arXiv subjects

Rajnish Kumar

Publications and source records attributed to Rajnish Kumar.

14 recordsLinked to original sources

arXiv2026

Integrating Proportionality and Egalitarianism in Claims Problems

We study the problem of allocating a finite estate among agents whose total claims exceed the available resources, a standard framework in the theory of claims problems. Two canonical rules embody competing fairness ideals: the Proportional rule allocates in proportion to claims, while the Constrained Equal Awards (CEA) rule equalizes awards as much as possible subject to claim-boundedness. We introduce the P-CEA family of compromise rules, which assigns each agent a fixed baseline award, capped by her claim, and distributes the remaining estate proportionally to residual claims. By varying the baseline parameter, this family generates a continuum of allocation rules that interpolates between the Proportional and CEA benchmarks. We provide an axiomatic characterization based on two threshold-dependent principles: No Advantageous Reallocation, which prevents agents with claims above the threshold from benefiting through coordinated claim redistribution that preserves the threshold condition, and Sustainable Lower Bound, which guarantees each agent at least the minimum of her claim and the threshold. We further develop a dual analysis that reallocates losses instead of awards and characterize the corresponding dual family using the dual versions of our axioms.

econ.TH↗

arXiv2026

Differentiable Normative Guidance for Nash Bargaining Solution Recovery

Autonomous artificial intelligence agents in negotiation systems must generate equitable utility allocations satisfying individual rationality (IR), ensuring each agent receives at least its outside option, and the Nash Bargaining Solution (NBS), which maximizes joint surplus. Existing generative models often learn suboptimal human behaviors, producing solutions far from Pareto efficiency, while classical methods require full Pareto frontier knowledge, which is unavailable in real datasets. We propose a guided graph diffusion framework that generates individually rational utility vectors while approximating the NBS without frontier knowledge at inference time. Negotiations are modeled as directed graphs with graph attention capturing asymmetric agent attributes, and a conditional diffusion model maps these to utility vectors. A differentiable composite guidance loss, applied in the final reverse diffusion steps, penalizes IR violations and Nash product gaps. We prove that, under sufficient penalty weighting, solutions enter the IR region in finite time. Across datasets, the method achieves 100% IR compliance. Nash efficiency reaches 99.45% on synthetic data (within 0.55 percentage points of an oracle), and 54.24% (CaSiNo) and 88.67% (Deal or No Deal), improving 20-60 percentage points over unconstrained generative baselines.

cs.GT↗

arXiv2025

Load-Aware Calibration of EMG-Driven Musculoskeletal Models for Accurate and Generalizable Joint Torque Estimation

Accurate EMG-driven musculoskeletal (MSK) modeling is critical for biomechanics, rehabilitation, and assistive technology. However, most models calibrate parameters under a single load, ignoring the fact that tasks with similar kinematics may differ in mechanical demand. This study introduces a load-aware calibration framework to improve joint torque prediction accuracy and generalizability. Surface EMG and joint kinematics were recorded from eleven participants during elbow flexion-extension under 0, 2, and 4\,kg loads. We evaluated three calibration strategies (load-specific, global, cross-load) and three optimization frameworks (simulated annealing (SA), particle swarm optimization (PSO), and hybrid PSO-pattern search (PSO-PS)). Results indicate that load-specific calibration significantly improves performance, with lower RMSE and higher correlation ($r > 0.75$). Parameters related to muscle force, fiber length, and activation dynamics showed high load sensitivity. PSO-based methods yielded more consistent and physiologically plausible estimates than simulated annealing. The proposed framework enables MSK models to distinguish between visually similar but mechanically distinct tasks, supporting robust subject-specific modeling for clinical and real-world applications.

physics.bio-ph↗

arXiv2025

Nanobubble size controls gas hydrate nucleation in supercooled water

Gas hydrates are crystalline compounds formed when water molecules encapsulate guest gas molecules under high pressure and low temperatures. They have gained significant interest due to their potential as alternative energy resources and their applications in gas storage, transportation, and carbon sequestration. However, the fundamental mechanisms governing their formation, especially the influence of gas bubbles, remain poorly understood. In this study, we use molecular dynamics (MD) simulations to examine how methane nanobubble size modulates hydrate formation in supercooled water. Nanobubbles of different sizes are generated by modulating the methane concentration in a methane-water mixture during equilibration under high-temperature and low-pressure conditions, followed by quenching to low temperature and high pressure to induce gas hydrate nucleation and subsequent growth. The simulations reveal a strong correlation between nanobubble size and the extent of hydrate formation. Specifically, the extent of hydrate formation increases with bubble size in the small-to-intermediate regime. However, beyond a critical bubble size threshold, the hydrate formation efficiency declines. The work provides new molecular-level insight into how nanobubble size modulates gas hydrate nucleation and growth dynamics.

