In today's fast-changing competitive environment, strategy is no longer a matter of positioning a fixed set of activities along that old industrial model, the value chain. Successful companies increasingly do not just add value, they reinvent it. The key strategic task is to reconfigure roles and relationships among a constellation of actors--suppliers, partners, customers--in order to mobilize the creation of value by new combinations of players. What is so different about this new logic of value? It breaks down the distinction between products and services and combines them into activity-based "offerings" from which customers can create value for themselves. But as potential offerings grow more complex, so do the relationships necessary to create them. As a result, a company's strategic task becomes the ongoing reconfiguration and integration of its competencies and customers. The authors provide three illustrations of these new rules of strategy. IKEA has blossomed into the world's largest retailer of home furnishings by redefining the relationships and organizational practices of the furniture business. Danish pharmacies and their national association have used the opportunity of health care reform to reconfigure their relationships with customers, doctors, hospitals, drug manufacturers, and with Danish and international health organizations to enlarge their role, competencies, and profits. French public-service concessionaires have mastered the art of conducting a creative dialogue between their customers--local governments in France and around the world--and a perpetually expanding set of infrastructure competencies.
Dynamic link failures disrupt the connectivity and geometric symmetry of the constellation structure, thereby increasing protocol overhead and degrading the effective capacity for traffic transport. The fundamental relationship between constellation size and effective capacity under protocol overhead constraints remains unclear. To this end, we define capacity scalability as the ratio of constellation capacity under non-failure conditions to protocol overhead. Specifically, if ISL states follow a two-state discrete Markov chain and the maintenance period is $k \geq 1$, the upper bound of capacity scalability under the uniform traffic pattern is $O(1/n)$, where $n$ is the number of satellites. With perfect information about the constellation topology, the upper bound can be achieved via shortest-path routing. For any given protocol, there exists an optimal constellation deployment scale in terms of capacity scalability. When the constellation size is below this optimum scale, capacity scalability increases with constellation size, thereby improving effective capacity. Increasing the maintenance period $k$ can improve capacity scalability, but it does not change the fact that the cap
Extending our work on the $k$-tuple conjecture, we previously applied those methods to the Engelsma counterexamples (narrow constellations) of length $J=459$ and span $|s|=3242$. Here we extend that analysis to the $116$ Engelsma counterexamples of length $J=458$ and $|s|=3240$. We track the evolution of these $116$ counterexamples from inadmissible driving terms starting in the cycle of gaps ${\mathcal G}(11^\#)$ up through their first appearance in ${\mathcal G}(113^\#)$. We continue developing primorial coordinates for each admissible instance through a breadth-first exhaustive search through ${\mathcal G}(211^\#)$. Each of the $(458,3240)$ constellations sits inside a $(459,3242)$ constellation, which we call its {\em parent}. We show that no $(458,3240)$ constellation occurs outside of its parent until the cycle ${\mathcal G}(227^\#)$. The early evolution of the $(458,3240)$ constellations is dominated by the evolution of their parents, which we have previously studied. For each $(458,3240)$-counterexample we calculate its asymptotic relative population, among other constellations of length $J=458$.
A constellation pattern is a finite increasing rational sequence \(Q=[0=q_0<q_1<\cdots<q_k=1]\), and a \(Q\)-constellation in \([n]\) is obtained by scaling and translating a rational pattern $Q$, with key examples including arithmetic progressions. In 2010, Butler, Costello, and Graham proposed a conjecture, that is, for any constellation pattern $Q$ there is a coloring pattern of $[n]$ that has $γn^2+o\left(n^2\right)$ monochromatic constellations, where $γ$ is smaller than the coefficient for a random coloring. In this paper, we confirm this conjecture. As applications of this conjecture, we obtain interval-uncommon translation-invariant linear systems associated with rational constellations and a ground-state bound for deterministic arithmetic hypergraph spin systems.
