FAME, a microprocessor based front-end analysis and modeling environment

Higher order software (HOS) is a methodology for the specification and verification of large scale, complex, real time systems. The HOS methodology was implemented as FAME (front end analysis and modeling environment), a microprocessor based system for interactively developing, analyzing, and displaying system models in a low cost user-friendly environment. The nature of the model is such that when completed it can be the basis for projection to a variety of forms such as structured design diagrams, Petri-nets, data flow diagrams, and PSL/PSA source code. The user's interface with the analyzer is easily recognized by any current user of a structured modeling approach; therefore extensive training is unnecessary. Furthermore, when all the system capabilities are used one can check on proper usage of data types, functions, and control structures thereby adding a new dimension to the design process that will lead to better and more easily verified software designs

Normal Coordinates and Primitive Elements in the Hopf Algebra of Renormalization

We introduce normal coordinates on the infinite dimensional group $G$ introduced by Connes and Kreimer in their analysis of the Hopf algebra of rooted trees. We study the primitive elements of the algebra and show that they are generated by a simple application of the inverse Poincar\'e lemma, given a closed left invariant 1-form on $G$. For the special case of the ladder primitives, we find a second description that relates them to the Hopf algebra of functionals on power series with the usual product. Either approach shows that the ladder primitives are given by the Schur polynomials. The relevance of the lower central series of the dual Lie algebra in the process of renormalization is also discussed, leading to a natural concept of $k$-primitiveness, which is shown to be equivalent to the one already in the literature.Comment: Latex, 24 pages. Submitted to Commun. Math. Phy

Barkhausen noise in the Random Field Ising Magnet Nd2_2Fe14_{14}B

With sintered needles aligned and a magnetic field applied transverse to its easy axis, the rare-earth ferromagnet Nd$_2$Fe$_{14}$B becomes a room-temperature realization of the Random Field Ising Model. The transverse field tunes the pinning potential of the magnetic domains in a continuous fashion. We study the magnetic domain reversal and avalanche dynamics between liquid helium and room temperatures at a series of transverse fields using a Barkhausen noise technique. The avalanche size and energy distributions follow power-law behavior with a cutoff dependent on the pinning strength dialed in by the transverse field, consistent with theoretical predictions for Barkhausen avalanches in disordered materials. A scaling analysis reveals two regimes of behavior: one at low temperature and high transverse field, where the dynamics are governed by the randomness, and the second at high temperature and low transverse field where thermal fluctuations dominate the dynamics.Comment: 16 pages, 7 figures. Under review at Phys. Rev.

Baby-Step Giant-Step Algorithms for the Symmetric Group

We study discrete logarithms in the setting of group actions. Suppose that $G$ is a group that acts on a set $S$. When $r,s \in S$, a solution $g \in G$ to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study the case where $G = S_n$, and develop analogs to the Shanks baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets $A, B \subseteq S_n$ such that every permutation of $S_n$ can be written as a product $ab$ of elements $a \in A$ and $b \in B$. Our deterministic procedure is optimal up to constant factors, in the sense that $A$ and $B$ can be computed in optimal asymptotic complexity, and $|A|$ and $|B|$ are a small constant from $\sqrt{n!}$ in size. We also analyze randomized "collision" algorithms for the same problem

Issues in health reform: How changes in eligibility may move millions back and forth between Medicaid and insurance exchanges

The Affordable Care Act will extend health insurance coverage by both expanding Medicaid eligibility and offering premium subsidies for the purchase of private health insurance through state health insurance exchanges. But by definition, eligibility for these programs is sensitive to income and can change over time with fluctuating income and changes in family composition. The law specifies no minimum enrollment period, and subsidy levels will also change as income rises and falls. Using national survey data, we estimate that within six months, more than 35 percent of all adults with family incomes below 200 percent of the federal poverty level will experience a shift in eligibility from Medicaid to an insurance exchange, or the reverse; within a year, 50 percent, or 28 million, will. To minimize the effect on continuity and quality of care, states and the federal government should adopt strategies to reduce the frequency of coverage transitions and to mitigate the disruptions caused by those transitions. Options include establishing a minimum guaranteed eligibility period and “dually certifying” some plans to serve both Medicaid and exchange enrollees

Inference with interference between units in an fMRI experiment of motor inhibition

An experimental unit is an opportunity to randomly apply or withhold a treatment. There is interference between units if the application of the treatment to one unit may also affect other units. In cognitive neuroscience, a common form of experiment presents a sequence of stimuli or requests for cognitive activity at random to each experimental subject and measures biological aspects of brain activity that follow these requests. Each subject is then many experimental units, and interference between units within an experimental subject is likely, in part because the stimuli follow one another quickly and in part because human subjects learn or become experienced or primed or bored as the experiment proceeds. We use a recent fMRI experiment concerned with the inhibition of motor activity to illustrate and further develop recently proposed methodology for inference in the presence of interference. A simulation evaluates the power of competing procedures.Comment: Published by Journal of the American Statistical Association at http://www.tandfonline.com/doi/full/10.1080/01621459.2012.655954 . R package cin (Causal Inference for Neuroscience) implementing the proposed method is freely available on CRAN at https://CRAN.R-project.org/package=ci

Strongly-coupled quantum critical point in an all-in-all-out antiferromagnet

Dimensionality and symmetry play deterministic roles in the laws of Nature. They are important tools to characterize and understand quantum phase transitions, especially in the limit of strong correlations between spin, orbit, charge, and structural degrees of freedom. Using newly-developed, high-pressure resonant x-ray magnetic and charge diffraction techniques, we have discovered a quantum critical point in Cd2Os2O7 as the all-in-all-out (AIAO) antiferromagnetic order is continuously suppressed to zero temperature and, concomitantly, the cubic lattice structure continuously changes from space group Fd-3m to F-43m. Surrounded by three phases of different time reversal and spatial inversion symmetries, the quantum critical region anchors two phase lines of opposite curvature, with striking departures from a mean-field form at high pressure. As spin fluctuations, lattice breathing modes, and quasiparticle excitations interact in the quantum critical region, we argue that they present the necessary components for strongly-coupled quantum criticality in this three-dimensional compound

Continuous and Discontinuous Quantum Phase Transitions in a Model Two-Dimensional Magnet

The Shastry-Sutherland model, which consists of a set of spin 1/2 dimers on a 2-dimensional square lattice, is simple and soluble, but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. We compress the model Shastry-Sutherland material, SrCu2(BO3)2, in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state. High-resolution x-ray measurements exploit what emerges as a remarkably strong spin-lattice coupling to both monitor the magnetic behavior and the absence or presence of structural discontinuities. In the low-pressure spin-singlet regime, the onset of magnetism results in an expansion of the lattice with decreasing temperature, which permits a determination of the pressure dependent energy gap and the almost isotropic spin-lattice coupling energies. The singlet-triplet gap energy is suppressed continuously with increasing pressure, vanishing completely by 2 GPa. This continuous quantum phase transition is followed by a structural distortion at higher pressure.Comment: 16 pages, 4 figures. Accepted for publication in PNA