Reduced-order modeling using Dynamic Mode Decomposition and Least Angle Regression

Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Regression (LARS). We modify LARS to be complex-valued and utilize LARS to select DMD modes. We refer to the resulting algorithm as Least Angle Regression for Dynamic Mode Decomposition (LARS4DMD). Sparsity-Promoting Dynamic Mode Decomposition (DMDSP), a popular mode-selection algorithm, serves as a benchmark for comparison. Numerical results from a Poiseuille flow test problem show that LARS4DMD yields reduced-order models that have comparable performance to DMDSP. LARS4DMD has the added benefit that the regularization weighting parameter required for DMDSP is not needed.Comment: 14 pages, 2 Figures, Submitted to AIAA Aviation Conference 201

Parameter estimation for heavy binary-black holes with networks of second-generation gravitational-wave detectors

The era of gravitational-wave astronomy has started with the discovery of the binary black hole coalescences (BBH) GW150914 and GW151226 by the LIGO instruments. These systems allowed for the first direct measurement of masses and spins of black holes. The component masses in each of the systems have been estimated with uncertainties of over 10\%, with only weak constraints on the spin magnitude and orientation. In this paper we show how these uncertainties will be typical for this type of source when using advanced detectors. Focusing in particular on heavy BBH of masses similar to GW150914, we find that typical uncertainties in the estimation of the source-frame component masses will be around 40\%. We also find that for most events the magnitude of the component spins will be estimated poorly: for only 10\% of the systems the uncertainties in the spin magnitude of the primary (secondary) BH will be below 0.7 (0.8). Conversely, the effective spin along the angular momentum can be estimated more precisely than either spins, with uncertainties below 0.16 for 10\% of the systems. We also quantify how often large or negligible primary spins can be excluded, and how often the sign of the effective spin can be measured. We show how the angle between the spin and the orbital angular momentum can only seldom be measured with uncertainties below 60$^\circ$. We then investigate how the measurement of spin parameters depends on the inclination angle and the total mass of the source. We find that when precession is present, uncertainties are smaller for systems observed close to edge-on. Contrarily to what happens for low-mass, inspiral dominated, sources, for heavy BBH we find that large spins aligned with the orbital angular momentum can be measured with small uncertainty. We also show how spin uncertainties increase with the total mass. Finally...Comment: 18 pages, 28 figures. The abstract is cut in the Arxiv metadata. Refer to PDF. Version accepted by PR

Annual Survey of Virginia Law: Criminal Law

This article summarizes all published criminal law decisions of the Supreme Court of Virginia and the major criminal law decisions of the Virginia Court of Appeals sitting en banc, issued between July 1, 1997, and July 1, 1998. Due to space limitations, however, the article includes only a few selected published panel opinions of the Virginia Court of Appeals. Also, this article includes a summary df the criminal law opinion from the Supreme Court of the United States which arose from a Virginia case during the period stated above. And finally, this article summarizes the most significant enactments from the 1998 session of the Virginia General Assembly in the field of criminal law

Performance Enhancement of a Vertical Tail Model with Sweeping Jet Actuators

Active Flow Control (AFC) experiments performed at the Caltech Lucas Adaptive Wall Wind Tunnel on a 12%-thick, generic vertical tail model indicated that sweeping jets emanating from the trailing edge (TE) of the vertical stabilizer significantly increased the side force coefficient for a wide range of rudder deflection angles and yaw angles at free-stream velocities approaching takeoff rotation speed. The results indicated that 2% blowing momentum coefficient (C_μ) increased the side force in excess of 50% at the maximum conventional rudder deflection angle in the absence of yaw. Even C_μ = 0.5% increased the side force in excess of 20% under these conditions. This effort was sponsored by the NASA Environmentally Responsible Aviation (ERA) project and the successful demonstration of this flow-control application could have far reaching implications. It could lead to effective applications of AFC technologies on key aircraft control surfaces and lift enhancing devices (flaps) that would aid in reduction of fuel consumption through a decrease in size and weight of wings and control surfaces or a reduction of the noise footprint due to steeper climb and descent

