On the stability of gravity with Dirichlet walls

Dirichlet walls - time-like boundaries at a finite distance from the bulk on which the induced metric is held fixed - have been used to model AdS spacetimes with a finite cutoff. In the context of gauge/gravity duality, such models are often described as dual to some novel UV-cutoff version of a corresponding CFT that maintains local Lorentz invariance. We study linearized gravity in the presence of such a wall and find it to differ significantly from the seemingly analogous case of Dirichlet boundary conditions for fields of spins zero and one. In particular, using the Kodama-Ishibashi formalism, the boundary conditions that must be imposed on the scalar-sector master field with harmonic time dependence depend explicitly on their frequency. That this feature first arises for spin-2 appears to be related to the second-order nature of the equations of motion. It gives rise to a number of novel instabilities, though both global and planar anti-de Sitter remain (linearly) stable in the presence of large-radius Dirichlet cutoffs. The instabilities arise on the outside of spherical Dirichlet walls, and also inside sufficiently large spherical walls in de Sitter space. We analyze both the inside and outside of flat and spherical walls in Minkowski, de Sitter, and anti-de Sitter space, as well as in certain black hole spacetimes, and find stability for the cases not mentioned above. In particular, we find no linear instabilities in the presence of flat walls. We also find evidence supporting the conjecture that neutral black holes are repelled by Dirichlet walls

SketchGen: Generating Constrained CAD Sketches

Computer-aided design (CAD) is the most widely used modeling approach for technical design. The typical starting point in these designs is 2D sketches which can later be extruded and combined to obtain complex three-dimensional assemblies. Such sketches are typically composed of parametric primitives, such as points, lines, and circular arcs, augmented with geometric constraints linking the primitives, such as coincidence, parallelism, or orthogonality. Sketches can be represented as graphs, with the primitives as nodes and the constraints as edges. Training a model to automatically generate CAD sketches can enable several novel workflows, but is challenging due to the complexity of the graphs and the heterogeneity of the primitives and constraints. In particular, each type of primitive and constraint may require a record of different size and parameter types. We propose SketchGen as a generative model based on a transformer architecture to address the heterogeneity problem by carefully designing a sequential language for the primitives and constraints that allows distinguishing between different primitive or constraint types and their parameters, while encouraging our model to re-use information across related parameters, encoding shared structure. A particular highlight of our work is the ability to produce primitives linked via constraints that enables the final output to be further regularized via a constraint solver. We evaluate our model by demonstrating constraint prediction for given sets of primitives and full sketch generation from scratch, showing that our approach significantly out performs the state-of-the-art in CAD sketch generation

Dynamical Autler-Townes control of a phase qubit

Routers, switches, and repeaters are essential components of modern information-processing systems. Similar devices will be needed in future superconducting quantum computers. In this work we investigate experimentally the time evolution of Autler-Townes splitting in a superconducting phase qubit under the application of a control tone resonantly coupled to the second transition. A three-level model that includes independently determined parameters for relaxation and dephasing gives excellent agreement with the experiment. The results demonstrate that the qubit can be used as a ON/OFF switch with 100 ns operating time-scale for the reflection/transmission of photons coming from an applied probe microwave tone. The ON state is realized when the control tone is sufficiently strong to generate an Autler-Townes doublet, suppressing the absorption of the probe tone photons and resulting in a maximum of transmission.Comment: 8 pages, 8 figure

Emergent dynamic chirality in a thermally driven artificial spin ratchet

Modern nanofabrication techniques have opened the possibility to create novel functional materials, whose properties transcend those of their constituent elements. In particular, tuning the magnetostatic interactions in geometrically frustrated arrangements of nanoelements called artificial spin ice1, 2 can lead to specific collective behaviour3, including emergent magnetic monopoles4, 5, charge screening6, 7 and transport8, 9, as well as magnonic response10, 11, 12. Here, we demonstrate a spin-ice-based active material in which energy is converted into unidirectional dynamics. Using X-ray photoemission electron microscopy we show that the collective rotation of the average magnetization proceeds in a unique sense during thermal relaxation. Our simulations demonstrate that this emergent chiral behaviour is driven by the topology of the magnetostatic field at the edges of the nanomagnet array, resulting in an asymmetric energy landscape. In addition, a bias field can be used to modify the sense of rotation of the average magnetization. This opens the possibility of implementing a magnetic Brownian ratchet13, 14, which may find applications in novel nanoscale devices, such as magnetic nanomotors, actuators, sensors or memory cells

