Inversion Rotation Research Articles

Matrix Isolation Spectroscopy and Nuclear Spin Conversion of NH3 and ND3 in Solid Parahydrogen

We present matrix isolation infrared absorption spectra of NH3 and ND3 trapped in solid parahydrogen (pH2) at temperatures around 1.8 K. We used the relatively slow nuclear spin conversion (NSC) of NH3 and ND3 in freshly deposited pH2 samples as a tool to assign the sparse vibration-inversion-rotation (VIR) spectra of NH3 in the regions of the ν2, ν4, 2ν4, ν1, and ν3 bands and ND3 in the regions of the ν2, ν4, ν1, and ν3 fundamentals. Partial assignments are also presented for various combination bands of NH3. Detailed analysis of the ν2 bands of NH3 and ND3 indicates that both isotopomers are nearly free rotors; that the vibrational energy is blue-shifted by 1-2%; and that the rotational constants and inversion tunneling splitting are 91-94% and 67-75%, respectively, of the gas-phase values. The line shapes of the VIR absorptions are narrow (0.2-0.4 cm(-1)) for upper states that cannot rotationally relax and broad (>1 cm(-1)) for upper states that can rotationally relax. We report and assign a number of NH3-induced infrared absorption features of the pH2 host near 4150 cm(-1), along with a cooperative transition that involves simultaneous vibrational excitation of a pH2 molecule and rotation-inversion excitation of NH3. The NSCs of NH3 and ND3 were found to follow first-order kinetics with rate constants at 1.8 K of k = 1.88(16) × 10(-3) s(-1) and k = 1.08(8) × 10(-3) s(-1), respectively. These measured rate constants are compared to previous measurements for NH3 in an Ar matrix and with the rate constants measured for other dopant molecules isolated in solid pH2.

Brain Regulation of Muscle Tone in Healthy and Functionally Unstable Ankles

Current research into the etiology of joint instability has yielded inconsistent results, limiting our understanding of how to prevent and treat ligamentous injury effectively. Recently, cortical reorganization was demonstrated in patients with ligamentous injury; however, these neural changes have not been assessed relative to joint laxity. The purpose of the current study was to determine if changes in cortical excitability and inhibition occur in subjects with functional ankle instability, as well as to investigate the relationship between these measures and joint laxity. Posttest only with control group. University laboratory. 12 subjects with no history of ankle sprain (CON) and 12 subjects with a history of unilateral functional ankle instability (UNS). Subjects were tested for joint laxity using an instrumented ankle arthrometer. Cortical excitability and inhibition were assessed using transcranial magnetic stimulation (TMS) to obtain motor-evoked potentials and the cortical silent period from the lower leg muscles. Joint laxity was quantified as peak anterior displacement and inversion rotation. Active motor threshold, slope, and intensity at 50% of peak slope of TMS-derived recruitment curves were used to quantify cortical excitability from lower leg muscles, while the cortical silent period from the peroneus longus was used to represent intracortical inhibition. No significant differences were observed between groups for laxity or cortical measures. CON demonstrated a significant relationship between laxity and tibialis anterior excitability, as well as laxity and silent period, while UNS ankles demonstrated significant relationships between peroneal and soleus excitability and laxity measures. Our results support relationships between laxity and measures of excitability and inhibition that differ between healthy and unstable subjects. Future research should further investigate the mechanisms behind these findings and consider cortical influences when investigating altered joint laxity.

Delayed Closure of the Palatal Defect Using Buccal Inversion and Palatal Rotation Flaps After Maxillectomy

Maxillectomy leaves oronasal and oroantral defects that result in functional impairment of mastication, deglutition, and speech. Many treatment options are suggested and tried including the palatal flap as local flap. Although palatal flaps have been used to repair various oral cavity defects, they have certain limitations due to the dimensions. The amount and location of the palatal tissues available are important for palatal repair. Secondary intentional healing after maxillectomy will allow the epithelialization of the defect margin adjacent to remained palate, and there will be more mucosa that is available for closure of the defect. We delayed the closure of the palatal defect, while the patient underwent prosthetic treatment for functional recovery in 5 maxillectomy patients. Delayed closure of palatal defect with local flap was done at 10.8 ± 7.9 months after the maxillectomy. While delayed closure in hemimaxillectomy patients left postoperative fistula, it provided separation of the oral cavity and nasal/sinus cavity and adequate surface for prosthesis in partial maxillectomy patients.

