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Register a new userWhat can be observed in real time PCR and when does it show?
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Real time, or quantitative, PCR typically starts from a very low concentration of initial DNA strands. During iterations the numbers increase, first essentially by doubling, later predominantly in a linear way. Observation of the number of DNA molecules in the experiment becomes possible only when it is substantially larger than initial numbers, and then possibly affected by the randomness in individual replication. Can the initial copy number still be determined? This is a classical problem and, indeed, a concrete special case of the general problem of determining the number of ancestors, mutants or invaders, of a population observed only later. We approach it through a generalised version of the branching process model introduced by Jagers and Klebaner, 2003 and based on Michaelis-Menten type enzyme kinetical considerations from Schnell and Mendoza, 1997. A crucial role is played by the Michaelis-Menten constant being large, as compared to initial copy numbers. In a strange way, determination of the initial number turns out to be completely possible if the initial rate $v$ is one, i.e all DNA strands replicate, but only partly so when $v<1$, and thus the initial rate or probability of successful replication is lower than one. Then, the starting molecule number becomes hidden behind a veil of uncertainty. This is a special case, of a hitherto unobserved general phenomenon in population growth processes, which will be addressed elsewhere.
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The concept of realism in quantum mechanics means that results of measurement are caused by physical variables, hidden or observable. Local hidden variables were proved unable to explain results of measurements on entangled particles tested far away from one another. Then, some physicists embraced the idea of nonlocal hidden variables. The present article proves that this idea is problematic, that it runs into an impasse vis-`a-vis the special relativity.
Numerous models for grounded language understanding have been recently proposed, including (i) generic models that can be easily adapted to any given task and (ii) intuitively appealing modular models that require background knowledge to be instantiated. We compare both types of models in how much they lend themselves to a particular form of systematic generalization. Using a synthetic VQA test, we evaluate which models are capable of reasoning about all possible object pairs after training on only a small subset of them. Our findings show that the generalization of modular models is much more systematic and that it is highly sensitive to the module layout, i.e. to how exactly the modules are connected. We furthermore investigate if modular models that generalize well could be made more end-to-end by learning their layout and parametrization. We find that end-to-end methods from prior work often learn inappropriate layouts or parametrizations that do not facilitate systematic generalization. Our results suggest that, in addition to modularity, systematic generalization in language understanding may require explicit regularizers or priors.
Models of language trained on very large corpora have been demonstrated useful for NLP. As fixed artifacts, they have become the object of intense study, with many researchers probing the extent to which linguistic abstractions, factual and commonsense knowledge, and reasoning abilities they acquire and readily demonstrate. Building on this line of work, we consider a new question: for types of knowledge a language model learns, when during (pre)training are they acquired? We plot probing performance across iterations, using RoBERTa as a case study. Among our findings: linguistic knowledge is acquired fast, stably, and robustly across domains. Facts and commonsense are slower and more domain-sensitive. Reasoning abilities are, in general, not stably acquired. As new datasets, pretraining protocols, and probes emerge, we believe that probing-across-time analyses can help researchers understand the complex, intermingled learning that these models undergo and guide us toward more efficient approaches that accomplish necessary learning faster.
While Bernoullis equation is one of the most frequently mentioned topics in Physics literature and other means of dissemination, it is also one of the least understood. Oddly enough, in the wonderful book Turning the world inside out [1], Robert Ehrlich proposes a demonstration that consists of blowing a quarter dollar coin into a cup, incorrectly explained using Bernoullis equation. In the present work, we have adapted the demonstration to show situations in which the coin jumps into the cup and others in which it does not, proving that the explanation based on Bernoullis is flawed. Our demonstration is useful to tackle the common misconception, stemming from the incorrect use of Bernoullis equation, that higher velocity invariably means lower pressure.
The development of neural networks and pretraining techniques has spawned many sentence-level tagging systems that achieved superior performance on typical benchmarks. However, a relatively less discussed topic is what if more context information is introduced into current top-scoring tagging systems. Although several existing works have attempted to shift tagging systems from sentence-level to document-level, there is still no consensus conclusion about when and why it works, which limits the applicability of the larger-context approach in tagging tasks. In this paper, instead of pursuing a state-of-the-art tagging system by architectural exploration, we focus on investigating when and why the larger-context training, as a general strategy, can work. To this end, we conduct a thorough comparative study on four proposed aggregators for context information collecting and present an attribute-aided evaluation method to interpret the improvement brought by larger-context training. Experimentally, we set up a testbed based on four tagging tasks and thirteen datasets. Hopefully, our preliminary observations can deepen the understanding of larger-context training and enlighten more follow-up works on the use of contextual information.
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