220 research outputs found
Measuring subdiffusion parameters
We propose a method to extract from experimental data the subdiffusion
parameter and subdiffusion coefficient which are defined by
means of the relation where
denotes a mean square displacement of a random walker starting from
at the initial time . The method exploits a membrane system where a
substance of interest is transported in a solvent from one vessel to another
across a thin membrane which plays here only an auxiliary role. Using such a
system, we experimentally study a diffusion of glucose and sucrose in a gel
solvent. We find a fully analytic solution of the fractional subdiffusion
equation with the initial and boundary conditions representing the system under
study. Confronting the experimental data with the derived formulas, we show a
subdiffusive character of the sugar transport in gel solvent. We precisely
determine the parameter , which is smaller than 1, and the subdiffusion
coefficient .Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.
Simplified Kripke style semantics for some very weak modal logics
In the present paper we examine very weak modal logics C1, D1, E1, S0.5◦, S0.5◦+(D), S0.5 and some of their versions which are closed under replacement of tautological equivalents (rte-versions). We give semantics for these logics, formulated by means of Kripke style models of the form , where w is a «distinguished» world, A is a set of worlds which are alternatives to w, and V is a valuation which for formulae and worlds assigns the truth-vales such that: (i) for all formulae and all worlds, V preserves classical conditions for truth-value operators; (ii) for the world w and any formula ϕ, V(⬜ϕ,w) = 1 iff ∀x∈A V(ϕ,x) = 1; (iii) for other worlds formula ⬜ϕ has an arbitrary value. Moreover, for rte-versions of considered logics we must add the following condition: (iv) V(⬜χ,w) = V(⬜χ[ϕ/ψ],w), if ϕ and ψ are tautological equivalent. Finally, for C1, D1and E1 we must add queer models of the form in which: (i) holds and (ii') V(⬜ϕ,w) = 0, for any formula ϕ. We prove that considered logics are determined by some classes of above models
Complex Reaction Kinetics in Chemistry: A unified picture suggested by Mechanics in Physics
Complex biochemical pathways or regulatory enzyme kinetics can be reduced to
chains of elementary reactions, which can be described in terms of chemical
kinetics. This discipline provides a set of tools for quantifying and
understanding the dialogue between reactants, whose framing into a solid and
consistent mathematical description is of pivotal importance in the growing
field of biotechnology. Among the elementary reactions so far extensively
investigated, we recall the socalled Michaelis-Menten scheme and the Hill
positive-cooperative kinetics, which apply to molecular binding and are
characterized by the absence and the presence, respectively, of cooperative
interactions between binding sites, giving rise to qualitative different
phenomenologies. However, there is evidence of reactions displaying a more
complex, and by far less understood, pattern: these follow the
positive-cooperative scenario at small substrate concentration, yet
negative-cooperative effects emerge and get stronger as the substrate
concentration is increased. In this paper we analyze the structural analogy
between the mathematical backbone of (classical) reaction kinetics in Chemistry
and that of (classical) mechanics in Physics: techniques and results from the
latter shall be used to infer properties on the former
Effects of topological constraints on globular polymers
Topological constraints can affect both equilibrium and dynamic properties of
polymer systems, and can play a role in the organization of chromosomes.
Despite many theoretical studies, the effects of topological constraints on the
equilibrium state of a single compact polymer have not been systematically
studied. Here we use simulations to address this longstanding problem. We find
that sufficiently long unknotted polymers differ from knotted ones in the
spatial and topological states of their subchains. The unknotted globule has
subchains that are mostly unknotted and form asymptotically compact crumples. However, crumples display high fractal dimension of the
surface , forming excessive contacts and interpenetrating each
other. We conclude that this topologically constrained equilibrium state
resembles a conjectured crumpled globule [Grosberg et al., Journal de Physique,
1988, 49, 2095], but differs from its idealized hierarchy of self-similar,
isolated and compact crumples
Rationalization and Design of the Complementarity Determining Region Sequences in an Antibody-Antigen Recognition Interface
Protein-protein interactions are critical determinants in biological systems. Engineered proteins binding to specific areas on protein surfaces could lead to therapeutics or diagnostics for treating diseases in humans. But designing epitope-specific protein-protein interactions with computational atomistic interaction free energy remains a difficult challenge. Here we show that, with the antibody-VEGF (vascular endothelial growth factor) interaction as a model system, the experimentally observed amino acid preferences in the antibody-antigen interface can be rationalized with 3-dimensional distributions of interacting atoms derived from the database of protein structures. Machine learning models established on the rationalization can be generalized to design amino acid preferences in antibody-antigen interfaces, for which the experimental validations are tractable with current high throughput synthetic antibody display technologies. Leave-one-out cross validation on the benchmark system yielded the accuracy, precision, recall (sensitivity) and specificity of the overall binary predictions to be 0.69, 0.45, 0.63, and 0.71 respectively, and the overall Matthews correlation coefficient of the 20 amino acid types in the 24 interface CDR positions was 0.312. The structure-based computational antibody design methodology was further tested with other antibodies binding to VEGF. The results indicate that the methodology could provide alternatives to the current antibody technologies based on animal immune systems in engineering therapeutic and diagnostic antibodies against predetermined antigen epitopes
What is Socialism Today? Conceptions of a Cooperative Economy
Socialism is back on the political agenda in the United States. Politicians and some economists who identify as socialists, however, do not discuss property relations, a topic that was central in the intellectual history of socialism, but rather limit themselves to advocacy of economic reforms, funded through taxation, that would tilt the income distribution in favor of the disadvantaged in society. In the absence of a more precise discussion of property relations, the presumption must be that ownership of firms would remain private or corporate with privately owned shares. This formula is identified with the Nordic and other western European social democracies. In this article, I propose several variants of socialism, which are characterized by different kinds of property relation in the ownership of society’s firms. In addition to varying property relations, I include as part of socialism a conception of what it means for a socialist society to possess a cooperative ethos, in place of the individualistic ethos of capitalist society. Differences in ethea are modeled as differences in the manner in which economic agents optimize. With an individualistic ethos, economic agents optimize in the manner of John Nash, while under a cooperative ethos, many optimize in the manner of Immanuel Kant. It is shown that Kantian optimization can decentralize resource allocation in ways that neatly separate issues of income distribution from those of efficiency. In particular, remuneration of labor and capital contributions to production need no longer be linked to marginal-product pricing of these factors, as is the key to efficiency with capitalist property relations. I present simulations of socialist income distributions, and offer some tentative conclusions concerning how we should conceive of socialism today
Effects of activator treatment - evidence for the occurrence of two different types of reaction
A longitudinal cephalometric study was made of 12 boys and 13 girls with Class 11, Division 1 malocclusion treated with activators. The findings were compared with an untreated control group of 24 boys and 15 girls. The children were aged about 9 years at the start of the investigation and they were treated, or observed, for about two years. Possible alterations of mandibular condylar growth were investigated and the results were compared with previously published hypotheses on the mode of action of the activator. Since there were significant differences in the growth increments of control boys and control girls, the sexes were treated statistically as separate groups. Mandibular growth was found to be altered by activator therapy; in the boys growth was increased and redirected posteriorly while in the girls growth was only redirected. The maxilla and the dental arches were differently affected by the treatment. The differences in the observed results are probably explained by variation in the amount of vertical activation of the appliance but the possibility that boys and girls generally react differently could not be excluded. It is also possible that at least some of the differences were due to special growth patterns associated with certain features in the initial cephalometric pattern. There was no indication that modes of appliance action led to the different reactions. The results as a whole support the concept of the activator as an appliance which transduces elastic soft tissue forces to the skeletal and dental unit
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