Convergence of program transformers in the metric space of trees

AbstractIn recent years increasing consensus has emerged that program transformers, e.g. partial evaluation and unfold/fold transformations, should terminate; a compiler should stop even if it performs fancy optimizations! A number of techniques to ensure termination of program transformers have been invented, but their correctness proofs are sometimes long and involved. We present a framework for proving termination of program transformers, cast in the metric space of trees. We first introduce the notion of an abstract program transformer; a number of well-known program transformers can be viewed as instances of this notion. We then formalize what it means that an abstract program transformer terminates and give a general sufficient condition for an abstract program transformer to terminate. We also consider some specific techniques for satisfying the condition. As applications we show that termination of some well-known program transformers either follows directly from the specific techniques or is easy to establish using the general condition. Our framework facilitates simple termination proofs for program transformers. Also, since our framework is independent of the language being transformed, a single correctness proof can be given in our framework for program transformers that use essentially the same technique in the context of different languages. Moreover, it is easy to extend termination proofs for program transformers to accommodate changes to these transformers. Finally, the framework may prove useful for designing new termination techniques for program transformers

Two-Dimensional Inversion Asymmetric Topological Insulators in Functionalized III-Bi Bilayers

The search for inversion asymmetric topological insulators (IATIs) persists as an effect for realizing new topological phenomena. However, so for only a few IATIs have been discovered and there is no IATI exhibiting a large band gap exceeding 0.6 eV. Using first-principles calculations, we predict a series of new IATIs in saturated Group III-Bi bilayers. We show that all these IATIs preserve extraordinary large bulk band gaps which are well above room-temperature, allowing for viable applications in room-temperature spintronic devices. More importantly, most of these systems display large bulk band gaps that far exceed 0.6 eV and, part of them even are up to ~1 eV, which are larger than any IATIs ever reported. The nontrivial topological situation in these systems is confirmed by the identified band inversion of the band structures and an explicit demonstration of the topological edge states. Interestingly, the nontrivial band order characteristics are intrinsic to most of these materials and are not subject to spin-orbit coupling. Owning to their asymmetric structures, remarkable Rashba spin splitting is produced in both the valence and conduction bands of these systems. These predictions strongly revive these new systems as excellent candidates for IATI-based novel applications.Comment: 17 pages,5figure

Phase diagram and spin Hamiltonian of weakly-coupled anisotropic S=1/2 chains in CuCl2*2((CD3)2SO)

Field-dependent specific heat and neutron scattering measurements were used to explore the antiferromagnetic S=1/2 chain compound CuCl2 * 2((CD3)2SO). At zero field the system acquires magnetic long-range order below TN=0.93K with an ordered moment of 0.44muB. An external field along the b-axis strengthens the zero-field magnetic order, while fields along the a- and c-axes lead to a collapse of the exchange stabilized order at mu0 Hc=6T and mu0 Hc=3.5T, respectively (for T=0.65K) and the formation of an energy gap in the excitation spectrum. We relate the field-induced gap to the presence of a staggered g-tensor and Dzyaloshinskii-Moriya interactions, which lead to effective staggered fields for magnetic fields applied along the a- and c-axes. Competition between anisotropy, inter-chain interactions and staggered fields leads to a succession of three phases as a function of field applied along the c-axis. For fields greater than mu0 Hc, we find a magnetic structure that reflects the symmetry of the staggered fields. The critical exponent, beta, of the temperature driven phase transitions are indistinguishable from those of the three-dimensional Heisenberg magnet, while measurements for transitions driven by quantum fluctuations produce larger values of beta.Comment: revtex 12 pages, 11 figure

Wideband digital phase comparator for high current shunts

A wideband phase comparator for precise measurements of phase difference of high current shunts has been developed at INRIM. The two-input digital phase detector is realized with a precision wideband digitizer connected through a pair of symmetric active guarded transformers to the outputs of the shunts under comparison. Data are first acquired asynchronously, and then transferred from on-board memory to host memory. Because of the large amount of data collected the filtering process and the analysis algorithms are performed outside the acquisition routine. Most of the systematic errors can be compensated by a proper inversion procedure. The system is suitable for comparing shunts in a wide range of currents, from several hundred of milliampere up to 100 A, and frequencies ranging between 500 Hz and 100 kHz. Expanded uncertainty (k=2) less than 0.05 mrad, for frequency up to 100 kHz, is obtained in the measurement of the phase difference of a group of 10 A shunts, provided by some European NMIs, using a digitizer with sampling frequency up to 1 MHz. An enhanced version of the phase comparator employs a new digital phase detector with higher sampling frequency and vertical resolution. This permits to decrease the contribution to the uncertainty budget of the phase detector of a factor two from 20 kHz to 100 kHz. Theories and experiments show that the phase difference between two high precision wideband digitizers, coupled as phase detector, depends on multiple factors derived from both analog and digital imprint of each sampling system.Comment: 20 pages, 9 figure

Small‐scale structure of the midlatitude storm enhanced density plume during the 17 March 2015 St. Patrick’s Day storm

Kilometer‐scale density irregularities in the ionosphere can cause ionospheric scintillation—a phenomenon that degrades space‐based navigation and communication signals. During strong geomagnetic storms, the midlatitude ionosphere is primed to produce these ∼1–10 km small‐scale irregularities along the steep gradients between midlatitude storm enhanced density (SED) plumes and the adjacent low‐density trough. The length scales of irregularities on the order of 1–10 km are determined from a combination of spatial, temporal, and frequency analyses using single‐station ground‐based Global Positioning System total electron content (TEC) combined with radar plasma velocity measurements. Kilometer‐scale irregularities are detected along the boundaries of the SED plume and depleted density trough during the 17 March 2015 geomagnetic storm, but not equatorward of the plume or within the plume itself. Analysis using the fast Fourier transform of high‐pass filtered slant TEC suggests that the kilometer‐scale irregularities formed near the poleward gradients of SED plumes can have similar intensity and length scales to those typically found in the aurora but are shown to be distinct phenomena in spacecraft electron precipitation measurements.Key PointsKilometer‐scale density irregularities measured in single‐station GPS TEC data from the 17 March 2015 storm enhanced density plume systemLocation, intensity, and length scales are estimated from spatial, temporal, and frequency analyses of multiple instrument dataFormation regions for small‐scale irregularities with length scales of 3‐10 km are identified for plasma velocities of 500–1200 m s−1Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136745/1/jgra53295_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136745/2/jgra53295.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136745/3/jgra53295-sup-0001-supplementary.pd