The recent advancement in research on distributed space systems that operate a large number of satellites as a single system urges the need for the investigation of satellite constellations. Communication constellations can be used to construct global or regional communication networks using inter-satellite and ground-to-satellite links. This study examines two challenges of communication constellations: continuous coverage and inter-satellite link connectivity. The bounded Voronoi diagram and APC decomposition are presented as continuous coverage analysis methods. For continuity analysis of the inter-satellite link, the relative motion between adjacent orbital planes is used to derive analytic solutions. The Walker-Delta constellation and common ground-track constellation design methods are introduced as examples to verify the analysis methods. The common ground-track constellations are classified into quasi-symmetric and optimal constellations. The optimal common ground-track constellation is optimized using the BILP algorithm. The simulation results compare the performance of the communication constellations according to various design methods.
This paper proposes a simple and effective method for constructing higher-order three-dimensional (3D) signal constellations, aiming to enhance the reliability of digital communication systems. The approach systematically extends the conventional two-dimensional hexagonal quadrature amplitude modulation (2D-HQAM) constellation into a 3D-HQAM signal space, forming structured lattice configurations. To address the increased decision complexity resulting from a larger number of constellation points, a dimension reduction (DR) technique is introduced, allowing the derivation of closed-form symbol error probability (SEP) expressions under additive white Gaussian noise (AWGN) conditions. Theoretical SEPs closely match simulation results, validating the accuracy of the proposed method. The minimum Euclidean distance (MED) of the 3D constellations shows a minimum increase of 12.14% over 2D constellation for 8-HQAM, reaching up to 160.81% for 1024-HQAM constellations. This significant improvement in MED leads to enhanced error performance. Therefore, the proposed 3D constellations are promising candidates for high-quality and reliable next-generation digital communication systems.
Low Earth Orbit (LEO) satellite constellations are emerging as a key component of non-terrestrial networks due to their low-latency and high-capacity communication capabilities. However, satellites in these orbits are characterized by a small coverage footprint and high orbital velocity compared to those in higher orbits. This results in constantly changing and dynamic constellations that require smart design of orbital parameters to ensure continuous coverage. Existing constellation deployments are typically optimized either for low- and mid-latitude regions or for full polar coverage, leaving high-latitude regional scenarios such as the North Atlantic insufficiently explored. This work provides insights into the key characteristics associated with the deployment of satellites in LEO for North Atlantic coverage. Therefore, we investigate how constellation inclination, minimum elevation angle, altitude, and satellite footprint jointly affect visibility probability, revisit time, path loss, and coverage continuity. Results show that the minimum elevation angle is a critical design parameter since a Walker Delta constellation with 64 satellites at 1000 km altitude can provide continu
6G communications systems are expected to integrate radar-like sensing capabilities enabling novel use cases. However, integrated sensing and communications (ISAC) introduces a trade-off between communications and sensing performance because the optimal constellations for each task differ. In this paper, we compare geometric, probabilistic and joint constellation shaping for orthogonal frequency division multiplexing (OFDM)-ISAC systems using an autoencoder (AE) framework. We first derive the constellation-dependent detection probability and propose a novel loss function to include the sensing performance in the AE framework. Our simulation results demonstrate that constellation shaping enables a dynamic trade-off between communications and sensing. Depending on whether sensing or communications performance is prioritized, geometric or probabilistic constellation shaping is preferred. Joint constellation shaping combines the advantages of geometric and probabilistic shaping, significantly outperforming legacy modulation formats.
A novel Gamma-distributed geometric constellation design framework for integrated sensing and communication (ISAC) is proposed in this paper. In this framework, constellation points are modeled as samples drawn from a parameterized two-dimensional distribution, with a Gamma distribution for the amplitude and a uniform distribution for the phase. End-task performance metrics, namely, the probability of detection for sensing and mutual information for communication, are used as objective functions of the optimization problem, and the problem is solved via particle swarm optimization. We further derive analytical performance bounds for the proposed design, including the union bound on the symbol error rate for communication and the Cramer--Rao bound for sensing parameter estimation. The proposed method is compared with constellations obtained via end-to-end neural network design, demonstrating competitive performance while requiring significantly fewer parameters and no training data. Moreover, the proposed geometric constellation is more compatible with conventional system architectures than probabilistic or neural network-based designs.
