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Though photonic computing systems offer advantages in speed, scalability, and power consumption, they often have a limited dynamic encoding range due to low signal-to-noise ratios. Compared to digital floating-point encoding, photonic fixed-point encoding limits the precision of photonic computing when applied to scientific problems. In the case of iterative algorithms such as those commonly applied in machine learning or differential equation solvers, techniques like precision decomposition and residue iteration can be applied to increase accuracy at a greater computing cost. However, the analog nature of photonic symbols allows for modulation of both amplitude and frequency, opening the possibility of encoding both the significand and exponent of floating-point values on photonic computing systems to expand the dynamic range without expending additional energy. With appropriate schema, element-wise floating-point multiplication can be performed intrinsically through the interference of light. Herein, we present a method for configurable, signed, floating-point encoding and multiplication on a limited precision photonic primitive consisting of a directly modulated Mach–Zehnder interferometer. We demonstrate this method using Newton's method to find the Golden Ratio within ±0.11%, with six-level exponent encoding for a signed trinary digit-equivalent significand, corresponding to an effective increase of 243× in the photonic primitive's dynamic range. 

We present a method for configurable, signed, floating-point encoding and multiplication on limited precision photonic primitives, demonstrating Newton’s method with improved accuracy and expanding the dynamic range of the photonic solver by over 200×. 

Abstract Solving linear systems, often accomplished by iterative algorithms, is a ubiquitous task in science and engineering. To accommodate the dynamic range and precision requirements, these iterative solvers are carried out on floating-point processing units, which are not efficient in handling large-scale matrix multiplications and inversions. Low-precision, fixed-point digital or analog processors consume only a fraction of the energy per operation than their floating-point counterparts, yet their current usages exclude iterative solvers due to the cumulative computational errors arising from fixed-point arithmetic. In this work, we show that for a simple iterative algorithm, such as Richardson iteration, using a fixed-point processor can provide the same convergence rate and achieve solutions beyond its native precision when combined with residual iteration. These results indicate that power-efficient computing platforms consisting of analog computing devices can be used to solve a broad range of problems without compromising the speed or precision. 

Abstract Fleshy macroalgae dominate the hard bottom, shallow waters along the Western Antarctic Peninsula (WAP). Although there are numerous reports on their ecology, geographic distribution, and to a lesser extent, vertical (depth) distribution in the northern portions of the WAP, much less is known farther south along the central portion of the WAP. Here we provide the first report of the vertical distributions of brown and red fleshy macroalgae in this region based on scuba-derived collections at 14 study sites between southern Anvers Island (64.8°S, 64.4°W) in the north and central Marguerite Bay (68.7°S, 67.5°W) in the south. Although several overstory brown macroalgal species that can be common along the northern WAP includingDesmarestia ancepsandCystosphaera jacquinotiiare mostly absent from the central WAP, the vertical distributions of the brown macroalgaeDesmarestia menziesiiandHimantothallus grandifoliusare similar to the northern WAP even though their percent cover is much lower. Likewise, the vertical distribution of the 14 most widespread red macroalgae, where they occur, mirrored those known from the northern part of the WAP even though macroalgal cover, biomass, and total species richness declined markedly to the south across this region due to increasing sea ice concentrations. 

Macroalgal forests dominate shallow hard bottom areas along the northern portion of the Western Antarctic Peninsula (WAP). Macroalgal biomass and diversity are known to be dramatically lower in the southern WAP and at similar latitudes around Antarctica, but few reports detail the distributions of macroalgae or associated macroinvertebrates in the central WAP. We used satellite imagery to identify 14 sites differing in sea ice coverage but similar in terms of turbidity along the central WAP. Fleshy macroalgal cover was strongly, negatively correlated with ice concentration, but there was no significant correlation between macroinvertebrate cover and sea ice. Overall community (all organisms) diversity correlated negatively with sea ice concentration and positively with fleshy macroalgal cover, which ranged from around zero at high ice sites to 80% at the lowest ice sites. Nonparametric, multivariate analyses resulted in clustering of macroalgal assemblages across most of the northern sites of the study area, although they differed greatly with respect to macroalgal percent cover and diversity. Analyses of the overall communities resulted in three site clusters corresponding to high, medium, and low fleshy macroalgal cover. At most northern sites, macroalgal cover was similar across depths, but macroalgal and macroinvertebrate distributions suggested increasing effects of ice scour in shallower depths towards the south. Hindcast projections based on correlations of ice and macroalgal cover data suggest that macroalgal cover at many sites could have been varying substantially over the past 40 years. Similarly, based on predicted likely sea ice decreases by 2100, projected increases in macroalgal cover at sites that currently have high ice cover and low macroalgal cover are substantial, often with only a future 15% decrease in sea ice. Such changes would have important ramifications to future benthic communities and to understanding how Antarctic macroalgae may contribute to future blue carbon sequestration.