Papers

The paper focuses on information theoretic converse bounds for the alignment of $m$ correlated graphs and for the detection of correlation among $m$ graphs. A simple idea for $m\geq 3$ is that if the alignment of $m-1$ of the graphs is revealed as extra information (by a genie for example) then it is still necessary to produce the alignment between the one remaining graph and the others, i.e. the last matching must be accomplished. For both Gaussian and Erdos-Renyi models, the last-matching problem is equivalent to one with two observed graphs, providing a path to extend converse bounds for $m=2$ to larger $m$. While the method is rather obvious for alignment, we show that the method can also be used to derive converse bounds for weak detection of correlation.

Flexible reflectors (FRs) have emerged as a low-cost and energy-efficient solution for reshaping electromagnetic propagation environments across a wide range of applications. This paper investigates FR-swarm-assisted target localization in scenarios where line-of-sight (LoS) paths are unavailable. By leveraging the virtual LoS paths created by the FRs, a simple yet accurate estimator is proposed for localization under severe blockage conditions. To characterize the performance limits of the proposed scheme, we derive the Cramer-Rao lower bound (CRLB) and use it to optimize the positions and orientations of the FRs. Furthermore, by accounting for random FR deployment, we characterize the CRLB distribution and reveal how different network configurations affect localization accuracy. Simulation results demonstrate that the developed scheme closely approaches the CRLB performance, while the derived analytical results provide useful guidelines for FR deployment and network design.

The active inference framework provides a principled approach to modeling sentient behavior. In this framework perception and action selection are treated in a unified way. The resulting agents form an internal generative model of the relevant dynamics of the world in order to infer their future observations, their internal states and to select actions. We combine this modeling framework with the Integrated Information Theory of consciousness and are therefore able to analyze the active inference agents from the perspective of integrated information. The Integrated Information Theory aims at quantifying the level of consciousness of a system by assessing its capability to integrate information. Here, we define a measure of integrated information for the generative model by making an additional structural assumption. Experiments with simulated agents reveal a correlation between integrated information measures and the free energy of the active inference agents that increases with the size of the generative model.

We consider the problem of sequential prediction of an $m$-ary sequence, where at each epoch, (i) the environment selects an outcome from an $m$-ary alphabet, (ii) the learner selects a probability distribution over the same alphabet (unaware of the outcome generated by the environment), and finally, (iii) the learner incurs a cost that depends on the probability assigned to the outcome. The cost function we consider captures the complexity of predicting the outcome generated by the environment, in a scenario where the aforementioned prediction is performed via comparative queries to a lying oracle. We consider both stochastic and adversarial environments, propose algorithms for both settings, and establish logarithmic upper bounds on their regret.

Entropy functionals and their associated divergences underlie many statistical methods, including maximum entropy inference, minimum divergence estimation, and goodness-of-fit testing, yet choosing among Shannon, Rényi, Tsallis, and more general entropies is often a matter of convention rather than structural principle. We introduce a measure theoretic framework in which admissibility requires the entropy of an input measure to be bounded above by that of its reference measure whenever the former is absolutely continuous with respect to the latter. Under generalized mean-value composition, we characterize all such entropy functionals and obtain a four-level hierarchy determined successively by the mean generator, entropy scale, and additivity assumptions. A continuous strictly monotone generator $g$ is admissible exactly when $t\mapsto g(1/t)$ is strictly convex for increasing $g$, or strictly concave for decreasing $g$. This resolves a question posed by Rényi (Proc. 4th Berkeley Sympos. Math. Statist. Prob., 1961) concerning which generalized means may replace the arithmetic mean in his entropy axiomatization. The same criterion is equivalent to strict convexity of an associated Csiszár $f$-divergence generator and therefore yields data processing under Markov kernels with an exact equality condition. Within this hierarchy, product additivity singles out the Rényi family, while internal additivity, or product additivity together with arithmetic mean-value composition, singles out Shannon entropy. The characterization is constructive and yields new admissible entropy and divergence families, including integral-transform examples.