Infrared spectroscopy of 15ND3: The ν2 and ν4 bending fundamental bands

The infrared spectrum of the ammonia isotopologue 15ND3 has been investigated by high resolution Fourier transform spectroscopy in the region from 450 to 1600cm−1. In total, 2217 transitions involving the (s) and (a) inversion–rotation–vibration levels have been identified and assigned to the ν2 and ν4 bending fundamentals. The assigned transitions have been fitted simultaneously using an inversion–rotation–vibration effective Hamiltonian which includes all symmetry allowed interactions between and within the excited state levels. The adopted model has been successful in rationalizing the complicated energy level pattern. Accurate values for the vibration and rotation spectroscopic constants, including 11 interaction coefficients, have been obtained for both inversion levels of the v2=1 and v4=1 states. The standard deviation of the fit, 0.00071cm−1, is about two times the estimated measurement precision.

Introducing Charge Hydration Asymmetry in the Realm of Continuum Solvation

Charge hydration asymmetry (CHA) manifests itself in the experimentally observed strong dependence of free energy of ion hydration on the sign of the ion charge. This asymmetry is not consistently accounted for by popular models of solvation; its magnitude varies greatly between the models. While it is clear that CHA is somehow related to charge distribution within a water molecule, the exact nature of this relationship is unknown. We propose a simple, yet general and rigorous criterion that relates rotational and charge inversion properties of a water molecule's charge distribution with its ability to cause CHA. We show which electric multipole components of a water molecule are key to explain its ability for asymmetric charge hydration. We then test several popular water models and explain why specific models show none, little, or strong CHA in simulations. We use the gained insight to derive an analogue of the Born equation that includes the missing physics necessary to account for CHA and does not rely on redefining the continuum dielectric boundary. The proposed formula is as simple as the original, does not contain any fitting parameters, and predicts hydration free energies and entropies of spherical cations and anions within experimental uncertainty. We further incorporate CHA into the framework of Generalized Born continuum solvation model; our findings suggest that the gap between the practical continuum electrostatics framework and the more fundamental explicit solvent treatment can be reduced considerably by explicitly introducing CHA into the existing framework.

Relationship between foot function and medial knee joint loading in people with medial compartment knee osteoarthritis

BackgroundDynamic joint loading, particularly the external knee adduction moment (KAM), is an important surrogate measure for the medio-lateral distribution of force across the knee joint in people with knee osteoarthritis (OA). Foot motion may alter the load on the medial tibiofemoral joint and hence affect the KAM. Therefore, this study aimed to investigate the relationship between tibia, rearfoot and forefoot motion in the frontal and transverse planes and the KAM in people with medial compartment knee OA.MethodMotion of the knee, tibia, rearfoot and forefoot and knee moments were evaluated in 32 patients with clinically and radiographically-confirmed OA, predominantly in the medial compartment. Pearson’s correlation coefficient was used to investigate the association between peak values of tibia, rearfoot and forefoot motion in the frontal and transverse planes and 1st peak KAM, 2nd peak KAM, and the knee adduction angular impulse (KAAI).ResultsLateral tilt of the tibia was significantly associated with increased 1st peak KAM (r = 0.60, p < 0.001), 2nd peak KAM (r = 0.67, p = 0.001) and KAAI (r = 0.82, p = 0.001). Increased peak rearfoot eversion was significantly correlated with decreased 2nd peak KAM (r = 0.59, p < 0.001) and KAAI (r = 0.50, p = 0.004). Decreased rearfoot internal rotation was significantly associated with increased 2nd peak KAM (r = −0.44, p = 0.01) and KAAI (r = −0.38, p = 0.02), while decreased rearfoot internal rotation relative to the tibia was significantly associated with increased 2nd peak KAM (r = 0.43, p = 0.01). Significant negative correlations were found between peak forefoot eversion relative to the rearfoot and 2nd peak KAM (r = −0.53, p = 0.002) and KAAI (r = −0.51, p = 0.003) and between peak forefoot inversion and 2nd peak KAM (r = −0.54, p = 0.001) and KAAI (r = −0.48, p = 0.005).ConclusionIncreased rearfoot eversion, rearfoot internal rotation and forefoot inversion are associated with reduced knee adduction moments during the stance phase of gait, suggesting that medial knee joint loading is reduced in people with OA who walk with greater foot pronation. These findings have implications for the design of load-modifying interventions in people with knee OA.

