Search Results (308)

This paper investigates the blind estimation problem of multiuser long-code Direct Sequence Spread Spectrum (DSSS) signals in non-cooperative reception scenarios. In a long-code DSSS system, the spreading-sequence length exceeds the spreading gain and is not an integer multiple of it, so each symbol interval contains only a fragment of the spreading sequence. Consequently, conventional short-code subspace methods cannot directly estimate the complete spreading-code subspace. To address this issue, a blind despreading method based on signal subspace reconstruction and iterative least-squares projection (ILSP) is proposed. First, symbol samples sharing identical spreading-sequence fragments are grouped, and subspace decomposition is applied to obtain multiple fragment subspace estimates. These fragment subspaces are then jointly combined through the periodic selection structure to reconstruct the complete spreading-code subspace. Finally, ILSP is employed to estimate the spreading sequences and recover the transmitted information sequences. Simulation results demonstrate that the proposed method remains effective under low signal-to-noise ratio (SNR) conditions and that its information-sequence bit error rate (BER) approaches that of cooperative reception as the SNR or sample size increases. Full article

A variable-to-variable (V2V) length code parses a source sequence into phrases of variable length and maps each phrase to a binary codeword of, generally, a different random length. After encoding n phrases, the realized compression ratio $R_n={\Lambda }_n/{\Sigma }_n$—total codeword length over total source-symbol count—is the finite-sample counterpart of the code’s asymptotic rate $\rho$, to which it converges only as $n\to \infty$. This paper first derives exact formulas for all integer moments of $R_n$ for a given discrete memoryless source (DMS). Specifically, we obtain a closed-form formula for every moment $\mathbb{E}\left\{R_n^k\right\}$ as a one-dimensional integral involving only single-phrase moment generating functions of the pair $(L,\mathcal{l})$—the phrase length, in source symbols, and codeword length, in bits. From these moments we derive an Edgeworth approximation to the cumulative distribution function (CDF) of $R_n$ that is substantially more accurate than the central limit theorem (CLT) approximation. Using the Laplace method of integration, we also derive explicit closed-form formulas for the bias constant $C={\lim }_{n\to \infty }n(\mathbb{E}\left\{R_n\right\}-\rho )$ and for the variance constant ${\lim }_{n\to \infty }n·\mathrm{Var}\left\{R_n\right\}$. The analysis extends to Markov sources via state-indexed matrices with a redundancy formula obtained in closed form. On the coding-theoretic side, we cast V2V length codes as finite-state encoders and apply a generalized Kraft inequality for a compression-rate lower bound, and give a structural decomposition of the bias coefficient that separates cleanly across variable-to-fixed (V2F) length codes, fixed-to-variable (F2V) length codes, and V2V length codes. Applied to the Khodak code of Bugeaud, Drmota, and Szpankowski, this decomposition shows that its improved performance is reflected in its smaller bias constant. Full article

This paper shows how the ideas of Archimedes about integrating “mechanical methods” and formal reasoning can be connected with the modern-day use of three computer programs—Wolfram Alpha, Maple, and Excel—in exploring topics related to the elementary theory of numbers. Explorations deal with the subsequences of integer sequences through the step-by-step elimination of every other term obtained in the previous step. This process, resembling the sieve of Eratosthenes and some modern-day sieving algorithms, is applied to tetrahedral numbers stemming from an ancient tradition to associate integers with geometric shapes and social contexts. It is demonstrated that symbolic computations in Wolfram Alpha enable generalization in the construction of sieves that is confirmed by Maple and a spreadsheet. This conceptual paper addresses one of the aims of the Special Issue by demonstrating the duality of mathematics and technology in the sense that whereas the latter facilitates new approaches to knowledge acquisition, the former can be used to improve the efficiency of computations by reflecting on the results made possible by these approaches. The activities conducted advocate for the value of a pedagogical framework that integrates ancient ideas, digital tools, and elementary number theory in the education of mathematics teachers. Reflective comments by teacher candidates are included as appropriate and linked to established educational frameworks to illustrate conformity. Full article

