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NASA NTRS2012

Improving Multiple Fault Diagnosability using Possible Conflicts

Multiple fault diagnosis is a difficult problem for dynamic systems. Due to fault masking, compensation, and relative time of fault occurrence, multiple faults can manifest in many different ways as observable fault signature sequences. This decreases diagnosability of multiple faults, and therefore leads to a loss in effectiveness of the fault isolation step. We develop a qualitative, event-based, multiple fault isolation framework, and derive several notions of multiple fault diagnosability. We show that using Possible Conflicts, a model decomposition technique that decouples faults from residuals, we can significantly improve the diagnosability of multiple faults compared to an approach using a single global model. We demonstrate these concepts and provide results using a multi-tank system as a case study.

multiple faults↗

DOE OSTI2024

Multiplicity and transverse momentum dependence of charge-balance functions in pPb and PbPb collisions at LHC energies

Measurements of the charge-dependent two-particle angular correlation function in proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{NN}}$ = 8.16 TeV and lead-lead (PbPb) collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are reported. The pPb and PbPb data sets correspond to integrated luminosities of 186 nb -1 and 0.607 nb -1 , respectively, and were collected using the CMS detector at the CERN LHC. The charge-dependent correlations are characterized by balance functions of same- and opposite-sign particle pairs. The balance functions, which contain information about the creation time of charged particle pairs and the development of collectivity, are studied as functions of relative pseudorapidity (Δη) and relative azimuthal angle (Δφ), for various multiplicity and transverse momentum (p T ) intervals. A multiplicity dependence of the balance function is observed in Δη and Δφ for both systems. The width of the balance functions decreases towards high-multiplicity collisions in the momentum region < 2 GeV, for pPb and PbPb results. Integrals of the balance functions are presented in both systems, and a mild dependence of the charge-balancing fractions on multiplicity is observed. No multiplicity dependence is observed at higher transverse momentum. The data are compared with HYDJET, HIJING, and AMPT generator predictions, none of which capture completely the multiplicity dependence seen in the data. The comparison of results with different center-of-mass energies suggests that the balance functions become narrower at higher energies, which is consistent with the idea of delayed hadronization and the effect of radial flow.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Harnessing emergent multiple scattering resonances in a photonic glass structure for photoelectrochemical energy conversion

Light trapping nanostructures are often necessary to improve carrier collection yields in semiconductor photoelectrodes with intrinsically poor electron transport. Photonic crystal templates can generate tailorable light trapping via periodic and precise nanostructure, though this is not a scalable strategy for photoelectrochemical (PEC) applications. It is therefore critical to identify alternative mechanisms for light trapping that tolerate disorder. Light trapping in disordered media is generated by the diffusive transport caused by multiple scattering. In some cases, multiple scattering can generate resonances that resemble those observed in photonic crystals. While resonant multiple scattering is a disorder tolerant light trapping mechanism, it is unclear if the effect is sufficiently adaptable, or even useful, for PEC applications. Here, we describe a photonic omission glass, a nanostructure that can controllably induce resonances in multiple scattering transport. We characterized the emergence of these resonances after coating a disordered SiO 2 colloidal structure with a layer of TiO 2 , which functions both as dielectric contrast and as a light absorbing semiconductor. We show in finite element simulations and spectroscopic characterization that the resonant multiple scattering effect improves light trapping near the interface between the structure and the bulk electrolyte. This effect, coupled with the increased electrochemically active surface area, results in a hierarchically structured TiO 2 photoanode with orders of magnitude higher photocurrents compared to an equivalent planar photoanode for PEC reactions such as alkaline water oxidation. We show that controlling this resonant multiple scattering effect can be advantageous for improving PEC energy conversion in disordered photoelectrodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Charged-particle multiplicity distributions over a wide pseudorapidity range in p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

