The Ising framework maps the decoding problem in quantum error correction onto ground-state optimization of a classical Hamiltonian, in which $X$-$Z$ error correlations enter as cross terms. Under phenomenological depolarizing noise, the exact joint formulation contains up to 8-body interactions for the toric code and 10-body for the $6.6.6$ color code. These high-order terms degrade solver convergence, inflate runtime, and raise the auxiliary spin overhead when embedding into native 2-body Ising hardware. In this work, we propose the iterative low-order decoding (ILOD) algorithm, which alternates between $X$- and $Z$-type sub-Hamiltonians, approximating cross-type correlations through Bayesian priors that reweight each type's couplings using the other type's inferred error configuration. This halves the maximum body count of interaction terms in the Hamiltonian, accelerating the solver, restoring convergence at larger code distances, and reducing the total spin count for 2-body embedding by a factor of $2.5$. For the toric code, ILOD attains a threshold of $4.73%$ versus $4.83%$ for the joint formulation, with the empirical runtime ratio scaling as $(0.81)^d$. For the $6.6.6$ color code, their thresholds agree within statistical uncertainty for small code distances, and ILOD remains convergent for larger distances where the joint formulation fails to converge despite a larger annealing budget.

The transition to next-generation mobile communication networks, particularly 6G, demands advanced technologies to meet the requirements for ultra-reliable, low-latency communication, massive connectivity, and intelligent applications. Reconfigurable antennas (RAs) play a crucial role in achieving these objectives by enabling dynamic adjustments to the radio frequency (RF) characteristics of antennas, such as gain, radiation pattern, impedance, and polarization. Unlike traditional fixed-position antennas, RAs can alter both their radiation patterns and positions, offering flexibility in response to varying communication environments. This paper presents a comprehensive survey and tutorial on RAs, with a focus on fluid antennas (FAs), movable antennas (MAs), pinching antennas (PAs), and reconfigurable holographic antennas (RHAs), examining their potential in next-generation mobile networks. We explore the channel modelling and estimation, performance analysis, resource allocation strategies, and their synergy with other emerging wireless technologies for each type of RA. Finally, we provide a comparative analysis of different RAs and discuss the open challenges and future research directions, offering insights and guidance for future investigations in the exciting research area.

Semantic communications enable AI-native wireless systems by mapping raw data into compressed task-oriented latent representations. However, independently trained agents often rely on heterogeneous latent spaces and background knowledge, leading to semantic mismatch that degrades mutual understanding and downstream task execution, especially in interferencelimited multi-user wireless networks. This paper investigates distributed latent-space alignment in multi-user semantic MIMO interference networks with cognitive radio constraints. We consider primary users and semantic-aware secondary users sharing the same wireless resources, where secondary agents must simultaneously mitigate interference and align heterogeneous semantic representations. To address this problem, we formulate semantic alignment as a non-cooperative game and derive a closed-form solution for the joint optimization of linear semantic MIMO transceivers under power and interference constraints. Exploiting the structure of the problem, we recast the original matrix valued optimization into a lower-dimensional power-allocation game, leading to an iterative semantic water-filling algorithm. We establish sufficient conditions for existence, uniqueness, and global convergence to a Nash equilibrium, explicitly relating semantic alignment properties and physical-channel interactions. Numerical results assess the performance of the proposed framework, revealing key trade-offs among semantic compression, task performance, and hierarchical spectrum access.

Lifted product codes are an important family of quantum low-density parity-check (QLDPC) codes, as they were the first QLDPC code family shown to be asymptotically good. Understanding the structure of their parity-check matrices $H_{\mathsf{X}}$ and $H_{\mathsf{Z}}$, as well as the associated Tanner graphs, is essential for analyzing their decoding behavior and error-floor performance. In this work, we show that the Tanner graphs of $H_{\mathsf{X}}$ and $H_{\mathsf{Z}}$ are indeed isomorphic, and investigate their graph-theoretical structure. We establish conditions ensuring the connectivity of these graphs and provide bounds on their minimal absorbing sets, providing new insight into the combinatorial structures influencing decoding performance.