Molecular Structure and Dimeric Organization of the Notch Extracellular Domain as Revealed by Electron Microscopy

Background: The Notch receptor links cell fate decisions of one cell to that of the immediate cellular neighbor. In humans, malfunction of Notch signaling results in diseases and congenital disorders. Structural information is essential for gaining insight into the mechanism of the receptor as well as for potentially interfering with its function for therapeutic purposes. Methodology/Principal Findings: We used the Affinity Grid approach to prepare specimens of the Notch extracellular domain (NECD) of the Drosophila Notch and human Notch1 receptors suitable for analysis by electron microscopy and three-dimensional (3D) image reconstruction. The resulting 3D density maps reveal that the NECD structure is conserved across species. We show that the NECD forms a dimer and adopts different yet defined conformations, and we identify the membrane-proximal region of the receptor and its ligand-binding site. Conclusions/Significance: Our results provide direct and unambiguous evidence that the NECD forms a dimer. Our studies further show that the NECD adopts at least three distinct conformations that are likely related to different functional states of the receptor. These findings open the way to now correlate mutations in the NECD with its oligomeric state and conformation

FIC/FEM formulation with matrix stabilizing terms for incompressible flows at low and high Reynolds numbers

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-006-0060-yWe present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.Peer ReviewedPostprint (author's final draft

Proliferation and estrogen signaling can distinguish patients at risk for early versus late relapse among estrogen receptor positive breast cancers

Introduction: We examined if a combination of proliferation markers and estrogen receptor (ER) activity could predict early versus late relapses in ER-positive breast cancer and inform the choice and length of adjuvant endocrine therapy. Methods: Baseline affymetrix gene-expression profiles from ER-positive patients who received no systemic therapy (n = 559), adjuvant tamoxifen for 5 years (cohort-1: n = 683, cohort-2: n = 282) and from 58 patients treated with neoadjuvant letrozole for 3 months (gene-expression available at baseline, 14 and 90 days) were analyzed. A proliferation score based on the expression of mitotic kinases (MKS) and an ER-related score (ERS) adopted from Oncotype DX® were calculated. The same analysis was performed using the Genomic Grade Index as proliferation marker and the luminal gene score from the PAM50 classifier as measure of estrogen-related genes. Median values were used to define low and high marker groups and four combinations were created. Relapses were grouped into time cohorts of 0-2.5, 0-5, 5-10 years. Results: In the overall 10 years period, the proportional hazards assumption was violated for several biomarker groups indicating time-dependent effects. In tamoxifen-treated patients Low-MKS/Low-ERS cancers had continuously increasing risk of relapse that was higher after 5 years than Low-MKS/High-ERS cancers [0 to 10 year, HR 3.36; p = 0.013]. High-MKS/High-ERS cancers had low risk of early relapse [0-2.5 years HR 0.13; p = 0.0006], but high risk of late relapse which was higher than in the High-MKS/Low-ERS group [after 5 years HR 3.86; p = 0.007]. The High-MKS/Low-ERS subset had most of the early relapses [0 to 2.5 years, HR 6.53; p < 0.0001] especially in node negative tumors and showed minimal response to neoadjuvant letrozole. These findings were qualitatively confirmed in a smaller independent cohort of tamoxifen-treated patients. Using different biomarkers provided similar results. Conclusions: Early relapses are highest in highly proliferative/low-ERS cancers, in particular in node negative tumors. Relapses occurring after 5 years of adjuvant tamoxifen are highest among the highly-proliferative/high-ERS tumors although their risk of recurrence is modest in the first 5 years on tamoxifen. These tumors could be the best candidates for extended endocrine therapy