A binary constant-weight code is a set of binary words of length $n$ such that each word has exactly weight $w$ and is at least Hamming distance $d$ from every other word in the set. $A(n,d,w)$ denotes the maximum size of a binary constant-weight code with parameters $(n,d,w)$. Using seeded initialization with bit-swap tabu search, we found 124 new constructions that improve existing lower bounds for $A(n,d,w)$. As a corollary of stronger bounds on $A(n,8,8)$ for $n \in \{ 32,33,34,37 \}$, we also improve lower bounds on kissing numbers $\tau_{32}$, $\tau_{33}$, $\tau_{34}$, and $\tau_{37}$.

The capacity region of the $K$-sender discrete memoryless multiple access channel (MAC) is fully characterized when non-signaling (NS) assistance is available to all $K$ transmitters and the receiver. It is shown to have the same form as the classical capacity region of the MAC, except that the input distribution is allowed to be arbitrarily dependent across the senders. In particular, the NS-assisted capacity region matches the natural generalization to $K$ senders of an outer bound that was previously established by Fawzi and Fermé for $K=2$ senders. Additionally, we provide examples of $K$-sender MACs where the multiplicative gain in capacity from NS-assistance is arbitrarily close to $K$. Combined with an upper bound from prior work, this establishes $K$ as the extremal value of the multiplicative gain from NS-assistance across all $K$-sender MAC settings.

We construct a zero-knowledge proof of knowledge for the CSIDH group action that exploits the Chinese Remainder Theorem (CRT) structure of the ideal class group, available whenever the group structure is known exactly, as for CSIDH-512. We prove perfect completeness, perfect special honest-verifier zero-knowledge, and 2-special soundness, in which the secret is recovered from two accepting transcripts by one subtraction and one modular inversion per CRT component; no rewinding loop, lattice reduction, or heuristic sampling appears in the extractor. Because each round admits exactly two responses, Unruh's transform yields a non-interactive proof with straight-line extraction in the quantum random oracle model (QROM), removing the multiplicative forking-lemma loss. We instantiate the scheme on the CSIDH-512 class group, verify the algebraic layer by machine over the exact 258-bit modulus ($10^4$ random instances, all passing), and report protocol-level simulations in the exponent model: Monte Carlo soundness rates matching the proven $2^{-t}$ bound within 95% confidence at every tested $t$, serialized signature sizes within 1.6% of the formulas, instrumented action counts, and a scaled meet-in-the-middle attack whose measured cost follows the predicted $\sqrt{q}$ law. We further prove two delimiting results: CRT decomposition cannot enlarge the per-round challenge space, and publishing the CRT hop curves lowers classical key-recovery cost from about $2^{128.6}$ to about $2^{67.3}$ group action evaluations. The construction is therefore correct and structurally complete today, but quantitatively secure only on future parameters whose class number has large prime factors. We compare against CSI-FiSh, CSI-Otter, and Tanuki; a tightly secure blind signature from this proof of knowledge is left to future work.

In this paper, we consider transmissions with superimposed (SI) demodulation-reference-symbol (DMRS) and data in orthogonal frequency-division multiplexing (OFDM) based multiple-input multiple-output (MIMO) systems. First, we derive an analytical framework to characterize the iterative behavior between the mean-square errors (MSEs) of channel estimation (CE) and MIMO detection (MD) within an iterative CE and detection (ICED) process. This framework is subsequently utilized to optimize power allocation and pilot patterns between the DMRS and data symbols for SI-DMRS transmission. Second, we design an artificial intelligence (AI) based receiver built upon Transformer encoders for SI-DMRS transmissions, which incorporates an iterative CE and detection (ICED) structure. Simulation results demonstrate that the proposed AI-ICED receiver, combined with SI-DMRS, effectively increases spectral efficiency (SE) compared to conventional systems using non-overlapped DMRS and data symbols.

A feedback loop that returns a message into the process it describes defines a quantum channel on the message. We ask when such a loop preserves entanglement with a reference, that is, when its channel is not entanglement breaking. For any qubit loop, the negativity of the Choi state is at most half the fidelity between the states that the two values of the message leave in the discarded registers, in any basis. This channel analogue of the duality between fringe visibility and which-way information is attained by pure dephasing, and a perfect record of the message in the discarded registers makes the loop entanglement breaking. We then solve a three-qubit loop in which the message steers a future event, a probe reads the event, and a partial swap feeds the probe back. Every partial feedback is a strict contraction, and the loop is entanglement breaking exactly when an explicit trigonometric polynomial in its coupling angles is not positive. A partial record of the message in the future event can restore entanglement that the feedback alone destroys. Stability, a coherent fixed point, information about the future event and entanglement preservation coexist on about three quarters of the parameter space.

Deep joint source-channel coding-enabled (DeepJSCC) semantic communication (SemCom) has excelled at delivering high perceptual quality at low channel-bandwidth ratios, which positions it as a pillar for next-generation wireless networks. However, the existing works have difficulty accommodating user heterogeneity in terms of communication channel quality, expected quality-of-service (QoS) targets, and the available local energy. Therefore, in this paper, we explicitly reflect the heterogeneity of user devices in terms of the differences in expected QoS, channel condition, and local energy, and then mathematically formulate the problem. Next, we propose an energy-aware compression-computation co-adaptation (CoCo) framework, in which the base station can meet the expected user QoS by transmitting a longer signal or offloading the task to a local device. The user has to dedicate energy to denoising the signal to recover higher-fidelity latent features before feeding it to the semantic decoder. To solve the formulated problem, we first decompose it into two sub-problems: parameter optimization and resource allocation problems. Specifically, we propose a robust codec that effectively works under a diversity of compression rates and channel noise without re-training, while the greedy sub-carrier allocation lowers the communication time. Finally, we present simulation results on standard image datasets over additive white Gaussian noise to demonstrate the effectiveness of CoCo, which reduces total latency relative to rate-only adaptive DeepJSCC or denoising-only, thereby ensuring the demands of each individual user are met.

Quantum technology has the potential to transform scientific discovery, but quantum advantages often require processing capabilities well beyond the reach of experimental platforms. We show that coupling a single controllable qubit to an otherwise conventional sensor can exponentially reduce the number of measurements required to learn classical signals. These rigorous quantum advantages apply to fundamental sensing tasks, including learning Fourier coefficients, extracting temporal correlations from time-varying signals, and estimating transformations of physical observables. Using a superconducting cavity–qubit architecture, we experimentally demonstrate $10^7$-fold reductions in the number of measurements required for Fourier-amplitude and time-varying signal learning. Our $\textit{quantum feature sensing}$ algorithms further enable orders-of-magnitude improvements in simulations of weak-signal dark matter detection and wireless communication applications. These quantum advantages are derived from Quantum Phase-Space Inference (Q$\Psi$), a unifying theory of quantum-enhanced experiments that simultaneously converts a set of experimental objectives and constraints into tight lower bounds and optimal quantum-enhanced learning algorithms while producing a certificate of quantum advantage. Q$\Psi$ extends beyond the regimes captured by quantum Fisher information and provides a framework for systematically identifying rigorous quantum advantages in practical experimental tasks. Together, our results establish that near-term quantum technology can exponentially enhance our ability to learn from classical signals.

We study masking diffusion for discrete sampling and introduce a path-resolved measure of data geometry called the unmasking growth complexity ({UGC\xspace}). Its local increments directly control Kullback–Leibler (KL) discretization error, yielding a unified analysis of Bernoulli-subset and fixed-cardinality unmasking schemes. In log-reveal-odds coordinates, this structure yields optimized single-block and multi-block schedules, and quantifies the gains from adapting computational effort to data geometry. Crucially, we show how {UGC\xspace} increments can be estimated from samples via KL increments along coupled reveal trajectories. This leads to certified-optimal samplers that achieve a prescribed KL error with high probability and iteration complexity within a constant factor of the corresponding oracle procedure. Collapsing the \ugc path yields the aggregate {UGC\xspace} mass, which connects to classical multivariate dependence measures and complexity measures from previous analyses of discrete diffusion. In the fine-partition limit, the squared integral of the square-root {UGC\xspace} density determines the sharp leading-order optimal Euler discretization error. Examples exhibit substantial dimension-dependent gains over coarse schedules, including $\widetilde{\Omega}(\sqrt{d})$ improvements achievable with a constant number of adaptively placed blocks.

Over-the-air computation (AirComp) enables low-latency wireless data aggregation, but its accuracy is limited by imperfect signal alignment over fading channels and receiver noise. Fully digital beamforming improves aggregation accuracy in multiple-input multiple-output (MIMO) AirComp systems but requires one radio-frequency (RF) chain per antenna. To reduce this hardware burden, we investigate microwave linear analog computer (MiLAC)-aided beamforming for MIMO AirComp. Under a lossless and reciprocal MiLAC model, we jointly optimize the transmit digital precoding matrices and the receive-side MiLAC aggregation matrix to minimize the mean squared error (MSE). An alternating optimization algorithm is developed, in which the precoding matrices are optimally updated using the Karush–Kuhn–Tucker conditions and bisection, while the resulting convex aggregation matrix subproblem is solved globally using projected gradient descent. Numerical results verify the algorithm's convergence and demonstrate that MiLAC-aided beamforming approaches the MSE performance of fully digital beamforming with substantially fewer RF chains and outperforms phase-shifter-based hybrid beamforming under the same RF-chain budget.

Fluid antenna arrays (FAAs) reconfigure a finite set of radiating ports within a prescribed aperture. In compact apertures, however, channel-driven placement may cluster ports, strengthen mutual coupling, degrade radiation conditioning, increase source-voltage demand, and produce uneven current loading. This paper studies downlink multi-user beamforming with jointly optimized port placement and current-domain transmission. An electromagnetic-guided graph network predicts port layouts from channel observations and refines them using geometric and mutual-impedance information. The training objective jointly considers communication performance and electromagnetic feasibility, while a common evaluation procedure is applied to all methods. The results show that, under a common feasibility standard, the proposed method provides a controllable tradeoff among communication rate, current loading, and configuration latency.

Semantic communication (SemCom) and task-oriented communication (TOC) can reduce wireless resource consumption by focusing on transmitting semantic or task-relevant information instead of raw messages. In practice, a main challenge is to make transmitting information robust to channel noise and fading while keeping it compact. Existing learning-based transceivers often improve reliability by using larger encoders or higher-dimensional channel features, which increase computation complexity and channel uses. Therefore, optimized system design needs explicit rate control to balance performance and transmitting resources e.g., bandwidth and power. For this purpose, we propose a manifold-constrained hyper-connection (mHC) coding scheme with an entropy bottleneck (EB) for resource-efficient SemCom and TOC over wireless channels. Instead of using a single residual path of existing encoders, the proposed mHC-based semantic encoder applies multiple residual streams and constrains their interaction by doubly stochastic (DS) mixing matrices. The new structure improves representation diversity and training stability with negligible parameter and floating-point overhead. The EB quantizes the channel features and estimates the entropy-coded rate, enabling end-to-end rate–distortion/task optimization under bandwidth and transmit-power constraints. We further show that DS-constrained stream mixing does not increase the differential entropy of the transmitted features. This implies no increase in the ideal EB coding length. Experiments on SemCom and TOC under additive white Gaussian noise (AWGN), Rayleigh fading, Rician fading, and imperfect channel state information (CSI) show that the proposed scheme improves semantic/task performance, communication robustness, and convergence stability over residual and unconstrained HC baselines, while requiring no additional channel uses.

Fluid antenna array (FAA) activation jointly determines the effective multi-user channel for precoding and the sparse physical aperture. Channel-oriented selection can concentrate high-gain ports and erode aperture quality, whereas geometry-oriented selection does not adapt to instantaneous channel state information (CSI). This paper formulates finite-port FAA activation as a rate–aperture–feasibility problem under an exact RF-chain budget. We propose impedance-aware zonal port activation (IA-ZPA), which couples compact CSI-conditioned port scoring with a checkerboard feasibility projection and inference-time mutual-impedance-aware selection. The learned scorer ranks ports, while the deterministic rule fixes the active aperture; a separate current-domain RZF backend then evaluates source-drive feasibility. Under a common induced-EMF protocol, IA-ZPA attains the largest constrained rate among the methods satisfying the prescribed mean-PSLL target with a substantially lower decision time than greedy selection.

We study pull-based remote state estimation of an arbitrary, multi-state Markov source while accounting for both freshness and correctness attributes of information. To that end, we formulate a discounted optimization problem in terms of the age of incorrect information (AoII), and express it as a joint source-AoII belief Markov decision process (MDP) under maximum a posteriori (MAP) estimation. We then exploit the information structure of the model and prove that every reachable belief is represented by the last successfully observed source state and the number of time slots elapsed since that observation. For numerical computation, we truncate the elapsed no-success duration at a finite level and derive an explicit error bound and a criterion for selecting the truncation parameter. For reliable links, we show that an optimal policy can be represented by a look-up table of waiting times. For unreliable links, we propose a persistent policy and derive computable performance bounds. We also show that the MAP estimate stabilizes after a finite number of time slots. To further reduce memory requirements, we introduce a hybrid estimator with an early stationary switch and derive a computable bound on the resulting difference in performance. Finally, we extend the framework to multiple sources, formulate the scheduling problem as a restless multi-armed bandit, establish a sufficient condition for indexability, and develop an approximate Whittle index policy based on interpolation. Our numerical results illustrate the structure of the optimal single-source policy, evaluate the performance of the multi-source policies, and verify that the proposed heuristic policies closely approach the optimal solution while substantially reducing computational efforts.

We present two counterexamples to the Markovity Conjecture of Gohari, Liu and Nair (ISIT 2025), which is a structural conjecture concerning the optimizers of the dual functional associated with Marton's inner bound and, if true, would greatly simplify the evaluation of Marton's inner bound. Both counterexamples are ternary-input broadcast channels with strictly positive transition probabilities and use the same nonrectangular $2\times2$ auxiliary structure. In each case, we exhibit an explicit non-Markov construction whose objective value is rigorously larger than that achievable by any construction satisfying the conjectured Markov structure. Both examples are obtained with the assistance of GPT-5.6 Sol and disprove the Markovity Conjecture.

Zero-knowledge (ZK) proofs certify that a message belongs to an allowed semantic class without revealing the message, but the certificate compares a high-dimensional embedding against class centroids, so its cost grows with the embedding dimension $d$. A Johnson–Lindenstrauss (JL) projection lowers $d$ to $m\ll d$ while preserving pairwise distances, yet a random JL matrix must be committed and its sampling proved inside the circuit, which is costly and a leakage risk. We construct a public deterministic projection from the standardized orbit of a Pisot $\beta$-transformation, analyzed through the spectral gap of the $\beta$-map, the geometric decay of its correlations, rather than equidistribution. We prove that the induced squared-norm estimator is unbiased up to a term decaying geometrically with a sampling gap, and that its variance is $V_0/m$ with a constant $V_0$ that is dimension-free in experiment and, under one stated concentration hypothesis, in theory. A single public seed preserving all pairwise centroid distances therefore exists and is found by search. Against six standard projections, including the chaotic-sequence matrix of Yu et al., the construction matches statistical quality to within measurement noise, and it is the only one simultaneously free of in-circuit randomness and exactly reproducible in a fixed finite field at a per-step cost $\log_2\beta$ rather than $2^{k}$.

The growing power demands and variability of AI workloads make electrical power delivery a critical constraint in data-center operation. Distributed energy storage can reduce the power capacity required to support stochastic loads, but its benefits depend fundamentally on the statistics and time scales of demand. This paper develops a probabilistic framework that jointly characterizes provisioned power, energy-storage capacity, and the probability of overdraw. We show that storage-assisted provisioning separates into two operating regimes. In the Small Battery Region, overdraw is dominated by short-lived demand excursions and storage provides nearly linear reductions in the required power margin. In the Large Battery Region, overdraw results from sustained demand fluctuations over longer spans of time, and the required margin exhibits diminishing returns with storage. For this regime we introduce effective power, an analogue of effective bandwidth that captures the temporal statistics of the demand and gives an asymptotically tight characterization of the required power. We further quantify how temporal correlation and spatial aggregation affect storage requirements and statistical multiplexing gains, and extend the analysis to loads with multiple demand time scales. Finally, we evaluate the framework using power-demand traces from three production data centers spanning HPC, GPU-training, and cloud-service workloads. Despite their heterogeneous, cyclo-stationary and multi-modal behavior, the measured workloads exhibit the predicted regimes, and a simple four-parameter two-state model captures the dynamics governing their storage-power tradeoffs. The resulting framework provides both a probabilistic foundation and practical dimensioning principles for storage-assisted power provisioning in next-generation AI data centers.

What a finite learning device has recorded and what will hold value for it on future tasks are not the same quantity. We develop a typed accounting for finite-state learning devices that separates four components: a training-side fit functional $\Phi_{\mathrm{fit}}$, the record-correlation stock $J_{D}=I(M;D)$, an update-side search ledger $\sigma_{M}$, and an operational capital value $V(M;T,b)$. This value is the work gap between an informed protocol class and a blind class obtained by deleting the memory-read port and re-optimizing from scratch. (I) Separation: for every $n$, there is a device family on which record correlation and world correlation grow by $n\ln 2$ while the capital gain is exactly zero. In the $\mathrm{flat}^{*}$ regime, data-free updates never increase $V$. (II) Capitalization ledger: an exact $\mathrm{flat}^{*}$ extraction identity and a universal ledger identity give, for (F5$'$)-stable $M$-local updates under a no-discarded-record-correlation condition (f), the bound $\eta_{\mathrm{cap}}\le 1$ for the capitalization efficiency $\eta_{\mathrm{cap}}=\Delta V/(k T\,\sigma_{M})$, together with necessary and sufficient conditions for equality. (III) Value retention: for the retention gap $L_{\mathrm{gen}}$ and retention ratio $\rho_{\mathrm{gen}}$ (the former carries no sign constraint; the latter is defined for positive training-side value and is not confined to $[0,1]$) we give a two-layer alignment domain: an exact exchange rate between value and the side-information-adjusted record fit $I(M';D\mid Y)$ without any record-side-information independence assumption, and a raw record-stock exchange rate under a joint side-information neutrality condition $(M,D)\perp Y$, whose boundary is marked by an explicit one-time-pad witness. These are statements about finite-device value retention under task-distribution shift, not a theory of statistical generalization.

We consider the uplink of a fronthaul-constrained cell-free massive MIMO system with a single multi-antenna user equipment (UE) transmitting multiple spatial streams to distributed access points (APs). Due to heterogeneous channel conditions and limited fronthaul capacity, uniform-resolution quantization across APs and streams is highly inefficient. To address this, we propose a stream- and AP-adaptive resolution control framework that jointly optimizes the transmit power and per-AP per-stream quantization resolutions. By leveraging a distributed implementation of singular-value decomposition (SVD)-based processing, the data streams are decoupled at the APs, enabling flexible fronthaul compression across both spatial streams and APs. The resulting non-convex optimization problem is tackled using a weighted minimum mean-squared error (WMMSE)-based block coordinate descent algorithm with semi-closed-form updates.

We study quantization-aware precoding for the downlink of cell-free massive MIMO systems with limited-resolution fronthaul. In such systems, the centrally designed precoder must be quantized before being conveyed to distributed access points (APs), creating a strong coupling between precoder design and fronthaul compression. To capture this effect, we develop an end-to-end signal model based on Bussgang decomposition, where the quantization distortion depends explicitly on the precoder coefficients. Building on this model, we formulate a joint precoding and bit allocation problem under per-AP power constraints and a total fronthaul bit budget. We propose an efficient block coordinate descent algorithm that iteratively updates the precoder, receive scaling, and distortion levels. Numerical results demonstrate that the proposed method significantly outperforms uniform bit allocation and quantization-unaware precoding schemes, particularly in fronthaul-limited regimes.