We describe a computational search for quadratic APN (Almost Perfect Nonlinear) functions in dimension 8 within a structured self-equivalence subspace. The search space is a 40-dimensional binary linear subspace consisting of all functions commuting with a linear automorphism of order 5 (class 22 in the taxonomy of Beierle, Brinkmann, and Leander, 2021), previously reported to contain no APN functions. Our approach combines random sampling via an explicit RREF parameterization (approximately 600 fresh APN-positive evaluations per core-hour) with Gröbner basis computation in Magma to enumerate all APN functions in a 24-dimensional hyperplane through each center (approximately 10 minutes per hyperplane). From 428 hyperplane computations, covering 0.65% of all 65,536 hyperplanes, we obtained 566 quadratic APN functions forming six CCZ-equivalence classes under the ortho-derivative invariant. Four classes, comprising 500 functions, match no entry in the 2025 database of 3,775,599 quadratic APN functions or in the pre-2020 compilation of 12,921 instances. Two classes (66 functions) are CCZ-equivalent to the Gold functions x^3 and x^9, confirming the correctness of the search pipeline. A membership analysis shows that the three new classes (B, C, D) lie entirely outside the original subspace and occur only in Gold-centered slices, demonstrating the essential role of the Gröbner basis stage. In 532 experiments using database functions as slice centers and 20 experiments with random centers, no APN neighbors were found, indicating that the gateway phenomenon is specific to the self-equivalence structure of the search space. Since the ortho-derivative invariant is a complete CCZ-invariant for quadratic APN functions, the absence of matching signatures provides a rigorous proof of CCZ-inequivalence.

Deep Joint Source-Channel Coding (JSCC) has emerged as a promising paradigm for overcoming the ``cliff effect" in wireless communications. However, existing Deep JSCC frameworks operate directly on raw analog data such as image pixels rather than the discrete semantic tokens that foundation models require. Moreover, traditional systems employ fixed, hand-designed constellations that treat all tokens equally, leading to catastrophic random errors under channel noise. In this paper, the Semantic Token Codebook Communication (STCC) is proposed as a unified source-channel semantic token coding framework designed to transmit the discrete semantic tokens of foundation models over noisy channels. The core of STCC is the Semantic Token Codec (STC). It accepts discrete tokens as input, which maintains compatibility with foundation models while employing a residual multiple layer perceptron, i.e., MLP-based encoder that learns geometrically structured constellations optimized with a triple-loss objective. This learned mapping forces the channel topology to align with the semantic embedding space, ensuring that channel noise results in topological errors rather than random corruption. This phenomenon is theoretically and empirically characterized, identifying ``Semantic Drift" in symbolic modalities and ``Structural Distortion" in perceptual modalities, where errors shift predictions to semantically or structurally similar tokens. Extensive experiments demonstrate that STCC significantly outperforms traditional systems in low-SNR regimes, effectively converting channel noise into semantic variations without requiring receiver-side modification.

We establish conditions for embedding a corpus of $N$ documents as $d$-dimensional vectors such that every $k$-subset $S \subseteq [N]$ is realizable as a result of top-$k$ retrieval by some query vector. Recent work shows that $d = O(k)$ suffices for such embeddings to exist in $\mathbb{R}^d$, independently of $N$. We theoretically prove that this corpus-independent bound is specific to infinite precision. With $B$ bits per coordinate, perfect top-$k$ retrieval requires $Bd = \Omega(k \ln N)$; thus, at any fixed precision, the dimension must grow at least logarithmically with $N$. Specializing to a $\ell_2$-normalized $B$-bit uniform scalar quantization model, we also identify a threshold on the precision $B^{*} = O(\ln \ln N)$ below which no dimension suffices, together with two further regimes that bound the feasible $(B, d)$ pairs. Our result implies that in practical vector databases and dense retrieval systems where quantization is standard, the embedding dimension and possibly the precision must grow with the corpus size.