This paper presents the primary charged-particle multiplicity distributions in proton–lead collisions at a centre-of-mass energy per nucleon–nucleon collision of $\sqrt{s_{NN}}$ = 5.02 TeV. The distributions are reported for non-single diffractive collisions in different pseudorapidity ranges. The measurements are performed using the combined information from the Silicon Pixel Detector and the Forward Multiplicity Detector of ALICE. The multiplicity distributions are parametrised with a double negative binomial distribution function which provides satisfactory descriptions of the distributions for all the studied pseudorapidity intervals. The data are compared to models and analyzed quantitatively, evaluating the first four moments (mean, standard deviation, skewness, and kurtosis). The shape evolution of the measured multiplicity distributions is studied in terms of KNO variables and it is found that none of the considered models reproduces the measurements. This paper also reports on the average charged-particle multiplicity, normalised by the average number of participating nucleon pairs, as a function of the collision energy. The multiplicity results are then compared to measurements made in proton–proton and nucleus–nucleus collisions across a wide range of collision energies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1993

Impact experiments into multiple-mesh targets: Concept development of a lightweight collisional bumper

The utility of multiple-mesh targets as potential lightweight shields to protect spacecraft in low-Earth orbit against collisional damage is explored. Earlier studies revealed that single meshes comminute hypervelocity impactors with efficiencies comparable to contiguous targets. Multiple interaction of projectile fragments with any number of meshes should lead to increased comminution, deceleration, and dispersion of the projectile, such that all debris exiting the mesh stack possesses low specific energies (ergs/sq cm) that would readily be tolerated by many flight systems. The study is conceptually exploring the sensitivity of major variables such as impact velocity, the specific areal mass (g/sq cm) of the total mesh stack (SM), and the separation distance (S) between individual meshes. Most experiments employed five or ten meshes with total SM typically less than 0.5 the specific mass of the impactor, and silicate glass impactors rather than metal projectiles. While projectile comminution increases with increasing impact velocity due to progressively higher shock stresses, encounters with multiple-meshes at low velocity (1-2 km/s) already lead to significant disruption of the glass impactors, with the resulting fragments being additionally decelerated and dispersed by subsequent meshes, and, unlike most contiguous single-plate bumpers, leading to respectable performance at low velocity. Total specific bumper mass must be the subject of careful trade-off studies; relatively massive bumpers will generate too much debris being dislodged from the bumper itself, while exceptionally lightweight designs will not cause sufficient comminution, deceleration, or dispersion of the impactor. Separation distance was found to be a crucial design parameter, as it controls the dispersion of the fragment cloud. Substantial mass savings could result if maximum separation distances were employed. The total mass of debris dislodged by multiple-mesh stacks is modestly smaller than that of single, contiguous-membrane shields. The cumulative surface area of all penetration holes in multiple mesh stacks is an order of magnitude smaller than that in analog multiple-foil shields, suggesting good long-term performance of the mesh designs. Due to different experimental conditions, direct and quantitative comparison with other lightweight shields is not possible at present.

Hoerz, Friedrich↗

NASA NTRS1994

Fourth Annual International Acquisitions Workshop: Access to Multiple Media Worldwide

Topics discussed during the workshop include: (1) Multinational-Multiple media collections and activities spanning many countries; (2) Multiple media in North American trade and commerce; (3) African spotlight; (4) Europe-Multiple media in national libraries and services; (5) Scandinavian spotlight; (6) Internet update; (7) Multiple media in US federal agencies; (8) Open-source multiple media in US federal agencies; and (9) Multiple media at US federal technical agencies-NIST and NOAA.

Source record↗

NASA NTRS1997

Sequential Test Strategies for Multiple Fault Isolation

In this paper, we consider the problem of constructing near optimal test sequencing algorithms for diagnosing multiple faults in redundant (fault-tolerant) systems. The computational complexity of solving the optimal multiple-fault isolation problem is super-exponential, that is, it is much more difficult than the single-fault isolation problem, which, by itself, is NP-hard. By employing concepts from information theory and Lagrangian relaxation, we present several static and dynamic (on-line or interactive) test sequencing algorithms for the multiple fault isolation problem that provide a trade-off between the degree of suboptimality and computational complexity. Furthermore, we present novel diagnostic strategies that generate a static diagnostic directed graph (digraph), instead of a static diagnostic tree, for multiple fault diagnosis. Using this approach, the storage complexity of the overall diagnostic strategy reduces substantially. Computational results based on real-world systems indicate that the size of a static multiple fault strategy is strictly related to the structure of the system, and that the use of an on-line multiple fault strategy can diagnose faults in systems with as many as 10,000 failure sources.

