In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases, models are sloppy, that is, exhibit an exponential hierarchy of parameter sensitivities. We propose a parameter classification scheme based on how the sensitivities scale at long observation times. We show that for oscillatory models, either with a limit cycle or a strange attractor, sensitivities can become arbitrarily large, which implies a high effective-dimensionality on the model manifold. Sloppy models with a single fixed point have model manifolds with low effective-dimensionality, previously described as a "hyper-ribbon". In contrast, models with high effective dimensionality translate into multimodal fitting problems. We define a measure of curvature on the model manifold which we call the winding frequency that estimates the density of local minima in the model's parameter space. We then show how alternative choices of fitting metrics can "unwind" the model manifold and give low winding frequencies. This prescription translates the model manifold from one of high effective-dimensionality into the "hyper-ribbon" structures observed elsewhere. This translation opens the door for applications of sloppy model analysis and model reduction methods developed for models with low effective-dimensionality.

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Superconducting radio‐frequency (SRF) resonators are critical components for particle accelerator applications, such as free‐electron lasers, and for emerging technologies in quantum computing. Developing advanced materials and their deposition processes to produce RF superconductors that yield nΩ surface resistances is a key metric for the wider adoption of SRF technology. Here, ZrNb(CO) RF superconducting films with high critical temperatures (Tc) achieved for the first time under ambient pressure are reported. The attainment of a Tc near the theoretical limit for this material without applied pressure is promising for its use in practical applications. A range of Tc, likely arising from Zr doping variation, may allow a tunable superconducting coherence length that lowers the sensitivity to material defects when an ultra‐low surface resistance is required. The ZrNb(CO) films are synthesized using a low‐temperature (100 – 200 °C) electrochemical recipe combined with thermal annealing. The phase transformation as a function of annealing temperature and time is optimized by the evaporated Zr‐Nb diffusion couples. Through phase control, one avoids hexagonal Zr phases that are equilibrium‐stable but degrade Tc. X‐ray and electron diffraction combined with photoelectron spectroscopy reveal a system containing cubic β‐ZrNb mixed with rocksalt NbC and low‐dielectric‐loss ZrO2. Proof‐of‐concept RF performance of ZrNb(CO) on an SRF sample test system is demonstrated. BCS resistance trends lower than reference Nb, while quench fields occur at approximately 35 mT. The results demonstrate the potential of ZrNb(CO) thin films for particle accelerators and other SRF applications.

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