The Casein Kinase I Family in Wnt Signaling

AbstractThe canonical Wnt-signaling pathway is critical for many aspects of development, and mutations in components of the Wnt pathway are carcinogenic. Recently, sufficiency tests identified casein kinase Iϵ (CKIϵ) as a positive component of the canonical Wnt/β-catenin pathway, and necessity tests showed that CKIϵ is required in vertebrates to transduce Wnt signals. In addition to CKIϵ, the CKI family includes several other isoforms (α, β, γ, and δ) and their role in Wnt sufficiency tests had not yet been clarified. However, in Caenorhabditis elegans studies, loss-of-function of a CKI isoform most similar to α produced the mom phenotype, indicative of loss-of-Wnt signaling. In this report, we examine the ability of the various CKI isoforms to activate Wnt signaling and find that all the wild-type CKI isoforms do so. Dishevelled (Dsh), another positive component of the Wnt pathway, becomes phosphorylated in response to Wnt signals. All the CKI isoforms, with the exception of γ, increase the phosphorylation of Dsh in vivo. In addition, CKI directly phosphorylates Dsh in vitro. Finally, we find that CKI is required in vivo for the Wnt-dependent phosphorylation of Dsh. These studies advance our understanding of the mechanism of Wnt action and suggest that more than one CKI isoform is capable of transducing Wnt signals in vivo

The Casein Kinase I Family: Roles in Morphogenesis

AbstractWnt signals play important roles in development and oncogenesis and are transduced through at least two pathways: a canonical β-catenin-dependent and a β-catenin-independent cascade. Casein kinase I (CKI) is required in both invertebrates and vertebrates to transduce canonical Wnt signals. However, its role in the β-catenin-independent pathway was unknown. During vertebrate embryogenesis, the β-catenin-independent cascade is thought to control cell movements and has been postulated to be analogous to the Drosophila planar cell polarity pathway, which signals through the JNK cascade. Here, we report that blocking CKI function inhibits embryonic morphogenesis and activates JNK in cell lines. These studies suggest that CKI might also act in the β-catenin-independent pathway and indicate a role for CKI during convergence extension in early vertebrate development

The Effects of Lower Body Positive Pressure Treadmill Running on Acute Femoral Cartilage Deformation

Purpose: Examine and compare the acute response of femoral cartilage in healthy individuals after running at full bodyweight (BW) (100%) and 80% BW on a lower body positive pressure treadmill. Methods: Crossover study consisted of 20 total healthy participants (10 males, 10 females). Femoral cartilage width was assessed using ultrasonography before and after the assigned running conditions. The control condition consisted of running at 6mph for 30 minutes at 100% BW, while the experimental condition consisted of running at 6mph for 30 minutes at 80% BW. Each participant ran both BW conditions, exactly one week apart. The order of conditions was randomly assigned to each participant. All running conditions were completed on the same AlterG Via X treadmill. Results: A significant reduction in cartilage width was found in both the right (p=0.001) and left (p=0.016) knees after running at 100% BW. Baseline cartilage measurements were comparative prior to each running condition and between limbs. There were no significant differences between limbs for either running condition. A significant reduction in cartilage width was seen after running at 80% body weight only in the right lateral compartment (p=0.006). Cartilage showed greater deformation after 100% BW than 80% BW in right (p=0.033) and left (p=0.011) knees. Conclusions: Cartilage thickness change proved to be lower after 80% BW running compared to 100% BW, which could have implications for long term cartilage health and future research into anti-gravity running

Influence of electron injection on performance of GaN photodetectors

It is demonstrated that short-time (up to 1200 s) electron injection into the p-region of GaN p-n junction, as a result of forward bias application, leads to a long-term multifold enhancement of the device peak responsivity as well as to a spectral broadening of the photoresponse. The effect is found to persist for several days and is related to an increased minority carrier diffusion length in the p region, due to an injected electron trapping on deep levels associated with Mg acceptors

Improving Rudder Effectiveness with Sweeping Jet Actuators

The application of active flow control on a vertical tail of a typical twin engine aircraft was investigated. Sweeping jets installed into the rudder surface were used and their effect was assessed by force measurements, flow visualization and local pressure distributions. The airfoil forming the tail is a NACA 0012 with a rudder using 35% of its chord. The tests were carried out at the Lucas Wind Tunnel at the California Institute of Technology at representative Reynolds numbers of up to Re=1.5 million. Multiple flap deflections and spanwise actuator configurations were tested resulting in an increase of up to 50-70% in side force depending on the free stream velocity and momentum input