Shakeri, M.↗

NASA NTRS1998

A Multiplicity Survey of Chromospherically Active and Inactive Stars

Surveys of the three samples of solar-type stars, segregated by chromospheric emission level, were made to determine their multiplicity fractions and to investigate the evolution of multiplicity with age. In total, 245 stars were searched for companions with DeltaV <= 3.0 and separations of 0.035" to 1.08" using optical speckle interferometry, By incorporating the visual micrometer survey for duplicity of the LamontHussey Observatory, the angular coverage was extended to 5.0" with no change in in the DeltaV limit. This magnitude difference allows mass ratios of 0.63 and larger to be detected throughout a search region of 2-127 AU for the stars observed. The 84 primaries observed in the chromospherically active sample are presumably part of a young population and are found to have a multiplicity fraction of 17.9% +/- 4.6%. The sample of 118 inactive, presumably older, primaries were selected and observed using identical methods and are found to have a multiplicity fraction of only 8.5% +/- 2.7%. Given the known link between chromospheric activity and age, these results tentatively imply a decreasing stellar multiplicity fraction from 1 to 4 Gyr, the approximate ages of the two samples. Finally, only two of the 14 very active primaries observed were found to have a companion meeting the survey detection parameters. In this case, many of the systems are either very young, or close, RS CVn type multiples that are unresolvable using techniques employed here.

Mason, Brian D.↗

NASA NTRS2006

PVM Enhancement for Beowulf Multiple-Processor Nodes

A recent version of the Parallel Virtual Machine (PVM) computer program has been enhanced to enable use of multiple processors in a single node of a Beowulf system (a cluster of personal computers that runs the Linux operating system). A previous version of PVM had been enhanced by addition of a software port, denoted BEOLIN, that enables the incorporation of a Beowulf system into a larger parallel processing system administered by PVM, as though the Beowulf system were a single computer in the larger system. BEOLIN spawns tasks on (that is, automatically assigns tasks to) individual nodes within the cluster. However, BEOLIN does not enable the use of multiple processors in a single node. The present enhancement adds support for a parameter in the PVM command line that enables the user to specify which Internet Protocol host address the code should use in communicating with other Beowulf nodes. This enhancement also provides for the case in which each node in a Beowulf system contains multiple processors. In this case, by making multiple references to a single node, the user can cause the software to spawn multiple tasks on the multiple processors in that node.

Springer, Paul↗

NASA NTRS2016

Sizing a Common Habitat for Multiple Environments and Mission Durations

A human mission to Mars and other deep space destinations will require a consistent habitation strategy that applies to disparate environments preferably using multiples of identical hardware. The crew will endure high-g forces during launch, microgravity during transit, and various partial gravities on the destination planet, moon, or asteroid. Habitable volume will likely need to be broken up into smaller modules that do not exceed the capacity of launch vehicles and entry-descent-landing technologies. Though it may be possible to design a different unique, optimized habitat for each environment that the crew may encounter, it is more likely that space agencies and other mission sponsors will only have the resources to develop and produce single multi-use hardware that can be used equally well in all environments, with minimal adaptation by the crew. When sizing habitable volume, mission duration and number of crew become important factors to consider. For example, a pressurized rover cabin may only need to support two crew members for a few days at a time, requiring less volume than a habitat that must support the same number of persons for an entire year. In this study the authors consider constraining factors such as launch vehicle capacity, mission duration, crew size, and Mars lander capacity and study how to divide total pressurized volume, subsystems, equipment, consumables, and supplies into multiple manifests. Preference has been given to solutions that use multiples of identical modules over unique optimized volumes. For example at one extreme, can all the habitat pressure vessels, logistic modules, Mars ascent stage cabins, rover cabins, and airlocks be constructed from multiples of the same small-diameter cylindrical modules? On the other extreme, can logistics, habitation volume, mobility, all be enclosed in a single monolithic volume habitat design? Though there may be advantages and disadvantages to either extreme, the conclusion of this study is that most functions can be distilled into two sizes for hardware: multiples of large diameter modules that generally stay in one place, and multiples of smaller volume cabins that can be moved around or function as cockpits for ascent stages, support vehicles, rovers, airlocks, and logistics delivery.

