Water is a critical resource for data centers and an efficient means of cooling. However, meeting the growing water demand of data centers requires substantial peak water withdrawals, which many communities in the United States cannot supply, especially during the hottest days of the year. This largely overlooked water capacity constraint is emerging as a bottleneck for data centers and can force operators to rely on less efficient dry cooling, further stressing the power grid during summer peaks. In this paper, we focus on the direct water withdrawal of U.S. data centers for cooling and examine their impacts on public water systems. Our analysis indicates that, if the 2024 water use intensity persists, U.S. data centers could collectively require 697-1,451 million gallons per day (MGD) of new water capacity through 2030, comparable to New York City's average daily supply of roughly 1,000 MGD. Under an optimistic scenario with a compound annual water use intensity reduction by 10%, the water capacity demand decreases to 227-604 MGD, although high-growth IT loads could still require enough capacity to hypothetically supply about half of New York City for most of the year. The total valuation of the new water capacity is on the order of \$10 billion, reaching up to \$58 billion in the high-growth case. These impacts are highly concentrated on communities hosting data centers. Finally, we provide recommendations to address the growing water capacity demand of U.S. data centers, including reporting peak water use, developing corporate-community partnerships, adopting a Water Capacity Neutral approach (colloquially "Pipe Neutral") to allow host communities to retain limited water capacity resources, and implementing coordinated water-power planning to responsibly leverage water for peak power reduction and opportunistically utilize surplus power to mitigate impacts on public water systems.
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.
Holger Boche, Andrea Grigorescu, Rafael F. Schaefer
et al.
This paper explores the computational complexity involved in determining the capacity of the band-limited additive colored Gaussian noise (ACGN) channel and its capacity-achieving power spectral density (p.s.d.). The study reveals that when the noise p.s.d. is a strictly positive computable continuous function, computing the capacity of the band-limited ACGN channel becomes a $\#\mathrm{P}_1$-complete problem within the set of polynomial time computable noise p.s.d.s. Meaning that it is even more complex than problems that are $\mathrm{NP}_1$-complete. Additionally, it is shown that the capacity-achieving distribution is also $\#\mathrm{P}_1$-complete. Furthermore, under the widely accepted assumption that $\mathrm{FP}_1 \neq \#\mathrm{P}_1$, it has two significant implications for the ACGN channel. The first implication is the existence of a polynomial time computable noise p.s.d. for which the computation of its capacity cannot be performed in polynomial time, i.e., the number of computational steps on a Turing Machine grows faster than all polynomials. The second one is the existence of a polynomial time computable noise p.s.d. for which determining its capacity-achieving p.s.d. cannot be done within polynomial time.
This paper studies whether risky borrowing will induce a supplier to expand capacity and thus mitigate a capacity underinvestment problem in supply chains. It demonstrates that the relationship between capacity and capital structure is not as simple as the existing literature suggests. If the supplier is very powerful, it will use a mixed capital structure and build less capacity than if it were equity financed. If the buyer is very powerful, the supplier will use all debt financing and overbuild capacity. In this case, the supplier would not agree to build capacity ex ante if it were prohibited from borrowing. Hence, borrowing is Pareto optimal. Under a more balanced power structure, the supplier may choose all debt financing and overbuild capacity or all equity financing and underbuild capacity, depending on the trade‐off of the bargaining benefits and costs of debt financing.
Holographic Multiple-Input and Multiple-Output (MIMO) is envisioned as a promising technology to realize unprecedented spectral efficiency by integrating a large number of antennas into a compact space. Most research on holographic MIMO is based on isotropic scattering environments, and the antenna gain is assumed to be unlimited by deployment space. However, the channel might not satisfy isotropic scattering because of generalized angle distributions, and the antenna gain is limited by the array aperture in reality. In this letter, we aim to analyze the holographic MIMO channel capacity under practical angle distribution and array aperture constraints. First, we calculate the spectral density for generalized angle distributions by introducing a wavenumber domain-based method. And then, the capacity under generalized angle distributions is analyzed and two different aperture schemes are considered. Finally, numerical results show that the capacity is obviously affected by angle distribution at high signal-to-noise ratio (SNR) but hardly affected at low SNR, and the capacity will not increase infinitely with antenna density due to the array aperture constraint.
