arXiv subjects

Stella Stylianou

Publications and source records attributed to Stella Stylianou.

4 recordsLinked to original sources

arXiv2026

Exact optimality of augmented order-of-addition designs

We prove that, for the pairwise-ordering model with at least three components, adding any run to an order-of-addition orthogonal array gives a $D$-optimal design among all exact designs of the enlarged size, allowing replication. We also establish the corresponding result for foldover designs: adding any reversal pair to a foldover order-of-addition orthogonal array gives a $D$-optimal design within the foldover class at the enlarged size. Both augmentations also minimise the average prediction variance and a covariance-scaled information discrepancy, and maximise the minimum relative efficiency. The key step represents the scaled discrepancy through signed comparisons of triples and derives a sharp integer lower bound; classical spectral inequalities then give the exact-size optima, and signed four-component relative-order counts characterise equality. Complete reversal pairs additionally protect the estimation of pairwise-ordering effects against arbitrary reversal-invariant nuisance means. At the smallest estimable five-component foldover size, exact enumeration identifies five determinant-optimal classes with different prediction and balance properties, and a seven-component example shows that deleting a reversal pair need not be optimal even when it minimises the discrepancy. Constructions through ten components illustrate the attained run sizes.

math.ST↗

arXiv2026

The complete existence spectrum of periodic complementary ternary pairs of weight nine

For two sequences with entries $0,\pm1$, periodic complementarity means that their periodic autocorrelation functions sum to zero at every nonzero shift. We give necessary and sufficient conditions on the length for the existence of such pairs of total weight nine, where weight counts nonzero entries. The conditions decide existence at any prescribed length by divisibility tests. The main new result bounds the length of primitive pairs with two nonzero components. A pair is primitive if it cannot be shortened by removing uniformly inserted zeros after independent cyclic permutations. We prove primitive-length bounds of $64,48,64$ for weight distributions $(5,4),(6,3),(7,2)$. These bounds make the classification finite and prove that the earlier searches contain every required case. Exhaustive enumeration gives $91$ primitive sequence-equivalence classes. Including the five known circulant classes gives $96$ representatives from which every pair can be generated. The same catalogue gives class counts at every length. For constructing one pair, $33$ displayed seeds suffice. The results settle earlier conjectures on the weight distributions and decide exactly which orders admit the associated two-circulant weighing-matrix construction.

math.CO↗

arXiv2026

An exact compression-and-lifting procedure and D-optimal designs of orders 198 and 170

We develop a compression-and-lifting procedure for constructing D-optimal complementary pairs on finite abelian groups of odd order. The procedure separates the Fourier conditions preserved by compression from those needed to recover the original binary sequences. For groups with a cyclic factor of order nine, integer matching conditions separate compatible classes of local sign assignments. Their exact sizes can be computed before full sequences are generated, allowing searches to discard incompatible pairs and select manageable classes. A bound on cosets on which a sequence is constant also excludes certain automorphisms as fixing symmetries. Applying the method yields supplementary difference sets with parameters $(99;43,42;36)$ and $(85;39,34;31)$, resolving two previously undecided parameter sets. These give the first D-optimal matrix of order $198$ and constructions with new parameters at the known order $170$. For the successful length-$99$ compression, the exact class condition removes $99.9888\%$ of candidate pairs while preserving every D-optimal lift. A reflection-invariant construction at length $85$ gives seven supplementary difference set classes and fourteen matrix classes under signed row and column permutations, paired by transposition. The class reductions guide computation; finding suitable compressions and matching their lifts remain search problems.

math.CO↗

arXiv2025

A pilot cohort study of a microfluidic-based point-of-care bilirubin measurement system

Objective The concentration of bilirubin in blood or serum is useful for assessing liver function as well as monitoring treatment. This study evaluates the clinical performance of a novel point-of-care (PoC) device for the detection of bilirubin in serum. The PoC device incorporates an integrated miniature optoelectronic sensing module and a microfluidic test cartridge. Methods Patients' serum total bilirubin concentrations, ranging from 2 μmol/L to 480 μmol/L, were measured using the PoC device and the standard laboratory method (n=20). Bland-Altman analysis and regression analysis using Passing-Bablok method were used to benchmark the PoC device against the standard laboratory measurements. The diagnostic capability of the PoC device in categorising the serum samples within clinically relevant bilirubin concentration thresholds of 200, 300, and 450 μmol/L was assessed using receiver operating characteristic (ROC) analysis. Results The mean difference between the PoC device and the standard laboratory method was -5.6 μmol/L, with a 95% confidence interval (CI) of -45.1 μmol/L to 33.9 μmol/L. The coefficient of determination (R2) was 0.986. The PoC device achieved a detection sensitivity of 90% and specificity of 97% in categorising bilirubin concentrations within bands used in clinical decision-making. Conclusions This study demonstrates that the proposed PoC device is capable of measuring bilirubin levels in patient samples with clinically acceptable accuracy.

physics.med-ph↗