Integrated Sensing and Communication (ISAC) refers to the capability for the network to provide communications services whilst also being able to sense the environment in a scalable manner. One of the key functions of ISAC is the accurate localization of passive and mobile sensing targets. This paper introduces a novel hybrid TRP-UE sensing mechanism that improves network-based sensing performance. Evaluation results are provided using 3GPP-compliant ISAC channel models. The results demonstrate the significant benefit in complimenting TRP-based sensing with UE-assisted sensing in challenging propagation environments such as indoor factory.

Semantic-aware communication has emerged as a transformative paradigm for next-generation communication systems, shifting the fundamental goal from transmitting bit-level symbols to reliably recovering and understanding the semantic meaning of information. Previous studies have demonstrated that representing the semantic content of source messages as graph-based structures can significantly improve communication efficiency and the accuracy of semantic inference at the receiver. However, existing solutions typically employ graphs that capture only pairwise relationships, thereby neglecting higher-order implicit correlations commonly observed in real-world scenarios, such as group interactions, multi-entity associations, and complex relational contexts. This limitation reduces semantic expressiveness and makes semantic inference susceptible to ambiguity and performance degradation, particularly under noisy or corrupted channel conditions. To address these issues, this paper proposes a novel hypergraph-based implicit semantic reasoning framework, HISR, which leverages hypergraphs to represent complex multi-entity relationships among semantic knowledge entities. In HISR, entities and their associated higher-order relations are mapped into dedicated semantic subspaces tailored to distinct relational contexts. This design not only disentangles diverse semantic interactions to mitigate the over-smoothing effects commonly found in traditional graph embedding methods but also enables robust semantic inference even when partial information loss occurs during transmission. Numerical results show that the proposed HISR achieves up to a 36.6% improvement in implicit semantic interpretation accuracy over the state-of-the-art benchmarks.

Dense Eisenstein--Jacobi (EJ) networks are degree-six algebraic interconnection networks whose finite quotient geometry is naturally represented by a hexagonal axial-coordinate ball. This paper studies non-redundant one-to-all broadcast repair in the dense EJ network generated by $α=(t+1)+tω$, where $t$ is the network diameter. We propose EJ-MOEM, a multi-orientation edge-minimum repair method that evaluates a constant-size family of hexagonal broadcast-tree orientations, selects a fault-aware candidate, contracts the fault-pruned tree into healthy components, and reconnects these components using external component-crossing repair edges. The resulting structure is a rooted spanning tree of the healthy subgraph: every healthy node receives the message exactly once, no faulty node is used, and the original healthy tree components are preserved. We prove that, for a chosen orientation whose fault-pruned component graph is connected, exactly $c-1$ external repair edges are necessary and sufficient, where $c$ is the number of healthy components. We also prove a depth-certificate theorem for EJ coordinate-reduction trees: every one-fault placement admits a repair of depth at most $t+1$, and every two-fault placement admits a repair of depth at most $t+2$. The proof uses the three-strip representation of EJ hexagons, a sector-suffix attachment lemma, a non-adjacent-sector separation lemma, and a six-direction shielding classification for paired cuts. Extended validation includes exhaustive one- and two-fault enumeration for $t=2,\ldots,12,14,16,18$ (up to $N=1027$ and 525,825 two-fault placements at $t=18$), structured theorem-critical tests through $t=30$, and large random tests through $t=200$, all with 100\% success and no violation of the theorem.

Circulant interconnection networks provide symmetric addressing, compact generator descriptions, and uniform local connectivity. This paper maps a degree--redundancy landscape for a fault-tolerant two-hop primitive in directed circulants: given $n$ nodes and degree budget $m$, how large can the worst-case shared-relay multiplicity $R(n,m)$ be? A node is a shared relay for an ordered terminal pair if it has outgoing links to both terminals; an $f$-relay-fault-tolerant circulant requires at least $f+1$ such relays for every pair. The underlying feasibility condition is a cyclic difference-multiplicity condition, which we use as a mathematical tool rather than claim as a new object. The contribution is the network-design framework around this tool: the parameters $R(n,m)$ and $D_f(n)$, a negative theorem for interval circulants, relay-table preprocessing and lookup algorithms, adversarial and random failure guarantees, load-balance scope, certified upper-bound interpretation of heuristic designs, exact small-$n$ calibration, a software lookup-versus-search microbenchmark, and a reproducible study of 526,539 generator sets. The results show that generator choice critically determines worst-case relay survivability: optimized threshold designs achieve $f$-relay-fault tolerance within about $1.16$--$1.63$ of the counting lower bound, while standard interval generators can fail structurally even at much larger degrees.

