Discontinuous

Discontinuous

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In this issue, Géraud et al. provide important insight into the transcriptional regulation of discontinuous liver sinusoid morphology (11). This group had previously determined that the transcription factor GATA4 is enriched in rat liver sinusoidal endothelial cells (LSECs) compared with rat lung microvascular endothelial cells (LMECs) (12). Géraud and colleagues have now employed transgenic mouse lines to define the function of GATA4 in murine LSECs (11). Specifically, they developed a line of mice harboring Cre driven by the stabilin 2 (Stab2) promoter (Stab2-Cre), which is expressed in mature LSECs (11), and exploited an existing Lyve1-Cre line (13), which is active in embryonic LSECs (14). Deletion of a floxed Gata4 allele in either line resulted in mutant embryos with hypoplastic livers, anemia, and prenatal lethality (11). Unlike the liver, other organs were not obviously affected by Gata4 deletion in either the Stab2-Cre or Lyve1-Cre line (11). GATA4-deficient livers exhibited microvessels with features of continuous capillaries rather than those of discontinuous sinusoids seen in WT livers (11). In particular, upregulation of endothelial cell junction proteins (CD31 and VE-cadherin) on LSECs was observed by immunostaining, and a more robust basement membrane was detected by electron microscopy and by immunostaining for extracellular matrix components (11). No effect of Gata4 deletion on LSEC fenestrae was reported, but it would be interesting to know whether this transcription factor affects the number or size of fenestrae or the presence of a diaphragm on the pores. As LSECs are highly endocytic (15), it would also be informative to know whether GATA4 impacts endocytic vesicle density on embryonic LSECs.

Géraud et al. also exploited primary rat LSECs and LMECs to establish a transcriptional profile for discontinuous and continuous capillaries, respectively (11). As rodent LSECs rapidly de-differentiate in culture, precluding knockdown or overexpression studies, Géraud and colleagues manipulated GATA4 expression in human umbilical vein endothelial cells (HUVECs), which are transcriptionally similar to continuous LMECs (11). Upon GATA4 overexpression, HUVECs acquired a transcriptional profile more similar to discontinuous LSECs, indicating that GATA4 can promote a discontinuous LSEC gene program across species and in different endothelial cell types (11).

Genetic deletion of the transcription factor Gata4 from liver sinusoidal endothelial cells (LSECs) causes upregulation of endothelial cell junction proteins and robust deposition of basement membrane proteins that prevent circulating hematopoietic progenitor or stem cells from colonizing the fetal liver (11). The consequences of this transition from discontinuous sinusoidal to continuous capillary morphology are liver hypoplasia, anemia, and lethality of Gata4 mutant embryos (11).

Another interesting question is whether GATA4 is important for the maintenance of discontinuous liver sinusoids once they are established, as Géraud and colleagues demonstrated that GATA4 is expressed in adult murine, rat, and human LSECs (11). An inducible Stab2-Cre or Lyve1-Cre line would help address the temporal influence of GATA4 over discontinuous hepatic sinusoidal characteristics. Such lines could also clarify whether GATA4 and discontinuous sinusoids are required for differentiated blood cells to egress from the fetal liver and reenter the circulation. Macrophage precursors require diaphragms on LSEC fenestrae for this egression process (9), but a robust basement membrane may serve as a critical impediment, even in the presence of diaphragmed fenestrae. An inducible Stab2-Cre line might also help clarify whether GATA4 promotes discontinuous sinusoidal development in other organs, such as the bone marrow and spleen, which undergo colonization by hematopoietic stem cells later in development (7). Géraud and colleagues report that GATA4 is not expressed on STAB2-positive endothelial cells in adult bone marrow and spleen (11), but whether it contributes to the initial development of those sinusoids is an open question. If GATA4 does not contribute to discontinuous sinusoidal development in these hematopoietic organs, identifying other transcription factors that act in lieu of GATA4 will clarify the organ-specific derivation of sinusoidal vessels.

For each of the following, consider a real valued function f {\displaystyle f} of a real variable x , {\displaystyle x,} defined in a neighborhood of the point x 0 {\displaystyle x_{0}} at which f {\displaystyle f} is discontinuous.

