In this work, we prove that the complement of the Brjuno set $\mathcal{B}$ has a zero capacity with respect to the kernel $k^1_σ(z,ξ)=\ln^2{|z-ξ|}\left|\ln{\ln{\left(e+\frac{1}{|z-ξ|}\right)}}\right|^σ$ for any$σ> 2$. Similarly, the complement of the Perez-Marco set $\mathcal{PM}$ has a zero capacity with respect to the kernel $k^2_σ(z,ξ) = \ln^{2}{\ln\left(e+\frac{1} {\left| {z - ξ}\right|}\right)}\cdot\ln^σ{\ln\ln\left(e^3+\frac{1} {\left| {z - ξ}\right|}\right)}$ for any $σ>2$.
The impact of local von Neumann measurements on quantum battery capacity is investigated in tripartite quantum systems. Two measurement-based protocols are proposed and the concept of optimal local projective operators is introduced. Specifically, explicit analytical expressions are derived for the protocols when applied to general three-qubit X-states. Furthermore, the negative effects of white noise and dephasing noise on quantum battery capacity are analyzed, proving that optimal local projective operators can improve the robustness of subsystem and total system capacity against both noise types for the general tripartite X-state. The performance of different schemes in capacity enhancement are numerically validated through detailed examples and it is found that these optimized operators can effectively enhance both subsystem and total system battery capacity. The results indicate that the local von Neumann measurement is a powerful tool to enhance the battery capacity in multipartite quantum systems.
Felix Parker, Diego A. Martínez, James Scheulen
et al.
Data-driven optimization models have the potential to significantly improve hospital capacity management, particularly during demand surges, when effective allocation of capacity is most critical and challenging. However, integrating models into existing processes in a way that provides value requires recognizing that hospital administrators are ultimately responsible for making capacity management decisions, and carefully building trustworthy and accessible tools for them. In this study, we develop an interactive, user-friendly, electronic dashboard for informing hospital capacity management decisions during surge periods. The dashboard integrates real-time hospital data, predictive analytics, and optimization models. It allows hospital administrators to interactively customize parameters, enabling them to explore a range of scenarios, and provides real-time updates on recommended optimal decisions. The dashboard was created through a participatory design process, involving hospital administrators in the development team to ensure practical utility, trustworthiness, transparency, explainability, and usability. We successfully deployed our dashboard within the Johns Hopkins Health System during the height of the COVID-19 pandemic, addressing the increased need for tools to inform hospital capacity management. It was used on a daily basis, with results regularly communicated to hospital leadership. This study demonstrates the practical application of a prospective, data-driven, interactive decision-support tool for hospital system capacity management.
Mohamed M S Nasser, Christopher C. Green, Matti Vuorinen
A boundary integral equation method is presented for fast computation of the analytic capacities of compact sets in the complex plane. The method is based on using the Kerzman--Stein integral equation to compute the Szegö kernel and then the value of the Ahlfors map at the point at infinity. The proposed method can be used for domains with smooth and piecewise smooth boundaries. When combined with conformal mappings, the method can be used for compact slit sets. Several numerical examples are presented to demonstrate the efficiency of the proposed method. We recover some known exact results and corroborate the conjectural subadditivity property of analytic capacity.
Thomas Bläsius, Adrian Feilhauer, Jannik Westenfelder
Dynamic network flows, sometimes called flows over time, extend the notion of network flows to include a transit time for each edge. While Ford and Fulkerson showed that certain dynamic flow problems can be solved via a reduction to static flows, many advanced models considering congestion and time-dependent networks result in NP-hard problems. To increase understanding of these advanced dynamic flow settings we study the structural and computational complexity of the canonical extensions that have time-dependent capacities or time-dependent transit times. If the considered time interval is finite, we show that already a single edge changing capacity or transit time once makes the dynamic flow problem weakly NP-hard. In case of infinite considered time, one change in transit time or two changes in capacity make the problem weakly NP-hard. For just one capacity change, we conjecture that the problem can be solved in polynomial time. Additionally, we show the structural property that dynamic cuts and flows can become exponentially complex in the above settings where the problem is NP-hard. We further show that, despite the duality between cuts and flows, their complexities can be exponentially far apart.
The capacity sharing problem in Radio Access Network (RAN) slicing deals with the distribution of the capacity available in each RAN node among various RAN slices to satisfy their traffic demands and efficiently use the radio resources. While several capacity sharing algorithmic solutions have been proposed in the literature, their practical implementation still remains as a gap. In this paper, the implementation of a Reinforcement Learning-based capacity sharing algorithm over the O-RAN architecture is discussed, providing insights into the operation of the involved interfaces and the containerization of the solution. Moreover, the description of the testbed implemented to validate the solution is included and some performance and validation results are presented.
Similar to the energy flowing process in traditional heat engines, information could be considered to flow in the communication systems with the form of energy and entropy. Combining the thermodynamic Carnot machine and the classical Shannon information theory, a generalized thermodynamic MIMO (multiple input multiple outputs) communication system is established to analyze the channel capacity using forward error correction codes. Based on the concepts of freedom and entropy in the communication system, the generalized channel capacity is proposed under the thermodynamic theory. Furthermore, the relationships between the proposed channel capacity and the noise freedom and coding overhead are derived and simulated. Simulation results verify the proposed channel capacity is coincident with the classical channel capacity.
Akshay Seshadri, Felix Leditzky, Vikesh Siddhu
et al.
