On the Complexity of Quantum ACC

For any q > 1, let MOD_q be a quantum gate that determines if the number of 1's in the input is divisible by q. We show that for any q,t > 1, MOD_q is equivalent to MOD_t (up to constant depth). Based on the case q=2, Moore has shown that quantum analogs of AC^(0), ACC[q], and ACC, denoted QAC^(0)_wf, QACC[2], QACC respectively, define the same class of operators, leaving q > 2 as an open question. Our result resolves this question, implying that QAC^(0)_wf = QACC[q] = QACC for all q. We also prove the first upper bounds for QACC in terms of related language classes. We define classes of languages EQACC, NQACC (both for arbitrary complex amplitudes) and BQACC (for rational number amplitudes) and show that they are all contained in TC^(0). To do this, we show that a TC^(0) circuit can keep track of the amplitudes of the state resulting from the application of a QACC operator using a constant width polynomial size tensor sum. In order to accomplish this, we also show that TC^(0) can perform iterated addition and multiplication in certain field extensions.

Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

Lovelock terms and BRST cohomology

Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of an order not higher than 2 (while generic polynomial scalar densities lead to Euler-Lagrange derivatives with derivatives of the metric of order 4). A characteristic feature of Lovelock terms is that their first nonvanishing term in the expansion g λμ = η λμ + h λμ of the metric around flat space is a total derivative. In this paper, we investigate generalized Lovelock terms defined as polynomial scalar densities in the Riemann curvature tensor and its covariant derivatives (of arbitrarily high but finite order) such that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. This is done by reformulating the problem as a BRST cohomological one and by using cohomological tools. We determine all the generalized Lovelock terms. We find, in fact, that the class of nontrivial generalized Lovelock terms contains only the usual ones. Allowing covariant derivatives of the Riemann tensor does not lead to a new structure. Our work provides a novel algebraic understanding of the Lovelock terms in the context of BRST cohomology. © 2005 IOP Publishing Ltd.

Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification

We propose and experimentally validate a first-principles based model for the nonlinear piezoelectric response of an electroelastic energy harvester. The analysis herein highlights the importance of modeling inherent piezoelectric nonlinearities that are not limited to higher order elastic effects but also include nonlinear coupling to a power harvesting circuit. Furthermore, a nonlinear damping mechanism is shown to accurately restrict the amplitude and bandwidth of the frequency response. The linear piezoelectric modeling framework widely accepted for theoretical investigations is demonstrated to be a weak presumption for near-resonant excitation amplitudes as low as 0.5 g in a prefabricated bimorph whose oscillation amplitudes remain geometrically linear for the full range of experimental tests performed (never exceeding 0.25% of the cantilever overhang length). Nonlinear coefficients are identified via a nonlinear least-squares optimization algorithm that utilizes an approximate analytic solution obtained by the method of harmonic balance. For lead zirconate titanate (PZT-5H), we obtained a fourth order elastic tensor component of c1111p =-3.6673× 1017 N/m2 and a fourth order electroelastic tensor value of e3111 =1.7212× 108 m/V. © 2010 American Institute of Physics.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Magnetic Resonance Imaging Biomarkers of Renal Structure and Function

The kidney's major role in filtration depends on its high blood flow, concentrating mechanisms, and biochemical activation. The kidney's greatest strengths also lead to vulnerability for drug-induced nephrotoxicity and other renal injuries. The current standard to diagnose renal injuries is with a percutaneous renal biopsy, which can be biased and insufficient. In one particular case, biopsy of a kidney with renal cell carcinoma can actually initiate metastasis. Tools that are sensitive and specific to detect renal disease early are essential, especially noninvasive diagnostic imaging. While other imaging modalities (ultrasound and x-ray/CT) have their unique advantages and disadvantages, MRI has superb soft tissue contrast without ionizing radiation. More importantly, there is a richness of contrast mechanisms in MRI that has yet to be explored and applied to study renal disease.