In this paper, we propose a segment-wise soft robotic antenna (SRA) system, where each soft robotic arm referred to as a tentacle, comprises multiple independently controllable segments with bending, elongation-retraction, and sweeping motions. By adjusting segment motion parameters, the positions of surface-mounted antennas are reconfigured, distinguishing it from conventional reconfigurable antenna (RA) systems. Based on this model, we propose two antenna deployment schemes: the segmented end-antenna configuration (SEAC), where fixed antennas are mounted at the segment ends and reconfigured via segment motions; and the hybrid end-and-intermediate antenna configuration (HEIAC), where RAs are further integrated as intra-segment antennas. In HEIAC, soft-robot segment deformation provides large-scale spatial reconfiguration, while RAs enable fine-grained adjustment. For SEAC, we formulate a sum-rate maximization problem accounting for inter-segment connectivity and the nonlinear mapping from segment deformation parameters to antenna coordinates, and develop a penalty dual decomposition-projected gradient ascent (PDD-PGA) algorithm. For HEIAC, we jointly optimize segment deformation, intra-segment antenna positions, and antenna activation using a block coordinate descent (BCD)-PDD-PGA algorithm with greedy backward antenna selection. Simulation results demonstrate that the proposed schemes substantially outperform fixed-position antenna arrays and conventional RA baselines. In particular, SEAC and HEIAC achieve 37.9% and 32.1% sum-rate gains over conventional 3D reconfigurable arrays, respectively, while SEAC provides up to a 49.3% gain in compact array deployments.

Recently, constructions of linear complementary pairs (LCPs) of codes and linear complementary dual (LCD) codes on function fields have attracted considerable attention due to the wide range of applications of these codes. Such constructions rely on non-special divisors of degrees $g$ and $g-1$. In this work, we investigate Kummer extensions defined by $y^m = f(x)$ with $f(x)\in\mathbb{F}_q(x)$ and establish an arithmetic characterization of non-special divisors whose support can contain non-totally ramified places. Based on this characterization, we explicitly construct non-special divisors of degree $g-1$ on the GK curve. Moreover, utilizing pure gaps, we explicitly provide several families of effective non-special divisors of degree $g$ on Kummer extensions with the same multiplicities. We then develop a general framework for constructing LCPs of algebraic geometry (AG) codes on Kummer extensions. By virtue of canonical divisors, we show that the security parameters of LCPs of AG codes can be determined within this framework, which also enables the construction of LCD AG codes. Finally, we illustrate our results with representative examples, including LCPs of codes on the GK curve and LCD codes on quotients of the Hermitian curve.

Low-Altitude Wireless Networks (LAWNs), composed of Unmanned Aerial Vehicles (UAVs) and other aerial platforms, provide integrated perception, communication, and computation services in low-altitude airspace. However, deploying large generative models in this domain faces three major challenges: 1) Limited embodied action mapping; 2) Inadequate physical environment modeling; 3) Insufficient closed-loop optimization. To address these challenges, this study proposes an Embodied Agentic UAV framework. Centered on a Vision-Language-Action (VLA) model as the execution core, the framework establishes an end-to-end embodied decision-making pipeline from multimodal environmental perception to continuous control generation. In addition, a World Model (WM) is introduced to capture the coupling between UAV actions and environmental state evolution, thereby supporting environment prediction, policy verification, and dynamic optimization. Furthermore, memory and reflection mechanisms are incorporated to form an adaptive closed-loop optimization paradigm of decision, execution, evaluation, and update, thereby enhancing the system's autonomous decision-making capability and continual evolution ability in complex dynamic environments. Experimental results validate its effectiveness in enabling robust, predictive, and sustainable autonomous control in LAWNs.

We study superspace concentration as a quantum resource, formalized through the focus measure F(\r{ho}) = {\lambda}_max(\r{ho}_super) - the largest eigenvalue of the reduced superspace state - which quantifies the capacity of a quantum system to concentrate informational weight into a preferred subspace of an extended degree-of-freedom space. We develop a complete resource-theoretic framework around this measure and validate its properties through GPU-accelerated numerical simulation. Analytic decoherence predictions are confirmed to machine precision (1.11 x 10^{-16}) for superspace dimensions dS in {2,4,8,16,32}. Focus monotonicity holds across 10,000 random states with zero violations under four focus-non-generating channels across six system configurations. Focused quantum states resist coherent unitary attacks with significantly greater resilience than standard fidelity predicts, with focus remaining above 0.9 at attack strength {\epsilon} = 0.302 versus {\epsilon} = 0.174 for fidelity. We further demonstrate that the focus measure and the U(dS)-asymmetry measure are operationally distinct: asymmetry remains near zero and provides no robustness signal under coherent and targeted attacks while focus tracks spectral concentration and remains robust until {\epsilon} > 0.3. The connection between Grover's algorithm and superspace concentration is made explicit via the identity F(|{\psi}_k><{\psi}_k|) = P(marked), providing a resource-theoretic interpretation of oracle query complexity. Finally, we provide the first numerical characterization of the focus capacity gap {\Delta}F, identifying a log_2(dS) scaling law confirmed for both product and correlated noise channels.

