Smooth Continuation Research Articles

Colonialism, Disability, and Possible Lives: The Residential Treatment of Children Whose Parents Survived Indian Residential Schools

This article performs an institutional autoethnography of working in a residential treatment center, proposing a moral economy in which the exaltation of white nondisabled professionals is tethered to the denigration of disabled Aboriginal children. It describes how resident and staff resistance, respectively, can be taken up so as to facilitate the smooth continuity of the status quo. And it raises questions about everyday institutional practices such as physical restraints, behavior modification, and life-skills curricula, suggesting they may not do what they are intended to do and may instead wither away knowledge and skills that residents had cultivated before their “intake.”

Retrievals of precipitable water vapor using star photometry: Assessment with Raman lidar and link to sun photometry

This work deals with the applicability of a star photometer to retrieve precipitable water vapor (W) at nighttime by means of direct irradiance from stars using a 940 nm narrowband filter. Retrievals are assessed with simultaneous data from a Raman lidar system and linked with daytime values from a sun photometer using measurements taken from March to May 2007 at an urban site. Calibration of both the star and sun photometers was performed by the Modified Astronomical Langley Method. The retrieval of W from photometers is based on a look up table using a simplified expression for the water vapor transmittance and the relative optical water vapor air mass. This methodology presents a systematic uncertainty in W below 3% and 6% for sun and star photometry, respectively. Retrievals of W from star photometry were 9% above those obtained from the Raman lidar technique, but with a great agreement in the temporal evolution from both instruments. The link of daytime and nighttime values of W using sun and star photometers for a more extended database showed a smooth continuity between consecutive periods.

Bone regeneration of canine artificial alveolar clefts using bone-marrow-derived mesenchymal stromal cells and β-tricalcium phosphate: A preliminary study

ObjectiveCleft lip and palate is a congenital disease showing the highest incidence in the maxillofacial field. In this study, bone regeneration in the canine artificial alveolar clefts using bone-marrow-derived mesenchymal stromal cells (MSCs) and β-tricalcium phosphate (β-TCP) was attempted. MethodsArtificial clefts were prepared in 2-year-old dogs and the animals were divided into three groups. Canine MSCs cultured on β-TCP were grafted in the MSCs/β-TCP group. β-TCP without cells was grafted in the β-TCP group. Nothing was grafted in the control group. ResultsSerial X-ray photographs showed that absorption of β-TCP and substitution with bone progressed favorably and regenerated bone had smooth continuity with the surrounding bone in the MSCs/β-TCP group. In contrast, a bone defect remained at 13 weeks after the cleft formation in the other two groups. Bone mineral density of regenerated bone in the MSCs/β-TCP group was between the density of normal bone and that of β-TCP. Bone mineral content of the cleft region in the MSCs/β-TCP group was three times higher than that in the other two groups. Histologically, the artificial bone in the MSCs/β-TCP group showed replacement with bone. In the control group, most of the cleft region was filled with fibrous tissue. ConclusionsBone regeneration using MSCs and β-TCP presents the possibility of a less-invasive new approach to alveolar bone reconstruction.

Second-order and fluctuation-induced first-order phase transitions with functional renormalization group equations

We investigate phase transitions in scalar field theories using the functional renormalization group (RG) equation. We analyze a system with $U(2)\times U(2)$ symmetry, in which there is a parameter $\lambda_2$ that controls the strength of the first-order phase transition driven by fluctuations. In the limit of $\lambda_2\to0$, the $U(2)\times U(2)$ theory is reduced to an $O(8)$ scalar theory that exhibits a second-order phase transition in three dimensions. We develop a new insight for the understanding of the fluctuation-induced first-order phase transition as a smooth continuation from the standard RG flow in the $O(8)$ system. In our view from the RG flow diagram on coupling parameter space, the region that favors the first-order transition emerges from the unphysical region to the physical one as $\lambda_2$ increases from zero. We give this interpretation based on the Taylor expansion of the functional RG equations up to the fourth order in terms of the field, which encompasses the $\epsilon$-expansion results. We compare results from the expansion and from the full numerical calculation and find that the fourth-order expansion is only of qualitative use and that the sixth-order expansion improves the quantitative agreement.