The focus of this work is to advance preclinical imaging tools to study the structure and function of the renal system. Studies were conducted in normal and disease models to understand general renal physiology as well as pathophysiology. This dissertation is separated into two parts--the first is the identification of renal architecture with ex vivo MRI; the second is the characterization of renal dynamics and function with in vivo MRI. High resolution ex vivo imaging provided several opportunities including: 1) identification of fine renal structures, 2) implementation of different contrast mechanisms with several pulse sequences and reconstruction methods, 3) development of image-processing tools to extract regions and structures, and 4) understanding of the nephron structures that create MR contrast and that are important for renal physiology. The ex vivo studies allowed for understanding and translation to in vivo studies. While the structure of this dissertation is organized by individual projects, the goal is singular: to develop magnetic resonance imaging biomarkers for renal system.

The work presented here includes three ex vivo studies and two in vivo studies:

1) Magnetic resonance histology of age-related nephropathy in sprague dawley.

2) Quantitative susceptibility mapping of kidney inflammation and fibrosis in type 1 angiotensin receptor-deficient mice.

3) Susceptibility tensor imaging of the kidney and its microstructural underpinnings.

4) 4D MRI of renal function in the developing mouse.

5) 4D MRI of polycystic kidneys in rapamycin treated Glis3-deficient mice.

Less wiring, more firing: low-performing older adults compensate for impaired white matter with greater neural activity.

The reliable neuroimaging finding that older adults often show greater activity (over-recruitment) than younger adults is typically attributed to compensation. Yet, the neural mechanisms of over-recruitment in older adults (OAs) are largely unknown. Rodent electrophysiology studies have shown that as number of afferent fibers within a circuit decreases with age, the fibers that remain show higher synaptic field potentials (less wiring, more firing). Extrapolating to system-level measures in humans, we proposed and tested the hypothesis that greater activity in OAs compensates for impaired white-matter connectivity. Using a neuropsychological test battery, we measured individual differences in executive functions associated with the prefrontal cortex (PFC) and memory functions associated with the medial temporal lobes (MTLs). Using event-related functional magnetic resonance imaging, we compared activity for successful versus unsuccessful trials during a source memory task. Finally, we measured white-matter integrity using diffusion tensor imaging. The study yielded 3 main findings. First, low-executive OAs showed greater success-related activity in the PFC, whereas low-memory OAs showed greater success-related activity in the MTLs. Second, low-executive OAs displayed white-matter deficits in the PFC, whereas low-memory OAs displayed white-matter deficits in the MTLs. Finally, in both prefrontal and MTL regions, white-matter decline and success-related activations occurred in close proximity and were negatively correlated. This finding supports the less-wiring-more-firing hypothesis, which provides a testable account of compensatory over-recruitment in OAs.

Cross-hemispheric collaboration and segregation associated with task difficulty as revealed by structural and functional connectivity.

Although it is known that brain regions in one hemisphere may interact very closely with their corresponding contralateral regions (collaboration) or operate relatively independent of them (segregation), the specific brain regions (where) and conditions (how) associated with collaboration or segregation are largely unknown. We investigated these issues using a split field-matching task in which participants matched the meaning of words or the visual features of faces presented to the same (unilateral) or to different (bilateral) visual fields. Matching difficulty was manipulated by varying the semantic similarity of words or the visual similarity of faces. We assessed the white matter using the fractional anisotropy (FA) measure provided by diffusion tensor imaging (DTI) and cross-hemispheric communication in terms of fMRI-based connectivity between homotopic pairs of cortical regions. For both perceptual and semantic matching, bilateral trials became faster than unilateral trials as difficulty increased (bilateral processing advantage, BPA). The study yielded three novel findings. First, whereas FA in anterior corpus callosum (genu) correlated with word-matching BPA, FA in posterior corpus callosum (splenium-occipital) correlated with face-matching BPA. Second, as matching difficulty intensified, cross-hemispheric functional connectivity (CFC) increased in domain-general frontopolar cortex (for both word and face matching) but decreased in domain-specific ventral temporal lobe regions (temporal pole for word matching and fusiform gyrus for face matching). Last, a mediation analysis linking DTI and fMRI data showed that CFC mediated the effect of callosal FA on BPA. These findings clarify the mechanisms by which the hemispheres interact to perform complex cognitive tasks.