Eisenstein--Jacobi (EJ) networks are degree-six quotient-lattice interconnection networks. For a generator $α=a+bρ$, let $N=a^2+ab+b^2$ and $d=\gcd(a,b)$. If $d=1$, the three natural unit directions already give three edge-disjoint Hamiltonian cycles. If $d>1$, each unit direction splits into $d$ cycles and the EDHC problem becomes a cycle-splicing problem. Existing non-coprime EJ decompositions prove existence by using a rectangular representation and exchange schedules. This paper develops a different, local switch calculus in the natural Cayley geometry. The first two Hamiltonian cycles are built using the minimum possible $d-1$ intercomponent switches each, and the third factor is obtained as the unused edge complement. The contribution is deliberately not a new existence theorem for all non-coprime EJ networks; rather, it is a compact, formula-driven, minimal-switch decomposition for Euclidean-residue families whose complement incidence is proved symbolically. The proof separates four ingredients: component-label collapse, anchor cancellation, noncollision of lifted switch representatives, and connected complement incidence. No infinite-family theorem in this manuscript is proved by finite witnesses or by computational enumeration. The theorem scope is stated for the parameter ranges where an algebraic complement-incidence certificate is written down. Tables and CSV data are used only to verify and reproduce the formulas, never as proof of an infinite-family theorem.

This paper investigates radio stripes (RSs) as a practical realization of generalized pinching antennas and proposes an RS-based generalized pinching-antenna (RS-GPA) framework. Unlike dielectric-waveguide-based passive pinching antennas that rely on passive coupling from a guided wave into free space, RSs employ active antenna processing units (APUs) deployed along a shared cable for local transmission, reception, and signal processing. This cable-like active architecture offers flexible installation and broad frequency applicability, while allowing selected APUs to act as discrete and controllable radiation or reception points for location-flexible wireless access. Based on the proposed RS-GPA framework, we establish the system and channel models by accounting for the distance-dependent APU-user channels. For downlink transmission, we formulate a circuit-power-aware sparse APU activation and beamforming problem and develop a reweighted group-sparse beamforming algorithm. To reveal the activation principle, we analyze the single-user downlink case and characterize when an additional APU should be activated by balancing transmit-power saving and circuit-power cost. Inspired by this insight, a geometry-guided low-complexity multiuser algorithm is proposed. For uplink transmission, we formulate a joint APU activation and user power control problem and develop a geometry-guided sparse activation design. Numerical results show that the proposed RS-GPA framework substantially reduces the total consumed power compared with benchmark schemes, while the geometry-guided algorithm achieves near-identical consumed-power performance to the group-sparse design with significantly lower runtime.

Pinching Waveguide Antennas (PWAs) offer significant potential for simultaneous wireless information and power transfer (SWIPT) by enabling precise near-field energy focusing. However, existing optimization frameworks are largely point-based (targeting a single coordinate for maximum gain), and thus highly sensitive to positioning errors and mobility, as near-field signals fluctuate significantly even over small spatial displacements. In this paper, we propose a spatially robust design framework based on discrete antenna selection optimized for service area (SA) coverage. Unlike point-based approaches, our model guarantees quality of service within predefined SAs for both information decoding (ID) and energy harvesting (EH) receivers, thereby improving robustness to user displacements. We formulate the problem as a non-convex binary quadratic program aimed at maximizing harvested energy within the EH SA subject to robust rate constraints in the ID SA. To characterize fundamental performance limits, we develop a semidefinite relaxation (SDR) framework that provides an upper bound on the achievable rate-energy (R-E) region. For the lower bound, we employ a low-complexity swap-based local search algorithm enforcing binary hardware constraints. Numerical results demonstrate that the proposed coverage-oriented design yields a robust R-E tradeoff and maintains stable performance across service regions, highlighting the advantages of discrete antenna activation over point-based near-field optimization approaches.

