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DOE OSTI2015

SU-E-P-14: Dosimetric Effects of Magnetic Field in MRI-Guided Radiation Therapy Delivery for Breast Cancer

Purpose: MRI-guided radiation therapy (RT) delivery would be beneficial for breast irradiation. The electron return effect due to the presence of a transverse magnetic field (TMF) may cause dosimetric issues on dose on skin and at the lung-tissue interface. The purpose of this study is to investigate these issues. Methods: IMRT plans with tangential beams and VMAT plans with 200 degree arcs to cover ipsilateral breast were generated for 10 randomly selected breast cancer cases using a research planning system (Monaco, Elekta) utilizing Monte Carlo dose calculation with or without a TMF of 1.5 T. Plans were optimized to deliver uniform dose to the whole breast with an exclusion of 5 mm tissue under the skin (PTV-EVAL). All four plans for each patient were re-scaled to have the same PTV-EVAL volume to receive the same prescription dose. The skin is defined as the first 5 mm of ipsilateral-breast tissue, plus extensions in the surrounding region. Results: The presence of 1.5 T TMF resulted in (1)increased skin dose, with the mean and maximum skin dose increase of 5% and 9%, respectively; (2) similar dose homogeneity within the PTV-EVAL; (3) the slightly improved (3%) dose homogeneity in the whole breast; (4) Averages of 9 and 16% increases in V5 and V20, respectively, for ipsilateral lung; and (5) increased the mean heart dose by 34%. VMAT plans don’t improve whole breast dose uniformity as compared that to the tangential plans. Conclusion: The presence of transverse magnetic field in MRI-guided RT delivery for whole breast irradiation can Result in slightly improved dose homogeneity in the whole breast, increased dose to the ipsilateral lung, heart, and skin. Plan optimization with additional specific dose volume constraints may eliminate/reduce these dose increases. This work is partially supported by Elekta Inc.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

IDENTIFYING STAR STREAMS IN THE MILKY WAY HALO

We develop statistical methods for identifying star streams in the halo of the Milky Way that exploit observed spatial and radial velocity distributions. Within a great circle, departures of the observed spatial distribution from random provide a measure of the likelihood of a potential star stream. Comparisons between the radial velocity distribution within a great circle and the radial velocity distribution of the entire sample also measure the statistical significance of potential streams. The radial velocities enable construction of a more powerful joint statistical test for identifying star streams in the Milky Way halo. Applying our method to halo stars in the Hypervelocity Star (HVS) survey, we detect the Sagittarius stream at high significance. Great circle counts and comparisons with theoretical models suggest that the Sagittarius stream comprises 10%-17% of the halo stars in the HVS sample. The population of blue stragglers and blue horizontal branch stars varies along the stream and is a potential probe of the distribution of stellar populations in the Sagittarius dwarf galaxy prior to disruption.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Chatter detection in simulated machining data: a simple refined approach to vibration data

Vibration monitoring is a critical aspect of assessing the health and performance of machinery and industrial processes. This study explores the application of machine learning techniques, specifically the Random Forest (RF) classification model, to predict and classify chatter—a detrimental self-excited vibration phenomenon—during machining operations. While sophisticated methods have been employed to address chatter, this research investigates the efficacy of a novel approach to an RF model. The study leverages simulated vibration data, bypassing resource-intensive real-world data collection, to develop a versatile chatter detection model applicable across diverse machining configurations. The feature extraction process combines time-series features and Fast Fourier Transform (FFT) data features, streamlining the model while addressing challenges posed by feature selection. By focusing on the RF model’s simplicity and efficiency, this research advances chatter detection techniques, offering a practical tool with improved generalizability, computational efficiency, and ease of interpretation. The study demonstrates that innovation can reside in simplicity, opening avenues for wider applicability and accelerated progress in the machining industry.