Harri Hakula, Mohamed M. S. Nasser, Matti Vuorinen
We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by polycircular domains. Experimental error estimates are provided for the computed capacity and, when possible, the rate of convergence under refinement of discretisation is analysed. The main ingredients of the computation are two computational methods, on one hand the boundary integral equation method combined with the fast multipole method and on the other hand the $hp$-FEM method. The results obtained with these two methods agree with high accuracy.
We propose a complexity measure of a neural network mapping function based on the diversity of the set of tangent spaces from different inputs. Treating each tangent space as a linear PAC concept we use an entropy-based measure of the bundle of concepts in order to estimate the conceptual capacity of the network. The theoretical maximal capacity of a ReLU network is equivalent to the number of its neurons. In practice however, due to correlations between neuron activities within the network, the actual capacity can be remarkably small, even for very big networks. Empirical evaluations show that this new measure is correlated with the complexity of the mapping function and thus the generalisation capabilities of the corresponding network. It captures the effective, as oppose to the theoretical, complexity of the network function. We also showcase some uses of the proposed measure for analysis and comparison of trained neural network models.
Logarithmic capacity is shown to be minimal for a planar set having $N$-fold rotational symmetry ($N \geq 3$), among all conductors obtained from the set by area-preserving linear transformations. Newtonian and Riesz capacities obey a similar property in all dimensions, when suitably normalized linear transformations are applied to a set having irreducible symmetry group. A corollary is Pólya and Schiffer's lower bound on capacity in terms of moment of inertia.
The zero-error channel capacity is the maximum asymptotic rate that can be reached with error probability exactly zero, instead of a vanishing error probability. The nature of this problem, essentially combinatorial rather than probabilistic, has led to various researches both in Information Theory and Combinatorics. However, the zero-error capacity is still an open problem, for example the capacity of the noisy-typewriter channel with 7 letters is unknown. In this article, we propose a new approach to construct optimal zero-error codes, based on the concatenation of words of variable-length, taken from a generator set. Three zero-error variable-length coding schemes, referred to as "variable-length coding", "intermingled coding" and "automata-based coding", are under study. We characterize their asymptotic performances via linear difference equations, in terms of simple properties of the generator set, e.g. the roots of the characteristic polynomial, the spectral radius of an adjacency matrix, the inverse of the convergence radius of a generator series. For a specific example, we construct an "intermingled" coding scheme that achieves asymptotically the zero-error capacity.
We initiate the study of the capacity constrained facility location problem from a mechanism design perspective. The capacity constrained setting leads to a new strategic environment where a facility serves a subset of the population, which is endogenously determined by the ex-post Nash equilibrium of an induced subgame and is not directly controlled by the mechanism designer. Our focus is on mechanisms that are ex-post dominant-strategy incentive compatible (DIC) at the reporting stage. We provide a complete characterization of DIC mechanisms via the family of Generalized Median Mechanisms (GMMs). In general, the social welfare optimal mechanism is not DIC. Adopting the worst-case approximation measure, we attain tight lower bounds on the approximation ratio of any DIC mechanism. The well-known median mechanism is shown to be optimal among the family of DIC mechanisms for certain capacity ranges. Surprisingly, the framework we introduce provides a new characterization for the family of GMMs, and is responsive to gaps in the current social choice literature highlighted by Border and Jordan (1983) and Barbar{à}, Mass{ó} and Serizawa (1998).
In this paper, we present an analytical lower bound on the ergodic capacity of optical multiple-input multiple-output (MIMO) channels. It turns out that the optical MIMO channel matrix which couples the mt inputs (modes/cores) into mr outputs (modes/cores) can be modeled as a sub-matrix of a m x m Haar-distributed unitary matrix where m > mt,mr. Using the fact that the probability density of the eigenvalues of a random matrix from unitary ensemble can be expressed in terms of the Christoffel-Darboux kernel. We provide a new analytical expression of the ergodic capacity as function of signal-to-noise ratio (SNR). Moreover, we derive a closed-form lower-bound expression to the ergodic capacity. In addition, we also derive an approximation to the ergodic capacity in low-SNR regimes. Finally, we present numerical results supporting the expressions derived.
