Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order. We establish a first global theory of existence and regularity for this shock diffraction problem. In particular, we establish that the optimal regularity for the solution is $C^{0,1}$ across the degenerate sonic boundary. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.Comment: 50 pages;7 figure

Semi-Automated SVG Programming via Direct Manipulation

Direct manipulation interfaces provide intuitive and interactive features to a broad range of users, but they often exhibit two limitations: the built-in features cannot possibly cover all use cases, and the internal representation of the content is not readily exposed. We believe that if direct manipulation interfaces were to (a) use general-purpose programs as the representation format, and (b) expose those programs to the user, then experts could customize these systems in powerful new ways and non-experts could enjoy some of the benefits of programmable systems. In recent work, we presented a prototype SVG editor called Sketch-n-Sketch that offered a step towards this vision. In that system, the user wrote a program in a general-purpose lambda-calculus to generate a graphic design and could then directly manipulate the output to indirectly change design parameters (i.e. constant literals) in the program in real-time during the manipulation. Unfortunately, the burden of programming the desired relationships rested entirely on the user. In this paper, we design and implement new features for Sketch-n-Sketch that assist in the programming process itself. Like typical direct manipulation systems, our extended Sketch-n-Sketch now provides GUI-based tools for drawing shapes, relating shapes to each other, and grouping shapes together. Unlike typical systems, however, each tool carries out the user's intention by transforming their general-purpose program. This novel, semi-automated programming workflow allows the user to rapidly create high-level, reusable abstractions in the program while at the same time retaining direct manipulation capabilities. In future work, our approach may be extended with more graphic design features or realized for other application domains.Comment: In 29th ACM User Interface Software and Technology Symposium (UIST 2016

Unlimited simultaneous discrimination intervals in regression Technical report no. 90

Unlimited simultaneous discrimination intervals in linear regression

Review of available synchronization and time distribution techniques

The methods of synchronizing precision clocks will be reviewed placing particular attention to the simpler techniques, their accuracies, and the approximate cost of equipment. The more exotic methods of synchronization are discussed in lesser detail. The synchronization techniques that will be covered will include satellite dissemination, communication and navigation transmissions via VLF, LF, HF, UHF and microwave as well as commercial and armed forces television. Portable clock trips will also be discussed

Power of Perspective: The Effects of Public Perceptions of Police and Fear of Crime on Attitudes Towards Aerial Drone Use

Historically, unmanned aerial systems (UAS; i.e., drones) have largely been used by the military and federal government. As UAS have become more affordable and easier to operate in recent years, state and local law enforcement agencies have become interested in adopting this technology to facilitate a wide range of police activities (e.g., search and rescue, surveillance, tactical operations, etc.). The Federal Aviation Administration (FAA) has begun to regulate the use of unmanned aerial systems, which will likely lead to the increased use of drone technology by law enforcement agencies across the country in upcoming years. However, previous research suggests that public perception of UAS use by the police is mixed, and in some cases there is considerable resistance to police departments adopting this technology. In the present research, we explore several personality factors related to public attitudes towards police UAS use. More specifically, we conducted a national survey examining the relationship between public perceptions of police legitimacy and effectiveness, as well as fear of crime and victimization, and police use of drone technology. The potential implications for public policy and law enforcement practices, particularly in terms of the introduction of UAS into local communities, are discussed

Development of the mammalian retinogeniculate pathway: Target finding, transient synapses and binocular segregation

This review is concerned with the development of the mammalian retinogeniculate projection from the perspective of our studies on the hamster and to a lesser extent on the cat. In these, and other mammalian species, axons from the two eyes initially spread throughout the dorsal lateral geniculate nucleus (dLGN) and thus completely overlap. Later they segregate, the axons from each eye coming to occupy discrete, non-overlapping territories within the dLGN. The process of segregation to establish the adult pattern coincides with the death of retinal ganglion cells projecting to inappropriate areas of the dLGN and with the loss, by degeneration or retraction, of the axons and/or axonal branches initially located within inappropriate territory of the dLGN. These events occur in the early postnatal period in hamsters, before the eyes have opened, and in cats and monkeys they occur entirely during embryonic life: thus, they do not depend on the onset of normal visual function. If one eye is removed before segregation has begun, the terminal fields of the crossed and uncrossed axons from the remaining eye do not segregate, suggesting that segregation in normal development may depend on some form of interaction between retinal ganglion cells from the two eyes. Attractive and/or repulsive influences exerted by the dLGN on retinogeniculate axons may also be involved in the formation of eye-specific territories. Experimental ultrastructural studies in hamster and cat show that the overlap phase is associated with the formation, by inappropriately located axons, of transient synapses similar to those made by retinogeniculate axons in appropriate parts of the dLGN. In the cat, the transient synapses are made by the axon trunk and by side branches of retinogeniculate axons with terminal arbors in appropriate parts of the nucleus; the transient synapses disappear as the side branches are shed or retracted during the segregation period. Because of good evidence that electrical activity of the retinogeniculate axons may be involved in binocular segregation of inputs, we suggest that the formation and elimination of transient synapses play a significant role in the development of the orderly retinogeniculate projections.published_or_final_versio

Non-adiabatic pumping in an oscillating-piston model

We consider the prototypical "piston pump" operating on a ring, where a circulating current is induced by means of an AC driving. This can be regarded as a generalized Fermi-Ulam model, incorporating a finite-height moving wall (piston) and non trivial topology (ring). The amount of particles transported per cycle is determined by a layered structure of phase-space. Each layer is characterized by a different drift velocity. We discuss the differences compared with the adiabatic and Boltzmann pictures, and highlight the significance of the "diabatic" contribution that might lead to a counter-stirring effect.Comment: 6 pages, 4 figures, improved versio

The Big Paper Network Supporting Doctoral Students to Degree Completion

Doctoral completion rates are a concern across disciplines.  This paper describes the way in which Curriculum Leadership faculty redesigned their doctoral program from coursework through completion to include a strong support system, intellectually and emotionally.  This culminated in the creation of the “Big Paper Network,” designed to support candidates from proposal writing through defense

Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom