In many complex systems, whether biological or artificial, the thermodynamic costs of communication among their components are large. These systems also tend to split information transmitted between any two components across multiple channels. A common hypothesis is that such inverse multiplexing strategies reduce total thermodynamic costs. So far, however, there have been no physics-based results supporting this hypothesis. This gap existed partially because we have lacked a theoretical framework that addresses the interplay of thermodynamics and information in off-equilibrium systems at any spatiotemporal scale. Here we present the first study that rigorously combines such a framework, stochastic thermodynamics, with Shannon information theory. We develop a minimal model that captures the fundamental features common to a wide variety of communication systems. We find that the thermodynamic cost in this model is a convex function of the channel capacity, the canonical measure of the communication capability of a channel. We also find that this function is not always monotonic, in contrast to previous results not derived from first principles physics. These results clarify when and how to split a single communication stream across multiple channels. In particular, we present Pareto fronts that reveal the trade-off between thermodynamic costs and channel capacity when inverse multiplexing. Due to the generality of our model, our findings could help explain empirical observations of how thermodynamic costs of information transmission make inverse multiplexing energetically favorable in many real-world communication systems.
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Deep neural networks (DNNs) are increasingly being deployed to perform safety-critical tasks. The opacity of DNNs, which prevents humans from reasoning about them, presents new safety and security challenges. To address these challenges, the verification community has begun developing techniques for rigorously analyzing DNNs, with numerous verification algorithms proposed in recent years. While a significant amount of work has gone into developing these verification algorithms, little work has been devoted to rigorously studying the computability and complexity of the underlying theoretical problems. Here, we seek to contribute to the bridging of this gap. We focus on two kinds of DNNs: those that employ piecewise-linear activation functions (e.g., ReLU), and those that employ piecewise-smooth activation functions (e.g., Sigmoids). We prove the two following theorems: 1) The decidability of verifying DNNs with a particular set of piecewise-smooth activation functions is equivalent to a well-known, open problem formulated by Tarski; and 2) The DNN verification problem for any quantifier-free linear arithmetic specification can be reduced to the DNN reachability problem, whose approximation is NP-complete. These results answer two fundamental questions about the computability and complexity of DNN verification, and the ways it is affected by the network's activation functions and error tolerance; and could help guide future efforts in developing DNN verification tools.
We prove a characterization of the structural conditions on matrices of sign-rank 3 and unit disk graphs (UDGs) which permit constant-cost public-coin randomized communication protocols. Therefore, under these conditions, these graphs also admit implicit representations. The sign-rank of a matrix $M \in \{\pm 1\}^{N \times N}$ is the smallest rank of a matrix $R$ such that $M_{i,j} = \mathrm{sign}(R_{i,j})$ for all $i,j \in [N]$; equivalently, it is the smallest dimension $d$ in which $M$ can be represented as a point-halfspace incidence matrix with halfspaces through the origin, and it is essentially equivalent to the unbounded-error communication complexity. Matrices of sign-rank 3 can achieve the maximum possible bounded-error randomized communication complexity $\Theta(\log N)$, and meanwhile the existence of implicit representations for graphs of bounded sign-rank (including UDGs, which have sign-rank 4) has been open since at least 2003. We prove that matrices of sign-rank 3, and UDGs, have constant randomized communication complexity if and only if they do not encode arbitrarily large instances of the Greater-Than communication problem, or, equivalently, if they do not contain arbitrarily large half-graphs as semi-induced subgraphs. This also establishes the existence of implicit representations for these graphs under the same conditions.
Terahertz (THz) integrated sensing and communication (ISAC) enables simultaneous data transmission with Terabit-per-second (Tbps) rate and millimeter-level accurate sensing. To realize such a blueprint, ultra-massive antenna arrays with directional beamforming are used to compensate for severe path loss in the THz band. In this paper, the time-frequency-space transmit design is investigated for THz ISAC to generate time-varying scanning sensing beams and stable communication beams. Specifically, with the dynamic array-of-subarray (DAoSA) hybrid beamforming architecture and multi-carrier modulation, two ISAC hybrid precoding algorithms are proposed, namely, a vectorization (VEC) based algorithm that outperforms existing ISAC hybrid precoding methods and a low-complexity sensing codebook assisted (SCA) approach. Meanwhile, coupled with the transmit design, parameter estimation algorithms are proposed to realize high-accuracy sensing, including a wideband DAoSA MUSIC (W-DAoSA-MUSIC) method for angle estimation and a sum-DFT-GSS (S-DFT-GSS) approach for range and velocity estimation. Numerical results indicate that the proposed algorithms can realize centi-degree-level angle estimation accuracy and millimeter-level range estimation accuracy, which are one or two orders of magnitudes better than the methods in the millimeter-wave band. In addition, to overcome the cyclic prefix limitation and Doppler effects in the THz band, an inter-symbol interference- and inter-carrier interference-tackled sensing algorithm is developed to refine sensing capabilities for THz ISAC.
We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This motivates the definition of the linarization complexity of $f$ as the minimum such $k$. Our theoretical contributions are the proof that random polynomials almost surely have a high linearization complexity and characterizations of its value in case we do or do not restrict the set of admissible Boolean functions. The practical relevance is shown by devising and evaluating integer linear programming models of two such linearizations for the low auto-correlation binary sequences problem. Still, many problems around this new concept remain open.
