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At least 235 records · Page 13

Boron biodistribution for BNCT in the hamster cheek pouch oral cancer model: Combined administration of BSH and BPA

Sodium mercaptoundecahydro-closo-dodecaborate (BSH) is being investigated clinically for BNCT. We examined the biodistribution of BSH and BPA administered jointly in different proportions in the hamster cheek pouch oral cancer model. The 3 assayed protocols were non-toxic, and showed preferential tumor boron uptake versus precancerous and normal tissue and therapeutic tumor boron concentration values (70–85 ppm). All 3 protocols warrant assessment in BNCT studies to contribute to the knowledge of (BSH+BPA)-BNCT radiobiology for head and neck cancer and optimize therapeutic efficacy.

99 GENERAL AND MISCELLANEOUS↗

Randomized Noninferiority Trial of Reduced High-Dose Volume Versus Standard Volume Radiation Therapy for Muscle-Invasive Bladder Cancer: Results of the BC2001 Trial (CRUK/01/004)

Purpose: To test whether reducing radiation dose to uninvolved bladder while maintaining dose to the tumor would reduce side effects without impairing local control in the treatment of muscle-invasive bladder cancer. Methods and Materials: In this phase III multicenter trial, 219 patients were randomized to standard whole-bladder radiation therapy (sRT) or reduced high-dose volume radiation therapy (RHDVRT) that aimed to deliver full radiation dose to the tumor and 80% of maximum dose to the uninvolved bladder. Participants were also randomly assigned to receive radiation therapy alone or radiation therapy plus chemotherapy in a partial 2 × 2 factorial design. The primary endpoints for the radiation therapy volume comparison were late toxicity and time to locoregional recurrence (with a noninferiority margin of 10% at 2 years). Results: Overall incidence of late toxicity was less than predicted, with a cumulative 2-year Radiation Therapy Oncology Group grade 3/4 toxicity rate of 13% (95% confidence interval 8%, 20%) and no statistically significant differences between groups. The difference in 2-year locoregional recurrence free rate (RHDVRT − sRT) was 6.4% (95% confidence interval −7.3%, 16.8%) under an intention to treat analysis and 2.6% (−12.8%, 14.6%) in the “per-protocol” population. Conclusions: In this study RHDVRT did not result in a statistically significant reduction in late side effects compared with sRT, and noninferiority of locoregional control could not be concluded formally. However, overall low rates of clinically significant toxicity combined with low rates of invasive bladder cancer relapse confirm that (chemo)radiation therapy is a valid option for the treatment of muscle-invasive bladder cancer.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Top-down mass spectrometry of native proteoforms and their complexes: a community study

The combination of native electrospray ionization with top-down fragmentation in mass spectrometry (MS) allows simultaneous determination of the stoichiometry of noncovalent complexes and identification of their component proteoforms and cofactors. Although this approach is powerful, both native MS and top-down MS are not yet well standardized, and only a limited number of laboratories regularly carry out this type of research. Further, to address this challenge, the Consortium for Top-Down Proteomics initiated a study to develop and test protocols for native MS combined with top-down fragmentation of proteins and protein complexes across 11 instruments in nine laboratories. Here we report the summary of the outcomes to provide robust benchmarks and a valuable entry point for the scientific community.

47 OTHER INSTRUMENTATION↗

Equilibration and analysis of first-principles molecular dynamics simulations of water

First-principles molecular dynamics (FPMD) simulations based on density functional theory are becoming increasingly popular for the description of liquids. In view of the high computational cost of these simulations, the choice of an appropriate equilibration protocol is critical. In this study, we assess two methods of estimation of equilibration times using a large dataset of first-principles molecular dynamics simulations of water. The Gelman-Rubin potential scale reduction factor [A. Gelman and D. B. Rubin, Stat. Sci. 7, 457 (1992)] and the marginal standard error rule heuristic proposed by White [Simulation 69, 323 (1997)] are evaluated on a set of 32 independent 64-molecule simulations of 58 ps each, amounting to a combined cumulative time of 1.85 ns. The availability of multiple independent simulations also allows for an estimation of the variance of averaged quantities, both within MD runs and between runs. We analyze atomic trajectories, focusing on correlations of the Kohn-Sham energy, pair correlation functions, number of hydrogen bonds, and diffusion coefficient. The observed variability across samples provides a measure of the uncertainty associated with these quantities, thus facilitating meaningful comparisons of different approximations used in the simulations. We find that the computed diffusion coefficient and average number of hydrogen bonds are affected by a significant uncertainty in spite of the large size of the dataset used. Lastly, a comparison with classical simulations using the TIP4P/2005 model confirms that the variability of the diffusivity is also observed after long equilibration times. Complete atomic trajectories and simulation output files are available online for further analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural magnetic glassiness in the spin ice Dy 2 Ti 2 O 7