42 ENGINEERING↗

DOE OSTI2015

TU-EF-304-03: 4D Monte Carlo Robustness Test for Proton Therapy

Purpose: Breathing motion and approximate dose calculation engines may increase proton range uncertainties. We address these two issues using a comprehensive 4D robustness evaluation tool based on an efficient Monte Carlo (MC) engine, which can simulate breathing with no significant increase in computation time. Methods: To assess the robustness of the treatment plan, multiple scenarios of uncertainties are simulated, taking into account the systematic and random setup errors, range uncertainties, and organ motion. Our fast MC dose engine, called MCsquare, implements optimized models on a massively-parallel computation architecture and allows us to accurately simulate a scenario in less than one minute. The deviations of the uncertainty scenarios are then reported on a DVH-band and compared to the nominal plan.The robustness evaluation tool is illustrated in a lung case by comparing three 60Gy treatment plans. First, a plan is optimized on a PTV obtained by extending the CTV with an 8mm margin, in order to take into account systematic geometrical uncertainties, like in our current practice in radiotherapy. No specific strategy is employed to correct for tumor and organ motions. The second plan involves a PTV generated from the ITV, which encompasses the tumor volume in all breathing phases. The last plan results from robust optimization performed on the ITV, with robustness parameters of 3% for tissue density and 8 mm for positioning errors. Results: The robustness test revealed that the first two plans could not properly cover the target in the presence of uncertainties. CTV-coverage (D95) in the three plans ranged respectively between 39.4–55.5Gy, 50.2–57.5Gy, and 55.1–58.6Gy. Conclusion: A realistic robustness verification tool based on a fast MC dose engine has been developed. This test is essential to assess the quality of proton therapy plan and very useful to study various planning strategies for mobile tumors. This work is partly funded by IBA (Louvain-la-Neuve, Belgium)

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Texture Manipulation and Its Impact on Electrical Properties of Zinc Phosphide Thin Films

Both randomly oriented and highly (220) textured thin films of zinc phosphide (Zn3P2) were grown by the close-space sublimation method. The effect of deposition parameters, such as pressure and substrate temperature, on the texture evolution has been established. It was found that the deposition temperature plays a dominant role in determining the preferred orientation whereas the ambient pressure (below 10 Torr) does not greatly affect the film texture. We further found that the microstrain changes from tensile at lower deposition temperatures to compressive at higher deposition temperatures. The preferred orientation also had a strong impact on the electrical resistivity of the films. The results provide guidance on the selection of substrate and deposition parameters to grow Zn3P2 thin films with desirable properties.

14 SOLAR ENERGY↗

DOE OSTI2021

A mechanistic damage model for solid oxide fuel cell ceramic materials - Part I: Constitutive modeling

A multiscale mechanistic damage model for solid oxide fuel cell (SOFC) ceramics that combines micromechanics of stiffness reduction due to material porosity change and microcracking with a continuum damage mechanics (CDM) description for the evolution of microcracks up to fracture is developed in this work. The model also accounts for volumetric swelling of the anode due to redox cycling. Porosity change and swelling during redox combined with normal operating thermomechanical loads could increase the stress, strain and damage distributions in SOFC stacks leading them to failure. The proposed model involves three governing parameters: (i) the porosity in terms of the pore or void volume fraction, (ii) material swelling magnitude prescribed at a given loading step, and (iii) the damage variable that describes microcracking caused by thermomechanical loads and swelling. Pores and microcracks in the ceramics are modeled as randomly distributed ellipsoidal inclusions with negligible stiffness by an Eshelby-Mori-Tanaka formulation combined with an inclusion orientation distribution method. Microcracking damage evolution is described by a CDM formulation. Volumetric swelling is treated in a similar way to thermal expansion in the constitutive relations. After validation and numerical checks, the damage model is used to analyze a simplified SOFC positive-electrode/electrolyte/negative-electrode (PEN) structure subjected a redox cycle in addition to thermomechanical loads experienced during normal operation of a SOFC stack.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2012