Howe, A Scott↗

NASA NTRS2019

Audibility of Multiple, Low-Frequency Tonal Signals in Noise

The main purpose of this study is to examine the audibility of multiple, low-frequency tones that are placed in distinct auditory channels. Three experiments are described, the goals of which are to determine if the presence of sound in multiple channels results in enhanced audibility and to assess the applicability of the Statistical Summation Model (SSM) to this frequency range. This model predicts that for the case of multiple signals that are in separate auditory channels, implying statistical independence, each with sensitivity value d prime of i, the resulting total sensitivity is given by the square root of the sum of the squares of the individual d prime of i values. In common with previous studies conducted at higher frequencies, the signals are pure tones and the maskers are broadband noise. The requirement that low frequency tones be placed in separate auditory filters limited the number of tones to a maximum of three. The first of the three experiments measured the change in masked thresholds for two- and three-tone signals relative to the level of the equally-detectable single tones. The multiple tone signals were composed of combinations of 55, 120 and 200 Hz tones. The measured changes in thresholds exceeded those predicted by the SSM, although they did not differ statistically from the model predictions. The second experiment employed the same overall approach but acquired more data and concentrated on the three-tone signal. Once again, the measured changes in masked threshold exceeded the model predictions, this time to a statistically-significant degree. Two issues were postulated with the potential to yield inflated changes in masked threshold: interaction between tones resulting in perceptible intermodulation/difference tones, and the assumption that the tones were in distinct auditory filters and statistically independent of one another. The third experiment used two sets of three-tone signals to address these latter concerns. The first set of three tones was composed of harmonically related tone frequencies of 55, 110 and 165 Hz, which was an attempt to reduce effects of intermodulation difference tones. The second set of three tones was chosen to be 110, 220 and 330 Hz, again reducing effects of difference tones, but also providing greater separation between tones. Results for the first set of three tones compared to those of the earlier experiments indicated that intermodulation was not an important effect. The second set of three tones (110, 220, 330 Hz) yielded changes in masked thresholds that, on average, were in good agreement with the SSM, although intersubject variability was large and prohibited a definitive conclusion regarding the concern that tone spacing was inadequate. The results of the three experiments showed that the masked threshold of sounds with multiple (two or three) equally-detectable low frequency tones was lower than those of the single tones. In other words, it is clear that audibility is enhanced by the presence of signals in multiple auditory filters. This finding is consistent with most previous research conducted at higher frequencies. In contrast with previous research, test subjects were, on average, able to detect multitone sounds at lower levels than those predicted using the SSM. Analyses that included Monte Carlo simulations showed that normally distributed errors in the single tone thresholds result in biased estimates of the thresholds of multitone sounds. This phenomenon is likely responsible for at least a substantial fraction of the unexpected deviation of measurements from SSM predictions.

Rafaelof, Menachem↗

DOE OSTI2026

Multiplicity dependence of K*(892) ± production in pp collisions at $\sqrt{s}$ = 13 TeV

The first results of K*(892) ± production at midrapidity (|y| < 0.5) in pp collisions at $\sqrt{s}$= 13 TeV as a function of the event multiplicity are presented. The K*(892) ± has been reconstructed via its hadronic decay channel K*(892) ± → π ± + K$^0_{\textrm{S}}$ using the ALICE detector at the LHC. For each multiplicity class, the differential transverse momentum (p T ) spectrum, the mean transverse momentum ⟨p T ⟩, the p T -integrated yield (dN/dy), and the ratio of the K*(892) ± to K$^0_{\textrm{S}}$ yields are reported. These are consistent with previous K*(892) 0 resonance results with a higher level of precision. Comparisons with phenomenological models such as PYTHIA6, PYTHIA8, EPOS-LHC, and DIPSY are also discussed. For the first time, a significant K*(892) ± /K$^0_{\textrm{S}}$ suppression in pp collisions is observed at a 7σ level passing from low to high multiplicity events. The ratios of the p T -differential yields of K*(892) ± and K$^0_{\textrm{S}}$ in high and low multiplicity events are also presented along with their double ratio. For p T ≲ 2 GeV/c this double ratio persists below unity by more than 3σ suggesting that the suppression affects mainly low p T resonances. The measured decreasing trend of the K*(892) ± /K$^0_{\textrm{S}}$ ratio with increasing multiplicity, which in heavy-ion collisions is typically attributed to the rescattering of decay particles of the short-lived resonances, is reproduced by the EPOS-LHC model without the use of hadronic afterburners.