This paper explores the use of generative models to synthesize high-quality, site-specific multiple-input multiple-output (MIMO) channel data, addressing the high cost of the extensive measurement campaigns required to acquire real-world data for AI-native wireless networks. Two location-conditioned generative paradigms are compared: a conditional denoising diffusion implicit model (cDDIM), and a conditional flow matching model (cFMM). Both these models generate MIMO channel matrices conditioned on user coordinates, to preserve the spatial structure of the deployment site. The approaches are evaluated across three dimensions: statistical fidelity (including beam consistency and effective rank), generation efficiency, and utility in downstream tasks such as channel-state information compression and beam alignment. Results across diverse propagation scenarios (28 GHz and 3.5 GHz, both line-of-sight and non-line-of-sight) demonstrate that both models accurately capture site-specific characteristics, even when trained on scarce ground-truth data. Notably, cFMM achieves a quality comparable to cDDIM with roughly an order of magnitude less inference time. Augmenting scarce site-specific datasets with these synthetic channels yields hefty performance gains in downstream physical layer tasks compared to using scarce data alone or stochastic channels.

Recent research on Doeblin coefficients has shed light on their usefulness as a multi-way generalization of the Dobrushin contraction coefficient for TV distance, in a separate vein from their classic role in the theory of Markov chain ergodicity. However, strong conditions, such as being bounded away from 0, are typically necessary for Doeblin coefficients to establish the existence of information contraction. Building on recently formulated concepts of nonlinear information contraction, we aim to propose a finer-grained Doeblin-based characterization of multi-way contraction behavior which yields non-vacuous contraction guarantees even for channels whose Doeblin coefficient is 0. To this end, we introduce the notion of a Doeblin curve -- a nonlinear function which quantifies the contraction behavior of a Markov kernel on collections of input distributions at specific levels of divergence and power. Through the course of our analysis, we develop a new variational characterization of Doeblin coefficients, present several properties of Doeblin curves, define several versions of power-constrained Doeblin curves, and derive upper and lower bounds using our aforementioned variational characterization. We then utilize these results in diverse areas, including generalization bounds for noisy iterative optimization, error bounds for reliable computation with noisy circuits, and differential privacy guarantees for online iterative algorithms. In particular, we extend results in these areas to broader domains or group settings, leveraging Doeblin curves to reveal finer-grained contraction phenomena than Doeblin coefficients.

Tight equalities between symmetric information and entropy production in driven steady states remain elusive. We show that they are forbidden by a parity selection rule for rotation-driven linear nonequilibrium steady states. Whenever the relaxation and diffusion matrices commute, the snapshot mutual information between two time slices is exactly even under drive reversal, and parity violation rises linearly in the commutator norm when alignment is broken. Full isotropy strengthens this to drive-independence, and the planar mutual information takes the closed-form value of about 0.145 nats. Under the same alignment, the entropy production is exactly quadratic in the drive, and its prefactor admits an explicit closed form in the traces and determinant of the two matrices. The orthogonality of even and odd sectors leaves only one-sided thermodynamic-uncertainty bounds. The rule rests on the rotational symmetry of the drift alone and survives heavy-tailed isotropic stable noise with tail index below two, where variance-based bounds become vacuous. A falsifiable test is proposed on an electrical Brownian gyrator augmented for independent drive control with circuit-level stable-noise injection.