We introduce the ladderpath index as a measure of language complexity grounded in algorithmic information theory. It counts the minimum steps needed to reconstruct a sequence through hierarchical reuse of repeated substructures, capturing an exactly computable but constrained form of algorithmic compressibility related to, but distinct from, Kolmogorov complexity. We apply the ladderpath approach to 21 parallel corpora from the Parallel Universal Dependencies dataset. The ladderpath index is approximately invariant across the languages, and varies much less than the corpus length. This is more pronounced when all corpora are mapped to a unified binary representation, providing evidence for the equi-complexity hypothesis from a representation-independent perspective. We also observe trade-offs between character inventory size and corpus length, and between vocabulary-level and corpus-level reconstruction complexity, supporting the trade-off hypothesis that total complexity is conserved and redistributed across linguistic levels. The reusable substructures identified by the ladderpath approach, without any linguistic input, overlap with words and morphological components attested in the natural vocabulary. The hierarchical reuse captured by the ladderpath approach parallels the chunking mechanisms proposed in cognitive science, where the human cognitive system compresses linguistic input into nested, reusable units under shared memory and processing constraints. This connection between cognitive chunking and the ladderpath approach provides a new interpretation for the equi-complexity and trade-off hypotheses, grounding both in the shared cognitive architecture that underlies language processing across human languages.

In this paper, we present a new approach for unmanned aerial vehicle (UAV) positioning and reconfigurable intelligent surface (RIS) partitioning to enhance connectivity of uplink RIS-assisted UAV networks. To achieve this, our approach optimizes RIS-aided link selection, RIS partitioning, and UAV positions to maximize network connectivity characterized by its Fiedler value. Meanwhile, it maintains a specific signal-to-interference plus noise ratio (SINR) constraint for user equipment (UE), which is influenced by RIS partitioning and UAV reliability. The network connectivity optimization problem is formulated using the Fiedler value subject to RIS elements allocation and SINR constraints. This problem is a computationally expensive combinatorial optimization, necessitating an efficient iterative approach. In particular, we propose a perturbation method for RIS-aided link selection, and derive a closed-form solution for RIS partitioning, with each partition tailored to optimize SINR for individual UAV. For the given RIS-aided links and RIS partitioning, we then show that the problem of UAV positioning can be formulated as a low complexity semi-definite programming (SDP) optimization problem, which can be solved using off-the-shelf CVX solvers. Our simulations show the potential gain of UAV positioning and RIS partitioning compared to the benchmark schemes from the literature.

This paper investigates the utility of the movable antenna (MA) and reconfigurable intelligent surface (RIS) framework for downlink wireless communications. In the considered scenario, a base station (BS) is equipped with two sub-arrays of MAs transmits signals to the users via the RIS. By jointly exploiting the antenna-positioning flexibility of MAs and the RIS element selection capability, the proposed joint MA-RIS framework introduces additional design degrees of freedom to enhance desired signals and mitigate inter-user interference, thereby maximizing the network sum-rate. To this end, we formulate a joint optimization problem involving MA positioning, sub-array beamforming, and RIS element selection, subject to the minimum antenna separation and transmit power constraints. The resulting problem is highly non-convex and challenging to solve directly. To address this issue, an alternating optimization framework is developed that decomposes the problem into three tractable subproblems. Specifically, zero-forcing beamforming is employed for transmit beamformer design, a low-complexity one-dimensional search is derived for RIS element selection, and the MA positioning problem is solved using block coordinate descent (BCD) and convex optimization techniques implemented via CVX. Simulation results demonstrate that the proposed joint MA-RIS framework significantly improves the achievable sum-rate compared with conventional fixed MAs and benchmark schemes with random configurations.

The success of large-scale deep learning models in neuroscience is fundamentally constrained by severe data heterogeneity. Native fMRI data aggregated from diverse sources exhibit substantial variation in both spatial and temporal resolutions. Consequently, most existing frameworks rely on lengthy, rigid preprocessing pipelines that enforce uniformity across datasets. This practice introduces two critical limitations: (1) potential degradation of subject-specific anatomical information; (2) significant computational overhead, often requiring hours of processing per subject. Here, we propose FlexiBrain, a resolution-agnostic voxel-level encoding framework for native fMRI based on Mamba-JEPA. FlexiBrain defines patch sizes in real-world physical units and employs a dynamic patch resizing, thereby bypassing destructive spatial standardization while enabling direct ingestion of data in native space. We instantiate the framework using an efficient Mamba-JEPA backbone to model high-dimensional 4D fMRI signals. Across five diverse downstream neuroscience tasks, FlexiBrain consistently outperforms recent state-of-the-art methods, achieving gains of up to 12 percentage points without external data augmentation. Importantly, FlexiBrain functions as a seamless plug-in module, substantially reducing preprocessing costs and accelerating the development of robust voxel-level fMRI foundation models. Code is available at this https URL.

Entanglement-assisted (EA) quantum QC-LDPC codes offer strong error-correction capabilities with structured parity-check matrices, but their practical use depends on efficient encoder circuits and the availability of pre-shared Bell pairs (ebits). In all encoder implementations based on the stabilizer formalism, the dominant contribution to this complexity comes from the use of controlled gates. In this paper, we adopt the Sharma-Kumar-Garani (SKG) encoder construction. We formulate the encoder optimization as a search over GF(2) row operations that decompose the binary matrix derived from its CNOT sub-sequence. We solve this problem using a beam search algorithm guided by a Hamming-distance heuristic. For the tested EA quantum QC-LDPC code families, the proposed method achieves CNOT-count reductions of 7.3-34.0% relative to the SKG baseline encoder. The optimized circuits also yield lower CNOT counts than Patel-Markov-Hayes synthesis on all tested instances and are verified by stabilizer-tableau simulation. These results show that substantial encoder simplification is possible for structured EA QC-LDPC codes.

Finite geometry (FG) codes combine the algebraic properties of classical block codes with the iterative belief propagation (BP) decoding ability of low-density parity-check~(LDPC) codes. However, exploiting both advantages in practice is hindered by the fact that the standard incidence matrix between $(\mu+1)$-flats and points is dense and contains many short cycles for any flat dimension $\mu\geq 1$. In this work, we propose to sparsify the decoding matrix based on pencil selection, formulated as a constant-dimension subspace packing problem and solved explicitly using lifted Gabidulin codes. For both affine and projective geometries, sparse parity-check matrices are constructed and verified for FG codes of lengths up to $1024$. Simulations on four FG codes show no visible error floor and around $0.5$~dB gain over corresponding 5G LDPC codes at a block error rate of $10^{-7}$.

We study the query complexity of Boolean functions $f: \{0, 1\}^n \rightarrow \{0, 1\}$ in the noisy query model introduced by Feige, Raghavan, Peleg and Upfal [SICOMP 1994]. In this model, an algorithm can adaptively query the bits of an input vector, but each query result is independently flipped with constant probability $p \in (0, 1/2)$; repeated queries are allowed. The noisy query complexity $\mathsf{N}_p(f)$ of a function $f$ is defined as the minimum expected number of queries needed to compute $f(x)$ with error probability at most $1/3$, for the worst case input $x$. We prove a general lower bound on $\mathsf{N}_p(f)$ based on degree statistics of certain subgraphs of the Boolean hypercube. This is the first general lower bound beyond those implied by the simple observation that $\mathsf{N}_p(f)$ is lower bounded by the randomized query complexity. We show that this recovers (up to a constant factor) most previously known lower bounds on the noisy query complexity of Boolean functions, providing a unified framework for understanding these results and simplifying the proofs in several cases. Furthermore, this resolves in the affirmative an open problem of Gu, Li and Xu [COLT 2025] that $\mathsf{N}_p(f) = \Omega(\mathsf{I}(f) \log \mathsf{I}(f))$, where $\mathsf{I}(f)$ denotes the total influence of $f$. We also apply our general lower bound to obtain tight bounds on the noisy query complexity for several new functions.

The cumulative distribution transform (CDT) is a quantile-based transport representation that exactly linearizes one-dimensional translations of positive densities. We study how this structure behaves under additive perturbations and how it can be exploited for shift recovery. Under a local nondegeneracy condition, we derive a first-order expansion showing that additive noise in physical space induces a nonlocal perturbation in CDT space through the primitive of the noise, weighted by the reciprocal density. This yields an explicit description of transform-domain sensitivity and shows, in particular, that perturbations are amplified in low-density regions. When the physical-space perturbation is modeled as a centered Gaussian random field, the induced first-order CDT perturbation is again Gaussian, with an explicit covariance kernel. We then use this structure to study recovery in CDT coordinates. In the known-template setting, the transport shift is obtained by projection onto the constant mode, giving an explicit estimator together with exactness in the noiseless case and a stability bound under perturbations. In the unknown-template setting, multiple observations permit joint recovery of the shifts and a common template up to the natural constant-mode gauge, leading to a simple de-shift--and--average procedure. We also consider a signed-signal analogue based on the signed cumulative distribution transform (SCDT), where shifts are estimated numerically by feature matching and unknown templates are recovered by alternating alignment and averaging. Numerical experiments validate the perturbation analysis and illustrate effective recovery for both density-valued and signed signals.

We propose a low-complexity Chase decoder for optical interconnects that formulates test pattern selection as a generalized maximum coverage problem. For concatenated RS-BCH and oFEC codes, our decoder achieves the standard Chase decoding performance with 25% and 61.3% fewer test patterns, respectively.

Combinatorial memory is a class of memory in which information is encoded in the set of paths through a structured mesh. In this work, we introduce a systematic encoding framework, referred to as the Color-Rule-Function (CRF) approach, for representing information in combinatorial memory. The method consists of four key steps: selecting a sequence of paths in the mesh, assigning values (e.g., colors) to each cell, defining a set of rules based on the values encountered along each path, and constructing a Boolean function that determines the state of each path.. The coding procedure is illustrated by several examples. The design space scales of the CRF scale fundamentally faster compared to conventional memory. This apparent advantage arises from the use of rule-based and functional representations but is accompanied by increased hardware complexity. A possible hardware realization of the CRF framework is discussed. Importantly, the hardware overhead can be substantially reduced through the use of customized modules. The examples of the customized design are described in the text. The combination of CRF coding with customized module design may lead to a practical advantage in data storage density. According to the estimates, the data storage density may exceed Exabit per centimeter squared. A key problem that requires further investigation is related to the minimum Hamming distance between an arbitrary target bit sequence and the closest sequence realizable within the CRF framework under fixed hardware constraints.

We study the Threshold Group Testing (TGT) problem in the noiseless and non-adaptive setting, where the objective is to exactly recover a sparse binary vector from pooled tests, using as few tests as possible. In TGT, each test applied to a subset of items returns a positive outcome if the number of 1's (defective items) in that subset meets or exceeds a specified threshold, and has a negative outcome otherwise. We investigate how the complexity of TGT compares to that of Classical Group Testing (CGT), corresponding to the special case of the threshold equal to one, and analyse the impact of increasing the threshold on the required number of tests. Our main contribution is the derivation of a sharp information-theoretic phase transition at $c_{\mathrm{inf}}^{\mathrm{TGT}}k\log(n/k)$ (non-adaptive) tests for TGT within the constant-column test design. The threshold constant $c_{\mathrm{inf}}^{\mathrm{TGT}}$ is expressed as a function of the prevalence of defectives and the threshold value. Our upper bound is derived under an analytic assumption, and we verify that this assumption is satisfied for a threshold value of 2. The value of $c_{\mathrm{inf}}^{\mathrm{TGT}}$ reveals that TGT on the constant-column design has the same information-theoretic behaviour as CGT in the low-prevalence regime. Yet, strikingly, at higher prevalences, the threshold leads to a significant reduction in the number of tests. On the other hand, we provide evidence that when the asymptotic proportion of defective items is positive, TGT actually becomes strictly harder than CGT (excluding trivial reductions).

