Related papers: The Voynich Codex Decoded: Statistical Symbolism a…
Numeral systems across the world's languages vary in fascinating ways, both regarding their synchronic structure and the diachronic processes that determined how they evolved in their current shape. For a proper comparison of numeral…
We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…
For a quantum state, or classical harmonic normal mode, of a system of spatial periodicity "R", Bloch character is encoded in a wavevector "K". One can ask whether this state has partial Bloch character "k" corresponding to a finer scale of…
This fourth and last tome is focusing on describing the envisioned works for a project that has been presented in the preceding tome. It is about a new approach dedicated to the coding of still and moving pictures, trying to bridge the…
We propose a general method for semantic representation of images and other data using progressive coding. Semantic coding allows for specific pieces of information to be selectively encoded into a set of measurements that can be highly…
Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, the equation itself…
A new score function is proposed for stack decoding of polar codes, which enables one to accurately compare paths of different lengths. The proposed score function includes bias, which reflects the average behaviour of the correct path.…
We present a detailed algorithm to construct symbolic encodings for chaotic attractors of three-dimensional flows. It is based on a topological analysis of unstable periodic orbits embedded in the attractor and follows the approach proposed…
Here we study an efficient algorithm for decoding the topological codes. It is based on a simple principle, which should allow straightforward generalization to complex decoding problems. It is benchmarked with the planar code for both…
We formulate code concatenation as the action of a unitary quantum circuit on an expanding tree geometry and find that for certain classes of gates, applied identically at each node, a binary tree circuit encodes a single logical qubit with…
Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…
Multimodal geometry reasoning requires models to jointly understand visual diagrams and perform structured symbolic inference, yet current vision--language models struggle with complex geometric constructions due to limited training data…
Most work on musical score models (a.k.a. musical language models) for music transcription has focused on describing the local sequential dependence of notes in musical scores and failed to capture their global repetitive structure, which…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
We propose a novel classification framework grounded in symbolic dynamics and data compression using chaotic maps. The core idea is to model each class by generating symbolic sequences from thresholded real-valued training data, which are…
Medical coding translates free-text clinical documentation into standardized codes drawn from classification systems that contain tens of thousands of entries and are updated annually. It is central to billing, clinical research, and…
Recently, interest has been emerging in the application of symbolic techniques to the specification and analysis of cryptosystems. These techniques, when accompanied by suitable proofs of soundness/completeness, can be used both to identify…
Since a quantum measurement generally disturbs the state of a quantum system, one might think that it should not be possible for a sender and receiver to communicate reliably when the receiver performs a large number of sequential…
Variable length codes exhibit de-synchronization problems when transmitted over noisy channels. Trellis decoding techniques based on Maximum A Posteriori (MAP) estimators are often used to minimize the error rate on the estimated sequence.…
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…