The origin and nature of glassy dynamics presents one of the central enigmas of condensed-matter physics across a broad range of systems ranging from window glass to spin glasses. The spin-ice compound Dy 2 Ti 2 O 7 , which is perhaps best known as hosting a three-dimensional Coulomb spin liquid with magnetically charged monopole excitations, also falls out of equilibrium at low temperature. How and why it does so remains an open question. Based on an analysis of low-temperature diffuse neutron-scattering experiments employing different cooling protocols alongside recent magnetic noise studies, combined with extensive numerical modeling, we argue that upon cooling, the spins freeze into what may be termed a “structural magnetic glass,” without an a priori need for chemical or structural disorder. Specifically, our model indicates the presence of frustration on two levels, first producing a near-degenerate constrained manifold inside which phase ordering kinetics is in turn frustrated. A remarkable feature is that monopoles act as sole annealers of the spin network and their pathways and history encode the development of glass dynamics, allowing the glass formation to be visualized. Our results suggest that spin ice Dy 2 Ti 2 O 7 provides one prototype of magnetic glass formation specifically and a setting for the study of kinetically constrained systems more generally.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SU-E-T-528: Robustness Evaluation for Fiducial-Based Accelerated Partial Breast Proton Therapy

Purpose: To investigate the robustness of the proton treatment plans in the presence of rotational setup error when patient is aligned with implanted fiducials. Methods: Five Stage I invasive breast cancer patients treated with the APBP protocol (PCG BRE007-12) were studied. The rotational setup errors were simulated by rotating the original CT images around the body center clockwise and counterclockwise 5 degrees (5CW and 5CCW). Manual translational registration was then performed to match the implanted fiducials on the rotated images to the original dataset. Patient contours were copied to the newly created CT set. The original treatment plan was applied to the new CT dataset with the beam isocenter placed at the geometrical center of PTV. The dose distribution was recalculated for dosimetric parameters comparison. Results: CTV and PTV (D95 and V95) coverages were not significantly different between the two simulated plans (5CW and 5CCW) and the original plan. PTV D95 and CTV D95 absolute difference among the three plans were relatively small, with maximum changes of 0.28 CGE and 0.15 CGE, respectively. PTV V95 and CTV V95 absolute differences were 0.79% and 0.48%. The dosage to the thyroid, heart, contralateral breast and lung remained zero for all three plans. The Dmax and Dmean to the volume of ipsilateral breast excluding CTV were compared, with maximum difference values of 1.02 CGE for Dmax and 3.56 CGE for Dmean. Ipsilateral lung Dmean maintained no significant changes through the three plan comparison, with the largest value 0.32 CGE. Ipsilateral lung Dmax was the most sensitive parameter to this simulation study, with a maximum difference at 20.2 CGE. Conclusion: Our study suggests that fiducial-based Accelerated Partial Breast Proton Therapy is robust with respect to +/− 5 degree patient setup rotational errors, as long as the internal fiducial markers are used for patient alignment.

60 APPLIED LIFE SCIENCES↗

MO-G-17A-08: Applications of Quantitative PET/CT Imaging of Yttrium-90: A Tool for Improving Radioembolization