Characterization of the t-Butyl Radical and Its Elusive Anion.

The t-butyl radical and its anion are studied theoretically using state-of-the-art quantum mechanical methods including coupled cluster theory with full single, double, and triple excitations (CCSDT) and CCSDT with perturbative quadruple excitations [CCSDT(Q)], in concert with large correlation-consistent cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5) basis sets. The relative energies are extrapolated to the complete basis set limit (CBS). The lowest energy structure of the t-butyl radical has a nonplanar carbon backbone with overall C3v symmetry. Low-lying C3h and Cs symmetry transition states, for pyramidal inversion and methyl group rotation, respectively, between equivalent C3v minima are investigated. The barriers for these interconversions are both less than 1 kcal mol(-1), but the corresponding barriers on the anion potential energy surface are more pronounced. Using the focal point analysis technique, we obtain a value of -0.48 kcal mol(-1) for the t-butyl radical adiabatic electron affinity at the CCSDT(Q)/CBS level of theory, where the negative sign indicates that the formation of the t-butyl anion is adiabatically unfavorable. We show that the electron affinity, whose sign has been the subject of debate, is very sensitive to both the basis set and the correlation treatment, and previous experimental and theoretical estimates of its value bracket the value computed herein. Our results indicate that the t-butyl anion is classically metastable with a vertical detachment energy of over 10 kcal mol(-1) to reach the neutral potential energy surface. However, the inclusion of the zero-point vibrational effects seems to favor its nonexistence.

Role of External Prophylactic Support in Restricting Accessory Ankle Motion after Exercise

To both prevent and accelerate recovery and return-to-play from ankle sprains, clinicians frequently employ the use of external prophylactic support (EPS), such as taping and bracing, to provide mechanical support to the ankle joint. While common practice clinically, research has been inconclusive in demonstrating the effectiveness of EPS in restricting accessory motion (laxity) throughout activity, as well as its efficacy in restricting laxity in patients with complaints of ankle instability, and patients with a history of ankle sprain. The purpose of this study was to investigate the effectiveness of EPS type (None, Tape, Brace) on ankle laxity before and after exercise in subjects with varying degrees of previous ankle injury. Ankles from 24 participants (age, 20.6 ± 1.6 years; height, 173.6 ± 8.3 cm; mass, 72.8 ± 12.2 kg) were placed into one of three groups: healthy control (CON), potential coper (COP), and functionally unstable (UNS). Ankle laxity was assessed using an ankle arthrometer at 4 points in time; prior to EPS application, immediately following EPS application, following a 20-minute functional exercise protocol with EPS, and following removal of EPS. Peak ankle anterior displacement (ANT), inversion rotation (INV), and eversion rotation (EVR) were compared between groups and across conditions using a three-way ANOVA. Taping and bracing each decreased laxity from pre-application to pre-exercise and post-exercise. Tape provided greater restriction post-exercise in inversion and eversion rotation. Additionally, the UNS group demonstrated significantly greater anterior displacement post-exercise following removal of the brace compared to other groups. Compared to pre-application and post-removal, EPS significantly decreased ankle laxity before and after physical activity, with taping providing better restriction in inversion and eversion rotation throughout exercise. Following EPS removal, bracing revealed a greater increase in post-exercise laxity in subjects with ankle instability, suggesting tape may be more beneficial for controlling laxity in these patients.

