Linearity no-threshold theory

M = total mortality rate from lung cancer Mr = lung cancer mortality rate due to radon Mn = lung cancer mortality rate due to non-radon causes including smoking and all other factors, known or unknown r = average radon level in a county Then, from the linear-no threshold theory,... 

Eq.(l) is not valid, which means that the linear-no threshold theory fails, grossly over-predicting the cancer risk at low doses. 

My research eventually convinced me (and a great many others) that radon in homes is very much less harmful than the widely publicized estimates that were based on extrapolating from the number of excess cancers seen in uranium miners who had very high radon exposures. Those estimates were (and are) based on the assumption that the cancer risk from radiation is proportional to the dose, the so-called linear-no threshold theory (LNT). 

Radon Cohen, B.L., Test of the linear-no-threshold theory of radiation carcinogenesis for inhaled radon decay products. Health Physics, 68,157-174 (1990). 

The principal research goal of our project is to test the linear-no threshold dose-response theory for radon-induced lung cancer. This... 

One theory is based on the concept that growth occurs layer by layer on the crystal face, and that each new layer begins as a two-dimensional nucleus attached to the face. This theory predicts that growth does not start until an appreciable threshold supersaturation is reached and that the rate of growth then increases rapidly until, at some fairly high value of supersaturation, it becomes linear with supersaturation. Actually, the growth rate of most crystals is linear with supersaturation at all supersaturations, even at very low values. There seems to be no threshold value required. 

A "committee machine uses several different classifiers for the same classification problem in a parallel manner. The classifiers may stem e.g. from different training processes with the same training set. The results (scalar products) are summarized to give the final classification. Threshold logical units are usually applied and the majority of votes determines the class membership. Correct classification for all members of the training set may be obtained by a committee machine even if the data set is not Linearly separable. Unfortunately, no exhaustive theory about the training of several parallel classifiers exists. 

At this time a few comments about the model of Parilis et al. is appropriate. Their theory predicts that no kinetic emission can occur up to a certain threshold energy the yield then increases linearly with energy until at higher energy the slope again changes and the yield finally becomes linear with velocity. The majority of experimental results appear to confirm these trends suggesting that there is some truth in the basic assumptions. 

With the input intensity changing slowly, the hysteresis loop is well reproducible. The upward transition BC in Fig. 2 is much faster than the downward transition DA The switching times are up— 1 s and down—15 s, respectively. The observed threshold power for up transition at point B was Pth 110 mW. With a beam cross section of 5x 10 cm at the sample, the corresponding threshold intensity was 7th 2.2 kW/cm. This transition should result from the field-induced molecular reorientation usually known as the Freedericksz transition. We found that the observed threshold for a circularly polarized input beam was twice that for a linearly polarized input beam, as expected from theory." However, no polarization rotation of the output was observed in the latter case. 

We can clearly consider a laser to be strong when its intensity becomes comparable to (4.113). In this regime, perturbation theory is no longer applicable, and the theorist has to resort to non-perturbative methods. When approaching these high intensities, a wealth of non-linear phenomena appear, like multi-photon ionization, above threshold ionization (ATI), high harmonic generation, etc. 

The chatter theory determining the threshold of stability is linear and hence the superposition of two solutions is feasible. However, once chatter exists, the amplitudes are stabilised by nonlinearities and it is by no means obvious that these will permit the coexistence of two separate chatter frequencies. 

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