A BPS Interpretation of Shape Invariance

We show that shape invariance appears when a quantum mechanical model is invariant under a centrally extended superalgebra endowed with an additional symmetry generator, which we dub the shift operator. The familiar mathematical and physical results of shape invariance then arise from the BPS structure associated with this shift operator. The shift operator also ensures that there is a one-to-one correspondence between the energy levels of such a model and the energies of the BPS-saturating states. These findings thus provide a more comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe

Influence of Phase Matching on the Cooper Minimum in Ar High Harmonic Spectra

We study the influence of phase matching on interference minima in high harmonic spectra. We concentrate on structures in atoms due to interference of different angular momentum channels during recombination. We use the Cooper minimum (CM) in argon at 47 eV as a marker in the harmonic spectrum. We measure 2d harmonic spectra in argon as a function of wavelength and angular divergence. While we identify a clear CM in the spectrum when the target gas jet is placed after the laser focus, we find that the appearance of the CM varies with angular divergence and can even be completely washed out when the gas jet is placed closer to the focus. We also show that the argon CM appears at different wavelengths in harmonic and photo-absorption spectra measured under conditions independent of any wavelength calibration. We model the experiment with a simulation based on coupled solutions of the time-dependent Schr\"odinger equation and the Maxwell wave equation, including both the single atom response and macroscopic effects of propagation. The single atom calculations confirm that the ground state of argon can be represented by its field free $p$ symmetry, despite the strong laser field used in high harmonic generation. Because of this, the CM structure in the harmonic spectrum can be described as the interference of continuum $s$ and $d$ channels, whose relative phase jumps by $\pi$ at the CM energy, resulting in a minimum shifted from the photoionization result. We also show that the full calculations reproduce the dependence of the CM on the macroscopic conditions. We calculate simple phase matching factors as a function of harmonic order and explain our experimental and theoretical observation in terms of the effect of phase matching on the shape of the harmonic spectrum. Phase matching must be taken into account to fully understand spectral features related to HHG spectroscopy

Fine-Scale Spatial Organization of Face and Object Selectivity in the Temporal Lobe: Do Functional Magnetic Resonance Imaging, Optical Imaging, and Electrophysiology Agree?

The spatial organization of the brain's object and face representations in the temporal lobe is critical for understanding high-level vision and cognition but is poorly understood. Recently, exciting progress has been made using advanced imaging and physiology methods in humans and nonhuman primates, and the combination of such methods may be particularly powerful. Studies applying these methods help us to understand how neuronal activity, optical imaging, and functional magnetic resonance imaging signals are related within the temporal lobe, and to uncover the fine-grained and large-scale spatial organization of object and face representations in the primate brain

Evidence for a nuclear compartment of transcription and splicing located at chromosome domain boundaries

The nuclear topography of splicing snRNPs, mRNA transcripts and chromosome domains in various mammalian cell types are described. The visualization of splicing snRNPs, defined by the Sm antigen, and coiled bodies, revealed distinctly different distribution patterns in these cell types. Heat shock experiments confirmed that the distribution patterns also depend on physiological parameters. Using a combination of fluorescencein situ hybridization and immunodetection protocols, individual chromosome domains were visualized simultaneously with the Sm antigen or the transcript of an integrated human papilloma virus genome. Three-dimensional analysis of fluorescence-stained target regions was performed by confocal laser scanning microscopy. RNA transcripts and components of the splicing machinery were found to be generally excluded from the interior of the territories occupied by the individual chromosomes. Based on these findings we present a model for the functional compartmentalization of the cell nucleus. According to this model the space between chromosome domains, including the surface areas of these domains, defines a three-dimensional network-like compartment, termed the interchromosome domain (ICD) compartment, in which transcription and splicing of mRNA occurs

Numerical Observation of a Tubular Phase in Anisotropic Membranes

We provide the first numerical evidence for the existence of a tubular phase, predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes without self-avoidance. Incorporating anisotropy into the bending rigidity of a simple model of a tethered membrane with free boundary conditions, we show that the model indeed has two phase transitions corresponding to the flat-to-tubular and tubular-to-crumpled transitions. For the tubular phase we measure the Flory exponent $\nu_F$ and the roughness exponent $\zeta$. We find $\nu_F=0.305(14)$ and $\zeta=0.895(60)$, which are in reasonable agreement with the theoretical predictions of RT --- $\nu_F=1/4$ and $\zeta=1$.Comment: 8 pages, LaTeX, REVTEX, final published versio

Healing of Tendon Defects Implanted with a Porous Collagen-GAG Matrix: Histological Evaluation

There is currently no method to restore normal function in tendon injuries that result in a gap. The objective of this study was to evaluate the early healing of tendon defects implanted with a porous collagen–glycosaminoglycan (CG) matrix, previously shown to facilitate the regeneration of dermis and peripheral nerve. A novel animal model that isolates the tendon defect site from surrounding tissue during healing was employed. This model used a silicone tube to entubulate the surgically produced tendon gap of 10 mm, allowing for the evaluation of the effects of the analog of extracellular matrix on healing of tendon, absent the influences of the external environment. The results showed that tendon stumps induced synthesis of a tissue cable inside the silicone tube in both the presence and absence of CG matrix. The presence of the CG matrix, however, altered the process of tendon healing. Tubes filled with CG matrix contained a significantly greater volume of tissue at the time periods of evaluation: 3, 6, and 12 weeks. Granulation tissue persisted for a longer period of time in the lesion site of CG-filled defects, and the amount of dense fibrous tissue increased continuously during the period of study in defects filled with CG matrix. In contrast, the amount of dense fibrous tissue decreased after 6 weeks in originally empty tubes. In tubes that did not contain the CG matrix, the new tissue consisted of dense aggregates of crimped fibers with a wavelength and fiber bundle thickness that were significantly shorter than those in normal tendon, and consistent with the type of scar that is the end result of repair of many connective tissues. Although, CG-filled tubes contained dense fibrous tissue by 12 weeks, the tissue had no crimp. The CG matrix may have prolonged the synthesis of granulation tissue and delayed or prevented the formation of scar.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63265/1/ten.1997.3.187.pd

Decomposition of Unitary Matrices for Finding Quantum Circuits: Application to Molecular Hamiltonians

Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems

Strongly dispersive transient Bragg grating for high harmonics

We create a transient Bragg grating in a high-harmonic generation medium using two counterpropagating pulses. The Bragg grating disperses the harmonics in angle and can diffract a large bandwidth with temporal resolution limited only by the source size. © 2010 Optical Society of America

Слабка збіжність сім'ї напівмарковських процесів до дифузійного процесу

Наведено основні критерії слабкої збіжності сім'ї напівмарковських процесів до ''чисто'' дифузійного процесу в умовах балансу та до дифузійного процесу Орнштейна–Уленбека за умови, що величина стрибка залежить від параметра серії ε.Приведены основные критерии слабой сходимости семейства полумарковских процессов к ''чисто'' диффузионному процессу в условиях баланса и к диффузионному процессу Орнштейна–Уленбека при условии, что величина скачка зависит от параметра серии ε.The basic criteria of weak convergence of a family of semi-Markov processes to the ''pure'' diffusion process under balance conditions and to the Ornstein–Uhlenbeck diffusion process provided that the value of jump depends on the series parameter ε are obtained

A quantum genetic algorithm with quantum crossover and mutation operations

In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm which has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.Comment: 21 pages, 1 table, v2: typos corrected, minor modifications in sections 3.5 and 4, v3: minor revision, title changed (original title: Semiclassical genetic algorithm with quantum crossover and mutation operations), v4: minor revision, v5: minor grammatical corrections, to appear in QI