Percutaneous Osteoplasty for the Treatment of a Painful Osteochondral Lesion of the Talus: A Case Report and Literature Review

An osteochondral lesion of the talus (OLT) is a lesion involving the talar articular cartilage and its subchondral bone. OLT is a known cause of chronic ankle pain after ankle sprains in the active population. The lesion causes deep ankle pain associated with weight-bearing, impaired function, limited range of motion, stiffness, catching, locking, and swelling. There are 2 common patterns of OLTs. Anterolateral talar dome lesions result from inversion and dorsiflexion injuries of the ankle at the area impacting against the fibula. Posteromedial lesions result from inversion, plantar flexion, and external rotation injuries of the ankle at the area impacting against the tibial ceiling of the ankle joint. Early diagnosis of an OLT is particularly important because the tibiotalar joint is exposed to more compressive load per unit area than any other joint in the body. Failure of diagnosis can lead to the evolution of a small, stable lesion into a larger lesion or an unstable fragment, which can result in chronic pain, joint instability, and premature osteoarthritis. A 43-year-old man, with a history of ankle sprain one year previously, visited our pain clinic for continuous right ankle pain after walking or standing for more than 30 minutes. There was a focal tenderness on the posteromedial area of the right talus. Imaging studies revealed a posteromedial OLT classified as having a geode form according to the FOG (fractures, osteonecroses, geodes) radiological classification and categorized as a stage 2a lesion on magnetic resonance imaging. The patient was scheduled for aspiration and osteoplasty with hydroxyapatite under arthroscopic and fluoroscopic guidance. A 26-gauge needle was inserted to infiltrate local anesthetics into the skin over the cyst and ankle joint. An arthroscope was placed into the joint to approach the OLT. The arthroscopic view showed that there was no connection between the OLT and the cyst of the talus body. A 13-gauge bone biopsy needle was inserted into the cyst, and aspiration was performed. Aspirated fluid from the cyst was originally white and clear; however, it changed to a blood-tinged, reddish color due to mixing with the incisional blood. After aspiration, contrast medium was injected, and the shape of the spread was observed. Bone cement comprising hydroxyapatite was injected to fill the bone defect of the cyst. A 1.5 mL volume of cement was injected into the talus under vigilant fluoroscopic and arthroscopic monitoring to prevent its dissemination into the joint. There was no cement leakage into the vessels or articular space. Postoperative fluoroscopy and computed tomography images showed bone cement filling of the defect. In the present case, arthroscopic and fluoroscopic guidance was used for aspiration of an OLT and for performing percutaneous osteoplasty with hydroxyapatite for one defect; this treatment decreased pain upon weight bearing and enabled a return to work without any restrictions one week after the procedure. The purpose of this report was to highlight the presence of OLT in chronic ankle pain and to review its management strategies. Key words: Ankle, bone fracture, cartilage fracture, calcium polyacrylate-hydroxyapatite cement, cementoplasty, endoscopy, osteochondritis dissecans, pain, sprain, talus.

