On the accuracy of solving confluent Prony systems

In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as frequency estimation and nonlinear Fourier inversion. Consequently, the question of stability of solution with respect to errors in the right-hand side becomes critical for the success of any particular application. We investigate the question of "maximal possible accuracy" of solving Prony-type systems, putting stress on the "local" behavior which approximates situations with low absolute measurement error. The accuracy estimates are formulated in very simple geometric terms, shedding some light on the structure of the problem. Numerical tests suggest that "global" solution techniques such as Prony's algorithm and ESPRIT method are suboptimal when compared to this theoretical "best local" behavior

A lower bound on CNF encodings of the at-most-one constraint

Constraint "at most one" is a basic cardinality constraint which requires that at most one of its $n$ boolean inputs is set to $1$. This constraint is widely used when translating a problem into a conjunctive normal form (CNF) and we investigate its CNF encodings suitable for this purpose. An encoding differs from a CNF representation of a function in that it can use auxiliary variables. We are especially interested in propagation complete encodings which have the property that unit propagation is strong enough to enforce consistency on input variables. We show a lower bound on the number of clauses in any propagation complete encoding of the "at most one" constraint. The lower bound almost matches the size of the best known encodings. We also study an important case of 2-CNF encodings where we show a slightly better lower bound. The lower bound holds also for a related "exactly one" constraint.Comment: 38 pages, version 3 is significantly reorganized in order to improve readabilit

Averages of bb-hadron, cc-hadron, and τ\tau-lepton properties as of summer 2014

This article reports world averages of measurements of $b$-hadron, $c$-hadron, and $\tau$-lepton properties obtained by the Heavy Flavor Averaging Group (HFAG) using results available through summer 2014. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, $CP$ violation parameters, parameters of semileptonic decays and CKM matrix elements.Comment: 436 pages, many figures and tables. Online updates available at http://www.slac.stanford.edu/xorg/hfag

Meeting user needs for sea level rise information: a decision analysis perspective

Despite widespread efforts to implement climate services, there is almost no literature that systematically analyses users' needs. This paper addresses this gap by applying a decision analysis perspective to identify what kind of mean sea‐level rise (SLR) information is needed for local coastal adaptation decisions. We first characterize these decisions, then identify suitable decision analysis approaches and the sea‐level information required, and finally discuss if and how these information needs can be met given the state‐of‐the‐art of sea‐level science. We find that four types of information are needed: i) probabilistic predictions for short term decisions when users are uncertainty tolerant; ii) high‐end and low‐end SLR scenarios chosen for different levels of uncertainty tolerance; iii) upper bounds of SLR for users with a low uncertainty tolerance; and iv) learning scenarios derived from estimating what knowledge will plausibly emerge about SLR over time. Probabilistic predictions can only be attained for the near term (i.e., 2030‐2050) before SLR significantly diverges between low and high emission scenarios, for locations for which modes of climate variability are well understood and the vertical land movement contribution to local sea‐levels is small. Meaningful SLR upper bounds cannot be defined unambiguously from a physical perspective. Low to high‐end scenarios for different levels of uncertainty tolerance, and learning scenarios can be produced, but this involves both expert and user judgments. The decision analysis procedure elaborated here can be applied to other types of climate information that are required for mitigation and adaptation purposes

The JAK/STAT3 Pathway Is a Common Inducer of Astrocyte Reactivity in Alzheimer's and Huntington's Diseases.

Astrocyte reactivity is a hallmark of neurodegenerative diseases (ND), but its effects on disease outcomes remain highly debated. Elucidation of the signaling cascades inducing reactivity in astrocytes during ND would help characterize the function of these cells and identify novel molecular targets to modulate disease progression. The Janus kinase/signal transducer and activator of transcription 3 (JAK/STAT3) pathway is associated with reactive astrocytes in models of acute injury, but it is unknown whether this pathway is directly responsible for astrocyte reactivity in progressive pathological conditions such as ND. In this study, we examined whether the JAK/STAT3 pathway promotes astrocyte reactivity in several animal models of ND. The JAK/STAT3 pathway was activated in reactive astrocytes in two transgenic mouse models of Alzheimer's disease and in a mouse and a nonhuman primate lentiviral vector-based model of Huntington's disease (HD). To determine whether this cascade was instrumental for astrocyte reactivity, we used a lentiviral vector that specifically targets astrocytes in vivo to overexpress the endogenous inhibitor of the JAK/STAT3 pathway [suppressor of cytokine signaling 3 (SOCS3)]. SOCS3 significantly inhibited this pathway in astrocytes, prevented astrocyte reactivity, and decreased microglial activation in models of both diseases. Inhibition of the JAK/STAT3 pathway within reactive astrocytes also increased the number of huntingtin aggregates, a neuropathological hallmark of HD, but did not influence neuronal death. Our data demonstrate that the JAK/STAT3 pathway is a common mediator of astrocyte reactivity that is highly conserved between disease states, species, and brain regions. This universal signaling cascade represents a potent target to study the role of reactive astrocytes in ND