The capacity of a channel characterizes the maximum rate at which information can be transmitted through the channel asymptotically faithfully. For a channel with multiple senders and a single receiver, computing its sum capacity is possible in theory, but challenging in practice because of the nonconvex optimization involved. To address this challenge, we investigate three topics in our study. In the first part, we study the sum capacity of a family of multiple access channels (MACs) obtained from nonlocal games. For any MAC in this family, we obtain an upper bound on the sum rate that depends only on the properties of the game when allowing assistance from an arbitrary set of correlations between the senders. This approach can be used to prove separations between sum capacities when the senders are allowed to share different sets of correlations, such as classical, quantum or no-signalling correlations. We also construct a specific nonlocal game to show that the approach of bounding the sum capacity by relaxing the nonconvex optimization can give arbitrarily loose bounds. Owing to this result, in the second part, we study algorithms for non-convex optimization of a class of functions we call Lipschitz-like functions. This class includes entropic quantities, and hence these results may be of independent interest in information theory. Subsequently, in the third part, we show that one can use these techniques to compute the sum capacity of an arbitrary two-sender MACs to a fixed additive precision in quasi-polynomial time. We showcase our method by efficiently computing the sum capacity of a family of two-sender MACs for which one of the input alphabets has size two. Furthermore, we demonstrate with an example that our algorithm may compute the sum capacity to a higher precision than using the convex relaxation.
Recent advancements in understanding the impulse response of the first arrival position (FAP) channel in molecular communication (MC) have illuminated its Shannon capacity. While Lee et al. shed light on FAP channel capacities with vertical drifts, the zero-drift scenario remains a conundrum, primarily due to the challenges associated with the heavy-tailed Cauchy distributions whose first and second moments do not exist, rendering traditional mutual information constraints ineffective. This paper unveils a novel characterization of the zero drift FAP channel capacity for both 2D and 3D. Interestingly, our results reveal a 3D FAP channel capacity that is double its 2D counterpart, hinting at a capacity increase with spatial dimension growth. Furthermore, our approach, which incorporates a modified logarithmic constraint and an output signal constraint, offers a simplified and more intuitive formula (similar to the well-known Gaussian case) for estimating FAP channel capacity.
This paper is devoted to the construction of analogues of higher Ekeland-Hofer symplectic capacities for $P$-symmetric subsets in the standard symplectic space $(\mathbb{R}^{2n},ω_0)$, which is motivated by Long and Dong's study $P$-symmetric closed characteristics on $P$-symmetric convex bodies. We study the relationship between these capacities and other capacities, and give some computation examples. Moreover, we also define higher real symmetric Ekeland-Hofer capacities as a complement of Jin and the second named author's recent study of the real symmetric analogue about the first Ekeland-Hofer capacity.
Conventional multi-user multiple-input multiple-output (MU-MIMO) mainly focused on Gaussian signaling, independent and identically distributed (IID) channels, and a limited number of users. It will be laborious to cope with the heterogeneous requirements in next-generation wireless communications, such as various transmission data, complicated communication scenarios, and massive user access. Therefore, this paper studies a generalized MU-MIMO (GMU-MIMO) system with more practical constraints, i.e., non-Gaussian signaling, non-IID channel, and massive users and antennas. These generalized assumptions bring new challenges in theory and practice. For example, there is no accurate capacity analysis for GMU-MIMO. In addition, it is unclear how to achieve the capacity optimal performance with practical complexity. To address these challenges, a unified framework is proposed to derive the GMU-MIMO capacity and design a capacity optimal transceiver, which jointly considers encoding, modulation, detection, and decoding. Group asymmetry is developed to make a tradeoff between user rate allocation and implementation complexity. Specifically, the capacity region of group asymmetric GMU-MIMO is characterized by using the celebrated mutual information and minimum mean-square error (MMSE) lemma and the MMSE optimality of orthogonal approximate message passing (OAMP)/vector AMP (VAMP). Furthermore, a theoretically optimal multi-user OAMP/VAMP receiver and practical multi-user low-density parity-check (MU-LDPC) codes are proposed to achieve the capacity region of group asymmetric GMU-MIMO. Numerical results verify that the gaps between theoretical detection thresholds of the proposed framework with optimized MU-LDPC codes and QPSK modulation and the sum capacity of GMU-MIMO are about 0.2 dB. Moreover, their finite-length performances are about 1~2 dB away from the associated sum capacity.
We study the conformal capacity by using novel computational algorithms based on implementations of the fast multipole method, and analytic techniques. Especially, we apply domain functionals to study the capacities of condensers $(G,E)$ where $G$ is a simply connected domain in the complex plane and $E$ is a compact subset of $G$. Due to conformal invariance, our main tools are the hyperbolic geometry and functionals such as the hyperbolic perimeter of $E$. Our computational experiments demonstrate, for instance, sharpness of established inequalities. In the case of model problems with known analytic solutions, very high precision of computation is observed.
In this correspondence, we illustrate among other things the use of the stationarity property of the set of capacity-achieving inputs in capacity calculations. In particular, as a case study, we consider a bit-patterned media recording channel model and formulate new lower and upper bounds on its capacity that yield improvements over existing results. Inspired by the observation that the new bounds are tight at low noise levels, we also characterize the capacity of this model as a series expansion in the low-noise regime. The key to these results is the realization of stationarity in the supremizing input set in the capacity formula. While the property is prevalent in capacity formulations in the ergodic-theoretic literature, we show that this realization is possible in the Shannon-theoretic framework where a channel is defined as a sequence of finite-dimensional conditional probabilities, by defining a new class of consistent stationary and ergodic channels.
The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not so trivial to predict statistical properties on the maximum flow of the network. In this paper, we present a probabilistic analysis for evaluating the accumulate distribution of the minimum s-t cut capacity on random graphs. The graph ensemble treated in this paper consists of weighted graphs with arbitrary specified degree distribution. The main contribution of our work is a lower bound for the accumulate distribution of the minimum s-t cut capacity. From some computer experiments, it is observed that the lower bound derived here reflects the actual statistical behavior of the minimum s-t cut capacity of random graphs with specified degrees.