Purpose: Yttrium-90 (Y90) PET/CT post-treatment imaging of radioembolization has fostered significant interest from both the interventional radiology and nuclear medicine communities over the past few years. Recent literature has demonstrated high quantitative accuracy of Y90 PET at the activity concentrations common in radioembolization. However, few have explored methods in which this information can be clinically applied toward improving patient care. Methods: IRB approval and informed consent was obtained for over 35 Y90 post-treatment imaging studies, performed under 2 distinct protocols. In protocol 1, Y90 PET/CT provided quantitative post-treatment imaging, which was then converted into 3D maps of absorbed-dose. Both images and absorbed dose maps were used to manage patient care. In protocol 2, tumor absorbed-dose measurements from Y90 PET/CT were compared to known tumoricidal thresholds. If insufficient absorbed dose was delivered to the tumor, the patient would have an additional Y90 infusion the same day, providing truly patient-specific Y90 PET/CT based treatment-planning. Results: Y90 PET/CT allowed for a superior post-radioembolization evaluation of technical success compared with conventional Y90 bremsstrahlung SPECT. Due to the exceptional resolution of PET, a direct comparison between the distribution of radioembolization and pre-treatment planning intentions can be made. Further, quantification of tumor absorbed-dose directly from PET/CT imaging allows for the prediction of treatment efficacy based on a comparison with known tumoricidal thresholds. This immediate evaluation allowed treating physicians to consider additional or alternate therapies before discovering clinical failure weeks later. One protocol 2 patient was found to have a subtumoricidal absorbed dose following radioembolization. This patient received a same-day infusion of additional Y90 with identical catheter placement to the first infusion. A robust treatment response was seen on follow-up imaging. Conclusion: Y90 PET/CT produces quantifiable image sets, which can be transformed into 3D maps of absorbed dose. This information can be utilized to improve patient care. SIRTeX Medical, Surefire Medical.

60 APPLIED LIFE SCIENCES↗

Comparison of internal dose estimates obtained using organ-level, voxel S value, and Monte Carlo techniques

Purpose: The authors’ objective was to compare internal dose estimates obtained using the Organ Level Dose Assessment with Exponential Modeling (OLINDA/EXM) software, the voxel S value technique, and Monte Carlo simulation. Monte Carlo dose estimates were used as the reference standard to assess the impact of patient-specific anatomy on the final dose estimate. Methods: Six patients injected with{sup 99m}Tc-hydrazinonicotinamide-Tyr{sup 3}-octreotide were included in this study. A hybrid planar/SPECT imaging protocol was used to estimate {sup 99m}Tc time-integrated activity coefficients (TIACs) for kidneys, liver, spleen, and tumors. Additionally, TIACs were predicted for {sup 131}I, {sup 177}Lu, and {sup 90}Y assuming the same biological half-lives as the {sup 99m}Tc labeled tracer. The TIACs were used as input for OLINDA/EXM for organ-level dose calculation and voxel level dosimetry was performed using the voxel S value method and Monte Carlo simulation. Dose estimates for {sup 99m}Tc, {sup 131}I, {sup 177}Lu, and {sup 90}Y distributions were evaluated by comparing (i) organ-level S values corresponding to each method, (ii) total tumor and organ doses, (iii) differences in right and left kidney doses, and (iv) voxelized dose distributions calculated by Monte Carlo and the voxel S value technique. Results: The S values for all investigated radionuclides used by OLINDA/EXM and the corresponding patient-specific S values calculated by Monte Carlo agreed within 2.3% on average for self-irradiation, and differed by as much as 105% for cross-organ irradiation. Total organ doses calculated by OLINDA/EXM and the voxel S value technique agreed with Monte Carlo results within approximately ±7%. Differences between right and left kidney doses determined by Monte Carlo were as high as 73%. Comparison of the Monte Carlo and voxel S value dose distributions showed that each method produced similar dose volume histograms with a minimum dose covering 90% of the volume (D90) agreeing within ±3%, on average. Conclusions: Several aspects of OLINDA/EXM dose calculation were compared with patient-specific dose estimates obtained using Monte Carlo. Differences in patient anatomy led to large differences in cross-organ doses. However, total organ doses were still in good agreement since most of the deposited dose is due to self-irradiation. Comparison of voxelized doses calculated by Monte Carlo and the voxel S value technique showed that the 3D dose distributions produced by the respective methods are nearly identical.