Kinematics Analysis of Ankle Inversion Ligamentous Sprain Injuries in Sports

Background: Ankle ligamentous sprain is common in sports. The most direct way to study the mechanism quantitatively is to study real injury cases; however, it is unethical and impractical to produce an injury in the laboratory. A recently developed, model-based image-matching motion analysis technique allows quantitative analysis of real injury incidents captured in televised events and gives important knowledge for the development of injury prevention protocols and equipment. To date, there have been only 4 reported cases, and there is a need to conduct more studies for a better understanding of the mechanism of ankle ligamentous sprain injury. Purpose: This study presents 5 cases in tennis and a comparison with 4 previous cases for a better understanding of the mechanism of ankle ligamentous sprain injury. Study Design: Case series; level of evidence, 4. Methods: Five sets of videos showing ankle sprain injuries in televised tennis competition with 2 camera views were collected. The videos were transformed, synchronized, and rendered to a 3-dimensional animation software. The dimensions of the tennis court in each case were obtained to build a virtual environment, and a skeleton model scaled to the injured athlete’s height was used for the skeleton matching. Foot strike was determined visually, and the profiles of the ankle joint kinematics were individually presented. Results: There was a pattern of sudden inversion and internal rotation at the ankle joint, with the peak values ranging from 48°-126° and 35°-99°, respectively. In the sagittal plane, the ankle joint fluctuated between plantar flexion and dorsiflexion within the first 0.50 seconds after foot strike. The peak inversion velocity ranged from 509 to 1488 deg/sec. Conclusion: Internal rotation at the ankle joint could be one of the causes of ankle inversion sprain injury, with a slightly inverted ankle joint orientation at landing as the inciting event. To prevent the foot from rolling over the edge to cause a sprain injury, tennis players who do lots of sideward cutting motions should try to land with a neutral ankle orientation and keep the center of pressure from shifting laterally.

Charge Hydration Asymmetry: The Basic Principle and How to Use It to Test and Improve Water Models

Charge hydration asymmetry (CHA) manifests itself in the experimentally observed strong dependence of free energy of ion hydration on the sign of the ion charge. This asymmetry is not consistently accounted for by popular models of solvation; its magnitude varies greatly between the models. While it is clear that CHA is somehow related to charge distribution within a water molecule, the exact nature of this relationship is unknown. We propose a simple, yet general and rigorous criterion that relates rotational and charge inversion properties of a water molecule's charge distribution with its ability to cause CHA. We show which electric multipole components of a water molecule are key to explain its ability for asymmetric charge hydration. We then test several popular water models and explain why specific models show none, little, or strong CHA in simulations. We use the gained insight to derive an analogue of the Born equation that includes the missing physics necessary to account for CHA and does not rely on redefining the continuum dielectric boundary. The proposed formula is as simple as the original, does not contain any fitting parameters, and predicts hydration free energies and entropies of spherical cations and anions within experimental uncertainty. Our findings suggest that the gap between the practical continuum electrostatics framework and the more fundamental explicit solvent treatment may be reduced considerably by explicitly introducing CHA into the existing continuum framework.

Exploring the Dynamics of Reaction C(3P) + C2H4 with Crossed Beam/Photoionization Experiments and Quantum Chemical Calculations

We investigated the title reaction at collision energy 3.5 kcal mol(-1) in a crossed molecular beam apparatus using undulator radiation as an ionization source. Time-of-flight (TOF) spectra of product C(3)H(3) were measured in laboratory angles from 20° to 100° using two photoionization energies 9.5 and 11.6 eV. These two sets of experimental data exhibit almost the same TOF distributions and laboratory angular distributions. From the best simulation, seven angle-specific kinetic-energy distributions and a nearly isotropic angular distribution are derived for product channel C(3)H(3) + H that has an average kinetic-energy release of 15.5 kcal mol(-1), corresponding to an average internal energy of 33.3 kcal mol(-1) in C(3)H(3). Furthermore, TOF spectra of product C(3)H(3) were measured at laboratory angle 52° with ionizing photon energies from 7 to 12 eV. The appearance of TOF spectra remains almost the same, indicating that a species exclusively contributes to product C(3)H(3); the species is identified as H(2)CCCH (propargyl) based on the ionization energy of 8.6 ± 0.2 eV and the maximal kinetic-energy release of 49 kcal mol(-1). Theoretical calculations indicate that the rapid inversion mechanism and rotation in intermediate H(2)CCCH(2) can result in a forward-backward symmetric angular distribution for product C(3)H(3) + H. The present work avoids the interference of reactions of C((1)D) and C(2) radicals with C(2)H(4) and rules out the probability of production of other isomers like c-C(3)H(3) and H(3)CCC proposed in the previous work at least at the investigated collision energy.