In the upcoming 5G Advanced and 6G technologies, joint sensing and communication (JSAC) will play a pivotal role in enabling the simultaneous utilization of hardware and spectrum resources for communication and sensing tasks. While current algorithms primarily focus on designing beampattern invariant covariance matrices for transmitting various symbols for communication, they often overlook the distances among these symbols. While these covariance matrices effectively facilitate ranging operations, they have adverse effects on communication performance. Designing beampattern invariance covariance matrices with maximal distances among themselves poses a challenging non-convex problem. In this paper, we introduce a novel waveform design method based on McCormick relaxation called McCormick-based JSAC (MJSAC). MJSAC sequentially solves an optimization problem to generate a set of covariance matrices by maximizing the distances (Frobenius norm) among themselves while ensuring a consistent beam pattern. Also, MJSAC eliminates the requirement for channel information to generate the covariance matrices. Through simulations, we demonstrate that MJSAC outperforms conventional algorithms, even those utilizing channel information at the transmitter.

Classical Game Theory underpins much of AI and multiagent research, but hybrid Human AI systems require a framework in which execution authority can alternate within a digital environment. We introduce NeoGame Theory, an extension of classical Game Theory for hybrid Human AI coalitions operating under Virtual Nature, the algorithmic analogue of classical (physical) Nature. The framework combines a lexicographic coalition utility with a delegation rule based on the Jensen-Shannon divergence between Human and AI policies. Two thresholds define agreement, contextual, and disagreement regions. In the contextual region, execution follows a scenario specific rule. Apart from the theory, in this paper we develop the first regime, Human arbitration, in which the AI learns by observation and frequency matching while the Human retains final execution authority. We establish the axiomatic basis of the framework and characterize a frequency convergence equilibrium, providing the foundation for later extensions and computational validation.

The joint rate-distortion framework of Stavrou and Kountouris (IEEE Transactions on Communications 2023) characterises dual-fidelity tradeoffs for semantic communication on stochastic semantic sources. Many task-oriented communication systems instead use designed sources, where the semantic object is a deterministic oracle allocation $\phi^(t)$ rather than a stochastic quantity given by nature. We isolate the subclass of designed sources under smooth concave utility with assumptions A1, A2 and Euclidean allocation codomain, and restrict the encoder class to deterministic common-category mappings. Within this subclass the SK exponential-tilting decoder and generalised Blahut--Arimoto iteration specialise to conditional-mean decoding and Lloyd--Max stationarity on $\phi^(t)$. When the second fidelity is a monotone single-letter distortion, the joint problem stays inside the SK admissible class; the common-category SK rate is lower-bounded by the max of the corresponding Shannon rate-distortion functions, with equality only when the common-category reconstruction is compatible and RDF-optimal. When the second fidelity is aggregate verification, the joint problem leaves the SK single-letter class and admits a constrained-design feasibility band $R_{\min}(\varepsilon^) \leq R \leq R_{\max}(\beta^)$ of width $\log_2(K_{\max}/K_{\min})$ bits in partition cardinality. The reduction and the band are scope statements on the SK apparatus, not modifications to it. A smart-grid economic-dispatch example with a non-technical-loss-detection contrast illustrates the band.

How much meaning does a text carry? Shannon's theory measures uncertainty over symbols and is intentionally indifferent to meaning, while pairwise metrics such as BERTScore compare two texts rather than characterizing one. We develop a geometric framework that measures semantic content from the structure of a text's sentence embeddings. The framework has three parts. First, within a fixed embedding and baseline, six natural axioms uniquely determine a scalar measure up to scale, a frame-conditional uniqueness theorem. The resulting scalar is empirically too coarse, motivating a richer representation. Second, we propose a three-coordinate semantic profile capturing novelty (displacement from generic discourse), breadth (diversity of distinct ideas), and integration (connectedness among them), together with a discrete minimal unit (the semantic quantum) whose resolution is fixed by a clustering threshold $\tau$. Third, we prove a no-go theorem: no scalar summary of the profile can simultaneously satisfy analytic stability under paraphrase and concatenation, ordinal robustness across text scales, and cross-representation comparability. We exhibit two practical scalars, $S_{\mathrm{minmax}}$ and $S_{\mathrm{rank}}$, each occupying a distinct corner of this trade-off triangle. Validation across 23 synthetic categories, 5 Project Gutenberg novels, and 3 embedding models confirms the trade-off. The recommended rank-normalized configuration passes 25 of 28 ordinal checks as point estimates (21 of 28 after Benjamini-Hochberg correction), outperforming seven baselines including unigram entropy and a BERTScore-based novelty signal. A separate variational result connects the breadth coordinate to the log-determinant of a determinantal point process (Spearman $\rho = 0.985$ over 507 Gutenberg chapters), giving an optimization-theoretic foundation for breadth.