60 APPLIED LIFE SCIENCES↗

WE-FG-202-03: Quantitative CT-Based Analysis to Assess Lung Injury Following Proton Radiotherapy

Purpose: Relative to photon alternatives, the increased dose-conformity associated with proton therapy is expected to reduce the extent of radiation-induced lung toxicity. However, analysis of follow-up data is yet to be published in this area. In this study we retrospectively analyzed late-phase HU changes for proton therapy cohorts of chest wall and lung patients. Methods: From our institution’s register of patients treated using double-scattered protons, all chest wall and stereotactic lung cases (treated 2011–2012 and 2008–2014 respectively) were initially considered. Follow-up CT data were accessible for 10 chest wall cases (prescribed 50.4 GyRBE in 28 fractions) and 16 lung cases (prescribed 42–50 GyRBE in 3–4 fractions). CT time-points ranged from 0.5–3.5 years post-treatment. Planning doses were recalculated using TOPAS Monte Carlo simulations and mapped onto the follow-up images using deformable registration. Excluding internal target volumes, changes in HU between each patient’s planning and follow-up CT(s) were evaluated for dose bins of 2–30 GyRBE (2 GyRBE increments). Results: Linear increases in HU per unit dose, with correlations statistically significant at the 1% level (one-sided Spearman’s rank test), were evident for all 10 chest wall cases and 14/16 lung cases. The mean changes in HU/Gy were: 1.76 (SD=0.73) for the chest wall cohort, and 1.40 (SD=0.87) for the lung cohort. The median scan times post treatment were 21 and 12 months respectively. All 26 patients developed solid consolidation (scar-like radiographic opacities) within the exposed lung(s). Conclusion: Analysis of follow-up CTs revealed statistically significant correlations in HU-change/dose for two proton cohorts (lung and chest wall). Quantitatively, the late-phase changes we report broadly match published photon data. Further analysis of such radiographic changes, particularly via matched cohort studies drawing upon consistent imaging protocols, could play an important role in elucidating inter-modality differences and provide insight into proton RBE for lung injury. Tracy Underwood gratefully acknowledges the support of the European Commission under an FP7 Marie Curie International Outgoing Fellowship for Career Development (#630064). This work was also funded under U19 grant CA 021239 (PI: Delaney).

60 APPLIED LIFE SCIENCES↗

Curation of Ground-Truth Validated Benchmarking Datasets for Fault Detection & Diagnostics Tools

Fault detection and diagnostics (FDD) analytical tools for heating, ventilation and air conditioning (HVAC) systems represent one of the most active areas of smart building technology development. A diversity of techniques is used for FDD analytics, spanning physical models, black box, and rule-based approaches, and researchers continuously strive to develop improved algorithms. With FDD algorithm numbers now in the hundreds, there is a need for performance evaluation of these algorithms in order to assess improvements, improve costeffectiveness, and to prioritize investment in the further development of these technologies. A persistent challenge of FDD advance has been the lack of common datasets to benchmark the performance accuracy of FDD algorithms. This paper summarizes the successful curation of HVAC operational data, paired with validated ground-truth information regarding the presence and absence of faults. The current dataset, consisting of both simulation and experimental data, will evolve to include a larger set of HVAC systems with the objective of creating the largest publicly available dataset to be used by FDD developers, users, and researchers to compare and contrast performance accuracy across FDD algorithms, helping to drive improvements that will spur greater market adoption of FDD tools. Furthermore, in order to avoid previously observed issues with contributed datasets and ensure high quality and consistency of future submissions, the development of data validation and ground-truth assessment protocol is detailed in this study.

Casillas, Armando↗

Securing Distributed Energy Resource Integration

The penetration of distributed energy resources (DER) is growing at much higher rates than predicted 20 years ago. Far from being used only in residential settings, DER are now installed on distribution and transmission circuits. In this position, they do not have the same properties as traditional generators and are more flexible in many cases. The growing penetration and range of uses for DER motivate the need to reliably and safely integrate them into the grid. Operators must be able to rely on them not only for normal operation, but also during abnormal conditions like black starts or adverse cyber scenarios. To that end, we study the communications, device interfaces, and potential consequences of DER operation under abnormal and adversarial conditions. The weaknesses of communications networks are studied based on the industrial protocols used, and the benefits of security features are examined. The device interfaces are found to be vulnerable to attack based on the requirements in the IEEE-1547 standard for DER interconnection and interoperability, which is expected to be adopted in the next ten years. In addition to exploring the requirements of the standard, we show that these vulnerabilities and others do exist and can be used maliciously in a modern storage system DER. Consequences of these vulnerabilities range from exacerbated grid instability, to simultaneous loss of large portions of DER penetration, to physical damage to inverters or DER themselves and other sensitive equipment. We tie these outcomes to specific attacker actions in an effort to give operators a better threat intelligence view that allows them to prioritize mitigations. Finally, we discuss mitigations that could prevent many of the adversarial scenarios described. Some solutions can be added to existing infrastructure, while others may require longer term planning for grid modernization with consideration for security.

