On the Hierarchy of Block Deterministic Languages

A regular language is $k$-lookahead deterministic (resp. $k$-block deterministic) if it is specified by a $k$-lookahead deterministic (resp. $k$-block deterministic) regular expression. These two subclasses of regular languages have been respectively introduced by Han and Wood ($k$-lookahead determinism) and by Giammarresi et al. ($k$-block determinism) as a possible extension of one-unambiguous languages defined and characterized by Br\"uggemann-Klein and Wood. In this paper, we study the hierarchy and the inclusion links of these families. We first show that each $k$-block deterministic language is the alphabetic image of some one-unambiguous language. Moreover, we show that the conversion from a minimal DFA of a $k$-block deterministic regular language to a $k$-block deterministic automaton not only requires state elimination, and that the proof given by Han and Wood of a proper hierarchy in $k$-block deterministic languages based on this result is erroneous. Despite these results, we show by giving a parameterized family that there is a proper hierarchy in $k$-block deterministic regular languages. We also prove that there is a proper hierarchy in $k$-lookahead deterministic regular languages by studying particular properties of unary regular expressions. Finally, using our valid results, we confirm that the family of $k$-block deterministic regular languages is strictly included into the one of $k$-lookahead deterministic regular languages by showing that any $k$-block deterministic unary language is one-unambiguous

Long-Distance Wind-Dispersal of Spores in a Fungal Plant Pathogen: Estimation of Anisotropic Dispersal Kernels from an Extensive Field Experiment

Given its biological significance, determining the dispersal kernel (i.e., the distribution of dispersal distances) of spore-producing pathogens is essential. Here, we report two field experiments designed to measure disease gradients caused by sexually- and asexually-produced spores of the wind-dispersed banana plant fungus Mycosphaerella fijiensis. Gradients were measured during a single generation and over 272 traps installed up to 1000 m along eight directions radiating from a traceable source of inoculum composed of fungicide-resistant strains. We adjusted several kernels differing in the shape of their tail and tested for two types of anisotropy. Contrasting dispersal kernels were observed between the two types of spores. For sexual spores (ascospores), we characterized both a steep gradient in the first few metres in all directions and rare long-distance dispersal (LDD) events up to 1000 m from the source in two directions. A heavy-tailed kernel best fitted the disease gradient. Although ascospores distributed evenly in all directions, average dispersal distance was greater in two different directions without obvious correlation with wind patterns. For asexual spores (conidia), few dispersal events occurred outside of the source plot. A gradient up to 12.5 m from the source was observed in one direction only. Accordingly, a thin-tailed kernel best fitted the disease gradient, and anisotropy in both density and distance was correlated with averaged daily wind gust. We discuss the validity of our results as well as their implications in terms of disease diffusion and management strategy

The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particles

The gradient of potential vorticity (PV) is an important quantity because of the way PV (denoted as $q$) tends to accumulate locally in the oceans and atmospheres. Recent analysis by the authors has shown that the vector quantity \bdB = \bnabla q\times \bnabla\theta for the three-dimensional incompressible rotating Euler equations evolves according to the same stretching equation as for \bom the vorticity and \bB, the magnetic field in magnetohydrodynamics (MHD). The \bdB-vector therefore acts like the vorticity \bom in Euler's equations and the \bB-field in MHD. For example, it allows various analogies, such as stretching dynamics, helicity, superhelicity and cross helicity. In addition, using quaternionic analysis, the dynamics of the \bdB-vector naturally allow the construction of an orthonormal frame attached to fluid particles\,; this is designated as a quaternion frame. The alignment dynamics of this frame are particularly relevant to the three-axis rotations that particles undergo as they traverse regions of a flow when the PV gradient \bnabla q is large.Comment: Dedicated to Raymond Hide on the occasion of his 80th birthda

Hyponatremia in patients with heart failure

Mild hyponatremia is encountered frequently in patients hospitalized for worsening heart failure. Admission plasma sodium concentration appears to be an independent predictor of increased mortality after discharge and rehospitalization. Recent studies have suggested that correction of hyponatremia may be associated with improved survival. This hypothesis is currently being studied in large prospective randomized clinical trials

To Learn or Not to Learn Features for Deformable Registration?

Feature-based registration has been popular with a variety of features ranging from voxel intensity to Self-Similarity Context (SSC). In this paper, we examine the question on how features learnt using various Deep Learning (DL) frameworks can be used for deformable registration and whether this feature learning is necessary or not. We investigate the use of features learned by different DL methods in the current state-of-the-art discrete registration framework and analyze its performance on 2 publicly available datasets. We draw insights into the type of DL framework useful for feature learning and the impact, if any, of the complexity of different DL models and brain parcellation methods on the performance of discrete registration. Our results indicate that the registration performance with DL features and SSC are comparable and stable across datasets whereas this does not hold for low level features.Comment: 9 pages, 4 figure

An Adiabatic Theorem without a Gap Condition

The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.Comment: Talk at QMath 7, Prague, 1998. 10 pages, 7 figure

London's weather and the everyday: two centuries of newspaper reports

This study surveys 200 years of London’s weather and its public reporting in newspapers to reveal some of the recurring modes of reporting and linguistic styles that are used to describe and make sense of the human experience of weather. These modes include: the cultural anxieties prompted by ‘unusual weather’; the visual dramas of ‘great storms’; the weather as culpable; and bench-marking extreme weather. Even as the broader processes and patterns of our climate are changing, at the level of the everyday the human and cultural experience of weather remains remarkably familiar

Properties of small molecular drug loading and diffusion in a fluorinated PEG hydrogel studied by ^1H molecular diffusion NMR and ^(19)F spin diffusion NMR

R_f-PEG (fluoroalkyl double-ended poly(ethylene glycol)) hydrogel is potentially useful as a drug delivery depot due to its advanced properties of sol–gel two-phase coexistence and low surface erosion. In this study, ^1H molecular diffusion nuclear magnetic resonance (NMR) and ^(19)F spin diffusion NMR were used to probe the drug loading and diffusion properties of the R_f-PEG hydrogel for small anticancer drugs, 5-fluorouracil (FU) and its hydrophobic analog, 1,3-dimethyl-5-fluorouracil (DMFU). It was found that FU has a larger apparent diffusion coefficient than that of DMFU, and the diffusion of the latter was more hindered. The result of ^(19)F spin diffusion NMR for the corresponding freeze-dried samples indicates that a larger portion of DMFU resided in the R_f core/IPDU intermediate-layer region (where IPDU refers to isophorone diurethane, as a linker to interconnect the R_f group and the PEG chain) than that of FU while the opposite is true in the PEG–water phase. To understand the experimental data, a diffusion model was proposed to include: (1) hindered diffusion of the drug molecules in the R_f core/IPDU-intermediate-layer region; (2) relatively free diffusion of the drug molecules in the PEG-water phase (or region); and (3) diffusive exchange of the probe molecules between the above two regions. This study also shows that molecular diffusion NMR combined with spin diffusion NMR is useful in studying the drug loading and diffusion properties in hydrogels for the purpose of drug delivery applications