Quantitative mapping of trimethyltin injury in the rat brain using magnetic resonance histology.

The growing exposure to chemicals in our environment and the increasing concern over their impact on health have elevated the need for new methods for surveying the detrimental effects of these compounds. Today's gold standard for assessing the effects of toxicants on the brain is based on hematoxylin and eosin (H&E)-stained histology, sometimes accompanied by special stains or immunohistochemistry for neural processes and myelin. This approach is time-consuming and is usually limited to a fraction of the total brain volume. We demonstrate that magnetic resonance histology (MRH) can be used for quantitatively assessing the effects of central nervous system toxicants in rat models. We show that subtle and sparse changes to brain structure can be detected using magnetic resonance histology, and correspond to some of the locations in which lesions are found by traditional pathological examination. We report for the first time diffusion tensor image-based detection of changes in white matter regions, including fimbria and corpus callosum, in the brains of rats exposed to 8 mg/kg and 12 mg/kg trimethyltin. Besides detecting brain-wide changes, magnetic resonance histology provides a quantitative assessment of dose-dependent effects. These effects can be found in different magnetic resonance contrast mechanisms, providing multivariate biomarkers for the same spatial location. In this study, deformation-based morphometry detected areas where previous studies have detected cell loss, while voxel-wise analyses of diffusion tensor parameters revealed microstructural changes due to such things as cellular swelling, apoptosis, and inflammation. Magnetic resonance histology brings a valuable addition to pathology with the ability to generate brain-wide quantitative parametric maps for markers of toxic insults in the rodent brain.

Botulinum toxin type A injections for the management of muscle tightness following total hip arthroplasty: a case series.

BACKGROUND: Development of hip adductor, tensor fascia lata, and rectus femoris muscle contractures following total hip arthroplasties are quite common, with some patients failing to improve despite treatment with a variety of non-operative modalities. The purpose of the present study was to describe the use of and patient outcomes of botulinum toxin injections as an adjunctive treatment for muscle tightness following total hip arthroplasty. METHODS: Ten patients (14 hips) who had hip adductor, abductor, and/or flexor muscle contractures following total arthroplasty and had been refractory to physical therapeutic efforts were treated with injection of botulinum toxin A. Eight limbs received injections into the adductor muscle, 8 limbs received injections into the tensor fascia lata muscle, and 2 limbs received injection into the rectus femoris muscle, followed by intensive physical therapy for 6 weeks. RESULTS: At a mean final follow-up of 20 months, all 14 hips had increased range in the affected arc of motion, with a mean improvement of 23 degrees (range, 10 to 45 degrees). Additionally all hips had an improvement in hip scores, with a significant increase in mean score from 74 points (range, 57 to 91 points) prior to injection to a mean of 96 points (range, 93 to 98) at final follow-up. There were no serious treatment-related adverse events. CONCLUSION: Botulinum toxin A injections combined with intensive physical therapy may be considered as a potential treatment modality, especially in difficult cases of muscle tightness that are refractory to standard therapy.

Signal Improvement and Contrast Enhancement in Magnetic Resonance Imaging

This thesis reports advances in magnetic resonance imaging (MRI), with the ultimate goal of improving signal and contrast in biomedical applications. More specifically, novel MRI pulse sequences have been designed to characterize microstructure, enhance signal and contrast in tissue, and image functional processes. In this thesis, rat brain and red bone marrow images are acquired using iMQCs (intermolecular multiple quantum coherences) between spins that are 10 μm to 500 μm apart. As an important application, iMQCs images in different directions can be used for anisotropy mapping. We investigate tissue microstructure by analyzing anisotropy mapping. At the same time, we simulated images expected from rat brain without microstructure. We compare those with experimental results to prove that the dipolar field from the overall shape only has small contributions to the experimental iMQC signal. Besides magnitude of iMQCs, phase of iMQCs should be studied as well. The phase anisotropy maps built by our method can clearly show susceptibility information in kidneys. It may provide meaningful diagnostic information. To deeply study susceptibility, the modified-crazed sequence is developed. Combining phase data of modified-crazed images and phase data of iMQCs images is very promising to construct microstructure maps. Obviously, the phase image in all above techniques needs to be highly-contrasted and clear. To achieve the goal, algorithm tools from Susceptibility-Weighted Imaging (SWI) and Susceptibility Tensor Imaging (STI) stands out superb useful and creative in our system.

