Three Inadequate Models

The connection between operational and denotational semantics is of longstanding interest in the study of programming languages. One naturally seeks positive results. For example in [FP94, Sim99] adequacy results are given for models in a variety of categories. Again, the failure of full abstraction in the standard models constructed using complete partial orders and continuous functions [Plo77, Mil77] prompted the exploration of other categories (see, e.g., [BCL85, FJM96, AM98, AC98]) with varying degrees of success. In this paper we interest ourselves in counterexamples in order to make a case that these natural avenues of research had a degree of necessity. To this end, we construct inadequate models and investigate whether one can do better than the standard model, but still stay in the category of complete partial orders. (In contrast, an inadequate standard model of PCF is given in [Sim99]—but in a specially constructed category.

Belief Revision in Science: Informational Economy and Paraconsistency

In the present paper, our objective is to examine the application of belief revision models to scientific rationality. We begin by considering the standard model AGM, and along the way a number of problems surface that make it seem inadequate for this specific application. After considering three different heuristics of informational economy that seem fit for science, we consider some possible adaptations for it and argue informally that, overall, some paraconsistent models seem to better satisfy these principles, following Testa (2015). These models have been worked out in formal detail by Testa, Cogniglio, & Ribeiro (2015, 2017)

A numerical code for a three-dimensional magnetospheric MHD equilibrium model

Two dimensional and three dimensional MHD equilibrium models were begun for Earth's magnetosphere. The original proposal was motivated by realizing that global, purely data based models of Earth's magnetosphere are inadequate for studying the underlying plasma physical principles according to which the magnetosphere evolves on the quasi-static convection time scale. Complex numerical grid generation schemes were established for a 3-D Poisson solver, and a robust Grad-Shafranov solver was coded for high beta MHD equilibria. Thus, the effects were calculated of both the magnetopause geometry and boundary conditions on the magnetotail current distribution

Models of cuspy triaxial stellar systems. III: The effect of velocity anisotropy on chaoticity

In several previous investigations we presented models of triaxial stellar systems, both cuspy and non cuspy, that were highly stable and harboured large fractions of chaotic orbits. All our models had been obtained through cold collapses of initially spherical $N$--body systems, a method that necessarily results in models with strongly radial velocity distributions. Here we investigate a different method that was reported to yield cuspy triaxial models with virtually no chaos. We show that such result was probably due to the use of an inadequate chaos detection technique and that, in fact, models with significant fractions of chaotic orbits result also from that method. Besides, starting with one of the models from the first paper in this series, we obtained three different models by rendering its velocity distribution much less radially biased (i.e., more isotropic) and by modifying its axial ratios through adiabatic compression. All three models yielded much higher fractions of regular orbits than most of those from our previous work. We conclude that it is possible to obtain stable cuspy triaxial models of stellar systems whose velocity distribution is more isotropic than that of the models obtained from cold collapses. Those models still harbour large fractions of chaotic orbits and, although it is difficult to compare the results from different models, we can tentatively conclude that chaoticity is reduced by velocity isotropy.Comment: 11 pages, 14 figures. Accepted for publication in MNRA

Toward connecting core-collapse supernova theory with observations: I. Shock revival in a 15 Msun blue supergiant progenitor with SN 1987A energetics

We study the evolution of the collapsing core of a 15 Msun blue supergiant supernova progenitor from the core bounce until 1.5 seconds later. We present a sample of hydrodynamic models parameterized to match the explosion energetics of SN 1987A. We find the spatial model dimensionality to be an important contributing factor in the explosion process. Compared to two-dimensional simulations, our three-dimensional models require lower neutrino luminosities to produce equally energetic explosions. We estimate that the convective engine in our models is 4% more efficient in three dimensions than in two dimensions. We propose that the greater efficiency of the convective engine found in three-dimensional simulations might be due to the larger surface-to-volume ratio of convective plumes, which aids in distributing energy deposited by neutrinos. We do not find evidence of the standing accretion shock instability nor turbulence being a key factor in powering the explosion in our models. Instead, the analysis of the energy transport in the post-shock region reveals characteristics of penetrative convection. The explosion energy decreases dramatically once the resolution is inadequate to capture the morphology of convection on large scales. This shows that the role of dimensionality is secondary to correctly accounting for the basic physics of the explosion. We also analyze information provided by particle tracers embedded in the flow, and find that the unbound material has relatively long residency times in two-dimensional models, while in three dimensions a significant fraction of the explosion energy is carried by particles with relatively short residency times.Comment: accepted for publication in Astrophysical Journa

Flavor Physics in SO(10) GUTs with Suppressed Proton decay Due to Gauged Discrete Symmetry

Generic SO(10) GUT models suffer from the problem that Planck scale induced non-renormalizable proton decay operators require extreme suppression of their couplings to be compatible with present experimental upper limits. One way to resolve this problem is to supplement SO(10) by simple gauged discrete symmetries which can also simultaneously suppress the renormalizable R-parity violating ones when they occur and make the theory "more natural". Here we discuss the phenomenological viability of such models. We first show that for both classes of models, e.g the ones that use ${\bf 16}_H$ or ${\bf 126}_H$ to break B-L symmetry, the minimal Higgs content which is sufficient for proton decay suppression is inadequate for explaining fermion masses despite the presence of all apparently needed couplings. We then present an extended ${\bf 16}_H$ model, with three {\bf 10} and three {\bf 45}-Higgs, where is free of this problem. We propose this as a realistic and "natural" model for fermion unification and discuss the phenomenology of this model e.g. its predictions for neutrino mixings and lepton flavor violation.Comment: 21 pages, 2 figure

The importance of distinct modeling strategies for gene and gene-specific treatment effects in hierarchical models for microarray data

When analyzing microarray data, hierarchical models are often used to share information across genes when estimating means and variances or identifying differential expression. Many methods utilize some form of the two-level hierarchical model structure suggested by Kendziorski et al. [Stat. Med. (2003) 22 3899-3914] in which the first level describes the distribution of latent mean expression levels among genes and among differentially expressed treatments within a gene. The second level describes the conditional distribution, given a latent mean, of repeated observations for a single gene and treatment. Many of these models, including those used in Kendziorski's et al. [Stat. Med. (2003) 22 3899-3914] EBarrays package, assume that expression level changes due to treatment effects have the same distribution as expression level changes from gene to gene. We present empirical evidence that this assumption is often inadequate and propose three-level hierarchical models as extensions to the two-level log-normal based EBarrays models to address this inadequacy. We demonstrate that use of our three-level models dramatically changes analysis results for a variety of microarray data sets and verify the validity and improved performance of our suggested method in a series of simulation studies. We also illustrate the importance of accounting for the uncertainty of gene-specific error variance estimates when using hierarchical models to identify differentially expressed genes.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS535 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The political economy of growth and distribution: A theoretical critique

This paper reconsiders the political economy approach to growth and distribution according to which (1) rising inequality induces more government redistribution; (2) more government redistribution is financed by higher distortionary taxation; and (3) higher distortionary taxes reduce economic growth. We present a variety of theoretical arguments demonstrating that all three propositions may be overturned by simply changing an assumption in a plausible way or adding a relevant real-world element to the basal models. The political economy models of growth and distribution, as well as the specific inequality-growth transmission channel they propose, must therefore be assessed as overly simplistic and inadequate with respect to the issues studied. --Political Economy,Redistribution,Inequality,Economic growth