Semantic communication has demonstrated significant potential for image transmission, especially in bandwidth-limited and low signal-to-noise ratio scenarios. However, most existing methods are based on analog transmission, which poses challenges to the compatibility with existing digital communication systems. Existing digital semantic communication methods commonly adopt conventional quadrature amplitude modulation constellations, which mismatch the empirical distribution of semantic features produced by the semantic encoder. This paper proposes a distribution-aware learnable modulation for semantic communication framework, which bridges semantic feature representations and discrete modulation through constellation learning. Specifically, a learnable constellation module, initialized with an amplitude phase shift keying geometric prior, is developed to refine the constellation geometry as a trainable codebook, enabling modulation symbols to better align with the distribution of semantic features. To enable end-to-end optimization, a two-stage training strategy is introduced, combining differentiable soft assignment with straight-through estimator. Simulation results show that the
This paper proposes a maintenance strategy for a satellite constellation that utilizes on-orbit servicing (OOS). Under this strategy, the constellation operator addresses satellite failures in two ways: by deploying new satellites and by recovering failed satellites through OOS. We develop an inventory management model with a parametric replenishment policy for the maintenance process, which can evaluate the performance of the satellite constellation system. Based on this model, we formulate the interaction between the constellation operator -- who seeks to maintain the required service level of the constellation while minimizing maintenance cost -- and the OOS provider -- who seeks to maximize profit by selecting service price and performance levels -- as a bi-objective optimization problem and identify the corresponding Pareto-optimal solutions. A case study based on real-world-scale constellation and launch service shows that, relative to the benchmark strategy without OOS, the OOS-integrated solutions can reduce annual maintenance cost by up to 14.5%, while reducing annual launch and manufacturing costs by approximately 25% each and maintaining the required service levels. The
In this work, we propose two methods to design zero constellations for binary modulation on conjugate-reciprocal zeros (BMOCZ). In the first approach, we treat constellation design as a multi-label binary classification problem and learn the zero locations for a direct zero-testing (DiZeT) decoder. In the second approach, we introduce a neural network (NN)-based decoder and jointly learn the decoder and zero constellation parameters. We show that the NN-based decoder can directly generalize to flat-fading channels, despite being trained under additive white Gaussian noise. Furthermore, the results of numerical simulations demonstrate that learned zero constellations outperform the canonical, Huffman BMOCZ constellation, with the proposed NN-based decoder achieving large performance gain at the expense of increased computational complexity.
Standard citation metrics treat all citations as equal, obscuring the social and structural pathways through which scholarly influence propagates. I introduce Citation-Constellation, a freely available no-code tool for citation network analysis with two complementary bibliometric scores that decompose a researcher's citation profile by network proximity between citing and cited authors. BARON (Boundary-Anchored Research Outreach Network score) is a strict binary metric counting only citations from outside the detected collaborative network. HEROCON (Holistic Equilibrated Research Outreach CONstellation score) applies graduated weights assigning partial credit to in-group citations based on relationship proximity. The gap between scores serves as a diagnostic of inner-circle dependence. An extended abstract with full details appears in the paper. The tool implements this through a phased architecture: (1) self-citation analysis, (2) co-authorship graph traversal, (3) temporal institutional affiliation matching via ROR, and (4) AI-agent-driven venue governance extraction using a local LLM. Phases 1-3 are fully operational; Phase 4 is under development. Key design choices include ORCI
In this paper, we present a general framework of designing geometrically shaped constellations for short-packet visible light communications with a peak- and an average-intensity constraints. By leveraging tools from large deviation theory, we first characterize the second-order asymptotics of the optimal constellation shaping region under aforementioned intensity constraints, which serves as a good performance measure for the best geometric shaping in finite blocklength. To further incorporate a sufficiently large coding gain and a nearly-maximum shaping gain, we construct multidimensional constellations by the nested structure of Construction B lattices, where the constellation shaping is implemented by controlling the boundary of the embedded sublattice, i.e., a strategy called coarsely shaping and finely coding. Fast algorithms for constellation mapping and demodulation are presented as well. As an illustrative example, we present an energy-efficient $24$-dimensional constellation design based on the Leech lattice, whose superiority over existing constellation designs is verified by numerical results.
TianQin is a proposed space-based gravitational-wave observatory mission that critically relies on the stability of an equilateral-triangle constellation. Comprising three satellites in high Earth orbits of a $ 10^5 $ km radius, this constellation's geometric configuration is significantly affected by gravitational perturbations, primarily originating from the Moon and the Sun. In this paper, we present an analytical model to quantify the effects of lunisolar perturbations on the TianQin constellation, derived using Lagrange's planetary equations. The model provides expressions for three kinematic indicators of the constellation: arm-lengths, relative line-of-sight velocities, and breathing angles. Analysis of these indicators reveals that lunisolar perturbations can distort the constellation triangle, resulting in three distinct variations: linear drift, bias, and fluctuation. Furthermore, it is shown that these distortions can be optimized to display solely fluctuating behavior, under certain predefined conditions. These results can serve as the theoretical foundation for numerical simulations and offer insights for engineering a stable constellation in the future.
With the incredible results achieved from generative pre-trained transformers (GPT) and diffusion models, generative AI (GenAI) is envisioned to yield remarkable breakthroughs in various industrial and academic domains. In this paper, we utilize denoising diffusion probabilistic models (DDPM), as one of the state-of-the-art generative models, for probabilistic constellation shaping in wireless communications. While the geometry of constellations is predetermined by the networking standards, probabilistic constellation shaping can help enhance the information rate and communication performance by designing the probability of occurrence (generation) of constellation symbols. Unlike conventional methods that deal with an optimization problem over the discrete distribution of constellations, we take a radically different approach. Exploiting the ``denoise-and-generate'' characteristic of DDPMs, the key idea is to learn how to generate constellation symbols out of noise, ``mimicking'' the way the receiver performs symbol reconstruction. By doing so, we make the constellation symbols sent by the transmitter, and what is inferred (reconstructed) at the receiver become as similar as possib
We give an algebraic characterisation of ordered groupoids, namely, we show that there is a categorical isomophism between the category of ordered groupoids and the category of $D$-inverse constellations. Here constellations are partial algebras in the sense that they possess a partial product, and a unary operation $D$. We consider constellations in which elements have a suitable notion of inverse, giving the notion of a D-inverse constellation.
The use of regional coverage satellite constellations is on the rise, urging the need for an optimal constellation design method for complex regional coverage. Traditional constellations are often designed for continuous global coverage, and the few existing regional constellation design methods lead to suboptimal solutions for periodically time-varying or spatially-varying regional coverage requirements. This paper introduces a new general approach to design an optimal constellation pattern that satisfies such complex regional coverage requirements. To this end, the circular convolution nature of the repeating ground track orbit and common ground track constellation is formalized. This formulation enables a scalable constellation pattern analysis for multiple target areas and with multiple sub-constellations. The formalized circular convolution relationship is first used to derive a baseline constellation pattern design method with the conventional assumption of symmetry. Next, a novel method based on binary integer linear programming is developed, which aims to optimally design a constellation pattern with the minimum number of satellites. This binary integer linear programming m
Deep learning-based joint source-channel coding (JSCC) has shown excellent performance in image and feature transmission. However, the output values of the JSCC encoder are continuous, which makes the constellation of modulation complex and dense. It is hard and expensive to design radio frequency chains for transmitting such full-resolution constellation points. In this paper, two methods of mapping the full-resolution constellation to finite constellation are proposed for real system implementation. The constellation mapping results of the proposed methods correspond to regular constellation and irregular constellation, respectively. We apply the methods to existing deep JSCC models and evaluate them on AWGN channels with different signal-to-noise ratios (SNRs). Experimental results show that the proposed methods outperform the traditional uniform quadrature amplitude modulation (QAM) constellation mapping method by only adding a few additional parameters.
In this paper, we investigate the optimal probabilistic constellation shaping design for covert communication systems from a practical view. Different from conventional covert communications with equiprobable constellations modulation, we propose nonequiprobable constellations modulation schemes to further enhance the covert rate. Specifically, we derive covert rate expressions for practical discrete constellation inputs for the first time. Then, we study the covert rate maximization problem by jointly optimizing the constellation distribution and power allocation. In particular, an approximate gradient descent method is proposed for obtaining the optimal probabilistic constellation shaping. To strike a balance between the computational complexity and the transmission performance, we further develop a framework that maximizes a lower bound on the achievable rate where the optimal probabilistic constellation shaping problem can be solved efficiently using the Frank-Wolfe method. Extensive numerical results show that the optimized probabilistic constellation shaping strategies provide significant gains in the achievable covert rate over the state-of-the-art schemes.