We study information transmission over a fully correlated amplitude damping channel acting on two qubits. We derive the single-shot classical channel capacity and show that entanglement is needed to achieve the channel best performance. We discuss the degradability properties of the channel and evaluate the quantum capacity for any value of the noise parameter. We finally compute the entanglement-assisted classical channel capacity.
Aslan Tchamkerten, Venkat Chandar, Gregory Wornell
Several aspects of the problem of asynchronous point-to-point communication without feedback are developed when the source is highly intermittent. In the system model of interest, the codeword is transmitted at a random time within a prescribed window whose length corresponds to the level of asynchronism between the transmitter and the receiver. The decoder operates sequentially and communication rate is defined as the ratio between the message size and the elapsed time between when transmission commences and when the decoder makes a decision. For such systems, general upper and lower bounds on capacity as a function of the level of asynchronism are established, and are shown to coincide in some nontrivial cases. From these bounds, several properties of this asynchronous capacity are derived. In addition, the performance of training-based schemes is investigated. It is shown that such schemes, which implement synchronization and information transmission on separate degrees of freedom in the encoding, cannot achieve the asynchronous capacity in general, and that the penalty is particularly significant in the high-rate regime.
We consider the Gaussian "diamond" or parallel relay network, in which a source node transmits a message to a destination node with the help of N relays. Even for the symmetric setting, in which the channel gains to the relays are identical and the channel gains from the relays are identical, the capacity of this channel is unknown in general. The best known capacity approximation is up to an additive gap of order N bits and up to a multiplicative gap of order N^2, with both gaps independent of the channel gains. In this paper, we approximate the capacity of the symmetric Gaussian N-relay diamond network up to an additive gap of 1.8 bits and up to a multiplicative gap of a factor 14. Both gaps are independent of the channel gains and, unlike the best previously known result, are also independent of the number of relays N in the network. Achievability is based on bursty amplify-and-forward, showing that this simple scheme is uniformly approximately optimal, both in the low-rate as well as in the high-rate regimes. The upper bound on capacity is based on a careful evaluation of the cut-set bound. We also present approximation results for the asymmetric Gaussian N-relay diamond network. In particular, we show that bursty amplify-and-forward combined with optimal relay selection achieves a rate within a factor O(log^4(N)) of capacity with pre-constant in the order notation independent of the channel gains.
The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an "ab initio" approach, using only the most basic tools in the quantum information theorist's toolkit: the Alicki-Fannes' inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the "quantum dynamic capacity formula" characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula simplifies the computation of the trade-off surface, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.
Hossein Bagheri, Abolfazl S. Motahari, Amir K. Khandani
In this paper, a dual-hop communication system composed of a source S and a destination D connected through two non-interfering half-duplex relays, R1 and R2, is considered. In the literature of Information Theory, this configuration is known as the diamond channel. In this setup, four transmission modes are present, namely: 1) S transmits, and R1 and R2 listen (broadcast mode), 2) S transmits, R1 listens, and simultaneously, R2 transmits and D listens. 3) S transmits, R2 listens, and simultaneously, R1 transmits and D listens. 4) R1, R2 transmit, and D listens (multiple-access mode). Assuming a constant power constraint for all transmitters, a parameter $Δ$ is defined, which captures some important features of the channel. It is proven that for $Δ$=0 the capacity of the channel can be attained by successive relaying, i.e, using modes 2 and 3 defined above in a successive manner. This strategy may have an infinite gap from the capacity of the channel when $Δ\neq$0. To achieve rates as close as 0.71 bits to the capacity, it is shown that the cases of $Δ$>0 and $Δ$<0 should be treated differently. Using new upper bounds based on the dual problem of the linear program associated with the cut-set bounds, it is proven that the successive relaying strategy needs to be enhanced by an additional broadcast mode (mode 1), or multiple access mode (mode 4), for the cases of $Δ$<0 and $Δ$>0, respectively. Furthermore, it is established that under average power constraints the aforementioned strategies achieve rates as close as 3.6 bits to the capacity of the channel.
New upper bounds on the sum capacity of the two-user Gaussian interference channel are derived. Using these bounds, it is shown that treating interference as noise achieves the sum capacity if the interference levels are below certain thresholds.