Large neuromorphic systems contain many processing tiles that may replicate a shared control parameter such as a threshold reference. If these copies diverge, identical inputs may be processed under different intended settings. We study how tiles can reduce this disagreement when communication carries only labeled spike times and up to \(f\) sender labels may be Byzantine. A raw event stream cannot supply the one-value-per-sender input required by classical approximate agreement because a faulty sender can remain silent, flood a receiver, or report different times to different receivers. We introduce the Spike-time Interface for Faults, or \SIF, which combines paced epochs, sender attribution, per-label \FirstSpike admission, bounded timing error, and a silence sentinel. For an affine one-spike code, midpoint decoding attains the exact deterministic minimax error \(\rho=\min\{1/2,\omega/L\}\), where \(\omega\) is the residual timing uncertainty and \(L\) is the usable encoding window. \SpikeTrim applies the classical mean-subsequence-reduced (MSR) rule to the sender-indexed decoded values. For \(n\ge3f+1\), it guarantees one-step robust validity, the tight noiseless contraction factor \(f/(n-2f)\) under direct updates, an explicit worst-case asymptotic disagreement bound, and finite recovery after transient agreement-state corruption. A closed-form test determines whether a validated timing budget meets a target disagreement. Simulations illustrate the fault threshold, timing dependence, flooding resistance, and recovery. A controlled spiking classifier experiment shows an association between faster control-state alignment and lower prediction disagreement under a finite maintenance budget.

Random spatial tessellations generated by point processes provide fundamental models for proximity, space partitioning, and local geometry in stochastic systems. Poisson–Voronoi and Poisson–Delaunay tessellations induced by homogeneous Poisson point processes form a canonical dual pair used in stochastic geometry, computational geometry, spatial statistics, and wireless-network analysis. Their typical-cell volume distributions provide important geometric inputs for modeling coverage, traffic load, clustering, connectivity, and other system characteristics. Despite extensive study, the literature remains analytically asymmetric. For Poisson–Voronoi cell volumes, exact integral representations exist in certain planar settings, while a recent scale–shape factorization provides an exact general-dimensional representation with conditional Gamma structure. However, the normalized shape laws and unbounded facet-count mixture remain implicit, and tractable unconditional closed-form distributions are unavailable. Practical modeling therefore relies largely on simulation, moment characterizations, and empirical approximations. By contrast, Poisson–Delaunay simplex volumes admit dimension-explicit PDFs, CDFs, and moment formulas derived through Mellin-transform analysis and Meijer's \(G\)-function representations. Motivated by this contrast, this paper surveys typical-cell volume distributions in Poisson–Voronoi and Poisson–Delaunay tessellations. We review the main analytical methods, synthesize exact and approximate results, summarize emerging high-dimensional limits, and discuss wireless-network applications, including load modeling, cooperative transmission, and three-dimensional architectures. We also identify open problems concerning unconditional Poisson–Voronoi distributions, non-Poisson spatial models, data-driven geometric inference, and dimension-aware network modeling.

Suppressive interference, high-dynamic motion of the receiving platform, and carrier-phase RTK lead satellite navigation to one fundamental question: when the receiver actively participates in observation formation through its array geometry, channel states, weights, and signal-processing rules, how can the resulting carrier observation continue to represent the same objective propagation process while preserving continuous phase and the integer-ambiguity structure? The physical world is not changed by a reconfiguration of the observer, but its complex representation in the observation world is. Without a strict separation between propagation-induced and observer-induced variations, anti-jamming, high dynamics, and precise carrier-phase positioning become structurally coupled at the observation-formation level. Finally, reproducible and falsifiable protocols are provided for static interference, dynamic rotation, inter-branch timing mismatch, near-null response, RF replay, and RTK integer-risk validation. The scoped novelty of SN-ASMO is the unification of observation formation, reference covariance, exact nuisance quotients, same-source transport, intrinsic statistical information, and preservation of the RTK integer structure in one mathematically closed and physically testable framework.

