Divide and color representations for threshold Gaussian and stable vectors

We study the question of when a (\{0,1\})-valued threshold process associated to a mean zero Gaussian or a symmetric stable vector corresponds to a {\it divide and color (DC) process}. This means that the process corresponding to fixing a threshold level $h$ and letting a 1 correspond to the variable being larger than $h$ arises from a random partition of the index set followed by coloring {\it all} elements in each partition element 1 or 0 with probabilities $p$ and $1-p$, independently for different partition elements. While it turns out that all discrete Gaussian free fields yield a DC process when the threshold is zero, for general $n$-dimensional mean zero, variance one Gaussian vectors with nonnegative covariances, this is true in general when $n=3$ but is false for $n=4$. The behavior is quite different depending on whether the threshold level $h$ is zero or not and we show that there is no general monotonicity in $h$ in either direction. We also show that all constant variance discrete Gaussian free fields with a finite number of variables yield DC processes for large thresholds. In the stable case, for the simplest nontrivial symmetric stable vector with three variables, we obtain a phase transition in the stability exponent $\alpha$ at the surprising value of $1/2$; if the index of stability is larger than $1/2$, then the process yields a DC process for large $h$ while if the index of stability is smaller than $1/2$, then this is not the case.Comment: 51 pages, 6 figures This paper together with arXiv:1911.00513, arXiv:1910.09813 and arXiv:1909.11322 replace the first version of this pape

Dynamic Evolution of Precise Regulatory Encodings Creates the Clustered Site Signature of Enhancers

Concentration gradients of morphogenic proteins pattern the embryonic axes of Drosophila by activating different genes at different concentrations. The neurogenic ectoderm enhancers (NEEs) activate different genes at different threshold levels of the Dorsal (Dl) morphogen, which patterns the dorsal/ventral axis. NEEs share a unique arrangement of highly constrained DNA-binding sites for Dl, Twist (Twi), Snail (Sna) and Suppressor of Hairless (Su(H)), and encode the threshold variable in the precise length of DNA that separates one well-defined Dl element from a Twi element. However, NEEs also possess dense clusters of variant Dl sites. Here, we show that these increasingly variant sites are eclipsed relic elements, which were superseded by more recently evolved threshold encodings. Given the divergence in egg size during Drosophila lineage evolution, the observed characteristic clusters of divergent sites indicate a history of frequent selection for changes in threshold responses to the Dl morphogen gradient and confirm the NEE structure/function model

Dynamic Evolution of Precise Regulatory Encodings Creates the Clustered Site Signature of Enhancers

Concentration gradients of morphogenic proteins pattern the embryonic axes of Drosophila by activating different genes at different concentrations. The neurogenic ectoderm enhancers (NEEs) activate different genes at different threshold levels of the Dorsal (Dl) morphogen, which patterns the dorsal/ventral axis. NEEs share a unique arrangement of highly constrained DNA-binding sites for Dl, Twist (Twi), Snail (Sna) and Suppressor of Hairless (Su(H)), and encode the threshold variable in the precise length of DNA that separates one well-defined Dl element from a Twi element. However, NEEs also possess dense clusters of variant Dl sites. Here, we show that these increasingly variant sites are eclipsed relic elements, which were superseded by more recently evolved threshold encodings. Given the divergence in egg size during Drosophila lineage evolution, the observed characteristic clusters of divergent sites indicate a history of frequent selection for changes in threshold responses to the Dl morphogen gradient and confirm the NEE structure/function model

Level statistics and localization in a 2D quantum percolation problem

A two dimensional model for quantum percolation with variable tunneling range is studied. For this purpose the Lifshitz model is considered where the disorder enters the Hamiltonian via the nondiagonal elements. We employ a numerical method to analyze the level statistics of this model. It turns out that the level repulsion is strongest around the percolation threshold. As we go away from the maximum level repulsion a crossover from a GOE type behavior to a Poisson like distribution is indicated. The localization properties are calculated by using the sensitivity to boundary conditions and we find a strong crossover from localized to delocalized states.Comment: 4 pages, 4 figure