This article proposes a formal epistemological and methodological framework for the analysis of lithic technology, moving beyond traditional optimization-oriented models and normative typologies. Grounded in Mario Bunge’s socio-natural science and Herbert Simon’s theory of bounded rationality, we introduce the concept of legaliform (law-like) principles. These principles are defined as stable, necessary relationships between technical procedures and morphological outcomes, dictated by the physics of brittle fracture and enacted through procedural memory. To enhance analytical precision and cross-cultural comparability, we develop a semi-formal symbolic notation that identifies the core “techno-scientific” operators underlying lithic reduction. We argue that stone tool morphology is not a static reflection of a “mental template,” but a dynamic sequence of technically adequate states achieved through satisficing behavior. By framing these legaliform regularities as epistemological meta-standards, this article establishes a standardized framework for data reproducibility, verification, and quality control in technological analysis. The framework identifies eight primary legaliform principles—including bifacial reduction (PBR), thermal alteration (PTT), and maintenance and reactivation (PMR)—illustrating how they structure technical action under material and cognitive constraints. The utility of this approach is demonstrated through a case study of Paleoindian Fell projectile points in South America. By operationalizing the Maintenance and Reactivation Principle (PMR), we explain the high morphological variability of these points as a predictable result of life-history and functional restoration rather than cultural “drift” or failed design. This perspective provides a rigorous basis for identifying Guided Convergence in the archaeological record, offering a scientific alternative to diffusionist explanations and purely morphological comparisons that often overlook the underlying techno-scientific regularities of lithic practice. Full article

Cultural heritage management today faces the challenge of addressing increasingly complex realities. In this context, international organisations focus on identifying heritage attributes that consider not only physical and artistic values, but also symbolic, social and environmental dimensions, a task that has been implemented in recent years and in which significant progress has been made. The aim of this research is to develop a detailed protocol for identifying heritage attributes, using the Alcázar of Seville, a World Heritage Site, as an example. Based on a consolidated methodology, the aim is to outline the work process by identifying the sequence of tasks from the collection, selection and distribution of information to the formation of the transdisciplinary team, the analysis process and the selection of attributes. The result shows a sequenced process in which a wide range of material is reviewed in depth from various disciplines, allowing the identification of attributes beyond cultural significance. This methodological update involves increasing the size of the transdisciplinary team and taking a more social approach to the management of this heritage. The proposal takes the form of a useful working tool for heritage professionals and public administrations responsible for managing world heritage properties. Full article

Post-socialist monotowns and mono-functional urban districts face interrelated economic, spatial, institutional, and identity crises, yet their transformation trajectories vary. Building on the previously developed methodological framework, the study implements its second stage by selecting reference cases and reconstructing transformation trajectories in Central and Eastern Europe. Seven weighted criteria—identity reframing, multi-level governance and actors, cultural vitality, economic diversification, heritage and architectural significance, positive physical transformation, and regional connectivity—were applied to nine purposively selected cases in Estonia, Lithuania, Poland, Germany, the Czech Republic, and Slovakia. Scores ranged from 1.40 to 4.05; five cases were retained, comprising a stable four-case core and a weight-sensitive fifth case selected for typological and target-context complementarity. Cross-case analysis identified four overlapping contours: crisis-adaptive, institutional-spatial, heritage-symbolic, and cultural-everyday. Transformation was asynchronous and non-linear: symbolic, institutional, cultural, spatial, and economic changes unfolded in different sequences, while economic diversification remained limited or moderate in most cases. Given theory-informed, author-assigned weights and a regionally bounded, typologically heterogeneous sample, the ranking is a case-selection tool rather than a measure of transformation success. The reconstructed trajectories provide the analytical basis for the subsequent assessment of their transferability to Piatykhatky (Kharkiv, Ukraine). Full article

Peptides are the most extensively studied bioactive compounds derived from food. They are analyzed using, e.g., in silico strategy. The BIOPEP-UWM database has become a standard tool in computer-aided peptide research. The aim of this study was to equip this database with a tool enabling the annotation and processing of peptide or protein sequences containing modified amino acid residues as well as other residues. The most recent section of the BIOPEP-UWM, i.e., the repository of amino acids and modifications, apart from 20 proteinogenic amino acids, annotates non-amino acid moieties or residues subjected to enzymatic or chemical modifications (phosphorylation, oxidation, hydroxylation, acylation, etc.). This part of BIOPEP-UWM provides the following information: Compound ID, name, symbol in a special code, InChIKey identifier, SMILES representation, number in the PubChem database (CID), formula, and IDs in other databases. The search options include ID in the repository, name, symbol in a biological code, InChIKey, PubChem Compound identifier (CID), and chemical formula. Peptide or protein sequences annotated using symbols from the repository are utilized by all applications available in the BIOPEP-UWM database. The database meets contemporary trends involving modifications of amino acid residues in the bioinformatic analysis of peptides and proteins. Full article

We present a short-preamble digital signal processing (DSP) architecture for downstream Alamouti coherent-lite passive optical network (PON) reception using a simplified optical network unit (ONU) receiver. A four-branch gear-shifted least-mean-square (LMS) equalizer uses a large step during quadrature phase-shift keying (QPSK) preamble training and a small step during decision-directed payload tracking. In 50 GBaud 16-ary quadrature amplitude modulation (16-QAM) simulations over 20 km single-mode fiber, a 2048-symbol preamble is the first cold-start point whose mean bit-error rate (BER) falls below the selected uncoded BER target of ${10}^{-2}$. A 20-realization-per-point sweep gives a sub-1 dB penalty for 2048 symbols and a mean offline mean-square-error (MSE) settling time below 100 ns, with low-gain locking events retained. However, frame-level reliability improves with longer training: in an indicative 20-frame Monte Carlo test, 13 of 20 frames met the BER target with a 2048-symbol preamble, compared with 17 of 20 using 4096 symbols. For repeated frames to the same ONU after initial acquisition, warm-start tap reuse allows frames 4–5 in the tested sequence to fall below target with 512-symbol preambles, corresponding to a later-frame nominal coded payload rate of 163 Gb/s instead of 123 Gb/s. The results quantify the preamble/reliability/payload-rate trade-off and indicate that downstream Alamouti coherent-lite reception can support short-training equalizer acquisition after preamble synchronization with one balanced detector and one analog-to-digital converter. Full article

We develop a non-Archimedean framework for the representation and analysis of genomic sequences based on the arithmetic and geometric structure of the ring of 5-adic integers. The proposed approach associates RNA sequences with points in a compact ultrametric space through an injective symbolic-to-arithmetic embedding that transforms genomic information into a hierarchical geometric object. We prove that the embedding is a global isometry between a natural symbolic prefix metric and the induced 5-adic metric, and we show that its image forms a compact Cantor-type subset of ${\mathbb{Z}}_5$. Building upon this representation, we formulate a continuous-time evolutionary model governed by a Vladimirov pseudo-differential operator. The resulting non-Archimedean diffusion equation provides a mathematically rigorous mechanism for describing evolutionary transitions across hierarchical genomic scales and admits an explicit fundamental solution obtained through 5-adic Fourier analysis. We further introduce a finite-resolution projection onto quotient rings of ${\mathbb{Z}}_5$ and develop an alignment-free phylogenetic inference framework based directly on the 5-adic valuation. The induced distance function is ultrametric and naturally encodes hierarchical relationships through shared symbolic prefixes. The proposed construction establishes a bridge between p-adic analysis, ultrametric geometry, pseudo-differential operators, and computational phylogenetics. As an illustration, we discuss its application to Hantavirus genomic sequences, demonstrating how hierarchical evolutionary organization can be represented within a unified non-Archimedean mathematical framework. Full article