Hadronic resonance production↗

DOE OSTI2025

Multiple Twinning in Nacre and Aragonite

Twinning occurs when two crystals share a coherent interface along which their lattices are mirror symmetric. Here, twinning is investigated in biogenic and geologic aragonite (CaCO 3 ) in columnar nacre from the red abalone Haliotis rufescens, sheet nacre from the black-lip pearl oyster Pinctada margaritifera, and geologic aragonite. All samples exhibit the expected single (110) twins, characterized by a 116.2° rotation of the aragonite a-axis. Surprisingly, multiple twins—double, triple, quadruple—are also observed, each involving successive 116.2° rotations of the a-axis around the c-axis. Multiple twinning is concomitant but distinct from the well-known cyclic twinning of aragonite. Multiple twinning is most prevalent in columnar nacre, reaching up to quadruple twins, most frequently occurring between nacre tablets in the same column, whereas sheet nacre and geologic aragonite exhibit up to triple twins. The frequency of twins decreases with increasing twin multiple, consistent with a physical rather than biological origin. This interpretation is supported by observations in geologic aragonite and by simulations of columnar nacre growth, which incorporate only nucleation rate, growth rate, and basic geometric constraints, yet they reproduce the observed twinning behavior in columnar nacre, reinforcing the conclusion that multiple twinning arises from physical growth mechanisms.

Schmidt, Connor A. [Univ. of Wisconsin, Madison, W↗

DOE OSTI2025

Search for jet quenching with dijets from high-multiplicity pPb collisions at $\sqrt{s_{NN}}$ = 8.16 TeV

The first measurement of the dijet transverse momentum balance xj in proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{NN}}$ = 8.16 TeV is presented. The xj observable, defined as the ratio of the subleading over leading jet transverse momentum in a dijet pair, is used to search for jet quenching effects. The data, corresponding to an integrated luminosity of 174.6 nb −1 , were collected with the CMS detector in 2016. The x j distributions and their average values are studied as functions of the charged-particle multiplicity of the events and for various dijet rapidity selections. The latter enables probing hard scattering of partons carrying distinct nucleon momentum fractions x in the proton- and lead-going directions. The former, aided by the high-multiplicity triggers, allows probing for potential jet quenching effects in high-multiplicity events (with up to 400 charged particles), for which collective phenomena consistent with quark-gluon plasma (QGP) droplet formation were previously observed. The ratios of x j distributions for high- to low-multiplicity events are used to quantify the possible medium effects. These ratios are consistent with simulations of the hard-scattering process that do not include QGP production. These measurements set an upper limit on medium-induced energy loss of the subleading jet of 1.26% of its transverse momentum at the 90% confidence level in high multiplicity pPb events.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Investigating strangeness enhancement with multiplicity in pp collisions using angular correlations

A study of strange hadron production associated with hard scattering processes and with the underlying event is conducted to investigate the origin of the enhanced production of strange hadrons in small collision systems characterised by large charged-particle multiplicities. For this purpose, the production of the single-strange meson ${\textrm{K}}_{\textrm{S}}^0$ and the double-strange baryon Ξ ± is measured, in each event, in the azimuthal direction of the highest-p T particle (“trigger” particle), related to hard scattering processes, and in the direction transverse to it in azimuth, associated with the underlying event, in pp collisions at $\sqrt{s}$ = 5.02 TeV and $\sqrt{s}$ = 13 TeV using the ALICE detector at the LHC. The per-trigger yields of ${\textrm{K}}_{\textrm{S}}^0$ and Ξ ± are dominated by the transverse-to-leading production (i.e., in the direction transverse to the trigger particle), whose contribution relative to the toward-leading production is observed to increase with the event charged-particle multiplicity. The transverse-to-leading and the toward-leading Ξ ± /${\textrm{K}}_{\textrm{S}}^0$ yield ratios increase with the multiplicity of charged particles, suggesting that strangeness enhancement with multiplicity is associated with both hard scattering processes and the underlying event. The relative production of Ξ ± with respect to ${\textrm{K}}_{\textrm{S}}^0$ is higher in transverse-to-leading processes over the whole multiplicity interval covered by the measurement. The ${\textrm{K}}_{\textrm{S}}^0$ and Ξ ± per-trigger yields and yield ratios are compared with predictions of three different phenomenological models, namely Pythia8.2 with the Monash tune, Pythia8.2 with ropes and EPOS LHC. The comparison shows that none of them can quantitatively describe either the transverse-to-leading or the toward-leading yields of ${\textrm{K}}_{\textrm{S}}^0$ and Ξ ± .

