The surging demand for batteries requires advanced battery management systems, where battery capacity modelling is a key functionality. In this paper, we aim to achieve accurate battery capacity prediction by learning from historical measurements of battery dynamics. We propose GiNet, a gated recurrent units enhanced Informer network, for predicting battery's capacity. The novelty and competitiveness of GiNet lies in its capability of capturing sequential and contextual information from raw battery data and reflecting the battery's complex behaviors with both temporal dynamics and long-term dependencies. We conducted an experimental study based on a publicly available dataset to showcase GiNet's strength of gaining a holistic understanding of battery behavior and predicting battery capacity accurately. GiNet achieves 0.11 mean absolute error for predicting the battery capacity in a sequence of future time slots without knowing the historical battery capacity. It also outperforms the latest algorithms significantly with 27% error reduction on average compared to Informer. The promising results highlight the importance of customized and optimized integration of algorithm and battery knowledge and shed light on other industry applications as well.
Quantum batteries, consisting of quantum cells, are anticipated to surpass their classical counterparts in performance because of the presence of quantum correlations. Recent theoretical study introduces the quantum battery capacity that is defined according to the highest and the lowest energy during the charging and discharging procedures. Here, we present an experimental verification of quantum battery capacity and its relationships with other quantum characters of battery by using two-photon states. This reveals a distinguished feature of quantum battery capacity and its trade-off relationship with the entropy of the battery state, as well as with measures of coherence and entanglement.
We consider the continuous-time ARMA(1,1) Gaussian channel and derive its feedback capacity in closed form. More specifically, the channel is given by $\boldsymbol{y}(t) =\boldsymbol{x}(t) +\boldsymbol{z}(t)$, where the channel input $\{\boldsymbol{x}(t) \}$ satisfies average power constraint $P$ and the noise $\{\boldsymbol{z}(t)\}$ is a first-order {\em autoregressive moving average} (ARMA(1,1)) Gaussian process satisfying $$ \boldsymbol{z}^\prime(t)+κ\boldsymbol{z}(t)=(κ+λ)\boldsymbol{w}(t)+\boldsymbol{w}^\prime(t), $$ where $κ>0,~λ\in\mathbb{R}$ and $\{\boldsymbol{w}(t) \}$ is a white Gaussian process with unit double-sided spectral density. We show that the feedback capacity of this channel is equal to the unique positive root of the equation $$ P(x+κ)^2 = 2x(x+\vert κ+λ\vert)^2 $$ when $-2κ<λ<0$ and is equal to $P/2$ otherwise. Among many others, this result shows that, as opposed to a discrete-time additive Gaussian channel, feedback may not increase the capacity of a continuous-time additive Gaussian channel even if the noise process is colored. The formula enables us to conduct a thorough analysis of the effect of feedback on the capacity for such a channel. We characterize when the feedback capacity equals or doubles the non-feedback capacity; moreover, we disprove continuous-time analogues of the half-bit bound and Cover's $2P$ conjecture for discrete-time additive Gaussian channels.
Florian Fischer, Matthias Keller, Anna Muranova
et al.
In this article we study the notion of capacity of a vertex for infinite graphs over non-Archimedean fields. In contrast to graphs over the real field monotone limits do not need to exist. Thus, in our situation next to positive and null capacity there is a third case of divergent capacity. However, we show that either of these cases is independent of the choice of the vertex and is therefore a global property for connected graphs. The capacity is shown to connect the minimization of the energy, solutions of the Dirichlet problem and existence of a Green's function. We furthermore give sufficient criteria in form of a Nash-Williams test, study the relation to Hardy inequalities and discuss the existence of positive superharmonic functions. Finally, we investigate the analytic features of the transition operator in relation to the inverse of the Laplace operator.
Traian Alexandru Buda, Emilia Calefariu, Flavius Aurelian Sarbu
et al.
Traian Alexandru Buda, EThis paper introduces a new model for computing the production capacity in a manufacturing system or in a supply chain. Solving the production capacity problem means to be able to answer the following question: how many parts, from each product, can be produced by a given manufacturing system in a given time span considering the product mix and a multi-stage Bill of Materials? The proposed model is able to determine the production capacity and the loading level per resource for a manufacturing system using as inputs the Bill of Materials, Routing file, time span and product mix. The novelty brought by this method consists in the adoption of the matrix calculus in order to manipulate the inputs to obtain the requested outputs. The opportunity of such a model is that it offers the complete view on the capacity problem with a full range of answers: the available and required capacity at resource and finished product level and the loading level for each resource. Also the facile implementation and integration in ERP systems is a vital point. The use of such a model is in the investment process, middle and long-term capacity planning and client order confirmation process. The model aims to solveany type of manufacturing system.
Let $X$ be a compact metric space and let $v$ be a sub-additive capacity defined on $X$. We show that Lusin's theorem with respect to $v$ holds if and only if $v$ is continuous from above.