Evaluating Foot Kinematics Using Magnetic Resonance Imaging: From Maximum Plantar Flexion, Inversion, and Internal Rotation to Maximum Dorsiflexion, Eversion, and External Rotation

The foot consists of many small bones with complicated joints that guide and limit motion. A variety of invasive and noninvasive means [mechanical, X-ray stereophotogrammetry, electromagnetic sensors, retro-reflective motion analysis, computer tomography (CT), and magnetic resonance imaging (MRI)] have been used to quantify foot bone motion. In the current study we used a foot plate with an electromagnetic sensor to determine an individual subject's foot end range of motion (ROM) from maximum plantar flexion, internal rotation, and inversion to maximum plantar flexion, inversion, and internal rotation to maximum dorsiflexion, eversion, and external rotation. We then used a custom built MRI-compatible device to hold each subject's foot during scanning in eight unique positions determined from the end ROM data. The scan data were processed using software that allowed the bones to be segmented with the foot in the neutral position and the bones in the other seven positions to be registered to their base positions with minimal user intervention. Bone to bone motion was quantified using finite helical axes (FHA). FHA for the talocrural, talocalcaneal, and talonavicular joints compared well to published studies, which used a variety of technologies and input motions. This study describes a method for quantifying foot bone motion from maximum plantar flexion, inversion, and internal rotation to maximum dorsiflexion, eversion, and external rotation with relatively little user processing time.

Multi-Rigid Image Segmentation and Registration for the Analysis of Joint Motion From Three-Dimensional Magnetic Resonance Imaging

We report an image segmentation and registration method for studying joint morphology and kinematics from in vivo magnetic resonance imaging (MRI) scans and its application to the analysis of foot and ankle joint motion. Using an MRI-compatible positioning device, a foot was scanned in a single neutral and seven other positions ranging from maximum plantar flexion, inversion, and internal rotation to maximum dorsiflexion, eversion, and external rotation. A segmentation method combining graph cuts and level set was developed. In the subsequent registration step, a separate rigid body transformation for each bone was obtained by registering the neutral position dataset to each of the other ones, which produced an accurate description of the motion between them. The segmentation algorithm allowed a user to interactively delineate 14 foot bones in the neutral position volume in less than 30 min total (user and computer processing unit [CPU]) time. Registration to the seven other positions took approximately 10 additional minutes of user time and 5.25 h of CPU time. For validation, our results were compared with those obtained from 3DViewnix, a semiautomatic segmentation program. We achieved excellent agreement, with volume overlap ratios greater than 88% for all bones excluding the intermediate cuneiform and the lesser metatarsals. For the registration of the neutral scan to the seven other positions, the average overlap ratio is 94.25%, while the minimum overlap ratio is 89.49% for the tibia between the neutral position and position 1, which might be due to different fields of view (FOV). To process a single foot in eight positions, our tool requires only minimal user interaction time (less than 30 min total), a level of improvement that has the potential to make joint motion analysis from MRI practical in research and clinical applications.

The ν 1 and ν 3 band system of 15NH3

The infrared spectrum of 15NH3 has been investigated by high-resolution Fourier transform infrared spectroscopy in the region of the stretching fundamentals. A large number of ro-vibration transitions in the 3050–3650 cm−1 spectral range has been recorded and assigned to the fundamentals ν 1 and ν 3, and to the 2ν 4 overtone bands. In total, 1606 transitions involving the (s) and (a) inversion–rotation–vibration levels have been identified and assigned. They include 256 perturbation-allowed transitions with selection rules ΔK = ±2, Δl = −1 in ν 3 and Δl = +2 in , and ΔK = ±3, Δl = 0 in ν 1 and . All assigned transitions were fitted simultaneously to a model Hamiltonian that includes all symmetry-allowed interactions between and within the excited state levels in order to obtain accurate sets of spectroscopic parameters for both inversion states. The standard deviation of the fit, 0.034 cm−1, is about 70 times larger than the estimated measurement precision. This result is similar to that reported for the same band system in 14NH3 by Kleiner et al. [J. Mol. Spectrosc. 193, 46 (1999)] and is a consequence of the neglect of vibration and ro-vibration interactions between the analysed states and vibrationally excited states with close energies.

