parameters cross country athletes showed ECG changes typical for cardiovascular endurance training compared to all other sports including sinus bradycardia, increased RR interval, and leftward axis shift. Discussion: Although marked differences in 12-lead ECG parameters were not found between sports in this sample, two athletes were sent for further echocardiogram evaluation due to abnormal ECGs, but were subsequently cleared to participate in their sport

Kinetic and Structural Analysis of Substrate Specificity in Two Copper Amine Oxidases from Hansenula polymorpha

The structural underpinnings of enzyme substrate specificity are investigated in a pair of copper amine oxidases (CAOs) from Hansenula polymorpha (HPAO-1 and HPAO-2). The X-ray crystal structure (to 2.0 Å resolution) and steady state kinetic data of the second copper amine oxidase (HPAO-2) are presented for comparison to HPAO-1. Despite 34 % sequence identity and superimposable active site residues implicated in catalysis, the enzymes vary considerably in their substrate entry channel. The previously studied CAO, HPAO-1, has a narrow substrate channel. In contrast HPAO-2 has a wide funnel-shaped substrate channel, which also contains a side-chamber. In addition, there are a number of amino acid changes within the channels of HPAO-2 and HPAO-1 that may sterically impact the ability of substrates to form covalent Schiff base catalytic intermediates and to initiate chemistry. These differences can partially explain the greatly different substrate specificities as characterized by kcat/Km value differences: in HPAO-1, the kcat/Km for methylamine is 330-fold greater than for benzylamine, whereas in HPAO-2 it is benzylamine that is the better substrate by 750-fold. In HPAO-2 an inflated Dkcat/Km(methylamine) in relation to Dkcat/Km(benzylamine) indicates that proton abstraction has been impeded more than substrate release. In HPAO-1, Dkcat/Km(S) changes little with the slow substrate, and indicates a similar increase in the energy barriers that control both substrate binding and subsequent catalysis. In neither case is kcat/Km for the second substrate, O2, significantly altered. These results reinforce the modular nature of the active sites of CAOs and show that multiple factors contribute to substrate specificity and catalytic efficiency. In HPAO-1, the enzyme with the smaller substrate binding pocket, both initial substrate binding and proton loss are affected by an increase in substrate size, while in HPAO-2, the enzyme with the larger substrate binding pocket, the rate of proton loss is differentially affected when a phenyl substituent in substrate is reduced to the size of a methyl group

A millimeter-wave kinetic inductance detector camera for long-range imaging through optical obscurants

Millimeter-wave imaging provides a promising option for long-range target detection through optical obscurants such as fog, which often occur in marine environments. Given this motivation, we are currently developing a 150 GHz polarization-sensitive imager using a relatively new type of superconducting pair-breaking detector, the kinetic inductance detector (KID). This imager will be paired with a 1.5 m telescope to obtain an angular resolution of 0.09° over a 3.5° field of view using 3,840 KIDs. We have fully characterized a prototype KID array, which shows excellent performance with noise strongly limited by the irreducible fluctuations from the ambient temperature background. Full-scale KID arrays are now being fabricated and characterized for a planned demonstration in a maritime environment later this year

A cryogenic waveplate rotator for polarimetry at mm and sub-mm wavelengths

Mm and sub-mm waves polarimetry is the new frontier of research in Cosmic Microwave Background and Interstellar Dust studies. Polarimeters working in the IR to MM range need to be operated at cryogenic temperatures, to limit the systematic effects related to the emission of the polarization analyzer. In this paper we study the effect of the temperature of the different components of a waveplate polarimeter, and describe a system able to rotate, in a completely automated way, a birefringent crystal at 4K. We simulate the main systematic effects related to the temperature and non-ideality of the optical components in a Stokes polarimeter. To limit these effects, a cryogenic implementation of the polarimeter is mandatory. In our system, the rotation produced by a step motor, running at room temperature, is transmitted down to cryogenic temperatures by means of a long shaft and gears running on custom cryogenic bearings. Our system is able to rotate, in a completely automated way, a birefringent crystal at 4K, dissipating only a few mW in the cold environment. A readout system based on optical fibers allows to control the rotation of the crystal to better than 0.1{\deg}. This device fulfills the stringent requirements for operation in cryogenic space experiments, like the forthcoming PILOT, BOOMERanG and LSPE.Comment: Submitted to Astronomy and Astrophysics. v1: 10 pages, 8 figures. v2: corrected labels for the bibliographic references (no changes in the bibliography). v3: revised version. 9 pages, 7 figures. Added a new figure. Updated with a more realistic simulation for the interstellar dust and with the latest cryogenic test