We study the cost of distributed MST construction in the setting where each edge has a latency and a capacity, along with the weight. Edge latencies capture the delay on the links of the communication network, while capacity captures their throughput (in this case, the rate at which messages can be sent). Depending on how the edge latencies relate to the edge weights, we provide several tight bounds on the time and messages required to construct an MST. When edge weights exactly correspond with the latencies, we show that, perhaps interestingly, the bottleneck parameter in determining the running time of an algorithm is the total weight $W$ of the MST (rather than the total number of nodes $n$, as in the standard CONGEST model). That is, we show a tight bound of $\tildeΘ(D + \sqrt{W/c})$ rounds, where $D$ refers to the latency diameter of the graph, $W$ refers to the total weight of the constructed MST and edges have capacity $c$. The proposed algorithm sends $\tilde{O}(m+W)$ messages, where $m$, the total number of edges in the network graph under consideration, is a known lower bound on message complexity for MST construction. We also show that $Ω(W)$ is a lower bound for fast MST constructions. When the edge latencies and the corresponding edge weights are unrelated, and either can take arbitrary values, we show that (unlike the sub-linear time algorithms in the standard CONGEST model, on small diameter graphs), the best time complexity that can be achieved is $\tildeΘ(D+n/c)$. However, if we restrict all edges to have equal latency $\ell$ and capacity $c$ while having possibly different weights (weights could deviate arbitrarily from $\ell$), we give an algorithm that constructs an MST in $\tilde{O}(D + \sqrt{n\ell/c})$ time. In each case, we provide nearly matching upper and lower bounds.
Assaf Ben-Yishai, Young-Han Kim, Or Ordentlich
et al.
The essential interactive capacity of a discrete memoryless channel is defined in this paper as the maximal rate at which the transcript of any interactive protocol can be reliably simulated over the channel, using a deterministic coding scheme. In contrast to other interactive capacity definitions in the literature, this definition makes no assumptions on the order of speakers (which can be adaptive) and does not allow any use of private / public randomness; hence, the essential interactive capacity is a function of the channel model only. It is shown that the essential interactive capacity of any binary memoryless symmetric (BMS) channel is at least $0.0302$ its Shannon capacity. To that end, we present a simple coding scheme, based on extended-Hamming codes combined with error detection, that achieves the lower bound in the special case of the binary symmetric channel (BSC). We then adapt the scheme to the entire family of BMS channels, and show that it achieves the same lower bound using extremes of the Bhattacharyya parameter.
Corsin Pfister, M. Adriaan Rol, Atul Mantri
et al.
One of the main figures of merit for quantum memories and quantum communication devices is their quantum capacity. It has been studied for arbitrary kinds of quantum channels, but its practical estimation has so far been limited to devices that implement independent and identically distributed (i.i.d.) quantum channels, where each qubit is affected by the same noise process. Real devices, however, typically exhibit correlated errors. Here, we overcome this limitation by presenting protocols that estimate a channel's one-shot quantum capacity for the case where the device acts on (an arbitrary number of) qubits. The one-shot quantum capacity quantifies a device's ability to store or communicate quantum information, even if there are correlated errors across the different qubits. We present a protocol which is easy to implement and which comes in two versions. The first version estimates the one-shot quantum capacity by preparing and measuring in two different bases, where all involved qubits are used as test qubits. The second version verifies on-the-fly that a channel's one-shot quantum capacity exceeds a minimal tolerated value while storing or communicating data, therefore combining test qubits and data qubits in one protocol. We discuss the performance of our method using simple examples, such as the dephasing channel for which our method is asymptotically optimal. Finally, we apply our method to estimate the one-shot capacity in an experiment using a transmon qubit.
The variational capacity cap_p in Euclidean spaces is known to enjoy the density dichotomy at large scales, namely that for every subset E of R^n, inf_{x in R^n} (cap_p(E \cap B(x,r),B(x,2r)) / cap_p(B(x,r),B(x,2r))) is either zero or tends to 1 as r tends to infinity. We prove that this property still holds in unbounded complete geodesic metric spaces equipped with a doubling measure supporting a p-Poincaré inequality, but that it can fail in nongeodesic metric spaces and also for the Sobolev capacity in R^n. It turns out that the shape of balls impacts the validity of the density dichotomy. Even in more general metric spaces, we construct families of sets, such as John domains, for which the density dichotomy holds. Our arguments include an exact formula for the variational capacity of superlevel sets for capacitary potentials and a quantitative approximation from inside of the variational capacity.
Jiayi Zhang, Linglong Dai, Wolfgang H. Gerstacker
et al.
The effective capacity of communication systems over generalized $κ$-$μ$ shadowed fading channels is investigated in this letter. A novel and analytical expression for the exact effective capacity is derived in terms of extended generalized bivariate Meijer's-$G$ function. To intuitively reveal the impact of the system and channel parameters on the effective capacity, we also derive closed-form expressions for the effective capacity in the asymptotically high signal-to-noise ratio regime. Our results demonstrate that the effective capacity is a monotonically increasing function of channel fading parameters $κ$ and $μ$ as well as the shadowing parameter $m$, while it decays to zero when the delay constraint $θ\rightarrow \infty$.
We consider the Gaussian channel with power constraint P. A gap exists between the channel capacity and the highest achievable rate of equiprobable uniformly spaced signal. Several approaches enable to overcome this limitation such as constellations with non-uniform probability or constellation shaping. In this letter, we focus on constellation shaping. We give a construction of amplitude and phase-shift keying (APSK) constellations with equiprobable signaling that achieve the Gaussian capacity as the number of constellation points goes to infinity.
In this note we present a universal formula in terms of theta functions for the Log- capacity of several segments on a line. The case of two segments was studied by N.I.Akhiezer (1930); three segments were considered by A.Sebbar and T.Falliero (2001).
We consider a wiretap channel and use previously transmitted messages to generate a secret key which increases the secrecy capacity. This can be bootstrapped to increase the secrecy capacity to the Shannon capacity without using any feedback or extra channel while retaining the strong secrecy of the wiretap channel.