Kinematics and kinetics of an accidental lateral ankle sprain

Ankle sprains are common during sporting activities and can have serious consequences. Understanding of injury mechanisms is essential to prevent injuries, but only two previous studies have provided detailed descriptions of the kinematics of lateral ankle sprains and measures of kinetics are missing. In the present study a female handball player accidentally sprained her ankle during sidestep cutting in a motion analysis laboratory. Kinematics and kinetics were calculated from 240 Hz recordings with a full-body marker setup. The injury trial was compared with two previous (non-injury) trials. The injury trial showed a sudden increase in inversion and internal rotation that peaked between 130 and 180 ms after initial contact. We observed an attempted unloading of the foot from 80 ms after initial contact. As the inversion and internal rotation progressed, the loads were likely to exceed injury threshold between 130 and 180 ms. There was a considerable amount of dorsiflexion in the injury trial compared to neutral flexion in the control trials, similar to the previously published kinematical descriptions of lateral ankle sprains. The present study also adds valuable kinetic information that improves understanding of the injury mechanism.

Kinematics and kinetics of accidental ankle sprain in 3D motion analysis lab

BackgroundAnkle sprain is among the most frequent sports injuries and a significant contributor to time lost from sports participation. The injury mechanism is traditionally described as an inversion trauma, but...

ROTATIONAL VARIABILITY OF EARTH'S POLAR REGIONS: IMPLICATIONS FOR DETECTING SNOWBALL PLANETS

We have obtained the first time-resolved, disc-integrated observations of Earth's poles with the Deep Impact spacecraft as part of the EPOXI Mission of Opportunity. These data mimic what we will see when we point next-generation space telescopes at nearby exoplanets. We use principal component analysis (PCA) and rotational lightcurve inversion to characterize color inhomogeneities and map their spatial distribution from these unusual vantage points, as a complement to the equatorial views presented in Cowan et al. (2009). We also perform the same PCA on a suite of simulated rotational multi-band lightcurves from NASA's Virtual Planetary Laboratory 3D spectral Earth model. This numerical experiment allows us to understand what sorts of surface features PCA can robustly identify. We find that the EPOXI polar observations have similar broadband colors as the equatorial Earth, but with 20-30% greater apparent albedo. This is because the polar observations are most sensitive to mid-latitudes, which tend to be more cloudy than the equatorial latitudes emphasized by the original EPOXI Earth observations. The cloudiness of the mid-latitudes also manifests itself in the form of increased variability at short wavelengths in the polar observations, and as a dominant gray eigencolor in the south polar observation. We construct a simple reflectance model for a snowball Earth. By construction, our model has a higher Bond albedo than the modern Earth; its surface albedo is so high that Rayleigh scattering does not noticeably affect its spectrum. The rotational color variations occur at short wavelengths due to the large contrast between glacier ice and bare land in those wavebands. Thus we find that both the broadband colors and diurnal color variations of such a planet would be easily distinguishable from the modern-day Earth, regardless of viewing angle.

Arthrometric measurement of ankle-complex motion: normative values.

