Detaching embedded points

We show that if $D \subset \mathbb P^N$ is obtained from a codimension two local complete intersection $C$ by adding embedded points of multiplicity $\leq 3$, then $D$ is a flat limit of $C$ and isolated points. As applications, we determine the irreducible components of Hilbert schemes of space curves with high arithmetic genus, show the smoothness of the Hilbert component whose general member is a plane curve union a point in $\mathbb P^3$, and construct a Hilbert component whose general member has an embedded point.Comment: 16 pages, amsart style. New examples added to show that hypotheses of main theorem are necessary, showing sharpness of resul

A structured argumentation framework for detaching conditional obligations

We present a general formal argumentation system for dealing with the detachment of conditional obligations. Given a set of facts, constraints, and conditional obligations, we answer the question whether an unconditional obligation is detachable by considering reasons for and against its detachment. For the evaluation of arguments in favor of detaching obligations we use a Dung-style argumentation-theoretical semantics. We illustrate the modularity of the general framework by considering some extensions, and we compare the framework to some related approaches from the literature.Comment: This is our submission to DEON 2016, including the technical appendi

Generalized Model of Migration-Driven Aggregate Growth - Asymptotic Distributions, Power Laws and Apparent Fractality

The rate equation for exchange-driven aggregation of monomers between clusters of size $n$ by power-law exchange rate ($\sim{n}^\alpha$), where detaching and attaching processes were considered separately, is reduced to Fokker-Planck equation. Its exact solution was found for unbiased aggregation and agreed with asymptotic conclusions of other models. Asymptotic transitions were found from exact solution to Weibull/normal/exponential distribution, and then to power law distribution. Intermediate asymptotic size distributions were found to be functions of exponent $\alpha$ and vary from normal ($\alpha=0$) through Weibull ($0<\alpha<1$) to exponential ($\alpha=1$) ones, that gives the new system for linking these basic statistical distributions. Simulations were performed for the unbiased aggregation model on the basis of the initial rate equation without simplifications used for reduction to Fokker-Planck equation. The exact solution was confirmed, shape and scale parameters of Weibull distribution (for $0<\alpha<1$) were determined by analysis of cumulative distribution functions and mean cluster sizes, which are of great interest, because they can be measured in experiments and allow to identify details of aggregation kinetics (like $\alpha$). In practical sense, scaling analysis of \emph{evolving series} of aggregating cluster distributions can give much more reliable estimations of their parameters than analysis of \emph{solitary} distributions. It is assumed that some apparent power and fractal laws observed experimentally may be manifestations of such simple migration-driven aggregation kinetics even.Comment: 11 pages, 7 figure

Transcription factor search for a DNA promoter in a three-states model

To ensure fast gene activation, Transcription Factors (TF) use a mechanism known as facilitated diffusion to find their DNA promoter site. Here we analyze such a process where a TF alternates between 3D and 1D diffusion. In the latter (TF bound to the DNA), the TF further switches between a fast translocation state dominated by interaction with the DNA backbone, and a slow examination state where interaction with DNA base pairs is predominant. We derive a new formula for the mean search time, and show that it is faster and less sensitive to the binding energy fluctuations compared to the case of a single sliding state. We find that for an optimal search, the time spent bound to the DNA is larger compared to the 3D time in the nucleus, in agreement with recent experimental data. Our results further suggest that modifying switching via phosphorylation or methylation of the TF or the DNA can efficiently regulate transcription.Comment: 4 pages, 3 figure

Generalized rabinowicz’ criterion for adhesive wear for elliptic micro contacts

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in AIP Conference Proceedings 1909, 020178 (2017) and may be found at https://doi.org/10.1063/1.5013859.This paper is devoted to an old idea suggested in 1958 by E. Rabinowicz in his paper “The effect of size on the looseness of wear fragments”. Rabinowicz assumed a circular shape for two asperities coming into contact and being destroyed due to relative sliding. We generalize his analysis for the case of non-circular contacts, in particular those having elliptical shape and discuss the general case of arbitrary contact shape