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Efficient algorithms for solving optimal transport problems are important for measuring and optimizing distances between functions. In the $L^2$ semi-discrete context, this problem consists of finding a map from a continuous density…
Time-reversal symmetry of most conservative forces constrains the properties of linear transport in most physical systems. Here, I study the efficiency of energy transfer in oscillator networks where time-reversal symmetry is broken locally…
We study the problem of networked online convex optimization, where each agent individually decides on an action at every time step and agents cooperatively seek to minimize the total global cost over a finite horizon. The global cost is…
We consider the problem of finding weights and biases for a two-layer fully connected neural network to fit a given set of data points as well as possible, also known as EmpiricalRiskMinimization. Our main result is that the associated…
Many real-world applications have the time-linkage property, and the only theoretical analysis is recently given by Zheng, et al. (TEVC 2021) on their proposed time-linkage OneMax problem, OneMax$_{(0,1^n)}$. However, only two elitist…
We utilize recently introduced linear programming bounds for the energy of periodic configurations in $\mathbb{R}^d$ to construct configurations which are universally optimal among those of the form $\omega_4+L_\beta$, where $\omega_4$ is a…
It was shown recently that the $K$ L1-norm principal components (L1-PCs) of a real-valued data matrix $\mathbf X \in \mathbb R^{D \times N}$ ($N$ data samples of $D$ dimensions) can be exactly calculated with cost $\mathcal{O}(2^{NK})$ or,…
Zermelo's navigation problem seeks the trajectory of minimal travel time between two points in a fluid flow. We address this problem for an agent -- such as a micro-robot or active particle -- that is advected by a two-dimensional flow,…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
In this paper, we derive the optimal user pairing and power allocation in uplink non orthogonal multiple access (NOMA) networks. The optimal power allocation that maximizes the sum rate is found for two user NOMA networks, while ensuring…
We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an…
In many complex systems, for the activity f(i) of the constituents or nodes i, a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) ~ <f(i)>^alpha; universal…
We compute the lowest operator dimension $\Delta(J;D)$ at large global charge $J$ in the $O(2)$ Wilson-Fisher model in $D=4-\epsilon$ dimensions, to leading order in both $1/J$ and $\epsilon$. The final result for $\Delta(J;D)$ in the…
In the recent years the Schr\"odinger problem has gained a lot of attention because of the connection, in the small-noise regime, with the Monge-Kantorovich optimal transport problem. Its optimal value, the \emph{entropic cost}…
In this paper, we present a novel algorithm for power allocation in the Amplify-and-Forward cooperative communication that minimizes the outage probability with a given value of total power. We present the problem with new formulation and…
Federated Learning (FL) is an intriguing distributed machine learning approach due to its privacy-preserving characteristics. To balance the trade-off between energy and execution latency, and thus accommodate different demands and…
On-line linear optimization on combinatorial action sets (d-dimensional actions) with bandit feedback, is known to have complexity in the order of the dimension of the problem. The exponential weighted strategy achieves the best known…
We study a modified version of a model previously proposed by Jackson and Wolinsky to account for communicating information and allocating goods in socioeconomic networks. In the model, the utility function of each node is given by a…
A weighted point-availability time-dependent network is a list of temporal edges, where each temporal edge has an appearing time value, a travel time value, and a cost value. In this paper we consider the single source Pareto problem in…
This paper investigates the optimal power allocation scheme for sum throughput maximization of non-orthogonal multiple access (NOMA) system with $\alpha$-fairness. In contrast to the existing fairness NOMA models, $\alpha$-fairness can only…