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Verification of program safety is often reducible to proving the unsatisfiability (i.e., validity) of a formula in Satisfiability Modulo Theories (SMT): Boolean logic combined with theories that formalize arbitrary first-order fragments. Zeroknowledge (ZK) proofs allow SMT formulas to be validated without revealing the underlying formulas or their proofs to other parties, which is a crucial building block for proving the safety of proprietary programs. Recently, Luo et al. studied the simpler problem of proving the unsatisfiability of pure Boolean formulas but does not support proofs generated by SMT solvers. This work presents ZKSMT, a novel framework for proving the validity of SMT formulas in ZK. We design a virtual machine (VM) tailored to efficiently represent the verification process of SMT validity proofs in ZK. Our VM can support the vast majority of popular theories when proving program safety while being complete and sound. To demonstrate this, we instantiate the commonly used theories of equality and linear integer arithmetic in our VM with theory-specific optimizations for proving them in ZK. ZKSMT achieves high practicality even when running on realistic SMT formulas generated by Boogie, a common tool for software verification. It achieves a three-order-of-magnitude improvement compared to a baseline that executes the proof verification code in a general ZK system. 

Z-RNA is a higher-energy, left-handed conformation of RNA, whose function has remained elusive. A growing body of work alludes to regulatory roles for Z-RNA in the immune response. Here, we review how Z-RNA features present in cellular RNAs—especially containing retroelements—could be recognized by a family of winged helix proteins, with an impact on host defense. We also discuss how mutations to specific Z-contacting amino acids disrupt their ability to stabilize Z-RNA, resulting in functional losses. We end by highlighting knowledge gaps in the field, which, if addressed, would significantly advance this active area of research. 

Despite structural differences between the right-handed conformations of A-RNA and B-DNA, both nucleic acids adopt very similar, left-handed Z-conformations. In contrast to their structural similarities and sequence preferences, RNA and DNA exhibit differences in their ability to adopt the Z-conformation regarding their hydration shells, the chemical modifications that promote the Z-conformation, and the structure of junctions connecting them to right-handed segments. In this review, we highlight the structural and chemical properties of both Z-DNA and Z-RNA and delve into the potential factors that contribute to both their similarities and differences. While Z-DNA has been extensively studied, there is a gap of knowledge when it comes to Z-RNA. Where such information is lacking, we try and extend the principles of Z-DNA stability and formation to Z-RNA, considering the inherent differences of the nucleic acids. 

Locomotion that is driven by muscle activity dominates the daily energetic expenditure in most animals. In fish, routine propulsion when swimming at low, steady speeds and at various gaits is powered primarily by red, oxidative muscle. In Bluegill Sunfish (Lepomis macrochirus), swimming speed is thought to reflect the most energetically efficient gait type. Since field observations of Bluegill suggest that intermittent swimming is the preferred gait, we hypothesized that intermittent locomotion would be more energetically efficient than steady swimming. To test this hypothesis, we used electromyography to analyze muscle activation intensity of Bluegill swimming steadily in a flume and volitionally intermittently in a pool. In the flume, muscle activation intensity and tailbeat frequency increased as a function of speed. However, when swimming volitionally in the pool, muscle activation intensity varied relative to average velocity and tailbeat frequency was lower than in the flume at the same velocities. Although we expected muscle activation intensity to be higher when steady swimming at a given speed, ~48% of fish (n=11) had higher muscle activation intensities when swimming volitionally when compared at the same speed in the flume. Also, there was a positive relationship between speed and glide duration, but there was no relationship between speed and muscle activation intensity when swimming intermittently. Instead, intermittent swimming may lower fatigue and enhance maneuverability, rather than increase energetic efficiency. 

Locomotion is vital to the survival and fitness of animals and dominates daily energy budgets. The main energy consuming process of locomotion is the muscle activity needed to maintain stability or generate propulsive forces. In fish, the speed of swimming is thought to depend on the gait type, which may reflect an energetically efficient locomotory behavior. Bluegill Sunfish (Lepomis macrochirus) exhibit either steady or intermittent (burst-coast) gaits when swimming in the field, but whether these gaits differ in their energetic efficiency is unknown. We analyzed the electromyography (EMG) of oxidative muscle in Bluegill swimming at low velocities to determine if steady swimming is more or less energetically efficient than intermittent swimming. EMG data were acquired using bipolar fine wire electrodes implanted into oxidative musculature at 2/3 tail length. Steady swimming EMGs were recorded in a flume (fish treadmill) at incrementally increasing speeds relative to body length, until nonoxidative muscle was recruited. As speed increased, EMG intensity increased, which corresponds to increased muscle recruitment. Fish reached maximum EMG intensity (100% oxidative muscle capacity) between 1.75 - 2.25 BL/s. Intermittent swimming EMGs were recorded while the fish swam volitionally in a pool. The burst phase consisted of 2-3 tailbeats, followed by a coast phase duration of 1 second or less. Based on preliminary results, fish in the pool swam at an average of 62.1% (n = 10) of their maximum oxidative capacity. When intermittently swimming, muscle activity was 37.9% more efficient than steady swimming at similar speeds. This demonstrates that when swimming volitionally Bluegill choose the most energetically effective gait. However, further analysis is needed to determine how individual variation affects swimming performance. Continued comparison of these methods of locomotion will broaden the understanding of energy decisions that fish make. These results suggest that intermittent swimming is the more energetically efficient form of aquatic locomotion. This work is supported by NSF grant award number 2135851.