hadron-hadron scattering↗

DOE OSTI2026

An algebraic convolution formulation for multiple-scattering correction in small-angle neutron scattering

Multiple scattering in small-angle neutron scattering (SANS) redistributes spectral weight and distorts structural interpretation, particularly for thick or strongly scattering samples. We develop a finite-dimensional spectral desmearing framework that corrects multiple scattering without resorting to integral transforms or model-dependent extrapolation. The primary intensity is expanded in an orthonormal basis adapted to the isotropic transverse-momentum measure, under which convolution reduces to a recursive tensor contraction, allowing the Poisson-weighted multiple-scattering series to be evaluated directly in a finite-dimensional basis representation. This formulation yields a stable forward–inverse mapping between apparent and primary spectra. Numerical tests demonstrate convergence under repeated convolution and accurate recovery of the single-scattering intensity. Application to SANS measurements collected at multiple neutron facilities, including the Spallation Neutron Source, the High Flux Isotope Reactor, and the Institut Laue-Langevin, shows the quantitative reconstruction of the underlying primary spectrum across a wide range of transmission conditions, including strongly attenuating samples. Here, the method provides a stable, model-agnostic framework for multiple-scattering correction in SANS and enables consistent structural interpretation across instruments and scattering regimes.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

DOE OSTI2025

Behavior of Multiple PV Plants in Future Power Grids During Events

As the integration of multiple photovoltaic (PV) plants into power grids grows, the dynamic response of each plant and their interactions during transient events demands a deeper understanding. In this paper, the dynamic behavior of multiple PV plants connected to future power grids is comprehensively explored using site-specific high-fidelity electromagnetic transient (EMT) PV plant models and generic high-fidelity EMT PV plant models. This research demonstrates the need to employ multiple high-fidelity EMT PV plant models to understand the intricate interactions between multiple PV plants during grid events. These models, developed in Fortran within the PSCAD environment, encompass a range of operational scenarios and plant configurations, offering invaluable insights crucial for future system planning with multiple PV plants to enhance grid stability.

Marthi, Phani Ratna Vanamali [ORNL] (ORCID:0000000↗

DOE OSTI2025

Fair Concurrent Training of Multiple Models in Federated Learning

Federated learning (FL) enables collaborative learning across multiple clients. In most FL work, all clients train a single learning task. However, the recent proliferation of FL applications may increasingly require multiple FL tasks to be trained simultaneously, sharing clients’ computing resources, which we call Multiple-Model Federated Learning (MMFL). Current MMFL algorithms use naïve average-based client-task allocation schemes that often lead to unfair performance when FL tasks have heterogeneous difficulty levels, as the more difficult tasks may need more client participation to train effectively. Furthermore, in the MMFL setting, we face a further challenge that some clients may prefer training specific tasks to others, and may not even be willing to train other tasks, e.g., due to high computational costs, which may exacerbate unfairness in training outcomes across tasks. We address both challenges by firstly designing FedFairMMFL, a difficulty-aware algorithm that dynamically allocates clients to tasks in each training round, based on the tasks’ current performance levels. We provide guarantees on the resulting task fairness and FedFairMMFL’s convergence rate. We then propose novel auction designs that incentivizes clients to train multiple tasks, so as to fairly distribute clients’ training efforts across the tasks, and extend our convergence guarantees to this setting. Here, we finally evaluate our algorithm with multiple sets of learning tasks on real world datasets, showing that our algorithm improves fairness by improving the final model accuracy and convergence speed of the worst performing tasks, while maintaining the average accuracy across tasks.

Federated learning↗