Context unification is in PSPACE

Contexts are terms with one `hole', i.e. a place in which we can substitute an argument. In context unification we are given an equation over terms with variables representing contexts and ask about the satisfiability of this equation. Context unification is a natural subvariant of second-order unification, which is undecidable, and a generalization of word equations, which are decidable, at the same time. It is the unique problem between those two whose decidability is uncertain (for already almost two decades). In this paper we show that the context unification is in PSPACE. The result holds under a (usual) assumption that the first-order signature is finite. This result is obtained by an extension of the recompression technique, recently developed by the author and used in particular to obtain a new PSPACE algorithm for satisfiability of word equations, to context unification. The recompression is based on performing simple compression rules (replacing pairs of neighbouring function symbols), which are (conceptually) applied on the solution of the context equation and modifying the equation in a way so that such compression steps can be in fact performed directly on the equation, without the knowledge of the actual solution.Comment: 27 pages, submitted, small notation changes and small improvements over the previous tex

Thermonuclear explosions of rapidly rotating white dwarfs - II. Detonations

Context: Superluminous type Ia supernovae (SNe Ia) may be explained by super-Chandrasekhar-mass explosions of rapidly rotating white dwarfs (WDs). In a preceding paper, we showed that the deflagration scenario applied to rapidly rotating WDs generates explosions that cannot explain the majority of SNe Ia. Aims: Rotation of the progenitor star allows super-Chandrasekhar-mass WDs to form that have a shallower density stratification. We use simple estimates of the production of intermediate and iron group elements in pure detonations of rapidly rotating WDs to assess their viability in explaining rare SNe Ia. Methods: We numerically construct WDs in hydrostatic equilibrium that rotate according to a variety of rotation laws. The explosion products are estimated by considering the density stratification and by evaluating the result of hydrodynamics simulations. Results: We show that a significant amount of intermediate mass elements is produced for theoretically motivated rotation laws, even for prompt detonations of WDs. Conclusions: Rapidly rotating WDs that detonate may provide an explanation of rare superluminous SNe Ia in terms of both burning species and explosion kinematics.Comment: 7 pages, 5 figures, accepted for publication by A&

Preferences of Indian Meal Moth Larvae for Different Dog Foods

Indian meal moths (IMM), Plodiainterpuntella, are persistent pests to our foods (Fasulo et al.1998; Plunkett’s Pest Control 2018). When IMMs infest a a food product the resulting value loss is the result of contamination by larvae that leave droppings and silken webs in grain and grain products (Jacob and Calvin 2001). The IMM is an important pest of high-value dog foods and the grain components of these food may influence their infestation. Experiments were conducted with eggs of the IMM to determine if moth larvae would choose and infest the grain-based dog food in comparison to dog foods with a higher meat content. IMM laboratory rearing diet was included for comparison. No-choice and choice tests confirmed the IMM diet to be the most preferred and best for larval development. Forced infestation of 50 IMM eggs on the four different dog foods found difference among them. In two-choice test that require newly hatched larvae to walk to and infest either lab diet or a dog food, the highest proportion of larvae selecting any of the dog foods was on product C, which was a medium quality, grain-free food. These results suggest that IMM infestations in warehouses or consumer’s homes could be prevalent on some dog foods more than others

Self-Consistent Cosmological Simulations of DGP Braneworld Gravity

We perform cosmological N-body simulations of the Dvali-Gabadadze-Porrati braneworld model, by solving the full non-linear equations of motion for the scalar degree of freedom in this model, the brane bending mode. While coupling universally to matter, the brane-bending mode has self-interactions that become important as soon as the density field becomes non-linear. These self-interactions lead to a suppression of the field in high-density environments, and restore gravity to General Relativity. The code uses a multi-grid relaxation scheme to solve the non-linear field equation in the quasi-static approximation. We perform simulations of a flat self-accelerating DGP model without cosmological constant. The results of the DGP simulations are compared with standard gravity simulations assuming the same expansion history, and with DGP simulations using the linearized equation for the brane bending mode. This allows us to isolate the effects of the non-linear self-couplings of the field which are noticeable already on quasi-linear scales. We present results on the matter power spectrum and the halo mass function, and discuss the behavior of the brane bending mode within cosmological structure formation. We find that, independently of CMB constraints, the self-accelerating DGP model is strongly constrained by current weak lensing and cluster abundance measurements.Comment: 21 pages; 10 figures. Revised version matching published versio

