arXiv subjects

Francesco De Rango

Publications and source records attributed to Francesco De Rango.

2 recordsLinked to original sources

arXiv2025

Entropy-Rank Ratio: A Novel Entropy-Based Perspective for DNA Complexity and Classification

Shannon entropy is widely used to measure the complexity of DNA sequences but suffers from saturation effects that limit its discriminative power for long uniform segments. We introduce a novel metric, the entropy rank ratio R, which positions a target sequence within the full distribution of all possible sequences of the same length by computing the proportion of sequences that have an entropy value equal to or lower than that of the target. In other words, R expresses the relative position of a sequence within the global entropy spectrum, assigning values close to 0 for highly ordered sequences and close to 1 for highly disordered ones. DNA sequences are partitioned into fixed-length subsequences and non-overlapping n-mer groups; frequency vectors become ordered integer partitions and a combinatorial framework is used to derive the complete entropy distribution. Unlike classical measures, R is a normalized, distribution-aware measure bounded in [0,1] at fixed (T,n), which avoids saturation to log2 4 and makes values comparable across sequences under the same settings. We integrate R into data augmentation for convolutional neural networks by proposing ratio-guided cropping techniques and benchmark them against random, entropy-based, and compression-based methods. On two independent datasets, viral genes and human genes with polynucleotide expansions, models augmented via R achieve substantial gains in classification accuracy using extremely lightweight architectures.

cs.IT↗

arXiv2025

The Noncomputability of Immune Reaction Complexity: Algorithmic Information Gaps under Effective Constraints

We introduce a validity-filtered, certificate-based view of reactions grounded in Algorithmic Information Theory. A fixed, total, input-blind executor maps a self-delimiting advice string to a candidate response, accepted only if a decidable or semi-decidable validity predicate V(x, r) holds. The minimum feasible realizer complexity M(x) = min_{r: V(x,r)=1} K(r), with K denoting prefix Kolmogorov complexity, measures the minimal information required for a valid outcome. We define the Normalized Advice Quantile (NAQ) as the percentile of M(x) across a reference pool, yielding a scale-free hardness index on [0, 1] robust to the choice of universal machine and comparable across task families. An Exact Realizer Identity shows that the minimal advice for any input-blind executor equals M(x) up to O(1), while a description plus selection upper bound refines it via computable feature maps, separating description cost K(y) from selection cost log i_y(x). In finite-ambiguity regimes M(x) approximately equals min_y K(y); in generic-fiber regimes the bound is tight. NAQ is quasi-invariant under bounded enumeration changes. An operational converse links NAQ to rate-distortion: communicating advice with error epsilon requires average length near the entropy of target features. Extensions include a resource-bounded variant NAQ_t incorporating time-penalized complexity (Levin's Kt) and an NP-style setting showing linear worst-case advice n - O(1). Finally, a DKW bound guarantees convergence of empirical NAQ estimates, enabling data-driven calibration via compressor-based proxies.

cs.IT↗