Localized shocks

We study products of precursors of spatially local operators, $W_{x_{n}}(t_{n}) ... W_{x_1}(t_1)$, where $W_x(t) = e^{-iHt} W_x e^{iHt}$. Using chaotic spin-chain numerics and gauge/gravity duality, we show that a single precursor fills a spatial region that grows linearly in $t$. In a lattice system, products of such operators can be represented using tensor networks. In gauge/gravity duality, they are related to Einstein-Rosen bridges supported by localized shock waves. We find a geometrical correspondence between these two descriptions, generalizing earlier work in the spatially homogeneous case.Comment: 23 pages plus appendices, 12 figures. v2: minor error in Appendix B corrected. v3: figure added to the introduction comparing the butterfly effect cone with the standard light con

Integral closures and weight functions over finite fields

AbstractCurves and surfaces of type I are generalized to integral towers of rank r. Weight functions with values in Nr and the corresponding weighted total-degree monomial orderings lift naturally from one domain Rj−1 in the tower to the next, Rj, the integral closure of Rj−1[xj]/〈φ(xj)〉. The qth power algorithm is reworked in this more general setting to produce this integral closure over finite fields, though the application is primarily that of calculating the normalizations of curves related to one-point AG codes arising from towers of function fields. Every attempt has been made to couch all the theory in terms of multivariate polynomial rings and ideals instead of the terminology from algebraic geometry or function field theory, and to avoid the use of any type of series expansion

Focused Anticoagulation Service in Family Medicine Residencies

A report on the creation of a new program to improve family medicine residents\u27 understanding, and quality of care, of anticoagulation patients. Patients requiring anticoagulation therapy pose unique issues requiring a systematic approach to their care, balancing the potential benefit from therapy with possible adverse events. Here, we describe a model that helps to standardize both the care received by patients on anticoagulation therapy as well as the training of family medicine residents caring for those patients. A team-based model of care (family medicine residents, clinical pharmacists, and nurses) is used to achieve the goals of improved care and education. Clinical pharmacists are used in concert with family medicine residents and attendings to assess patients\u27 medication profiles and help direct patient care and resident learning. Both the idea itself and the formal structure are presented in a model for possible adaptation to other program

Eternal Symmetree

In this paper we introduce a simple discrete stochastic model of eternal inflation that shares many of the most important features of the continuum theory as it is now understood. The model allows us to construct a multiverse and rigorously analyze its properties. Although simple and easy to solve, it has a rich mathematical structure underlying it. Despite the discreteness of the space-time the theory exhibits an unexpected non-perturbative analog of conformal symmetry that acts on the boundary of the geometry. The symmetry is rooted in the mathematical properties of trees, p-adic numbers, and ultrametric spaces; and in the physical property of detailed balance. We provide self-contained elementary explanations of the unfamiliar mathematical concepts, which have have also appeared in the study of the p-adic string. The symmetry acts on a huge collection of very low dimensional "multiverse fields" that are not associated with the usual perturbative degrees of freedom. They are connected with the late-time statistical distribution of bubble-universes in the multiverse. The conformal symmetry which acts on the multiverse fields is broken by the existence of terminal decays - to hats or crunches - but in a particularly simple way. We interpret this symmetry breaking as giving rise to an arrow of time. The model is used to calculate statistical correlations at late time and to discuss the measure problem. We show that the natural cutoff in the model is the analog of the so-called light-cone-time cutoff. Applying the model to the problem of the cosmological constant, we find agreement with earlier work.Comment: 39 pages plus appendices, with 11 figures. Journal version (PRD). A discussion of the arrow of time added, along with various other minor clarifications suggested by an anonymous referee. References also adde

Evidence for the involvement of more than one mRNA species in controlling the inactivation process of rat and rabbit brain Na channels expressed in Xenopus oocytes

The properties of rat and rabbit brain sodium (Na) channels expressed in Xenopus oocytes following either unfractionated or high-molecular- weight mRNA injections were compared to assess the relative contribution of different size messages to channel function. RNA was size-fractionated on a sucrose gradient and a high-molecular-weight fraction (7–10 kilobase) encoding the α-subunit gave rise to functional voltage-dependent Na channels in the oocyte membrane. Single- channel conductance, mean open time, and time to first opening were all similar to the values for channels following injection of unfractionated RNA. In contrast, inactivation properties were markedly different; Na currents from high-molecular-weight RNA inactivated with a several-fold smaller macroscopic inactivation rate and showed a steady-state voltage dependence that was shifted in the depolarizing direction by at least 10 mV relative to that for unfractionated RNA. Single-channel recording revealed that the kinetic difference arose from a greater probability for high-molecular-weight RNA induced channels to reopen during a depolarizing voltage step. Pooling all gradient fractions and injecting this RNA into oocytes led to the appearance of Na channels with inactivation properties indistinguishable from those following injection of unfractionated RNA. These results suggest that mRNA species not present in the high- molecular-weight fraction can influence the inactivation process of rat brain Na channels expressed in Xenopus oocytes. This mRNA may encode β-subunits or other proteins that are involved in posttranslational processing of voltage-dependent Na channels

Evidence for the involvement of more than one mRNA species in controlling the inactivation process of rat and rabbit brain Na channels expressed in Xenopus oocytes

The properties of rat and rabbit brain sodium (Na) channels expressed in Xenopus oocytes following either unfractionated or high-molecular- weight mRNA injections were compared to assess the relative contribution of different size messages to channel function. RNA was size-fractionated on a sucrose gradient and a high-molecular-weight fraction (7–10 kilobase) encoding the α-subunit gave rise to functional voltage-dependent Na channels in the oocyte membrane. Single- channel conductance, mean open time, and time to first opening were all similar to the values for channels following injection of unfractionated RNA. In contrast, inactivation properties were markedly different; Na currents from high-molecular-weight RNA inactivated with a several-fold smaller macroscopic inactivation rate and showed a steady-state voltage dependence that was shifted in the depolarizing direction by at least 10 mV relative to that for unfractionated RNA. Single-channel recording revealed that the kinetic difference arose from a greater probability for high-molecular-weight RNA induced channels to reopen during a depolarizing voltage step. Pooling all gradient fractions and injecting this RNA into oocytes led to the appearance of Na channels with inactivation properties indistinguishable from those following injection of unfractionated RNA. These results suggest that mRNA species not present in the high- molecular-weight fraction can influence the inactivation process of rat brain Na channels expressed in Xenopus oocytes. This mRNA may encode β-subunits or other proteins that are involved in posttranslational processing of voltage-dependent Na channels