Code and exact certificate data for 'Variance and local log-concavity of Poisson-binomial laws'
October, 2026 • Software
Reynolds, Brett
Code, exact certificate data and Lean 4 formalizations supporting the paper 'Variance and local log-concavity of Poisson-binomial laws' by Brett Reynolds.
Computations the proof needs: scripts/verify_…
Code, exact certificate data and Lean 4 formalizations supporting the paper 'Variance and local log-concavity of Poisson-binomial laws' by Brett Reynolds.
Computations the proof needs: scripts/verify_pb_compact_monotone.py checks the 32 exact rational inequalities of Section 4.1 using only the Python standard library, and scripts/verify_pb_large_h_range.py checks the expansions for H >= 16 in exact arithmetic (SymPy). scripts/verify_pb_cue_threshold.py certifies the variance threshold in the Haar unitary example with rational bounds on pi.
Additional check: a certificate by Bernstein expansions for 3 < H <= 16 (275 positive rational coefficients), with a SymPy generator and an independently written standard-library checker.
Formalizations (Lean 4, Mathlib v4.28.0): a proof of Proposition 3.1, and a proof of Theorem 1.1 from the probability-generating polynomial, including the Hillion-Johnson cubic inequalities, strict log-concavity and the maximal-mass bound. Both depend only on Lean's three standard axioms. An earlier conditional formalization is also included.
CERTIFICATE.md gives the replay commands, file hashes and the provenance of AI contributions; MANIFEST.sha256 lists the digest of every file.
Multi-locus alignments and phylogenetic trees of the mycobiota of Euterpe edulis
October, 2026 • Dataset
Pereira da Silva, Nívia Maria, Branco Rocha, Fabiano, Pereira, Caio, Salcedo Sarmiento, Sara, Barreto, Robert
The alignment of the sequences from each database was performed using MUSCLE, implemented in the MEGA X software (FASTA format), and the concatenated alignment was generated using the SequenceMatrix v…
The alignment of the sequences from each database was performed using MUSCLE, implemented in the MEGA X software (FASTA format), and the concatenated alignment was generated using the SequenceMatrix ver. 1.8 software.
The concatenated matrix was opened in AliView to export the final input files for phylogenetic analyses: - NEXUS format (.nex): Exported via AliView for the Bayesian Inference analysis. NEXUS file includes a MrBayes command block. - PHYLIP/PARTITIONS format (.partitions/.phy): Exported via AliView for the Maximum Likelihood analysis.
Both methods were analysed using tools implemented in the CIPRES Science Gateway web portal. For the ML analysis, the RAxML-HPC ver. 8.2.12 software was used, generating the RAxML tree (.nwk format). For the BI analysis, the MrBayes v.3.2.7a program was used, generating the consensus tree file (.nex.con).
Maximum LikelihoodBayesian InferenceMycologyPhylogeny
Reversals is a poem by Muhammad Dattijo Usman, preserved in the Muhammad Dattijo Usman Archive as a surviving typescript dating from 1998.
This record presents a 2026 digital archival edition prepared…
Reversals is a poem by Muhammad Dattijo Usman, preserved in the Muhammad Dattijo Usman Archive as a surviving typescript dating from 1998.
This record presents a 2026 digital archival edition prepared from the surviving document. The edition includes archival metadata, a facsimile of the source document and a diplomatic transcription preserving the wording of the surviving text.
No evidence establishing an earlier publication of the work has yet been located. The 1998 date therefore records the date of the original work rather than a verified historical publication.
Archive reference: MDU-L002.
Muhammad Dattijo UsmanReversalsNigerian poetryNigerian literatureAfrican literature
This study examines the association between the reproductive policy environment and female labor force participation (FLFP) in Canada and Sri Lanka using panel data from 2013-2023. The analysis introd…
This study examines the association between the reproductive policy environment and female labor force participation (FLFP) in Canada and Sri Lanka using panel data from 2013-2023. The analysis introduces a Reproductive Policy Restrictiveness Index (RPRI), a ten-component composite integrating three externally sourced legal variables (abortion legality, contraception access, and the World Bank Women, Business and the Law composite) with seven institutional indicators. The analytical approach in this work uses correlation analysis, Principal Component Analysis, Random Forest feature ranking, and ARIMA forecasting. Findings document a 55.7-point RPRI gap between Canada (mean = 90.6) and Sri Lanka (mean = 34.9), co-varying with a 13.4-percentage-point FLFP gap (pooled r = 0.996). Within-country temporal correlation is essentially zero, indicating the RPRI-FLFP association is between-country. The study contributes the first integrated legal-institutional restrictiveness index for these countries, framed associational rather than causally.
There is an increasing interest in upgrading the EModel, a parametric tool for speech quality estimation, to the wideband and super-wideband contexts. The
Contemporary models of Unmanned Aerial Vehicles (UAVs) are largely developed using simulators. In a typical scheme, a flight simulator is dovetailed with a
Undertaking engineering research can be compounding for beginning graduate students and thwarting even for seasoned researchers. With a wealth of academic
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