physics.chem-ph↗

arXiv2025

Deep Muscle EMG construction using A Physics-Integrated Deep Learning approach

Electromyography (EMG)--based computational musculoskeletal modeling is a non-invasive method for studying musculotendon function, human movement, and neuromuscular control, providing estimates of internal variables like muscle forces and joint torques. However, EMG signals from deeper muscles are often challenging to measure by placing the surface EMG electrodes and unfeasible to measure directly using invasive methods. The restriction to the access of EMG data from deeper muscles poses a considerable obstacle to the broad adoption of EMG-driven modeling techniques. A strategic alternative is to use an estimation algorithm to approximate the missing EMG signals from deeper muscle. A similar strategy is used in physics-informed deep learning, where the features of physical systems are learned without labeled data. In this work, we propose a hybrid deep learning algorithm, namely the neural musculoskeletal model (NMM), that integrates physics-informed and data-driven deep learning to approximate the EMG signals from the deeper muscles. While data-driven modeling is used to predict the missing EMG signals, physics-based modeling engraves the subject-specific information into the predictions. Experimental verifications on five test subjects are carried out to investigate the performance of the proposed hybrid framework. The proposed NMM is validated against the joint torque computed from 'OpenSim' software. The predicted deep EMG signals are also compared against the state-of-the-art muscle synergy extrapolation (MSE) approach, where the proposed NMM completely outperforms the existing MSE framework by a significant margin.

cs.LG↗

arXiv2024

sEMG-Driven Physics-Informed Gated Recurrent Networks for Modeling Upper Limb Multi-Joint Movement Dynamics

Exoskeletons and rehabilitation systems have the potential to improve human strength and recovery by using adaptive human-machine interfaces. Achieving precise and responsive control in these systems depends on accurately estimating joint movement dynamics, such as joint angle, velocity, acceleration, external mass, and torque. While machine learning (ML) approaches have been employed to predict joint kinematics from surface electromyography (sEMG) data, traditional ML models often struggle to generalize across dynamic movements. In contrast, physics-informed neural networks integrate biomechanical principles, but their effectiveness in predicting full movement dynamics has not been thoroughly explored. To address this, we introduce the Physics-informed Gated Recurrent Network (PiGRN), a novel model designed to predict multi-joint movement dynamics from sEMG data. PiGRN uses a Gated Recurrent Unit (GRU) to process time-series sEMG inputs, estimate multi-joint kinematics and external loads, and predict joint torque while incorporating physics-based constraints during training. Experimental validation, using sEMG data from five participants performing elbow flexion-extension tasks with 0 kg, 2 kg, and 4 kg loads, showed that PiGRN accurately predicted joint torques for 10 novel movements. RMSE values ranged from 4.02\% to 11.40\%, with correlation coefficients between 0.87 and 0.98. These results underscore PiGRN's potential for real-time applications in exoskeletons and rehabilitation. Future work will focus on expanding datasets, improving musculoskeletal models, and investigating unsupervised learning approaches.

cs.LG↗

arXiv2024

Weighted Myerson value for Network games

We study the weighted Myerson value for Network games extending a similar concept for communication situations. Network games, unlike communication situations, treat direct and indirect links among players differently and distinguish their effects in both worth generation and allocation processes. The weighted Myerson value is an allocation rule for Network games that generalizes the Myerson value of Network games. Here, the players are assumed to have some weights measuring their capacity to form links with other players. Two characterization of the weighted Myerson value are provided. Finally, we propose a bidding mechanism to show that the weighted Myerson value is a subgame-perfect Nash equilibrium under a non-cooperative framework.

econ.TH↗

arXiv2023

Predicting Multi-Joint Kinematics of the Upper Limb from EMG Signals Across Varied Loads with a Physics-Informed Neural Network