In this paper, we introduce and study Hermite–Kampé de Fériet Hahn–Appell polynomial sequences (HKdF Hahn–Appell sequences) within the unified framework of the Hahn difference operator. We establish three equivalent characterisations of these sequences: an operational definition via the Hahn difference condition, an explicit summation formula involving $\alpha$-binomial coefficients and the falling Hahn basis, and a generating-function criterion. A three-term recurrence relation, a second-order difference equation, and the determinantal representation are also derived for these polynomials. The d-orthogonality of the family is characterised via truncation conditions on the recurrence coefficients $\left\{{\sigma }_k\right\}$; the generating functions of d-orthogonal members are identified as products of $\alpha$-Pochhammer symbols, and the d-dimensional functional vector is expressed in closed form. As principal examples, the HKdF Hahn–Bernoulli, HKdF Hahn–Euler, and HKdF Hahn–Genocchi polynomial sequences are introduced, and for each family, four limiting cases are established. A unifying summary table is provided. Graphical and numerical analysis of the zero distribution for all three families confirms the analytical results and illustrates the convergence of zeros to the classical Hermite–Kampé de Fériet setting as the parameters approach their limiting values. Full article

Code Index Modulation (CIM) schemes usually rely on large orthogonal spreading codebooks to improve their index-carrying capability, resulting in high codebook resource consumption and a rapidly increasing receiver-side detection complexity. To address this problem, this paper proposes a Cyclic-Shift Code Index Modulation (CSCIM) scheme based on fast cyclic-correlation detection. Unlike conventional CIM, which carries information through the codebook indices of multiple independent spreading codes, CSCIM transforms the index-bearing mechanism from multi-code selection into cyclic-shift state selection of a single spreading code. At the transmitter, index bits control the cyclic-shift offset of a single spreading code to generate candidate index states. A composite frame structure consisting of a Zadoff–Chu (ZC) synchronization header and spread-spectrum data blocks is designed to eliminate code-offset ambiguity during fast correlation acquisition. At the receiver, an FFT-based fast cyclic-correlation mechanism obtains full-shift-domain correlation peaks through a single detection path, and the index information is recovered from the detected peak position. A local spreading code with the corresponding cyclic-shift phase is then generated to complete despreading and symbol decision. The simulation results show that CSCIM exhibits a stable BER reduction trend over both AWGN and flat Rayleigh fading channels, and maintains effective data-detection performance under high-order index configurations. The proposed CSCIM scheme requires only one spreading code sequence to generate all candidate spreading codes, effectively reducing the codebook resource consumption and receiver-side detection complexity while maintaining a competitive BER performance. Full article

We investigate functional behavioural differentiation in genetically homogeneous animal collectives using the $ϵ$-machine and $ϵ$-transducer frameworks from symbolic dynamics. Long-term tracking of unmarked individuals in colonies of the clonally reproducing ant Pristomyrmex punctatus reveals two distinct movement modes—clustering within the group and solitary exploration outside it. Reconstructed individual $ϵ$-transducers expose a sharp asymmetry in computational structure between these modes: solitary explorers are described by a deterministic machine, whereas clustering ants require stochastic machines to capture their complex patterns of micro-movement. A population-level (universal) $ϵ$-transducer, inferred from pooled data, captures the shared behavioural repertoire across all individuals. Individual differences are parsimoniously explained as biased and partial traversals of a common state space rather than as distinct generative programs. We compare three predictive models: the $ϵ$-machine, which relies solely on an ant’s own output history; a memoryful $ϵ$-transducer, which additionally conditions on changes in the local neighbour count as social input; and a memoryless $ϵ$-transducer, which uses this social input alone. The memoryful transducer matches the $ϵ$-machine in prediction accuracy despite requiring ten times as many states, while the memoryless transducer performs substantially worse. This shows that an ant’s own behavioural history is the essential predictor of its future movement at the temporal resolution examined here. We argue, however, that this predictive redundancy does not entail the causal irrelevance of social input: the behavioural history itself accumulates the trace of past social encounters so that any role differentiation established through prior interactions is already inscribed in the output sequence that the $ϵ$-machine reads, and mode transitions—the moments at which social input most plausibly exerts causal influence—are rare events that contribute negligibly to aggregate one-step accuracy. Agent-based simulations driven by the universal $ϵ$-transducer reproduce basic motion statistics and transient aggregations but fail to generate the stable macroscopic clusters observed experimentally, pointing to the role of additional mechanisms such as longer-term memory or stigmergic coupling. Nevertheless, ants do respond to their social environment: an explorer encountering an increase in neighbours is absorbed into the cluster and ceases directed movement. Together, our results suggest a two-level organisation: within each behavioural mode, individual dynamics are self-sufficient for one-step prediction, while transitions between modes are environmentally triggered and represent switches between fundamentally different classes of dynamical organisation. Full article