Solving parametric piecewise polynomial systems

We deal with C r smooth continuity conditions for piecewise polynomial functions on Δ , where Δ is an algebraic hypersurface partition of a domain Ω in R n . Piecewise polynomial functions of degree, at most, k on Δ that are continuously differentiable of order r form a spline space C k r . We present a method for solving parametric systems of piecewise polynomial equations of the form Z ( f 1 , … , f n ) = { X ∈ Ω ∣ f 1 ( V , X ) = 0 , … , f n ( V , X ) = 0 } , where f ω ∈ C k ω r ω ( Δ ) , and f ω ∣ σ i ∈ Q [ V ] [ X ] for each n -cell σ i in Δ , V = ( u 1 , u 2 , … , u τ ) is the set of parameters and X = ( x 1 , x 2 , … , x n ) is the set of variables; σ 1 , σ 2 , … , σ m are all the n -dimensional cells in Δ and Ω = ⋃ i = 1 m σ i . Based on the discriminant variety method presented by Lazard and Rouillier, we show that solving a parametric piecewise polynomial system Z ( f 1 , … , f n ) is reduced to the computation of discriminant variety of Z . The variety can then be used to solve the parametric piecewise polynomial system. We also propose a general method to classify the parameters of Z ( f 1 , … , f n ) . This method allows us to say that if there exist an open set of the parameters’ space where the system admits exactly a given number of distinct torsion-free real zeros in every n -cells in Δ .

Cooperation and competition in multidisciplinary optimization

This article aims to contribute to numerical strategies for PDE-constrained multiobjective optimization, with a particular emphasis on CPU-demanding computational applications in which the different criteria to be minimized (or reduced) originate from different physical disciplines that share the same set of design variables. Merits and shortcuts of the most-commonly used algorithms to identify, or approximate, the Pareto set are reviewed, prior to focusing on the approach by Nash games. A strategy is proposed for the treatment of two-discipline optimization problems in which one discipline, the primary discipline, is preponderant, or fragile. Then, it is recommended to identify, in a first step, the optimum of this discipline alone using the whole set of design variables. Then, an orthogonal basis is constructed based on the evaluation at convergence of the Hessian matrix of the primary criterion and constraint gradients. This basis is used to split the working design space into two supplementary subspaces to be assigned, in a second step, to two virtual players in competition in an adapted Nash game, devised to reduce a secondary criterion while causing the least degradation to the first. The formulation is proved to potentially provide a set of Nash equilibrium solutions originating from the original single-discipline optimum point by smooth continuation, thus introducing competition gradually. This approach is demonstrated over a testcase of aero-structural aircraft wing shape optimization, in which the eigen-split-based optimization reveals clearly superior. Thereafter, a result of convex analysis is established for a general unconstrained multiobjective problem in which all the gradients are assumed to be known. This results provides a descent direction common to all criteria, and adapting the classical steepest-descent algorithm by using this direction, a new algorithm is defined referred to as the multiple-gradient descent algorithm (MGDA). The MGDA realizes a phase of cooperative optimization yielding to a point on the Pareto set, at which a competitive optimization phase can possibly be launched on the basis of the local eigenstructure of the different Hessian matrices.

Qualitative analysis of solutions to discrete static contact problems with Coulomb friction

We analyze properties of solutions to discrete contact problems with Coulomb friction which are parametrized by the coefficient of friction F . Using a generalized variant of the implicit-function theorem we establish conditions under which there exists a local Lipschitz continuous branch of solutions around a reference point. Finally, a piecewise smooth continuation algorithm which allows to follow such branches of solutions is proposed.