In this research, we present an innovative method known as a physics-informed neural network (PINN) model to predict multi-joint kinematics using electromyography (EMG) signals recorded from the muscles surrounding these joints across various loads. The primary aim is to simultaneously predict both the shoulder and elbow joint angles while executing elbow flexion-extension (FE) movements, especially under varying load conditions. The PINN model is constructed by combining a feed-forward Artificial Neural Network (ANN) with a joint torque computation model. During the training process, the model utilizes a custom loss function derived from an inverse dynamics joint torque musculoskeletal model, along with a mean square angle loss. The training dataset for the PINN model comprises EMG and time data collected from four different subjects. To assess the model's performance, we conducted a comparison between the predicted joint angles and experimental data using a testing data set. The results demonstrated strong correlations of 58% to 83% in joint angle prediction. The findings highlight the potential of incorporating physical principles into the model, not only increasing its versatility but also enhancing its accuracy. The findings could have significant implications for the precise estimation of multi-joint kinematics in dynamic scenarios, particularly concerning the advancement of human-machine interfaces (HMIs) for exoskeletons and prosthetic control systems.

eess.SP↗

arXiv2023

The Expected Shapley value on a class of probabilistic games

We study a class of probabilistic cooperative games which can be treated as an extension of the classical cooperative games with transferable utilities. The coalitions have an exogenous probability of being realized. This probability distribution is known beforehand and the distribution of the expected worth needs to be done before the realization of the state. We obtain a value for this class of games and present three characterizations of this value using natural extensions of the axioms used in the seminal axiomatization of the Shapley value. The value, which we call the Expected Shapley value, allocates the players their expected worth with respect to a probability distribution.

econ.TH↗

arXiv2023

Weighted position value for Network games

In Network games under cooperative framework, the position value is a link based allocation rule. It is obtained from the Shapley value of an associated cooperative game where the links of the network are considered players. The Shapley value of each of the links is then divided equally among the players who form those links. The inherent assumption is that the value is indifferent to the weights of the players in the network. Depending on how much central a player is in the network, or the ability of making links with other players etc., for example, players can be considered to have weights. Thus, in such situations, dividing the Shapley value equally among the players can be an over-simplistic notion. We propose a generalised version of the position value: the weighted position value that allocates the Shapley shares proportional to the players' weights. These weights of the players are exogenously given. We provide two axiomatic characterizations of our value. Finally, a bidding mechanism is formulated to show that any sub-game perfect equilibrium (SPE) of this mechanism coincides with the weighted position value.

econ.TH↗

arXiv2022

Consolidating Marginalism and Egalitarianism: A New Value for Transferable Utility Games

In cooperative games with transferable utilities, the Shapley value is an extreme case of marginalism while the Equal Division rule is an extreme case of egalitarianism. The Shapley value does not assign anything to the non-productive players and the Equal Division rule does not concern itself to the relative efficiency of the players in generating a resource. However, in real life situations neither of them is a good fit for the fair distribution of resources as the society is neither devoid of solidarity nor it can be indifferent to rewarding the relatively more productive players. Thus a trade-off between these two extreme cases has caught attention from many researchers. In this paper, we obtain a new value for cooperative games with transferable utilities that adopts egalitarianism in smaller coalitions on one hand and on the other hand takes care of the players' marginal productivity in sufficiently large coalitions. Our value is identical with the Shapley value on one extreme and the Equal Division rule on the other extreme. We provide four characterizations of the value using variants of standard axioms in the literature. We have also developed a strategic implementation mechanism of our value in sub-game perfect Nash equilibrium.

econ.TH↗

arXiv2021

Multi-task Learning with Metadata for Music Mood Classification

Mood recognition is an important problem in music informatics and has key applications in music discovery and recommendation. These applications have become even more relevant with the rise of music streaming. Our work investigates the research question of whether we can leverage audio metadata such as artist and year, which is readily available, to improve the performance of mood classification models. To this end, we propose a multi-task learning approach in which a shared model is simultaneously trained for mood and metadata prediction tasks with the goal to learn richer representations. Experimentally, we demonstrate that applying our technique on the existing state-of-the-art convolutional neural networks for mood classification improves their performances consistently. We conduct experiments on multiple datasets and report that our approach can lead to improvements in the average precision metric by up to 8.7 points.

cs.SD↗

arXiv2021

Expected Values for Variable Network Games

A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatizations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatization of the Position Value based on the balanced link contribution property to the Expected Position Value.

cs.GT↗

arXiv2020

Fairness and Efficiency in Cake-Cutting with Single-Peaked Preferences

We study the cake-cutting problem when agents have single-peaked preferences over the cake. We show that a recently proposed mechanism by Wang-Wu (2019) to obtain envy-free allocations can yield large welfare losses. Using a simplifying assumption, we characterize all Pareto optimal allocations, which have a simple structure: are peak-preserving and non-wasteful. Finally, we provide simple alternative mechanisms that Pareto dominate that of Wang-Wu, and which achieve envy-freeness or Pareto optimality.

cs.GT↗