A 2011 Updated Systematic Review and Clinical Practice Guideline for the Management of Malignant Extradural Spinal Cord Compression

Purpose: To update the 2005 Cancer Care Ontario practice guidelines for the diagnosis and treatment of adult patients with a suspected or confirmed diagnosis of extradural malignant spinal cord compression (MESCC). Methods: A review and analysis of data published from January 2004 to May 2011. The systematic literature review included published randomized control trials (RCTs), systematic reviews, meta-analyses, and prospective/retrospective studies. Results: An RCT of radiation therapy (RT) with or without decompressive surgery showed improvements in pain, ambulatory ability, urinary continence, duration of continence, functional status, and overall survival. Two RCTs of RT (30 Gy in eight fractions vs. 16 Gy in two fractions; 16 Gy in two fractions vs. 8 Gy in one fraction) in patients with a poor prognosis showed no difference in ambulation, duration of ambulation, bladder function, pain response, in-field failure, and overall survival. Retrospective multicenter studies reported that protracted RT schedules in nonsurgical patients with a good prognosis improved local control but had no effect on functional or survival outcomes. Conclusions: If not medically contraindicated, steroids are recommended for any patient with neurologic deficits suspected or confirmed to have MESCC. Surgery should be considered for patients with a good prognosis who are medically and surgically operable. RT should be given to nonsurgical patients. For those with a poor prognosis, a single fraction of 8 Gy should be given; for those with a good prognosis, 30 Gy in 10 fractions could be considered. Patients should be followed up clinically and/or radiographically to determine whether a local relapse develops. Salvage therapies should be introduced before significant neurologic deficits occur.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2013

Effect of Recombinant Human Deoxyribonuclease on Oropharyngeal Secretions in Patients With Head-and-Neck Cancers Treated With Radiochemotherapy

Purpose: The current study examined the effect of recombinant human deoxyribonuclease (rhDNase) on quality of life (QOL) measures, clinical improvement, and DNA content of thick oropharyngeal secretions (OPS) in patients with head-and-neck (H and N) cancers. Methods and Materials: Thirty-six patients with local-regional advanced H and N cancer receiving chemoradiationtherapy (CRT) were randomized to receive either placebo or rhDNase. Endpoints included MD Anderson Symptom Inventory-Head and Neck (MDASI-HN) and Functional Assessment of Cancer Therapy–Head and Neck (FACT-NH) scores, along with clinical assessment and DNA concentration of OPS. Results: There were no statistically significant differences in patients' QOL outcomes over the study period. Both groups showed an increase in symptom and interference scores, although patients in the rhDNase group showed a greater decline in both scores during the 3 months posttreatment. Similarly, both groups showed a decline in physical and functional well being but recovered in the 3 months posttreatment follow-up, with the rhDNase group exhibiting speedier recovery. Patients in the rhDNase group exhibited significant clinical improvement in OPS, blindly assessed by a physician, compared with the placebo group (67% vs 27%, respectively; P=.046). The rhDNase group showed no change in OPS-DNA concentration, although the placebo group showed a significant increase in DNA concentration during the drug trial (P=.045). There was no differences in acute toxicities between the 2 groups. Conclusions: Our preliminary data suggest that rhDNase did not significantly improve study primary endpoints of QOL measures compared with the placebo group. However, there was a significant improvement in secondary endpoints of clinically assessed OPS and DNA concentration compared with placebo in H and N cancer patients treated with CRT. Further investigation in larger numbers of patients is warranted.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2016

Mild Lung Restriction in Breast Cancer Patients After Hypofractionated and Conventional Radiation Therapy: A 3-Year Follow-Up