Period-luminosity relations of pulsating M giants in the solar neighbourhood and the Magellanic Clouds

We analyse the results of a 5.5-yr photometric campaign that monitored 247 southern, semi-regular variables with relatively precise Hipparcos parallaxes to demonstrate an unambiguous detection of Red Giant Branch (RGB) pulsations in the solar neighbourhood. We show that Sequence A' contains a mixture of AGB and RGB stars, as indicated by a temperature related shift at the TRGB. Large Magellanic Cloud (LMC) and Galactic sequences are compared in several ways to show that the P-L sequence zero-points have a negligible metallicity dependence. We describe a new method to determine absolute magnitudes from pulsation periods and calibrate the LMC distance modulus using Hipparcos parallaxes to find \mu (LMC) = 18.54 +- 0.03 mag. Several sources of systematic error are discussed to explain discrepancies between the MACHO and OGLE sequences in the LMC. We derive a relative distance modulus of the Small Magellanic Cloud (SMC) relative to the LMC of \Delta \mu = 0.41 +- 0.02 mag. A comparison of other pulsation properties, including period-amplitude and luminosity-amplitude relations, confirms that RGB pulsation properties are consistent and universal, indicating that the RGB sequences are suitable as high-precision distance indicators. The M giants with the shortest periods bridge the gap between G and K giant solar-like oscillations and M-giant pulsation, revealing a smooth continuity as we ascend the giant branch.

Physical Activity Is Necessary to Prevent Deterioration of the Walking Ability of Patients Undergoing Maintenance Hemodialysis

Maintenance of the walking ability is very important for smooth continuation of maintenance hemodialysis (HD). The aim of the present study was to clarify the physical activity level in daily living that HD patients should maintain to prevent deterioration of their walking ability. Outpatients undergoing maintenance HD, consisting of 65 males and 88 females with a mean age of 64 +/- 11 years, were recruited for the present study. Their physical activity level was recorded over a week with an accelerometer. The physical activity level in daily living was defined as the sum of the lengths of time for which the patients were engaged in physical activity of light or greater intensity during the day, and expressed as the average duration per day. The walking ability was assessed by the normal walking speed and maximum walking speed. Data were analyzed using the receiver operating characteristic (ROC) curve, and the cut-off point for the physical activity time was determined to predict deterioration of the walking ability. In the prediction of deterioration of the normal and maximum walking speeds, the areas under the ROC curve for the physical activity time were 0.78 (95% confidence interval, 0.69-0.87, P < 0.001) and 0.75 (95% confidence interval, 0.63-0.86, P < 0.001), respectively. Moreover, the ROC curve revealed that the cut-off point for the physical activity time to prevent deterioration of the normal and maximum walking speeds was 50 min/day. Thus, HD patients should engage in physical activity for at least 50 min/day to prevent deterioration of their walking ability.

The smooth continuation method in optimal control with an application to quantum systems

The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system is depending upon three physical parameters, which can be used as homotopy parameters, and the time-minimizing trajectory for a prescribed couple of extremities can be analyzed by making a deformation of the Grushin metric on a two-sphere of revolution.

Fixation of Detached Osteochondritis Dissecans Lesions With Bioabsorbable Pins: Clinical and Histologic Evaluation

The purpose was to evaluate the effect of fixation of detached free fragments of osteochondritis dissecans (OCD) (International Cartilage Repair Society OCD IV) on not only the clinical outcome, including functional and radiographic assessment, but also postoperative second-look arthroscopic and histologic evaluation. Nine International Cartilage Repair Society OCD IV fragments were fixed with bioabsorbable pins made of poly-L-lactic acid after curettage of the bed and bone grafting. In 4 cases with severe cartilage damage in the fragments, after resection of the damaged part, trimmed fragments were fixed and osteochondral autologous transplantation was performed to cover the remaining defects. The follow-up period was at least 2 years (range, 2 to 3 years). Lysholm score and computed tomography (CT)/magnetic resonance imaging (MRI), second-look arthroscopy, and biopsy findings were examined postoperatively. All patients ultimately could return to previous sports activity, and the mean postoperative Lysholm score was 97 (range, 90 to 100). At 6 months, CT/MRI scans showed complete union and smooth continuity of articular surface in all cases. Second-look arthroscopy in 7 cases showed that fixed fragments were stable and that there were no progressive degenerative changes in the cartilage. Postoperative histologic examination in 4 cases showed almost normal cartilage from surface to bottom in terms of viability and quality. In addition, new bone trabeculae were covering dead bone trabeculae, which is called creeping substitution. Our study shows good short-term clinical results, as well as confirmation of healing on CT/MRI and second-look arthroscopy. Level IV, therapeutic case series.