Variable Flavor Number Scheme for Final State Jets

We discuss a variable flavor number scheme (VFNS) for final state jets which can account for the effects of arbitrary finite quark masses in inclusive jet observables. The scheme is a generalization of the VFNS scheme for PDFs applied to setups with additional dynamical scales and relies on appropriate renormalization conditions for the matrix elements in the factorization theorem. We illustrate general properties by means of the example of deep-inelastic scattering (DIS) in the endpoint region $x\rightarrow 1$ and event shapes in the dijet limit, in particular the calculations of threshold corrections, consistency conditions and relations to mass singularities found in fixed-order massive calculations.Comment: 7 pages, 4 figures, Proceedings of the XXII. International Workshop on Deep-Inelastic Scattering and Related Subjects, 28 April - 2 May 2014, Warsaw, Polan

A P wave-based, on-site method for earthquake early warning

A new strategy for a P wave-based, on-site earthquake early warning system has been developed and tested on Japanese strong motion data. The key elements are the real-time, continuous measurement of three peak amplitude parameters and their empirical combination to predict the ensuing peak ground velocity. The observed parameters are compared to threshold values and converted into a single, dimensionless variable. A local alert level is issued as soon as the empirical combination exceeds a given threshold. The performance of the method has been evaluated by applying the approach to the catalog of Japanese earthquake records and counting the relative percentage of successful, missed, and false alarms. We show that the joint use of three peak amplitude parameters improves the performance of the system as compared to the use of a single parameter, with a relative increase of successful alarms of about 35%. The proposed methodology provides a more reliable prediction of the expected ground shaking and improves the robustness of a single-station, threshold-based earthquake early warning system

Fast Projection onto the Simplex and the l1 Ball

International audienceA new algorithm is proposed to project, exactly and in finite time, a vector of arbitrary size onto a simplex or an l1-norm ball. It can be viewed as a Gauss-Seidel-like variant of Michelot’s variable fixing algorithm; that is, the threshold used to fix the variables is updated after each element is read, instead of waiting for a full reading pass over the list of non-fixed elements. This algorithm is empirically demonstrated to be faster than existing methods

Research on variable threshold transistor storage systems

A fully integrated, electrically alterable, nonvolatile, nondestructive readout control memory was developed, using as storage elements metal-nitride-silicon variable threshold transistors. An optimum approach to such a memory was developed in which a three dimensional selection technique was used, both for read and write operations. Electrical isolation of writing and memory circuits was obtained by means of separate memory and write circuit chips. This method provided protection from voltage breakdowns, increased circuit flexibility, and greater ease of testing of interim and final circuit elements

A resilience checklist to evaluate coastal dune vulnerability

The aim of the proposed resilience checklist is to easily evaluate foredune vulnerability when applied to management. It focus on: (i) the definition of the level of pressure for each use in relation to the foredune resilience threshold, (ii) the direct identification of the system components more vulnerable and (iii) the recognition of management readjustments needed, in order to prevent or minimise impacts. The resilience checklist structure is based on a selection of relevant coastal dune vulnerability descriptors, giving information about the system sensitivity and resilience. All variables selected describe observable signs of foredune degradation or regeneration and are related to system elements susceptible of receiving management intervention. hree major degrees of biophysical vulnerability are recognised: a) Degree 0 - low sensitivity and resilience threshold not exceeded; b) Degree 1 - variable sensitivity and at the resilience threshold; c) Degree 2- high sensitivity and resilience threshold exceeded. Each degree takes into account the system’s level of degradation and the corresponding desirable level of conservation. The application example- Mira’s beach southern sector- is a site under a very high summer pressure (seaside recreation and tourism). Three management phases were monitored, between 1996 and 1998. Checklist results show dune management inefficiency and an ineffective sand retention by vegetation as determinants to this foredune site vulnerability and that a planting program is still in need. However, a clear vulnerability decrease in this site was recognised.info:eu-repo/semantics/publishedVersio