A low-latency, low-complexity digital demodulator is presented for chirp spread spectrum (CSS)-modulated RF packets targeting low-power IoT wireless systems operating in spectrally congested environments. Conventional CSS receivers rely on fast-fourier transform (FFT)-based synchronization and long preamble sequences, resulting in increased latency and computational complexity. To address these limitations, the proposed receiver employs amplitude-domain synchronization using oversampled sub-chirp windows and maximum likelihood estimation without requiring FFT processing. A digital demodulator co-designed with receiver’s fractional-N phase-locked loop (PLL) architecture enables rapid sub-chirp generation and fast frequency settling, while compensation techniques mitigate symbol boundary offset (SBO) error due to PLL non-idealities during synchronization. The proposed system achieves packet synchronization within 17.5 preamble symbol cycles while maintaining symbol boundary offset estimation error below ±1%. Simulation results demonstrate a syncword misdetection probability below 10⁻³ at SNRs of 9 dB and 1 dB without and with 8× repetition, respectively. In the presence of interferences, the receiver tolerates worst-case in-band signal-to-noise ratio (SIR) levels down to −16.2 dB while consuming 877 µW and 830 µW average power at the digital demodulator, and fractional-N PLL, respectively. Implemented in 65 nm CMOS, the proposed architecture occupies 0.195 mm² active area. Full article

Words occurring in similar contexts have been observed to have similar meanings. A natural and established method within computational linguistics implements this observation by representing words as vectors with dimensions determined by words that are witnessed in fixed positions in relation to the target word. We generalize this context vector approach to part-of-speech (POS) sequences appropriate to word sequences. As with words, the context of a POS tag (considering the POS tags occurring before and after any target tag) reflects its syntactic constraints and may approximate the “meaning” of the target tag, from a distributional perspective. We use the 111-million-word British National Corpus (BNC) and the sequence of POS labels lifted from those texts to calculate POS context vectors. We observed significant agreement between the clusters of POS context vectors and the supercategories of corresponding POS tags, and examined potential categorization of the POS categories that emerged from the vector clusters. We also found that though vector measures partially align with the predictions of generativist linguistic theories, the approach suggests a more complex relation between syntactic categories. We conclude that a mutual-information-based approach better approximates the distributional “meaning” of syntactic categories than the conditional probability distribution of POS symbols. Full article

Virtual reality can support the preparation and rehearsal of assembly tasks by providing a safe and repeatable digital representation of workstations. This study presents the development and laboratory feasibility validation of a geometry- and procedure-oriented VR simulation model for the assembly and disassembly of end-effectors on an industrial robot. The workflow was implemented using the Almega AX-V6 robotic workstation as a case study and included geometric acquisition of the real robot, CAD modelling in SolidWorks, redesign of the original end-effector connection using a quick-change flange concept, creation of two alternative end-effector models, modelling of the laboratory workspace in SketchUp, and scene enhancement in Twinmotion. The resulting robot and environment models were integrated in Pixyz Review and deployed through an Oculus Rift-based VR setup. Compared with the original flange concept, which required twelve screws, the redesigned training concept used two screws and two nuts, reducing the number of fastening elements by 66.7% and the number of screw positions by 83.3%. The VR implementation supported visual inspection, controller-based placement and alignment, and symbolic confirmation of fastening steps; it did not include force feedback, threaded fastening physics, automatic error scoring, or quantified transfer-of-training evaluation. Laboratory feasibility validation confirmed correct asset integration, spatial correspondence with the physical workplace, and functional executability of the target exchange sequence. The results show that the workflow is useful as a case-study pipeline for CAD-to-VR modelling and assembly rehearsal, while controlled user studies are still required before claims about training effectiveness can be made. Full article