Bluetooth Low Energy (BLE) direction-finding is promising for indoor industrial localization, but its accuracy degrades in multipath environments where reflections and scattering bias angle estimates. Although line-of-sight (LOS) and non-line-of-sight (NLOS) detection is well studied for wide-band radios, BLE direction-finding still lacks narrow-band channel-feature representations, scalable kernel-based feature transformations, and dedicated datasets for data-driven, lightweight channel classification. To address this gap, the work introduces a controlled BLE measurement setup that generates labeled LOS/NLOS data in two distinct propagation environments. A quality-driven machine learning (ML)-based pipeline is then developed for BLE Constant Tone Extension (CTE) In-phase-Quadrature (IQ) features. First, robust quantile-based standardization is applied to reduce the influence of outliers and heavy-tailed effects. The standardized features are then analyzed using Principal Component Analysis (PCA) and Adaptive Kernel Density Estimation (AKDE) to verify scenario-dependent statistics and reveal LOS/NLOS separability. Next, Nyström Kernel Approximation (NKA) constructs low-rank nonlinear feature maps followed by a lightweight Support Vector Classifier (SVC) head for LOS/NLOS detection. This classifier is compared with Random Forest (RF) and Multilayer Perceptron (MLP) models. Results show that NKA improves accuracy by about 7-14% relative to the raw baseline. Although the MLP achieves higher absolute accuracy, the Nyström--SVC approach offers a more favorable trade-off between training complexity, inference cost, and memory footprint. Finally, several pipeline-calibrated posterior probabilities are utilized for cost-aware threshold selection and efficient real-time LOS/NLOS detection in resource-constrained localization systems.

We introduce the Frontier decoder, a pruned dynamic-programming decoder for sparse quantum decoding problems. Frontier processes error variables in a chosen order, merges prefixes with the same residual syndrome and logical label, and approximates logical-coset posterior masses by retaining only a narrow scored frontier. Without pruning, the recursion is exact ordered inference with exponential complexity. In the code-capacity setting, the decoder reaches thresholds close to optimal for the surface code and the color code. In the circuit-level noise model, it achieves state-of-the-art performance with a very small average retained list size: less than 100 for the gross code $[[144,12,12]]$ at a physical error rate of $0.001$. When the list size is constant, the decoder has linear complexity, suggesting the possibility of low-latency implementations.

Characterizing the features of a Hamiltonian that governs a quantum system serves as a fundamental subroutine of quantum device calibration, signal sensing, and error correction. Recent works proposed protocols have achieved the optimal Heisenberg-limited scaling learning ansatz-free Hamiltonians from their real-time evolutions without fully specifying interaction structures. However, these protocols rely on both deep circuits with interleaving probes and control, and extremely short time resolution, making them difficult to implement on near- and intermediate-term in situ quantum experiments. In this work, we propose a computationally efficient, control-free, and ancilla-free algorithm that uses only Pauli product state preparation and measurement, and learns an ansatz-free Hamiltonian $H$ with $||H||\leqΛ$ in total evolution time of $Θ(\fracΛ{ε^2}\log(\fracΛε))$. The evolution time cost of our algorithm is optimal for any control-free protocols as we further prove a lower bound of $Ω(\fracΛ{ε^2}\log(\fracΛε))$. Technically, our method introduces a randomized-sampling framework that combines band-limited kernel-based time sampling with a displacement sieve for Hamiltonian structure learning. The characteristic probe time resolution depends only on $Λ$ instead of $\varepsilon$, which makes our protocol especially appealing in the high-precision regime for sensing and calibration applications. We also show that the algorithm maintains the same asymptotic total evolution time in the presence of state-preparation-and-measurement (SPAM) noise when the Hamiltonian is local after calibration. Our results demonstrate the fundamental cost of experimentally friendly Hamiltonian learning and provide a practical route to rigorous in situ characterization of near-term quantum platforms.

The Bures--Helstrom metric is the minimal monotone Riemannian metric on the state space of a qubit. With the quantum Fisher normalization used here, it identifies the Bloch ball with a geodesic hemisphere of the unit round three--sphere. We describe its Ricci flow explicitly. In a general rotationally symmetric gauge the flow is a coupled system for the radial lapse and warping factor; a single scalar equation appears only after a Hamilton--DeTurck gauge choice. In the corresponding moving DeTurck frame the squared warping function $Ψ=Φ^2$ satisfies the linear forced heat equation \begin{equation*} D_tΨ=Ψ_{ss}-2, \end{equation*} while the fixed-lapse coordinate form contains the associated transport term. Since the Bures--Helstrom metric is Einstein, the geometric flow itself is the homothetic shrinker \begin{equation*} g(t)=(1-4t)g_{\mathrm{BH}}, \end{equation*} with scalar curvature $6/(1-4t)$ and extinction time $T=1/4$. Thus the metric remains inside the monotone cone for all $t<T$ and leaves the cone of nondegenerate Riemannian metrics only through the collapsed limit. We also record the volume--normalized flow, for which the Bures--Helstrom metric is a fixed point. Its linearization is the shifted round--sphere Laplacian $Δ_{\mathbb S^3}+3$, with spectrum \begin{equation*} σ_\ell=-(\ell-1)(\ell+3), \end{equation*} and spectral gap $5$ after removal of the scaling mode.