Purpose: To assess the effect of radiation therapy on lung function over the course of 3 years. Methods and Materials: Evolution of restrictive and obstructive lung function parameters was investigated in 108 breast cancer participants in a randomized, controlled trial comparing conventional radiation therapy (CR) and hypofractionated tomotherapy (TT) (age at inclusion ranging 32-81 years). Spirometry, plethysmography, and hemoglobin-corrected diffusing capacity were assessed at baseline and after 3 months and 1, 2, and 3 years. Natural aging was accounted for by considering all lung function parameters in terms of percent predicted values using the most recent reference values for women aged up to 80 years. Results: In the patients with negligible history of respiratory disease or smoking (n=77), the greatest rate of functional decline was observed during the initial 3 months, this acute decrease being more marked in the CR versus the TT arm. During the remainder of the 3-year follow-up period, values (in terms of percent predicted) were maintained (diffusing capacity) or continued to decline at a slower rate (forced vital capacity). However, the average decline of the restrictive lung function parameters over a 3-year period did not exceed 9% predicted in either the TT or the CR arm. Obstructive lung function parameters remained unaffected throughout. Including also the 31 patients with a history of respiratory disease or more than 10 pack-years showed a very similar restrictive pattern. Conclusions: In women with breast cancer, both conventional radiation therapy and hypofractionated tomotherapy induce small but consistent restrictive lung patterns over the course of a 3-year period, irrespective of baseline respiratory status or smoking history. The fastest rate of lung function decline generally occurred in the first 3 months.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2017

Estimating the Effective System Dead Time Parameter for Correlated Neutron Counting

We present that neutron time correlation analysis is one of the main technical nuclear safeguards techniques used to verify declarations of, or to independently assay, special nuclear materials. Quantitative information is generally extracted from the neutron-event pulse train, collected from moderated assemblies of 3 He proportional counters, in the form of correlated count rates that are derived from event-triggered coincidence gates. These count rates, most commonly referred to as singles, doubles and triples rates etc., when extracted using shift-register autocorrelation logic, are related to the reduced factorial moments of the time correlated clusters of neutrons emerging from the measurement items. Correcting these various rates for dead time losses has received considerable attention recently. The dead time losses for the higher moments in particular, and especially for large mass (high rate and highly multiplying) items, can be significant. Consequently, even in thoughtfully designed systems, accurate dead time treatments are needed if biased mass determinations are to be avoided. In support of this effort, in this paper we discuss a new approach to experimentally estimate the effective system dead time of neutron coincidence counting systems. It involves counting a random neutron source (e.g. AmLi is a good approximation to a source without correlated emission) and relating the second and higher moments of the neutron number distribution recorded in random triggered interrogation coincidence gates to the effective value of dead time parameter. We develop the theoretical basis of the method and apply it to the Oak Ridge Large Volume Active Well Coincidence Counter using sealed AmLi radionuclide neutron sources and standard multiplicity shift register electronics. The method is simple to apply compared to the predominant present approach which involves using a set of 252 Cf sources of wide emission rate, it gives excellent precision in a conveniently short time, and it yields consistent results as a function of the order of the moment used to extract the dead time parameter. In addition, this latter observation is reassuring in that it suggests the assumptions underpinning the theoretical analysis are fit for practical application purposes. However, we found that the effective dead time parameter obtained is not constant, as might be expected for a parameter that in the dead time model is characteristic of the detector system, but rather, varies systematically with gate width.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2023

A Machine Learning Model for Predicting Composition of Catalytic Coprocessing Products from Molecular Beam Mass Spectra

