Fractional regularization matrices for linear discrete ill-posed problems

The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore the use of fractional powers of the matrices {Mathematical expression} (for Tikhonov regularization) and A (for Lavrentiev regularization) as regularization matrices, where A is the matrix that defines the linear discrete ill-posed problem. Both small- and large-scale problems are considered. © 2013 Springer Science+Business Media Dordrecht

Telemedicine of family-based treatment for adolescent anorexia nervosa: A protocol of a treatment development study.

BackgroundFamily-based treatment is an efficacious treatment available for adolescents with anorexia nervosa. Yet the implementation of this treatment, at least in the United States, is challenging due to a limited number of trained family-based treatment therapists and the concentration of these therapists in a limited number of urban centers. The use of telemedicine in the delivery of family-based treatment can increase access to this therapy for this patient population.Methods/designThis two-year treatment development study (December 2013-November 2015) follows a two-wave iterative case series design. The study is ongoing and addresses the treatment needs of families in remote, rural, or underrepresented parts of the United States by delivering family-based treatment via telemedicine (video chat). The first six months of the study was dedicated to selecting a cloud-based secure telemedicine portal for use with participants. Recruitment for the first of two consecutive case series (N = 5) began during month seven. After these five patients completed treatment, a systematic review of treatment via feedback from participants and therapists related to the delivery of this model and use of technology was completed. A second wave of recruitment is underway (N = 5). At the end of both waves (N = 10), and after a second review of treatment, we should be able to establish the feasibility and acceptability of family-based treatment delivered via telemedicine for this patient population.DiscussionThis study is the first attempt to deliver family-based treatment for adolescents with anorexia nervosa via telemedicine. If delivering family-based treatment in this format is feasible, it will provide access to an evidence-based treatment for families heretofore unable to participate in specialist treatment for their child's eating disorder

Resonator-Aided Single-Atom Detection on a Microfabricated Chip

We use an optical cavity to detect single atoms magnetically trapped on an atom chip. We implement the detection using both fluorescence into the cavity and reduction in cavity transmission due to the presence of atoms. In fluorescence, we register 2.0(2) photon counts per atom, which allows us to detect single atoms with 75% efficiency in 250 microseconds. In absorption, we measure transmission attenuation of 3.3(3)% per atom, which allows us to count small numbers of atoms with a resolution of about 1 atom.Comment: 4.1 pages, 5 figures, and submitted to Physical Review Letter

Dynamical Instability in a Trimeric Chain of Interacting Bose-Einstein Condensates

We analyze thoroughly the mean-field dynamics of a linear chain of three coupled Bose-Einstein condensates, where both the tunneling and the central-well relative depth are adjustable parameters. Owing to its nonintegrability, entailing a complex dynamics with chaos occurrence, this system is a paradigm for longer arrays whose simplicity still allows a thorough analytical study.We identify the set of dynamics fixed points, along with the associated proper modes, and establish their stability character depending on the significant parameters. As an example of the remarkable operational value of our analysis, we point out some macroscopic effects that seem viable to experiments.Comment: 5 pages, 3 figure

Cavity-enhanced optical detection of carbon nanotube Brownian motion

Optical cavities with small mode volume are well-suited to detect the vibration of sub-wavelength sized objects. Here we employ a fiber-based, high-finesse optical microcavity to detect the Brownian motion of a freely suspended carbon nanotube at room temperature under vacuum. The optical detection resolves deflections of the oscillating tube down to 50pm/Hz^1/2. A full vibrational spectrum of the carbon nanotube is obtained and confirmed by characterization of the same device in a scanning electron microscope. Our work successfully extends the principles of high-sensitivity optomechanical detection to molecular scale nanomechanical systems.Comment: 14 pages, 11 figure

Isotopic difference in the heteronuclear loss rate in a two-species surface trap

We have realized a two-species mirror-magneto-optical trap containing a mixture of $^{87}$Rb ($^{85}$Rb) and $^{133}$Cs atoms. Using this trap, we have measured the heteronuclear collisional loss rate $\beta_{Rb-Cs}'$ due to intra-species cold collisions. We find a distinct difference in the magnitude and intensity dependence of $\beta_{Rb-Cs}'$ for the two isotopes $^{87}$Rb and $^{85}$Rb which we attribute to the different ground-state hyperfine splitting energies of the two isotopes.Comment: 4 pages, 2 figure

Cold atoms in videotape micro-traps

We describe an array of microscopic atom traps formed by a pattern of magnetisation on a piece of videotape. We describe the way in which cold atoms are loaded into one of these micro-traps and how the trapped atom cloud is used to explore the properties of the trap. Evaporative cooling in the micro-trap down to a temperature of 1 microkelvin allows us to probe the smoothness of the trapping potential and reveals some inhomogeneity produced by the magnetic film. We discuss future prospects for atom chips based on microscopic permanent-magnet structures.Comment: Submitted for EPJD topical issue "Atom chips: manipulating atoms and molecules with microfabricated structures

Fiber-Cavity-Based Optomechanical Device

We describe an optomechanical device consisting of a fiber-based optical cavity containing a silicon nitiride membrane. In comparison with typical free-space cavities, the fiber-cavity's small mode size (10 {\mu}m waist, 80 {\mu}m length) allows the use of smaller, lighter membranes and increases the cavity-membrane linear coupling to 3 GHz/nm and quadratic coupling to 20 GHz/nm^2. This device is also intrinsically fiber-coupled and uses glass ferrules for passive alignment. These improvements will greatly simplify the use of optomechanical systems, particularly in cryogenic settings. At room temperature, we expect these devices to be able to detect the shot noise of radiation pressure.Comment: 4 pages, 3 figures; the following article has been submitted to Applied Physics Letter

Coherence in Microchip Traps

We report the coherent manipulation of internal states of neutral atoms in a magnetic microchip trap. Coherence lifetimes exceeding 1 s are observed with atoms at distances of $5-130 \mu$m from the microchip surface. The coherence lifetime in the chip trap is independent of atom-surface distance within our measurement accuracy, and agrees well with the results of similar measurements in macroscopic magnetic traps. Due to the absence of surface-induced decoherence, a miniaturized atomic clock with a relative stability in the $10^{-13}$ range can be realized. For applications in quantum information processing, we propose to use microwave near-fields in the proximity of chip wires to create potentials that depend on the internal state of the atoms.Comment: Revised version, accepted for publication in Phys. Rev. Lett., 4 pages, 4 figure