Fabrication and Characterization of NiCr/NiSi Functional Thin Films on Temperature Measurement of Cutter Sensor

NiCr/NiSi functional thin films of temperature measurement of cutter sensor were prepared by means of advanced Twinned microwave ECR plasma source enhanced Radio Frequency (RF) reaction non-balance magnetron sputtering technique. Fabrication technologies of NiCr/NiSi thin films were studied. The Compositions, micro-morphology, general structure and depth of NiCr/NiSi thin films were analyzed by means of Electron Probe, SEM, AFM, step profiler and stereo vision micro operation system. The results showed that NiCr/NiSi thin-films were small depth, uniform compact, smooth and good continuity, composition of which was close to target.

DUST EMISSION FROM A PARSEC-SCALE STRUCTURE IN THE SEYFERT 1 NUCLEUS OF NGC 4151

We report mid-infrared interferometric measurements (based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile, programme number 081.B-0092(A)) with ∼10 mas resolution, which resolve the warm (T = 285+25−50 K) thermal emission at the center of NGC 4151. Using pairs of Very Large Telescope 8.2 m telescopes with the Mid-infrared interferometric instrument and by comparing the data to a Gaussian model, we determined the diameter of the dust emission region, albeit only along one position angle, to be (2.0 ± 0.4) pc (FWHM). This is the first size and temperature estimate for the nuclear warm dust distribution in a Seyfert 1 galaxy. The parameters found are comparable to those in Seyfert 2 galaxies, thus providing direct support for the unified model. Using simple analytic temperature distributions, we find that the mid-infrared emission is probably not the smooth continuation of the hot nuclear source that is marginally resolved with K-band interferometry. We also detected weak excess emission around 10.5 μm in our shorter baseline observation, possibly indicating that silicate emission is extended to the parsec scale.

Realistic analytic model for the prompt and high-latitude emission in GRBs

Most gamma-ray bursts (GRBs) observed by the Swift satellite show an early rapid decay phase (RDP) in their X-ray lightcurve, which is usually a smooth continuation of the prompt gamma-ray emission, strongly suggesting that it is its tail. However, the mechanism behind it is still not clear. The most popular model for this RDP is High Latitude Emission (HLE). While HLE is expected in many models for the prompt GRB emission, such as the popular internal shocks model, there are models in which it is not expected, such as sporadic magnetic reconnection events. Therefore, testing whether the RDP is consistent with HLE can help distinguish between different prompt emission models. We address this question by modeling the prompt emission as the sum of its individual pulses with their HLE tails. Analytic expressions for the observed flux density are obtained for power-law and Band function emission spectra. For internal shocks the observed instantaneous spectrum is very close to the emitted one, and should be well described by a Band function also during the RDP. Our model naturally produces, the observed spectral softening and steepening of the flux decay. The observed flux during the RDP is initially dominated by the tail of the last pulse, but the tails of one or more earlier pulses can become dominant later on. Moreover, modeling several overlapping pulses as a single wider pulse would over-predict the emission tail. Thus, one should be very careful when testing the predictions of HLE and do a combined temporal and spectral fit of the prompt GRB emission and the RDP.

Gauge theories with time dependent couplings and their cosmological duals

We consider the $N=4$ super Yang-Mills theory in flat $3+1$-dimensional space-time with a time dependent coupling constant which vanishes at $t=0$, like ${g}_{\mathrm{YM}}^{2}={t}^{p}$. In an analogous quantum mechanics toy model we find that the response is singular. The energy diverges at $t=0$, for a generic state. In addition, if $pg1$ the phase of the wave function has a wildly oscillating behavior, which does not allow it to be continued past $t=0$. A similar effect would make the gauge theory singular as well, though nontrivial effects of renormalization could tame this singularity and allow a smooth continuation beyond $t=0$. The gravity dual in some cases is known to be a time dependent cosmology which exhibits a spacelike singularity at $t=0$. Our results, if applicable in the gauge theory for the case of the vanishing coupling, imply that the singularity is a genuine sickness and does not admit a meaningful continuation. When the coupling remains nonzero and becomes small at $t=0$, the curvature in the bulk becomes of order string scale. The gauge theory now admits a time evolution beyond this point. In this case, a finite amount of energy is produced which possibly thermalizes and leads to a black hole in the bulk.