25 ENERGY STORAGE↗

Production and Targeting of Monovalent Quantum Dots

The multivalent nature of commercial quantum dots (QDs) and the difficulties associated with producing monovalent dots have limited their applications in biology, where clustering and the spatial organization of biomolecules is often the object of study. We describe here a protocol to produce monovalent quantum dots (mQDs) that can be accomplished in most biological research laboratories via a simple mixing of CdSe/ZnS core/shell QDs with phosphorothioate DNA (ptDNA) of defined length. After a single ptDNA strand has wrapped the QD, additional strands are excluded from the surface. Production of mQDs in this manner can be accomplished at small and large scale, with commercial reagents, and in minimal steps. These mQDs can be specifically directed to biological targets by hybridization to a complementary single stranded targeting DNA. We demonstrate the use of these mQDs as imaging probes by labeling SNAP-tagged Notch receptors on live mammalian cells, targeted by mQDs bearing a benzylguanine moiety.

59 BASIC BIOLOGICAL SCIENCES↗

Investigating Bacterial-Fungal Interactions using Fungal Highway Columns in Diverse Environments and Substrates

Bacterial-fungal interactions (BFIs) play an integral role in shaping microbial community composition, biogeochemical functions, spatial dynamics, and microbial dispersal. Mycelial networks created by filamentous fungi or other filamentous microorganisms (e.g., Oomycetes) act as 'fungal highways' that can be utilized by bacteria for transport throughout heterogeneous environments, greatly facilitating their mobility and granting them access to regions that may be challenging or impossible to reach on their own (e.g., due to air pockets within the soil). Several devices and experimental protocols have been created to study these fungal highways, including fungal highway columns. The fungal highway column designed by our group can be used for a variety of in situ or in vitro applications, as well as with diverse environmental and host-associated sample types. Herein, we describe the methods for performing experiments with these columns, including designing, printing, sterilizing, and preparing the devices. The options for analyzing data obtained from the use of these devices are also discussed here, and troubleshooting advice regarding potential pitfalls associated with experiments using fungal highway columns is offered. These devices can be used to gain a more comprehensive understanding of the diversity, mechanisms, and dynamics of fungal highway BFIs to provide valuable insights into the structural and functional dynamics within complex environments (e.g., soils) and across diverse habitats in which bacteria and fungi co-exist.

59 BASIC BIOLOGICAL SCIENCES↗

Geochemical Characterization of Rare Earth Elements in Coal Combustion Byproducts Utilizing Synchrotron Technology

Coal combustion by-products (CCBs) are being examined as a potential domestic resource for rare earth element (REE) recovery. In particular, fly ash is being explored due to its relatively abundant REE content, low-to-no-cost availability as a waste product, fine particle size, and enrichment with critical REEs. In order to develop an effective protocol for REE recovery, this study characterized speciation and distribution of REE in CCBs collected from various states.

Lopano, Christina↗

Rotating Disk Electrode Standardization and Best Practices in Acidic Oxygen Evolution for Low-Temperature Electrolysis

Efforts in oxygen evolution catalyst development have significantly increased and often use rotating disk electrode half-cells to evaluate intrinsic kinetics and screen materials for short-term durability. Standardizing rotating disk electrode test protocols is critical to experimental accuracy, to realistically assess their potential impact at a device level and to assess how different catalyst approaches and concepts are prioritized. The goal of this study is to provide standardized test protocols and suggest best practices to help reduce variability in ex situ materials characterization in the broader community. Specifically, these protocols focus on test cleanliness and materials choices, including how electrodes are prepared and tested, and the impact on activity observations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large Scale Study of Ligand–Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols

The accurate and reliable prediction of protein–ligand binding affinities can play a central role in the drug discovery process as well as in personalized medicine. Of considerable importance during lead optimization are the alchemical free energy methods that furnish an estimation of relative binding free energies (RBFE) of similar molecules. Recent advances in these methods have increased their speed, accuracy, and precision. This is evident from the increasing number of retrospective as well as prospective studies employing them. However, such methods still have limited applicability in real-world scenarios due to a number of important yet unresolved issues. Here, we report the findings from a large data set comprising over 500 ligand transformations spanning over 300 ligands binding to a diverse set of 14 different protein targets which furnish statistically robust results on the accuracy, precision, and reproducibility of RBFE calculations. We use ensemble-based methods which are the only way to provide reliable uncertainty quantification given that the underlying molecular dynamics is chaotic. These are implemented using TIES (Thermodynamic Integration with Enhanced Sampling). Results achieve chemical accuracy in all cases. Ensemble simulations also furnish information on the statistical distributions of the free energy calculations which exhibit non-normal behavior. We find that the “enhanced sampling” method known as replica exchange with solute tempering degrades RBFE predictions. We also report definitively on numerous associated alchemical factors including the choice of ligand charge method, flexibility in ligand structure, and the size of the alchemical region including the number of atoms involved in transforming one ligand into another. Our findings provide a key set of recommendations that should be adopted for the reliable application of RBFE methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Characterisation of [11C]PR04.MZ in Papio anubis baboon: A selective high-affinity radioligand for quantitative imaging of the dopamine transporter

N-(4-fluorobut-2-yn-1-yl)-2{beta}-carbomethoxy-3{beta}-(4{prime}-tolyl)nortropane (PR04.MZ, 1) is a PET radioligand for the non-invasive exploration of the function of the cerebral dopamine transporter (DAT). A reliable automated process for routine production of the carbon-11 labelled analogue [{sup 11}C]PR04.MZ ([{sup 11}C]-1) has been developed using GMP compliant equipment. An adult female Papioanubis baboon was studied using a test-retest protocol with [{sup 11}C]-1 in order to assess test-retest reliability, metabolism and CNS distribution profile of the tracer in non-human primates. Blood sampling was performed throughout the studies for determination of the free fraction in plasma (fP), plasma input functions and metabolic degradation of the radiotracer [{sup 11}C]-1. Time-activity curves were derived for the putamen, the caudate nucleus, the ventral striatum, the midbrain and the cerebellum. Distribution volumes (VT) and non-displaceable binding potentials (BPND) for various brain regions and the blood were obtained from kinetic modelling. [{sup 11}C]-1 shows promising results as aselective marker of the presynaptic dopamine transporter. With the reliable visualisation of the extra-striatal dopaminergic neurons and no indication on labelled metabolites, the tracer provides excellent potential for translation into man.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Investigating parameter trainability in the SNAP-displacement protocol of a qudit system

Here, in this study, we explore the universality of Selective Number-dependent Arbitrary Phase (SNAP) and Displacement gates for quantum control in qudit-based systems. However, optimizing the parameters of these gates poses a challenging task. Our main focus is to investigate the sensitivity of training any of the SNAP parameters in the SNAP-Displacement protocol. We analyze conditions that could potentially lead to the Barren Plateau problem in a qudit system and draw comparisons with multi-qubit systems. The parameterized ansatz we consider consists of blocks, where each block is composed of hardware operations, namely SNAP and Displacement gates [Fösel et al 2020 Efficient cavity control with snap gates arXiv:2004.14256]. Applying Variational Quantum algorithm (VQA) with observable and gate cost functions, we utilize techniques similar to those in [McClean et al 2018 Barren plateaus in quantum neural network training landscapes Nat. Commun.9 1–6] and [Cerezo et al 2021 Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat. Commun.12 1–12] along with the concept of t − design. Through this analysis, we make the following key observations: (a) The trainability of a SNAP-parameter does not exhibit a preference for any particular direction within our cost function landscape, (b) By leveraging the first and second moments properties of Haar measures, we establish new lemmas concerning the expectation of certain polynomial functions, and (c) utilizing these new lemmas, we identify a general condition that indicates an expected trainability advantage in a qudit system when compared to multi-qubit systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