Thermonuclear explosions of rapidly rotating white dwarfs - I. Deflagrations

Context: Turbulent deflagrations of Chandrasekhar mass White Dwarfs are commonly used to model Type Ia Supernova explosions. In this context, rapid rotation of the progenitor star is plausible but has so far been neglected. Aims: The aim of this work is to explore the influence of rapid rotation on the deflagration scenario. Methods: We use three dimensional hydrodynamical simulations to model turbulent deflagrations ignited within a variety of rapidly rotating CO WDs obeying rotation laws suggested by accretion studies. Results: We find that rotation has a significant impact on the explosion. The flame develops a strong anisotropy with a preferred direction towards the stellar poles, leaving great amounts of unburnt matter along the equatorial plane. Conclusions: The large amount of unburnt matter is contrary to observed spectral features of SNe Ia. Thus, rapid rotation of the progenitor star and the deflagration scenario are incompatible in order to explain SNe Ia.Comment: 13 pages, 10 figures, accepted for publication by A&

Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory

An overview of several recent developments in density functional theory for classical inhomogeneous liquids is given. We show how Levy's constrained search method can be used to derive the variational principle that underlies density functional theory. An advantage of the method is that the Helmholtz free energy as a functional of a trial one-body density is given as an explicit expression, without reference to an external potential as is the case in the standard Mermin-Evans proof by reductio ad absurdum. We show how to generalize the approach in order to express the internal energy as a functional of the one-body density distribution and of the local entropy distribution. Here the local chemical potential and the bulk temperature play the role of Lagrange multipliers in the Euler-Lagrange equations for minimiziation of the functional. As an explicit approximation for the free-energy functional for hard sphere mixtures, the diagrammatic structure of Rosenfeld's fundamental measure density unctional is laid out. Recent extensions, based on the Kierlik-Rosinberg scalar weight functions, to binary and ternary non-additive hard sphere mixtures are described.Comment: 15 pages, 6 figure

Intranasal insulin to improve developmental delay in children with 22q13 deletion syndrome: an exploratory clinical trial

Background: The 22q13 deletion syndrome (Phelan– McDermid syndrome) is characterised by a global developmental delay, absent or delayed speech, generalised hypotonia, autistic behaviour and characteristic phenotypic features. Intranasal insulin has been shown to improve declarative memory in healthy adult subjects and in patients with Alzheimer disease. Aims: To assess if intranasal insulin is also able to improve the developmental delay in children with 22q13 deletion syndrome. Methods: We performed exploratory clinical trials in six children with 22q13 deletion syndrome who received intranasal insulin over a period of 1 year. Short-term (during the first 6 weeks) and long-term effects (after 12 months of treatment) on motor skills, cognitive functions, or autonomous functions, speech and communication, emotional state, social behaviour, behavioural disorders, independence in daily living and education were assessed. Results: The children showed marked short-term improvements in gross and fine motor activities, cognitive functions and educational level. Positive long-term effects were found for fine and gross motor activities, nonverbal communication, cognitive functions and autonomy. Possible side effects were found in one patient who displayed changes in balance, extreme sensitivity to touch and general loss of interest. One patient complained of intermittent nose bleeding. Conclusions: We conclude that long-term administration of intranasal insulin may benefit motor development, cognitive functions and spontaneous activity in children with 22q13 deletion syndrome