Can intelligence be measured? We propose that intelligence can be defined as the lawful amplification of rare but valid futures: a system increases the probability of outcomes that would be unlikely under passive dynamics but remain admissible under the constraints of the domain. We start with the premise that an intelligent system must model the world and its own place within it. Because the system is part of the world it models, this leads naturally to recursive self-simulation: the system represents futures in which its own actions are part of the trajectory. Our central results give a necessity statement and a conditional near-sufficiency statement connecting this architecture to a precise thermodynamic measure of lawful amplification of rare-valid futures: high rare-valid lift is impossible unless the internal simulation identifies rare-valid futures with high fidelity; conversely, when rare-valid fidelity is high and the simulation contains an effective policy, the achievable lift approaches the actuation-limited optimum. Thus recursive self-simulation is not merely a plausible feature of intelligence but, under the stated assumptions, is necessary and nearly sufficient for high thermodynamic intelligence. The resulting framework makes intelligence measurable on a universal scale, from passive matter and feedback controllers, large language models, and humans as text generators to Maxwell-demon-like information engines.

Could two worlds localised on neighbouring branes communicate through gravity alone? We investigate this question in a minimal higher-dimensional framework in which Standard Model fields are confined to our brane while gravity propagates through the bulk. From the brane-to-brane graviton propagator we derive the retarded transfer kernel of the inter-brane link and identify the transition from evanescent to propagating Kaluza-Klein modes. The central idea is to give the Kaluza-Klein tower a new role: not only as a spectrum of massive gravitational states, but as a set of communication carriers. Below the first KK threshold the channel is effectively four-dimensional and is mediated only by the massless graviton. Above threshold, massive KK modes open as additional propagating subchannels, and information may be encoded in their occupation pattern, relative phases, and arrival-time structure as well as in ordinary signal variables. The compactification determines the KK masses, wavefunctions, brane overlap factors, and propagation phases, which together define a multi-input multi-output (MIMO) channel matrix. In the resolved-mode limit, the tower yields approximate parallel subchannels, to which standard information-theoretic notions such as capacity bounds, water-filling, effective rank, and sparse occupancy codes apply. The production and detection of such signals are highly model-dependent and not assumed to be feasible with known technology. Nevertheless, the channel structure is well defined: a neighbouring brane-world could be separated from us by a microscopic distance in the compact space while remaining hidden because the only shared interaction is gravity. The first observable signature may not be a deliberate message, but the spectral and modal structure of the Kaluza-Klein tower itself, revealing partial information about the geometry of a nearby hidden world.

We develop indexed Bellman information complexity, a representation-level theory of interactive decision making centered on information indices and reference histories. The representation strips away problem-specific syntax and retains only the ingredients needed for dynamic programming and information accounting, thereby unifying the earlier framework of indexed algorithmic information ratios (AIR). On the upper-bound side, regret is controlled by Bellman supersolutions or potential identities whose gradient bracket is paid for by indexed information. Upper-confidence-bound (UCB), estimation-to-decision/decision-estimation-coefficient (E2D/DEC), and adaptive-minimax-sampling or exploration-by-optimization (AMS/EBO) methods appear as three relaxations of this same identity. On the lower-bound side, the posterior-reference trajectory supplies both the information telescope and the ghost quantile of small-regret trajectories. The resulting critical radius in the lower bound is an effective-dimension-scale quantity, as in Fano and local-prior-mass lower bounds, rather than the constant radius of a two-point Le Cam argument. The examples show that DEC is best viewed as a one-step relaxation of indexed Bellman information complexity, not as a universally tight conversion mechanism. We illustrate the framework through several applications, with particular emphasis on kernel bandits. In this setting, the active action marginal provides a concrete basis for comparing UCB, E2D, and AMS/EBO.

