Our Work

Corrected edition — 24 September 2026Readers of an earlier edition should download the revised PDF or EPUB and replace their previous copy.This coordinated edition refresh corrects the companion-volum…

Corrected edition — 24 September 2026Readers of an earlier edition should download the revised PDF or EPUB and replace their previous copy.This coordinated edition refresh corrects the companion-volume title and source wording while preserving the 23 September Klein-quartic sewing and twist-convention corrections. Existing illustrations and earlier corrections are preserved.This volume introduces the mathematical language of the G2 brane-bulk theory: octonions and quaternionic subalgebras, exceptional symmetry, the Fano plane, the Klein quartic, geometric projections and brane-bulk transit. It develops the geometric constructions used in the companion volumes on cosmology, gravitation, matter and quantum mechanics.Edition and revisions. These volumes are evolving works. This release preserves the edited text as a dated edition. Future corrections, clarifications and extensions will be published as new versions, with earlier versions retained for citation. Readers should cite the specific version consulted.The PDF is the current edited interior; the EPUB contains the illustrated cover. A separate cover image is also provided.Rights. Copyright © 2026 Bharathi Dasan Jagadeesan. Free reading and download for private use; other rights, including redistribution, are retained by the rights holder, except as permitted by law or by permissions previously granted. Earlier editions published under CC BY retain that licence for the material covered by those releases; this notice does not revoke those permissions.

This record contains the supplemental materials  for the technical paper "Equitable Infrastructure Maintenance Planning under Fiscal and Intervention Rule Constraints" (Manuscript No. MEENG-8224)…

This record contains the supplemental materials  for the technical paper "Equitable Infrastructure Maintenance Planning under Fiscal and Intervention Rule Constraints" (Manuscript No. MEENG-8224).

This study aims to systematically review and synthesize recent empirical evidence on socioemotional skill interventions for preschool children with autism spectrum disorder (ASD) from an educational e…

This study aims to systematically review and synthesize recent empirical evidence on socioemotional skill interventions for preschool children with autism spectrum disorder (ASD) from an educational evaluation perspective. Guided by the preferred reporting items for systematic reviews and meta-analyses (PRISMA) framework, a systematic search of Scopus and Web of Science (WoS) identified 15 peer-reviewed studies published between 2019 and 2025. The included studies were thematically analyzed and appraised using the mixed methods appraisal tool (MMAT). The findings revealed three dominant intervention themes: i) relationship-based and developmental interventions; ii) structured and skill-focused interventions; and iii) creative, expressive, and technology-supported approaches, demonstrating overall positive effects on socioemotional outcomes. However, the strength of evidence remains moderate due to methodological heterogeneity, small sample sizes, and limited longitudinal designs. These findings highlight the importance of developmentally appropriate and flexible intervention designs in inclusive early childhood education. The review offers practical implications for educators, curriculum developers, and policymakers. Specifically, it emphasizes the need for evidence-based socioemotional programs to strengthen inclusive preschool practices for children with ASD.

O aleitamento materno é a estratégia mais eficaz para promover a saúde infantil, e sua proteção depende, entre outros fatores, do cumprimento da Norma Bras…

O aleitamento materno é a estratégia mais eficaz para promover a saúde infantil, e sua proteção depende, entre outros fatores, do cumprimento da Norma Brasileira de Comercialização de Alimentos para Lactentes e Crianças de Primeira Infância, Bicos, Chupetas e Mamadeiras (NBCAL). Este estudo avaliou a adequação da promoção comercial de produtos concorrentes do aleitamento materno em drogarias de Barbacena–MG, Brasil. Trata-se de um estudo observacional transversal, realizado em 22 drogarias localizadas nas regiões central, hospitalar e periférica do município. Por meio de checklists, foi realizada coleta de dados sobre a publicidade e propaganda de produtos substitutos do leite materno, bicos, mamadeiras e protetores de mamilo, visando avaliar a conformidade à NBCAL. Observou-se que 90 % das drogarias utilizavam estratégias de marketing persuasivas. As principais não conformidades foram prêmios e brindes após a compra (40,9 %), ofertas especiais (22,7 %), cupons de desconto (18,18 %), exposição especial (13,6 %).  A maioria das irregularidades (71,4 %) foi observada na região central, onde há maior circulação de pessoas. A elevada frequência de inadequações evidenciou o descumprimento da NBCAL nas drogarias de Barbacena–MG, principalmente nas regiões central e hospitalar. Ressalta-se a necessidade de ações de fiscalização, educação e conscientização de gestores, profissionais de saúde e proprietários dos estabelecimentos.

