Perpendicular magnetic tunnel junction (pMTJ)-based true-random number generators (RNGs) can consume orders of magnitude less energy per bit than CMOS pseudo-RNGs. Here, we numerically investigate with a macrospin Landau–Lifshitz-Gilbert equation solver the use of pMTJs driven by spin–orbit torque to directly sample numbers from arbitrary probability distributions with the help of a tunable probability tree. The tree operates by dynamically biasing sequences of pMTJ relaxation events, called ‘coinflips’, via an additional applied spin-transfer-torque current. Specifically, using a single, ideal pMTJ device we successfully draw integer samples on the interval [0, 255] from an exponential distribution based on
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Abstract p -value distribution analysis. In order to investigate device-to-device variations, the thermal stability of the pMTJs are varied based on manufactured device data. It is found that while repeatedly using a varied device inhibits ability to recover the probability distribution, the device variations average out when considering the entire set of devices as a ‘bucket’ to agnostically draw random numbers from. Further, it is noted that the device variations most significantly impact the highest level of the probability tree, with diminishing errors at lower levels. The devices are then used to draw both uniformly and exponentially distributed numbers for the Monte Carlo computation of a problem from particle transport, showing excellent data fit with the analytical solution. Finally, the devices are benchmarked against CMOS and memristor RNGs, showing faster bit generation and significantly lower energy use. -
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Abstract Background and Aims CAM photosynthesis is hypothesized to have evolved in atmospheres of low CO2 concentration in recent geological time because of its ability to concentrate CO2 around Rubisco and boost water use efficiency relative to C3 photosynthesis. We assess this hypothesis by compiling estimates of when CAM clades arose using phylogenetic chronograms for 73 CAM clades. We further consider evidence of how atmospheric CO2 affects CAM relative to C3 photosynthesis.
Results Where CAM origins can be inferred, strong CAM is estimated to have appeared in the past 30 million years in 46 of 48 examined clades, after atmospheric CO2 had declined from high (near 800 ppm) to lower (<450 ppm) values. In turn, 21 of 25 clades containing CAM species (but where CAM origins are less certain) also arose in the past 30 million years. In these clades, CAM is probably younger than the clade origin. We found evidence for repeated weak CAM evolution during the higher CO2 conditions before 30 million years ago, and possible strong CAM origins in the Crassulaceae during the Cretaceous period prior to atmospheric CO2 decline. Most CAM-specific clades arose in the past 15 million years, in a similar pattern observed for origins of C4 clades.
Conclusions The evidence indicates strong CAM repeatedly evolved in reduced CO2 conditions of the past 30 million years. Weaker CAM can pre-date low CO2 and, in the Crassulaceae, strong CAM may also have arisen in water-limited microsites under relatively high CO2. Experimental evidence from extant CAM species demonstrates that elevated CO2 reduces the importance of nocturnal CO2 fixation by increasing the contribution of C3 photosynthesis to daily carbon gain. Thus, the advantage of strong CAM would be reduced in high CO2, such that its evolution appears less likely and restricted to more extreme environments than possible in low CO2.
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Cook, S. ; Katz, B. ; Moore-Russo, D. (Ed.)Inquiry and active learning instructional methods have largely been regarded as equitable and beneficial for students. However, researchers have highlighted math classrooms as racialized and gendered spaces that can negatively impact marginalized students’ experiences in such spaces. In this study, I examine the development of one argument, and whose ideas are solicited and leveraged, in an inquiry-oriented linear algebra course with an eye toward participatory equity. I found that gender related most to the inequity of participation in argumentation and that only men participated in generalizing activity. This study adds to the growing literature addressing equity in inquiry and active learning math settings.more » « less
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Cook, S. ; Katz, B. ; Moore-Russo, D. (Ed.)Inquiry and active learning instructional methods have largely been regarded as equitable and beneficial for students. However, researchers have highlighted math classrooms as racialized and gendered spaces that can negatively impact marginalized students’ experiences in such spaces. In this study, I examine the development of one argument, and whose ideas are solicited and leveraged, in an inquiry-oriented linear algebra course with an eye toward participatory equity. I found that gender related most to the inequity of participation in argumentation and that only men participated in generalizing activity. This study adds to the growing literature addressing equity in inquiry and active learning math settings.more » « less
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Cook, S. ; Katz, B. ; Moore-Russo, D. (Ed.)Inquiry and active learning instructional methods have largely been regarded as equitable and beneficial for students. However, researchers have highlighted math classrooms as racialized and gendered spaces that can negatively impact marginalized students’ experiences in such spaces. In this study, I examine the development of one argument, and whose ideas are solicited and leveraged, in an inquiry-oriented linear algebra course with an eye toward participatory equity. I found that gender related most to the inequity of participation in argumentation and that only men participated in generalizing activity. This study adds to the growing literature addressing equity in inquiry and active learning math settings.more » « less
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