This manuscript contains preprint of a chapter under consideration for inclusion in the forthcoming third edition of {\em Cover and Thomas's Elements of Information Theory}, posted with permission from Wiley. The table of contents EIT-3 ToC of the new edition can be found at: https://docs.google.com/document/d/1L-m4oQEJw1PJhoxBeMwrrBD8S_HmvzMEkPbYvS24980/edit?usp=sharing . For feedback, please contact abbas@ee.stanford.edu Learning and information theory intersect in both model training and the characterization of fundamental performance limits. This manuscript provides a concise and accessible treatment of the first intersection, requiring only basic background in information theory and statistics at the senior undergraduate or first-year graduate level. End-of-chapter exercises make the material well suited for classroom use as well as self-study. The chapter focuses on the role of divergence measures in model training, with examples ranging from linear and logistic regression to autoregressive models, variational autoencoders, diffusion models, generative adversarial networks, and score-based models. It introduces the evidence lower bound (ELBO), f-divergences, and the Fisher divergence. In particular, the treatment of the generative diffusion model provides a more systematic and explicit derivation than is typical in the literature.

We extend the algebraic diversity (AD) framework from classical signal processing to quantum measurement theory. The Quantum Algebraic Diversity (QAD) Theorem establishes that a group-structured positive operator-valued measure (POVM) applied to a single copy of a quantum state produces a full-rank, group-averaged density matrix estimator whose eigenbasis and eigenvalue ordering track those of the true density matrix, with a bias toward the symmetrized state, analogous to the classical recovery of covariance eigenstructure from a single observation. We establish a Classical-Quantum Duality Map connecting classical covariance estimation to quantum state tomography, and an Optimality Inheritance Theorem showing that classical group optimality transfers to quantum settings via the Born map within the group-averaged family. SIC-POVMs are identified as AD with the Heisenberg-Weyl group and mutually unbiased bases as AD with the Clifford group, revealing the hierarchy $\mathrm{HW}(d) \subseteq \mathcal{C}(d) \subseteq S_d$ that mirrors the classical $\mathbb{Z}_M \subseteq G_{\min} \subseteq S_M$. The double-commutator eigenvalue theorem gives polynomial-time adaptive POVM selection. A worked qubit example shows the group-averaged estimator from a single computational-basis measurement, averaged over a matched $\mathbb{Z}_2$ group, reaching fidelity 0.99 where standard single-basis tomography gives a rank-1 estimate of fidelity 0.80. Monte Carlo simulations for $d = 2$ to $13$ confirm fidelity above 0.90 from a single outcome while standard fidelity degrades as $\sim 1/d$. The growing ratio reflects collapse of the rank-1 standard estimator, not fewer copies per parameter: the biased single-copy estimator reduces the number of distinct measurement settings, not the per-parameter sampling cost, and a genuine copy reduction holds only under exact symmetry.

Given $m \ge 2$ discrete probability distributions over $n$ states each, the minimum-entropy coupling is the minimum-entropy joint distribution whose marginals are the same as the input distributions. Computing the minimum-entropy coupling is NP-hard, but there has been significant progress in designing approximation algorithms; prior to this work, the best known polynomial-time algorithms attain guarantees of the form $H(\operatorname{ALG}) \le H(\operatorname{OPT}) + c$, where $c \approx 0.53$ for $m=2$, and $c \approx 1.22$ for general $m$ [CKQGK '23]. A main open question is whether this task is APX-hard, or whether there exists a polynomial-time approximation scheme (PTAS). In this work, we design an algorithm that produces a coupling with entropy $H(\operatorname{ALG}) \le H(\operatorname{OPT}) + \varepsilon$ in running time $n^{O(\operatorname{poly}(1/\varepsilon) \cdot \operatorname{exp}(m) )}$: showing a PTAS exists for constant $m$.