Python/numba code for manipulating time-dependent functions of spin-weighted spherical harmonics on future null infinity

Say a prime p is Artin base a if a is a primitive root modulo p. This paperstudies the joint behaviour of Artin status across bases at the same prime. We first record adeterministic exclusion law: for…

Say a prime p is Artin base a if a is a primitive root modulo p. This paperstudies the joint behaviour of Artin status across bases at the same prime. We first record adeterministic exclusion law: for any two bases a, b, writing d = sqf(ab) for the squarefree partof ab, no prime p with  dp= −1 is simultaneously Artin for a and for b. That condition is aunion of residue classes modulo 4d, so whenever d > 1 — equivalently, whenever a and b donot have the same squarefree part — half of all primes are barred outright; the proof is twolines from the multiplicativity of quadratic characters. A corollary is the triple form of the law:if sqf(c) = sqf(ab) then no odd prime is simultaneously Artin for a, b and c — for instance, noodd prime has 2, 5 and 10 all as primitive roots. Over all 66 pairs of the base set below and all50,847,524 primes below 109, the number of primes violating the pair law is zero, as it must be.We then measure, for all 66 pairs from the twelve bases {2, 3, 5, 6, 7, 10, 11, 13, 15, 17, 21, 29}and all 50,847,532 primes up to 109, the same-prime correlation ϕ(a, b) between the indicatorvariables of Artin status. Three empirical findings emerge. First, the correlation is positive for64 of the 66 pairs (mean ϕ = 0.0352, individual ϕ/σ0 up to 476 against the benchmark scaleσ0 = N −1/2 — which reflects the 5 × 107 primes enumerated rather than a large effect; thecorrelations explain about 0.1% of variance), despite the exclusion law: the common causep − 1 dominates. The only negative pairs are (2, 10) and (3, 15), the two for which the barringcharacter has conductor 5, the smallest occurring. Second, conditioning on the number ofprime factors ω(p − 1) removes only 55% of the mean correlation, but conditioning on a finersignature of p − 1 — the 2-adic valuation, the divisibility of p − 1 by each prime up to 13, andthe number of larger factors — removes 95%: the cross-base correlation is, almost entirely,a reflection of the fact that all bases see the same factorisation of p − 1. Third, the residualthat survives fine conditioning is concentrated on the triple-completed pairs (mean absoluteresidual 0.018 within those pairs, or 0.008 excluding one large positive outlier, versus 0.001 fornon-completed pairs), and is localised in the quadratic-character channel, which is where theexclusion law of Theorem 3 acts; we read this as the law’s statistical trace, visible once thecommon cause is conditioned away, while noting that a support restriction of this kind doesnot by itself determine the size or sign of a residual. Finally we evaluate the joint densitiespredicted by the Matthews–Moree–Stevenhagen Kummer-degree heuristic for all 66 pairs: withno fitted parameters they match the measured densities to a mean relative error of 0.012%,and they reproduce the sign reversal on the two negatively correlated pairs. Both the pointwiseobstruction and the Kummer-degree heuristic are governed by the same quadratic class sqf(ab),which appears in the first as a congruence barring half the primes and in the second as amember of the group of quadratic classes that can reduce the degree. We do not claim theseare the same phenomenon: the product class belongs to that group for every pair, whereas itlowers a degree only when its conductor divides the relevant cyclotomic level, and we exhibitpairs separating the two.

Environmental sustainability has become crucial, especially in tropical environments that act as lungs for the world. Therefore, exploring the pro-environmental behavior (PEB) of young citizens o…

Environmental sustainability has become crucial, especially in tropical environments that act as lungs for the world. Therefore, exploring the pro-environmental behavior (PEB) of young citizens of Eastern Borneo in Indonesia is beneficial. Exploration focused on the PEB category of students, the PEB aspect (preservation, utilization, appreciation), and student responses to the local environmental issues. This study surveyed 651 9th-grade students (15-year-olds) in six cities around Eastern Borneo. The measurement of PEB was carried out using the adapted two major environmental values model with an added scale for appreciation. Additional open-ended questions were applied to clarify the students’ perspectives on the significant environmental issues in Eastern Borneo. The result showed that only half of the students (51.31%) had advanced PEB, with the rest classified as transitional (48.23%) and naive (0.46%). Among the three PEB aspects, utilization scored the highest, indicating that the students were strongly inclined to endorse the importance of environmental utilization for human welfare. Moreover, the majority favored relocating the capital city, which highlights the importance of a new capital city owing to the overcrowded state of the current capital city (Jakarta) and the decentralization of the development of Indonesia. Nevertheless, it was found that they are concerned about preservation and sustainability regarding coal mining and palm plantations. Therefore, it was considered that environmental education for students needs enhancement to shape their PEB with contextual environmental issues.