Valid and reliable measurements of ankle-complex motion have been reported using the Hollis Ankle Arthrometer. No published normative data of ankle-complex motion obtained from ankle arthrometry are available for use as a reference for clinical decision making. To describe the distribution variables of ankle-complex motion in uninjured ankles and to establish normative reference values for use in research and to assist in clinical decision making. Descriptive laboratory study. University research laboratory. Both ankles of 50 men and 50 women (age = 21.78 ± 2.0 years [range, 19-25 years]) were tested. Each ankle underwent anteroposterior (AP) and inversion-eversion (I-E) loading using an ankle arthrometer. Recorded anterior, posterior, and total AP displacement (millimeters) at 125 N and inversion, eversion, and total I-E rotation (degrees) at 4 Nm. Women had greater ankle-complex motion for all variables except for posterior displacement. Total AP displacement of the ankle complex was 18.79 ± 4.1 mm for women and 16.70 ± 4.8 mm for men (U = 3742.5, P < .01). Total I-E rotation of the ankle complex was 42.10 degrees ± 9.0 degrees for women and 34.13 degrees ± 10.1 degrees for men (U = 2807, P < .001). All variables were normally distributed except for anterior displacement, inversion rotation, eversion rotation, and total I-E rotation in the women's ankles and eversion rotation in the men's ankles; these variables were skewed positively. Our study increases the available database on ankle-complex motion, and it forms the basis of norm-referenced clinical comparisons and the basis on which quantitative definitions of ankle pathologic conditions can be developed.

Rovibrational spectra of ammonia. II. Detailed analysis, comparison, and prediction of spectroscopic assignments for 14NH3,15NH3, and 14ND3

Several aspects of ammonia rovibrational spectra have been investigated using the new HSL-2 potential energy surface that includes an approximate correction for nonadiabatic effects. The unprecedented accuracy of rovibrational energy levels and transition energies computed using HSL-2 was demonstrated in Part I of this study. For (14)NH(3), new assignments for a few ν(3) + ν(4) band transitions and energy levels are suggested, and discrepancies between computed and HITRAN energy levels in the 2ν(4) band are analyzed (2ν(4) is the most difficult band below 5000 cm(-1)). New assignments are suggested for existing or missing 2ν(4) levels. Several new vibrational bands are identified from existing, unassigned HITRAN data, including 2ν(2) + ν(4), (ν(3) + ν(4)) -A(')∕A("), ν(1) + 2ν(2), and 2ν(2) + 2ν(4). The strong mixing between the 2ν(4) and 2ν(2) + ν(4) bands is carefully examined and found to be the source of the difficulties in the experimental modeling of 2ν(4). Discussion is presented for preliminary J = 10 results, where the overall root-mean-square error is estimated to be less than 0.039 cm(-1). The analysis of the 4ν(2) band demonstrates both the reliability and the accuracy of predictions from HSL-2. The full list of computed J = 0 band origins (with assignments) and the inversion splittings up to 7000-8000 cm(-1) above the zero-point energy are presented. J = 0-2 levels are reported for those bands below 5100 cm(-1) that are missing from the HITRAN database. For (15)NH(3), excellent agreement is found for the available ν(2) and ν(3) + ν(4)(E) transition energies, but significant deficiencies are shown for HITRAN levels and several corrections are suggested. The (15)N isotopic effects are presented for the J = 0-6 levels of 13 HITRAN bands. For (14)ND(3), we reproduce the pure rotational inversion spectra line frequencies with an accuracy similar to that for (14)NH(3). However, it is not possible to reproduce simultaneously all four pairs of inversion-split vibrational fundamentals to better than 0.05 cm(-1) uncertainty. It is suggested that a reanalysis of some suspicious (14)ND(3) fundamental bands is required. The analyses presented here and in Part I show that rovibrational energy levels and transition frequencies computed with HSL-2 (with nonadiabatic corrections) remain highly accurate well beyond the experimental data used in the refinement procedure. Calculations using HSL-2 are capable of revealing many deficiencies in experimental analyses of ammonia spectra and provide reliable predictions with similar accuracy. It is expected that the results of this study will be useful in the future interpretation of high-resolution spectra from laboratory experiments or from astronomical observations. The present work represents a very significant advance in the state of our knowledge of the spectroscopy of ammonia and its isotopologues.