Demand for the development of an automated and integrated refining process for biofuels has increased in recent years due to the lack of generalized process inspection tools. In bio-oil upgrading processes, all process variables are maintained based on the offline specification of intermediates and products. A lack of real-time product specifications in batch-wise monitoring can cause process failure and wasted resources. Therefore, there is a need for a fast and accurate intermediates/product specification tool that can be used for real-time specification to reduce waste and mitigate the risk of process failure. Here, to address this gap, we developed a machine learning (ML) model for predicting speciated bio-oil composition, including paraffin, iso-paraffins, olefins, naphthene, and aromatics. The model is trained using the mass spectra from upgraded products collected in the vapor phase before condensation and predicts the composition of the condensed product. Training ML models using raw mass spectra is challenging due to numerous overlapped peaks originating from different parent compounds. With this in mind, we propose a protocol that (i) transforms raw mass spectra to chemistry-inspired predefined features and (ii) trains decision tree-based models using these features. Our results show that the random forest model was robust against overfitting and had the highest accuracy compared to other models. Moreover, a stochastic ablation method determined the eight most significant features while maximizing the accuracy. Our protocol facilitates real-time compositional analysis of upgraded bio-oils and thus real-time process monitoring. Additionally, this protocol enables the rational design of efficient catalysts and the determination of optimal process conditions.

09 BIOMASS FUELS↗

DOE OSTI2014

Unraveling chaotic attractors by complex networks and measurements of stock market complexity

We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel–Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Simulating sticky particles: A Monte Carlo method to sample a stratification

Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample probability distributions subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. More generally, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications of the method in polymer physics, self-assembly of colloids, and volume calculation in high dimensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Lattice collective modes from a continuum model of magic-angle twisted bilayer graphene

Here, we show that the insulating states of magic-angle twisted bilayer graphene support a series of collective modes corresponding to local particle-hole excitations on triangular lattice sites. Our theory is based on a continuum model of the magic angle flat bands. When the system is insulating at moiré band filling ν = -3, our calculations show that the ground state supports seven low-energy modes that lie well below the charge gap throughout the moiré Brillouin zone, one of which couples strongly to THz photons. The low-energy collective modes are faithfully described by a model with a local SU(8) degree of freedom in each moiré unit cell that we identify as the direct product of spin, valley, and an orbital pseudospin. Apart from spin and valley-wave modes, the collective mode spectrum includes a low-energy intraflavor exciton mode associated with transitions between flat valence and conduction band orbitals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Postselection-Free Entanglement Dynamics via Spacetime Duality

The dynamics of entanglement in 'hybrid' non-unitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply postselection on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of non-unitary circuits by taking advantage of spacetime duality. This method maps the purification dynamics of a mixed state under non-unitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code formed by the mixed phase in this class of hybrid dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2014

SU-E-J-190: Characterization of Radiation Induced CT Number Changes in Tumor and Normal Lung During Radiation Therapy for Lung Cancer

Purpose: To measure CT number (CTN) changes in tumor and normal lung as a function of radiation therapy (RT) dose during the course of RT delivery for lung cancer using daily IGRT CT images and single respiration phase CT images. Methods: 4D CT acquired during planning simulation and daily 3D CT acquired during daily IGRT for 10 lung cancer cases randomly selected in terms of age, caner type and stage, were analyzed using an in-house developed software tool. All patients were treated in 2 Gy fractions to primary tumors and involved nodal regions. Regions enclosed by a series of isodose surfaces in normal lung were delineated. The obtained contours along with target contours (GTVs) were populated to each singlephase planning CT and daily CT. CTN in term of Hounsfield Unit (HU) of each voxel in these delineated regions were collectively analyzed using histogram, mean, mode and linear correlation. Results: Respiration induced normal lung CTN change, as analyzed from single-phase planning CTs, ranged from 9 to 23 (±2) HU for the patients studied. Normal lung CTN change was as large as 50 (±12) HU over the entire treatment course, was dose and patient dependent and was measurable with dose changes as low as 1.5 Gy. For patients with obvious tumor volume regression, CTN within the GTV drops monotonically as much as 10 (±1) HU during the early fractions with a total dose of 20 Gy delivered. The GTV and CTN reductions are significantly correlated with correlation coefficient >0.95. Conclusion: Significant RT dose induced CTN changes in lung tissue and tumor region can be observed during even the early phase of RT delivery, and may potentially be used for early prediction of radiation response. Single respiration phase CT images have dramatically reduced statistical noise in ROIs, making daily dose response evaluation possible.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