Amodal Completion is Not Completed Only behind the Occluder

We investigated amodal completion with changes in two parameters: figure orientation, and the shape of the occluding and occluded figures. First, Markovich's [2002, Visual Mathematics 4(1); http://www.mi.sanu.ac.rs/vismath/fila] figure was presented in vertical, horizontal, and diagonal orientations. The results supported Markovich's finding of amodal completion by smooth continuity and symmetry. Amodal completion was also affected by orientation: symmetrical shape tended to appear when the pattern had vertical axis whilst smooth continuity appeared in diagonal orientation. Next, the shape of the exposed side of the occluded figure was changed from straight to curved. Finally, the shape of the grey occluder was changed from a disk to a half-disk or a quarter-disk. The results then showed the influence of the visible contour on amodal completion. This shows that the contextual relation of the whole figure is significant in amodal completion.

Relative Smooth Topological Spaces

In 1992, Ramadan introduced the concept of a smooth topological space and relativeness between smooth topological space and fuzzy topological space in Chang's (1968) view points. In this paper we give a new definition of smooth topological space. This definition can be considered as a generalization of the smooth topological space which was given by Ramadan. Some general properties such as relative smooth continuity and relative smooth compactness are studied.

Questioning the Rules of Continuity Editing: An Empirical Study

We investigated phenomenal continuity across mid-action cuts in motion pictures. When a change of perspective is used in the midst of a dynamic event, film directors tend to agree that a straight-match cut is not advisable if the impression of smooth continuity is desired. Such a cut would embody an instantaneous transition from one camera angle or position to the next. Some film theorists recommend that some overlap of the action is desirable, surmising that the visual system needs time to digest the cut and to reorient. Others disagree and prefer a gap. We report two experiments that provide an empirical test of competing continuity hypotheses. We systematically varied the temporal parameters of a dynamic scene that continued across a camera jump. Computer-animated sequences had to be adjusted until they looked maximally smooth and temporally correct. Observers very consistently preferred gaps (ellipses). Implications for film editing and film theory are discussed.

Semiclassical theory of the structure of the hydrogen spectrum in near-perpendicular electric and magnetic fields: Derivations and formulas for Einstein-Brillouin-Keller-Maslov quantization and description of monodromy

In a previous paper [Schleif and Delos, Phys. Rev. A 76, 013404 (2007)] we described the spectrum of hydrogen atoms in near-perpendicular electric and magnetic fields. We displayed a number of previously unrecognized structures in the spectrum, most of which are connected with a classical phenomenon called ``nontrivial monodromy of action and angle variables in a Hamiltonian system,'' or simply ``monodromy.'' In that paper, we presented only the results, giving predictions of what to look for in various ranges of electric and magnetic fields. Here we present the underlying theory. Starting from Kepler action and angle variables, we give a derivation of a classical Hamiltonian to second order in perturbation theory; the derivation is different from, but the final result agrees with, previous work. We focus especially on the topological structure of the reduced phase space and on the resulting topological structure of the trajectories. We show that construction of action variables by the obvious methods leads to variables that have discontinuous derivatives. Smooth continuation of these ``primitive'' action variables leads to action variables that are multivalued. We show how these multivalued actions lead to lattice defects in the quantum spectrum. Finally we present a few correlation diagrams which show how quantum eigenvalues evolve from one region of near-perpendicular parameter space to another.

Simplified models for anharmonic numbers and densities of vibrational states. Part III: Resonance states of HO 2

Anharmonic rovibrational numbers and densities of resonance states of HO 2 are determined for a number of potential energy surfaces and employing a variety of methods. It is shown that the results present smooth analytical continuations of the expressions derived for the bound states [Part II of this series, J. Troe, V.G. Ushakov, Chem. Phys. 346 (2008) 186] and that no major changes of these expressions arise at the energies where the dissociations to H + O 2 and HO + O open up. The results are also used to test the empirical local mode model of part I of this series [J. Troe, Chem. Phys. 190 (1995) 381] which allows one to approximately predict anharmonic densities of states without using explicit potential energy surfaces.