Abstract. Call a prime p an Artin prime for base 10 if 10 is a primitive root modulo p. Weinvestigate the dependence between the Artin statuses of consecutive primes. Computing Artinstatus for all 50,…

Abstract. Call a prime p an Artin prime for base 10 if 10 is a primitive root modulo p. Weinvestigate the dependence between the Artin statuses of consecutive primes. Computing Artinstatus for all 50,847,531 primes 7 ≤ p ≤ 109, we find that consecutive primes are measurablyanticorrelated: P(Artn+1 | Artn) = 0.36514 versus P(Artn+1 | ¬Artn) = 0.37928, a deficit δ =−0.01414 (Pearson statistic 10,167 on one degree of freedom; signed square root −100.8 under anominal independent-status reference model; over 50,847,530 consecutive pairs). The dependencehas striking gap structure. We prove an elementary exclusion law: if p,p + g > 5 are both primewith g ≡ 20 (mod 40), then 10 is a quadratic residue modulo exactly one of them, so they cannever both be Artin primes for base 10; empirically, among 2,195,882 consecutive pairs with gap20 or 60 there is indeed not a single doubly-Artin pair; an independent recomputation extends thisto 194,296,748 such pairs below 1011, again with none. Conversely, gaps g ≡ 0 (mod 40) forceequal quadratic-residue status and exhibit strong positive dependence (P(Artn+1 | Artn) = 0.899at g = 40). Conditioning on the joint residues of (pn,pn+1) modulo 120 or 840 substantially reducesa selected-cell signed residual association; the remaining association is small in that metric but isnot established to vanish. These results are consistent with a substantial role for arithmetic residuestructure in the observed anticorrelation; they do not constitute a complete decomposition or anindependent quantitative verification of the Hardy–Littlewood explanation. As an intermediatelink we report the (apparently unreported) anticorrelation rω(pn −1),ω(pn+1 −1) = −0.041. Atfour decade-spaced cutoffs x = 108,109,1010,1011 the deficit grows in magnitude with decreasingincrements, δ = −0.01336,−0.01414,−0.01472,−0.01500, and no turnover is observed; we drawno asymptotic conclusion from this, and in particular these finite-range values do not distinguisheventual decay to zero from persistence of a nonzero correlation. We formulate open questions anddiscuss extensions to general bases.

spectrl defines and implements a URL-safe interchange format for individual mass spectra. A spectrl.v3 token contains peak arrays, array units, precursor information, modeled metadata based on mzML co…

spectrl defines and implements a URL-safe interchange format for individual mass spectra. A spectrl.v3 token contains peak arrays, array units, precursor information, modeled metadata based on mzML controlled-vocabulary terms. The payload is encoded as CBOR and Base64url text with a CRC-32 integrity checksum. Peak arrays use four versioned numeric encodings: raw words, byte shuffle, modular delta plus byte shuffle, and quantized words. Fixed profiles support exact recovery or controlled numerical loss. Compression applies once to the complete CBOR document, with zlib as the default and raw and Brotli alternatives. Applications can register namespaced custom numeric encodings and extensions. PSI-MS accessions retain scientific array and metadata identity. Selected source, instrument, software, and processing context can accompany each spectrum. Because the spectrum is carried in the token, it can be placed in URL fragments, query parameters, data URIs, QR codes, notebooks, and publication supplements without requiring a repository lookup or application backend. The Python package provides encoding, decoding, validation, URL helpers, a command-line interface, and conversion from mzmlpy spectrum objects. A separate TypeScript implementation supports browsers and Node, and shared conformance vectors test agreement between the two implementations. spectrl is intended for self-contained spectrum exchange and application handoffs. Repository-based identifiers remain more appropriate when persistent archival lookup is the primary goal.