Consistent deformations of [p,p]-type gauge field theories

Using BRST-cohomological techniques, we analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p > 1. Under the assumptions of locality and Poincaré invariance, we find that there is no consistent deformation of these theories that non-trivially modifies the gauge algebra and/or the gauge transformations. Adding the requirement that the deformation contains no more than two derivatives, the only possible deformation is a cosmological-constant-like term. © SISSA/ISAS 2004.

No self-interaction for two-column massless fields

We investigate the problem of introducing consistent self-couplings in free theories for mixed tensor gauge fields whose symmetry properties are characterized by Young diagrams made of two columns of arbitrary (but different) lengths. We prove that, in flat space, these theories admit no local, Poincaré-invariant, smooth, selfinteracting deformation with at most two derivatives in the Lagrangian. Relaxing the derivative and Lorentz-invariance assumptions, there still is no deformation that modifies the gauge algebra, and in most cases no deformation that alters the gauge transformations. Our approach is based on a Becchi-Rouet-Stora-iyutin (BRST) -cohomology deformation procedure. © 2005 American Institute of Physics.

Spin three gauge theory revisited

We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension 3$">n>3. Under the sole assumptions of Poincaré and parity invariance, local and perturbative deformation of the free theory, we determine all nontrivial consistent deformations of the abelian gauge algebra and classify the corresponding deformations of the quadratic action, at first order in the deformation parameter. We prove that all such vertices are cubic, contain a total of either three or five derivatives and are uniquely characterized by a rank-three constant tensor (an internal algebra structure constant). The covariant cubic vertex containing three derivatives is the vertex discovered by Berends, Burgers and van Dam, which however leads to inconsistencies at second order in the deformation parameter. In dimensions 4$">n>4 and for a completely antisymmetric structure constant tensor, another covariant cubic vertex exists, which contains five derivatives and passes the consistency test where the previous vertex failed. © SISSA 2006.

Variaciones termométricas en la planta del pie y piernas valorada en corredores antes y después de correr 30 km

La termometría es una técnica no invasiva que permite cuantificar los cambios en la temperatura cutánea y evaluarla de forma cuantitativa. El aumento significativo de la temperatura puede indicar la existencia de patología. Se ha demostrado que la actividad muscular induce procesos de transferencia de calor entre los músculos y las capas superficiales de tejido. En este estudio queremos cuantificar los cambios de temperatura que se producen en los músculos del pie y miembro inferior tras una carrera de 30 km, para ello hemos utilizado una cámara termográfica de alta resolución. Contamos con la colaboración voluntaria de 32 sujetos sanos a los que procedimos a tomar fotografías de la planta del pie, parte anterior de la pierna, parte posterior de la pierna, parte anterior del muslo y parte posterior del muslo en dos etapas, primero antes de la carrera y segunda toma después de la carrera de 30 km, de esta manera pudimos valorar si había o no variación de temperatura en las zonas seleccionadas. Tras el análisis de los datos obtenidos encontramos significativas variaciones térmicas en Talón, cabeza primer metatarsiano, cabeza segundo metatarsiano, cabeza tercer metatarsiano, cabeza cuarto metatarsiano, cabeza quinto metatarsiano, apófisis estiloides quinto metatarsiano, arco longitudinal interno, maléolo interno, maléolo externo, peroneo lateral largo, vasto interno, vasto externo, recto femoral, tensor de la fascia lata, inserción cuádriceps, gemelo interno, tendón de Aquiles y Biceps femoral.