Semantic communication has gained significant attention from researchers as a promising technique to replace conventional communication in the next generation of communication systems, primarily due to its ability to reduce communication costs. However, little literature has studied its effectiveness in multi-user scenarios, particularly when there are variations in the model architectures used by users and their computing capacities. To address this issue, we explore a semantic communication system that caters to multiple users with different model architectures by using a multi-purpose transmitter at the base station (BS). Specifically, the BS in the proposed framework employs semantic and channel encoders to encode the image for transmission, while the receiver utilizes its local channel and semantic decoder to reconstruct the original image. Our joint source-channel encoder at the BS can effectively extract and compress semantic features for specific users by considering the signal-to-noise ratio (SNR) and computing capacity of the user. Based on the network status, the joint source-channel encoder at the BS can adaptively adjust the length of the transmitted signal. A longer signal ensures more information for high-quality image reconstruction for the user, while a shorter signal helps avoid network congestion. In addition, we propose a hybrid loss function for training, which enhances the perceptual details of reconstructed images. Finally, we conduct a series of extensive evaluations and ablation studies to validate the effectiveness of the proposed system.
In wireless security, cognitive adversaries are known to inject jamming energy on the victim's frequency band and monitor the same band for countermeasures thereby trapping the victim. Under the class of cognitive adversaries, we propose a new threat model wherein the adversary, upon executing the jamming attack, measures the long-term statistic of Kullback-Leibler Divergence (KLD) between its observations over each of the network frequencies before and after the jamming attack. To mitigate this adversary, we propose a new cooperative strategy wherein the victim takes the assistance for a helper node in the network to reliably communicate its message to the destination. The underlying idea is to appropriately split their energy and time resources such that their messages are reliably communicated without disturbing the statistical distribution of the samples in the network. We present rigorous analyses on the reliability and the covertness metrics at the destination and the adversary, respectively, and then synthesize tractable algorithms to obtain near-optimal division of resources between the victim and the helper. Finally, we show that the obtained near-optimal division of energy facilitates in deceiving the adversary with a KLD estimator.
Electrical Distribution Systems are extensively penetrated with Distributed Energy Resources (DERs) to cater the energy demands with the general perception that it enhances the system's resilience. However, integration of DERs may adversely affect the grid operation and affect the system resilience due to various factors like their intermittent availability, dynamics of weather conditions, non-linearity, complexity, number of malicious threats, and improved reliability requirements of consumers. This paper proposes a methodology to evaluate the planning and operational resilience of power distribution systems under extreme events and determines the withstand capability of the electrical network. The proposed framework is developed by effectively employing the complex network theory. Correlated networks for undesirable configurations are developed from the time series data of active power monitored at nodes of the electrical network. For these correlated networks, computed the network parameters such as clustering coefficient, assortative coefficient, average degree and power law exponent for the anticipation; and percolation threshold for the determination of the network withstand capability under extreme conditions. The proposed methodology is also suitable for identifying the hosting capacity of solar panels in the system while maintaining resilience under different unfavourable conditions and identifying the most critical nodes of the system that could drive the system into non-resilience. This framework is demonstrated on IEEE 123 node test feeder by generating active power time-series data for a variety of electrical conditions using simulation software, GridLAB-D. The percolation threshold resulted as an effective metric for the determination of the planning and operational resilience of the power distribution system.
Elementary trapping sets (ETSs) are the main culprits for the performance of LDPC codes in the error floor region. Due to the large quantity, complex structures, and computational difficulties of ETSs, how to eliminate dominant ETSs in designing LDPC codes becomes a pivotal issue to improve the error floor behavior. In practice, researchers commonly address this problem by avoiding some special graph structures to free specific ETSs in Tanner graph. In this paper, we deduce the accurate Tur\'an number of $\theta(1,2,2)$ and prove that all $(a,b)$-ETSs in Tanner graph with variable-regular degree $d_L(v)=\gamma$ must satisfy the bound $b\geq a\gamma-\frac{1}{2}a^2$, which improves the lower bound obtained by Amirzade when the girth is 6. For the case of girth 8, by limiting the relation between any two 8-cycles in the Tanner graph, we prove a similar inequality $b\geq a\gamma-\frac{a(\sqrt{8a-7}-1)}{2}$. The simulation results show that the designed codes have good performance with lower error floor over additive white Gaussian noise channels.
The Chinese Remainder Theorem for the integers says that every system of congruence equations is solvable as long as the system satisfies an obvious necessary condition. This statement can be generalized in a natural way to arbitrary algebraic structures using the language of Universal Algebra. In this context, an algebra is a structure of a first-order language with no relation symbols, and a congruence on an algebra is an equivalence relation on its base set compatible with its fundamental operations. A tuple of congruences of an algebra is called a Chinese Remainder tuple if every system involving them is solvable. In this article we study the complexity of deciding whether a tuple of congruences of a finite algebra is a Chinese Remainder tuple. This problem, which we denote CRT, is easily seen to lie in coNP. We prove that it is actually coNP-complete and also show that it is tractable when restricted to several well-known classes of algebras, such as vector spaces and distributive lattices. The polynomial algorithms we exhibit are made possible by purely algebraic characterizations of Chinese Remainder tuples for algebras in these classes, which constitute interesting results in their own right. Among these, an elegant characterization of Chinese Remainder tuples of finite distributive lattices stands out. Finally, we address the restriction of CRT to an arbitrary equational class $\mathcal{V}$ generated by a two-element algebra. Here we establish an (almost) dichotomy by showing that, unless $\mathcal{V}$ is the class of semilattices, the problem is either coNP-complete or tractable.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
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