An e-detector for a pre-change class $\mathcal P$ is a nonnegative process $M$ such that $\mathbb E_P[M_\tau] \leq \mathbb E_P[\tau]$ for all stopping times $\tau$ and all $P \in \mathcal P$. Thresholding e-detectors controls the average run length (ARL): declaring a change at the first time $T_b$ when $M$ crosses $b$ ensures that $\inf_{P \in \mathcal P}\mathbb E_P[T] \geq b$. But e-detectors do substantially more than control the ARL; they also satisfy a optional-horizon inequality: \[ P(T_b\leq\sigma)\leq \mathbb E_P[\sigma]/b \] for every data-dependent stopping time (monitoring horizon) \(\sigma\) and $P\in \mathcal P$. In particular, every e-detector-based procedure obeys $P(T\leq t)\leq t/b$ at each fixed $t$, thus avoiding early false alarms. Remarkably, the converse also holds: every stopping time $T$ that satisfies the optional-horizon inequality must in fact arise from thresholding an e-detector. We also derive a universal representation of stopping times that satisfy (only) ARL control. These are represented by weak e-detectors, that only require $\mathbb E_P[M_\tau] \leq \mathbb E_P[\tau]$ to hold at all threshold stopping times $T_b$. Appendices present universal representations for other (less common) change detection metrics.

We study (binary) nearly-perfect covering codes, which are codes that attain the Van Wee bound with equality. They act as the covering counterparts to nearly-perfect error-correcting codes, which attain the Johnson bound with equality. These codes have been completely classified for covering radius $R=1$. We prove that no code with $R\geq 2$ can attain the original Van Wee bound with equality, since it omits the dependence on the minimum distance of the code. We refine the bound to account for the minimum distance and show some nearly-perfect covering codes. By proving some structural properties of such codes, we prove all nearly-perfect covering codes with $R=2,3$ must be equivalent to the codes we showed. We also prove that for any $R\geq 3$, there are at most a finite number of nearly-perfect covering codes.

Cardinality estimation - counting the number of distinct elements in a data stream - requires a tradeoff between memory and accuracy. ExaLogLog recently established the state of the art for this tradeoff by combining wide registers with a Fisher-information-optimal maximum likelihood (ML) estimator, achieving the best known memory-variance product (MVP) among HyperLogLog variants. Here we present Arithmetic Variable LogLog (AVLL), which surpasses ExaLogLog at every memory point tested using arithmetic encoding and eliminating uncommon states to consume 64-bit words completely with 11 registers each, yielding a 5.5x register-count advantage. Its four-component blended estimator, HLDLC, exploits this density advantage to surpass ExaLogLog's ML accuracy without iterative solving. At 1 KB, AVLL achieves 1.63% width-weighted mean absolute error compared to ExaLogLog's 1.71% - a 4.7% improvement. The corresponding empirical MVP is 3.4, surpassing ExaLogLog's practical MVP of 3.78 and its theoretical optimum of 3.67. This holds at every tested size from 0.25 to 4 KB. AVLL inherits DynamicLogLog's early exit mechanism, which filters most elements before any register is touched. With thousands of simultaneous sketches per thread, AVLL is 2.7-4.5x faster than ExaLogLog due to the reduced memory bandwidth from early exits. Like DynamicLogLog, AVLL stores relative NLZ values with a shared offset, so its memory scales as O(B + log log C) rather than O(B x log log C) - decoupling maximum representable cardinality from register width. These results hold under both high-complexity (all-unique) and low-complexity (nonuniformly high duplication rate) data distributions, with zero accuracy degradation from duplication. AVLL is implemented as a single self-contained Java class with all correction formulas embedded, available in the BBTools suite at https://bbmap.org.