Cancer treatment is at the core a sequential decision-making problem with partial observability, latent patient heterogeneity, and explicit constraints on the budget for medical measurements. Unlike standard Reinforcement Learning (RL) approaches that control state trajectories, cancer treatments permanently modify patients' transition dynamics, changing how states evolve over time. We model cancer treatment as a belief-space planning problem using active inference, deriving an expected free-energy objective that unifies goal-directed control and information acquisition under measurement budgets without. We implement this framework using real clinical cancer data from the AACR Project GENIE Biopharma Collaborative dataset. Results on clinical data demonstrate a simultaneous patient categorization and high treatment efficacy, under real measurement and treatment constraints.

We study local pure coordination games on finite social networks, continuing the framework of Hutchcroft, Rospuskova, and Tamuz. They showed that low inefficiency in local coordination forces the underlying graph to be amenable, with a square-root loss in the amenability parameter. We improve this loss in the binary unbiased setting. Using Shapley values of a mutual-information game associated with the players' local outputs, we prove that if the average disagreement is at most $\varepsilon$, then the graph is $(O(\varepsilon\log(1/\varepsilon)),r)$-amenable. This gives a sharper quantitative converse between local coordination and graph amenability.

Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebraic compatibility between quantum homomorphic encryption and quantum error correction, determining precise conditions under which encrypted encoded states remain inside the relevant code space during storage and computation. Our work establishes a necessary and sufficient criterion for an $[[n,1,d]]$ stabilizer code to remain compatible with the restricted transversal block-Pauli masking $U_{\rm enc}(a,b)=(X^aZ^b)^{\otimes n}$, stated explicitly for $[[n,1,d]]$ codes and extending directly to code-space preservation for $[[n,k,d]]$ codes. We verify this condition for standard examples (bit-flip and Shor codes, with the phase-flip repetition code following analogously), derive a practical criterion for Calderbank-Shor-Steane codes, and extend the analysis to three-dimensional color codes. A critical challenge emerges for non-Clifford gate implementation: the Shor code lacks a naive transversal $T$-gate implementation of the desired logical operation on encrypted encoded data. We present two routes around this obstruction. First, suitable triorthogonal codes admit transversal $T$-type logical implementations, up to Clifford corrections. Second, logical-gate masking gives code-space compatibility for arbitrary stabilizer codes, provided that suitable unitary representatives of the required logical gates are available. These results separate code-space compatibility from a full cryptographic security proof and provide explicit criteria for combining error correction with homomorphic processing in cloud quantum computing.

While diffusion models have emerged as a powerful class of generative models, their learning dynamics remain poorly understood. We address this issue first by empirically showing that standard diffusion models trained on natural images exhibit a distributional simplicity bias, learning simple, pair-wise input statistics before specializing to higher-order correlations. We reproduce this behaviour in simple denoisers trained on a minimal data model, the mixed cumulant model, where we precisely control both pair-wise and higher-order correlations of the inputs. We identify a scalar invariant of the model that governs the sample complexity of learning pair-wise and higher-order correlations that we call the diffusion information exponent, in analogy to related invariants in different learning paradigms. Using this invariant, we prove that the denoiser learns simple, pair-wise statistics of the inputs at linear sample complexity, while more complex higher-order statistics, such as the fourth cumulant, require at least cubic sample complexity. We also prove that the sample complexity of learning the fourth cumulant is linear if pair-wise and higher-order statistics share a correlated latent structure. Our work describes a key mechanism for how diffusion models can learn distributions of increasing complexity.