Thomae's function is discontinuous at every non-zero rational point, but continuous at every irrational point. One easily sees that those discontinuities are all essential of the first kind, that is E 1 = Q . {\displaystyle E_{1}=\mathbb {Q} .} By the first paragraph, there does not exist a function that is continuous at every rational point, but discontinuous at every irrational point.

We have collected cases of discontinuous technological progress to inform our understanding of whether artificial intelligence performance is likely to undergo such a discontinuity. This page details our investigation.

We are interested in learning whether artificial intelligence is likely to see discontinuous progress in the lead-up to human-level capabilities, or to produce discontinuous change in any other socially important metrics (e.g. percent of global wealth possessed by a single entity, economic value of hardware). We are interested because we think this informs us about the plausibility of different future scenarios and about which research and other interventions are best now, and also because it is a source of disagreement, and so perhaps fruitful for resolution.1We seek to answer this question by investigating the prevalence and nature of discontinuities in other technological progress trends. The prevalence can then act as a baseline for our expectations about AI, which can be updated with any further AI-specific evidence, including that which comes from looking at the nature of other discontinuities (for instance, whether they arise in circumstances that are predicted by the arguments that are made for predicting discontinuous progress in AI).

As a secondary goal, we are interested in learning about the circumstances that have surrounded discontinuous technological change in the past, insofar as it may inform our expectations about the consequences of discontinuous progress in AI, should it happen.

This is a list of areas of technological progress which we have tentatively determined to either involve discontinuous technological progress, or not. Note that we largely investigate cases that looked likely to be discontinuous.

High impact epidemics constitute one of the largest threats humanity is facing in the 21st century. In the absence of pharmaceutical interventions, physical distancing together with testing, contact tracing and quarantining are crucial in slowing down epidemic dynamics. Yet, here we show that if testing capacities are limited, containment may fail dramatically because such combined countermeasures drastically change the rules of the epidemic transition: Instead of continuous, the response to countermeasures becomes discontinuous. Rather than following the conventional exponential growth, the outbreak that is initially strongly suppressed eventually accelerates and scales faster than exponential during an explosive growth period. As a consequence, containment measures either suffice to stop the outbreak at low total case numbers or fail catastrophically if marginally too weak, thus implying large uncertainties in reliably estimating overall epidemic dynamics, both during initial phases and during second wave scenarios.

Researchers and policy makers often implicitly assume that the peak, i.e., the largest fraction of simultaneously infected individuals, continuously varies with epidemic parameters and with the level of countermeasures implemented. In this article, we demonstrate that this fundamental assumption is incorrect once testing resources are limited. We reveal that the nature of the epidemic dynamics changes drastically from this naive picture and has unexpected, severe consequences. In particular, limited testing generically yields a discontinuous transition in the fraction of infected individuals in a population, a phenomenon dynamically accompanied by an interval of faster than exponential growth. Similar to related types of phase transitions in statistical physics such as discontinuous or explosive percolation transitions5,6,7,8, limited testing effectively delays the transition, such that the fraction of infected individuals explosively becomes macroscopically large once effective epidemic parameters even only marginally cross a threshold. As a consequence, in the presence of limited testing, slight changes in countermeasures may induce huge macroscopic changes in the fraction of infected individuals, severely restricting the predictability of the epidemic transition. Discontinuous epidemic transitions have previously been pointed out in the context of limited vaccination supplies9, limited control10, and limited resources11.

Cannon discontinuous panel production stations and lines for insulated panels are the result of the 20 years technological successful partnership between Cannon expertise in PU/PIR dosing and foaming and Manni presses production capabilities.

The discontinuous production process is the best fitting one in many situations: tailor made shapes, different thickness, low volume production, very variable production mix for dimensions and geometry, introduction of inserts, need of high level of finishing or of frames on more than two sides, special shapes to avoid cold bridge in joining, as for corner panels.

After spending a tremendous amount of time digging, I believe the chngpt package is the way to go. It can do both continuous and discontinuous segmented regressions. Link here: -project.org/web/packages/chngpt/vignettes/chngpt-vignette.pdf 2b1af7f3a8