Classical logic, continuation semantics and abstract machines

One of the goals of this paper is to demonstrate that denotational semantics is useful for operational issues like implementation of functional languages by abstract machines. This is exemplified in a tutorial way by studying the case of extensional untyped call-by-name λ-calculus with Felleisen's control operator 𝒞. We derive the transition rules for an abstract machine from a continuation semantics which appears as a generalization of the ¬¬-translation known from logic. The resulting abstract machine appears as an extension of Krivine's machine implementing head reduction. Though the result, namely Krivine's machine, is well known our method of deriving it from continuation semantics is new and applicable to other languages (as e.g. call-by-value variants). Further new results are that Scott's D∞-models are all instances of continuation models. Moreover, we extend our continuation semantics to Parigot's λμ-calculus from which we derive an extension of Krivine's machine for λμ-calculus. The relation between continuation semantics and the abstract machines is made precise by proving computational adequacy results employing an elegant method introduced by Pitts

Where the linearized Poisson-Boltzmann cell model fails: (I) spurious phase separation in charged colloidal suspensions

We perform a linearization of the Poisson-Boltzmann (PB) density functional for spherical Wigner-Seitz cells that yields Debye-H\"uckel-like equations agreeing asymptotically with the PB results in the weak-coupling (high-temperature) limit. Both the canonical (fixed number of microions) as well as the semi-grand-canonical (in contact with an infinite salt reservoir) cases are considered and discussed in a unified linearized framework. In the canonical case, for sufficiently large colloidal charges the linearized theory predicts the occurrence of a thermodynamical instability with an associated phase separation of the homogeneous suspension into dilute (gas) and dense (liquid) phases. In the semi-grand-canonical case it is predicted that the isothermal compressibility and the osmotic-pressure difference between the colloidal suspension and the salt reservoir become negative in the low-temperature, high-surface charge or infinite-dilution (of polyions) limits. As already pointed out in the literature for the latter case, these features are in disagreement with the exact nonlinear PB solution inside a Wigner-Seitz cell and are thus artifacts of the linearization. By using explicitly gauge-invariant forms of the electrostatic potential we show that these artifacts, although thermodynamically consistent with quadratic expansions of the nonlinear functional and osmotic pressure, may be traced back to the non-fulfillment of the underlying assumptions of the linearization.Comment: 32 pages, 3 PostScript figures, submitted to J. Chem. Phy

Contribution of common and rare variants to bipolar disorder susceptibility in extended pedigrees from population isolates.

Current evidence from case/control studies indicates that genetic risk for psychiatric disorders derives primarily from numerous common variants, each with a small phenotypic impact. The literature describing apparent segregation of bipolar disorder (BP) in numerous multigenerational pedigrees suggests that, in such families, large-effect inherited variants might play a greater role. To identify roles of rare and common variants on BP, we conducted genetic analyses in 26 Colombia and Costa Rica pedigrees ascertained for bipolar disorder 1 (BP1), the most severe and heritable form of BP. In these pedigrees, we performed microarray SNP genotyping of 838 individuals and high-coverage whole-genome sequencing of 449 individuals. We compared polygenic risk scores (PRS), estimated using the latest BP1 genome-wide association study (GWAS) summary statistics, between BP1 individuals and related controls. We also evaluated whether BP1 individuals had a higher burden of rare deleterious single-nucleotide variants (SNVs) and rare copy number variants (CNVs) in a set of genes related to BP1. We found that compared with unaffected relatives, BP1 individuals had higher PRS estimated from BP1 GWAS statistics (P = 0.001 ~ 0.007) and displayed modest increase in burdens of rare deleterious SNVs (P = 0.047) and rare CNVs (P = 0.002 ~ 0.033) in genes related to BP1. We did not observe rare variants segregating in the pedigrees. These results suggest that small-to-moderate effect rare and common variants are more likely to contribute to BP1 risk in these extended pedigrees than a few large-effect rare variants

Exploring elite soccer teams’ performances during different match-status periods of close matches’ comebacks

The aim of the present study was to examine winning and losing teams’ performances during the four different match-status periods that occur in close soccer matches’ comebacks (1° drawing; 2° winning/losing; 3° drawing; and 4° losing/winning). The variables (i.e., shots, passing effectiveness and ball possession) were gathered from 17 matches of the Spanish professional soccer league. Relative-phase analysis of ball possession between teams revealed a shift from anti-phase to in-phase relations from period 1 to 4. Pass efficacy revealed a particular trend of anti-phase relations in period 2 and the analysis of shots revealed similar phase relations between periods. Statistically significant differences were observed between winning and losing teams in Period 3 for ball possession and passing effectiveness. Also, statistically significant differences among periods were observed for winning teams in ball possession with period 4 as the most differentiated from the other periods. Besides, winning teams also showed significant differences between periods in passing effectiveness (period 4 vs 3), and in shots (period 3 vs periods 1, 2 and 4). On the other hand, ball possession showed significant differences for losing teams with periods 3 and 4 different than periods 1 and 2. The current findings can be used when controlling match-status scenarios and key performance indicators along the match

Effective Interactions and Volume Energies in Charged Colloids: Linear Response Theory

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out from the partition function the degrees of freedom of all microions, and assuming linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the DLVO screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy -- a natural consequence of the one-component reduction -- contributes to the total free energy and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.Comment: 14 pages, including 3 figure

On the fluid-fluid phase separation in charged-stabilized colloidal suspensions

We develop a thermodynamic description of particles held at a fixed surface potential. This system is of particular interest in view of the continuing controversy over the possibility of a fluid-fluid phase separation in aqueous colloidal suspensions with monovalent counterions. The condition of fixed surface potential allows in a natural way to account for the colloidal charge renormalization. In a first approach, we assess the importance of the so called ``volume terms'', and find that in the absence of salt, charge renormalization is sufficient to stabilize suspension against a fluid-fluid phase separation. Presence of salt, on the other hand, is found to lead to an instability. A very strong dependence on the approximations used, however, puts the reality of this phase transition in a serious doubt. To further understand the nature of the instability we next study a Jellium-like approximation, which does not lead to a phase separation and produces a relatively accurate analytical equation of state for a deionized suspensions of highly charged colloidal spheres. A critical analysis of various theories of strongly asymmetric electrolytes is presented to asses their reliability as compared to the Monte Carlo simulations

The osmotic pressure of charged colloidal suspensions: A unified approach to linearized Poisson-Boltzmann theory

We study theoretically the osmotic pressure of a suspension of charged objects (e.g., colloids, polyelectrolytes, clay platelets, etc.) dialyzed against an electrolyte solution using the cell model and linear Poisson-Boltzmann (PB) theory. From the volume derivative of the grand potential functional of linear theory we obtain two novel expressions for the osmotic pressure in terms of the potential- or ion-profiles, neither of which coincides with the expression known from nonlinear PB theory, namely, the density of microions at the cell boundary. We show that the range of validity of linearization depends strongly on the linearization point and proof that expansion about the selfconsistently determined average potential is optimal in several respects. For instance, screening inside the suspension is automatically described by the actual ionic strength, resulting in the correct asymptotics at high colloid concentration. Together with the analytical solution of the linear PB equation for cell models of arbitrary dimension and electrolyte composition explicit and very general formulas for the osmotic pressure ensue. A comparison with nonlinear PB theory is provided. Our analysis also shows that whether or not linear theory predicts a phase separation depends crucially on the precise definition of the pressure, showing that an improper choice could predict an artificial phase separation in systems as important as DNA in physiological salt solution.Comment: 16 pages, 5 figures, REVTeX4 styl