IEEE Computer Society

Achieving inclusive mathematics education remains a distinctive challenge due to the discipline’s hierarchical structure, high degree of abstraction, and dense symbolism. These disciplinary features create unique cognitive barriers for students with special educational needs, requiring a precise intersection of content expertise and pedagogical scaffolding. While collaboration between mathematics and special education (SPED) teachers is vital to dismantling these barriers, the success of such teams is mediated by the teachers’ mental models—the internal assumptions that dictate their collaborative engagement. Utilizing a multi-case study design, this study examined teacher mental models through cross-disciplinary Lesson Study (LS) focused specifically on making abstract mathematical concepts accessible. Based on data collected before, during, and after four LS cycles, findings reveal that participants’ initial mental models of collaboration were limited to rudimentary idea-sharing. However, the LS experience facilitated a shift toward reciprocal learning, where participating teachers engaged in a mutual exchange of disciplinary expertise to co-create lesson resources and strategies. This shift is framed as a theoretical insight into cognitive syncretism: the restructuring of compartmentalized professional identities into a shared, integrated schema. Specifically, SPED teachers acquired the technical mathematical depth necessary to navigate cumulative curriculum demands, while mathematics teachers adopted differentiated strategies to decode complex mathematical symbols for diverse learners. Ultimately, this research positions mental models as primary mediators of educational reform, suggesting that sustainable inclusion in mathematics requires a fundamental cognitive reorganization of how teachers perceive the intersection of mathematical rigor and instructional accessibility.

We introduce the Sakib Renormalization–Projection Commutator (SRPC), a KL-valued commutativity defect that quantifies the inconsistency between (i) coarse- graining a data-defined distribution and then projecting onto a truncated model/basis, versus (ii) projecting first and then coarse-graining. Although KL divergence, coarse-graining maps, and information projections are individually classical, SRPC is proposed here as a single operational diagnostic for basis closure and missing- operator detection in multiscale modeling. We define the Sakib Index SI := − log10(SRPC + ε) (higher SI indicates closer- to-commutative, more closed truncations), and a data-driven operator-ranking score based on ∆SRPC under basis augmentation. Using only open observational datasets— (a) Planck 2018 CMB TT power-spectrum bins, (b) the NOAA Mauna Loa CO2 monthly record, and (c) the SILSO International Sunspot Number series—we pro- vide 10 dataset-based figures and show that SRPC is reproducible, scale-sensitive, and interpretable as a closure diagnostic.

This manuscript introduces a monotone finite-window extremal functional for Gaus- sian primes in the ring Z[i] under the boxcar (Manhattan, L1) metric, and proposes a calibrated extreme-value constant and a dimensionless normalization (the Sakib Index) for nearest-prime distance fields. While boxcar-metric “prime gap” frameworks in Z[i] exist in the literature, the present work isolates a distinct monotone diamond (increasing-window) covering-radius functional, provides a dataset-based computational study (no schematic/simulated plots in the 10 principal figures), and packages a norm- generalized constant law that reduces to a candidate constant cSakib = π/2 for the L1-ball geometry. All principal illustrations are generated directly from computed Gaussian-prime data (sieve + exact distance transform), with additional conceptual diagrams provided for clarity.

Greetings, YP readers! I hope your 2026 is off to a great start. Our EMC Society YP volunteers have been busy finalizing the details for our major events this year. In fact, 2026 will be the first year we hold YP events at all three major conferences sponsored by our Society: APEMC, the EMC+SIPI Symposium, and EMC Europe. If you're a YP and plan to attend one (or more) of these events, don't forget to sign up and seize the opportunity to meet other YPs. Relationships formed within the EMC Society can lead to future collaborations and provide valuable contacts when you need a friend to bounce ideas off.

A classical theorem of H. J. S. Smith states that the determinant of the n × n GCD matrix (gcd(i, j))1≤i,j≤n equals Qn k=1 φ(k). Building on the standard meet/poset (Smith–Wilf–Lindstr¨om) determinant factorization framework for ma- trices of the form (f (gcd(i, j))), we introduce a 2-adically weighted family A(c) n = cv2(gcd(i,j)) gcd(i, j) 1≤i,j≤n, and derive a closed-form determinant factorization depending only on the 2-adic valuation counts up to n. The resulting correction factor (normalized by Qn k=1 φ(k)) is named the Sakib Index. A key parity-twisted specialization yields the explicit factor SI(n) = (−1)⌈n/2⌉ 3⌊(n+2)/4⌋, producing an unexpectedly simple 2-adic amplification of Smith’s determinant. Ten data-driven figures (OEIS-based and exact integer computations) and six concep- tual diagrams are provided.

<title>Abstract</title> Hypertension prevalence in low-income populations globally is increasing rapidly and may have unique poverty-related determinants. Factors related to stress may be important contributors to hypertension in these populations in addition to traditional factors such as age and obesity. We examined stress-related and traditional hypertension risk factors among urban poor in Pune, India. We used cluster area random sampling to enroll adults aged ≥18 years from urban slum communities, collecting demographics, psychological distress (Kessler-6), tobacco use, anthropometrics, and blood pressure. Psychological distress was defined as Kessler-6 ≥11. Hypertension was defined as systolic blood pressure ≥140, diastolic blood pressure ≥90 or taking hypertension medications. We conducted multivariable logistic regression on hypertension, adjusting for age, BMI, and tobacco use. Among 502 adults, median age was 44 years (IQR 31-53), 75.5% (n=379) were female, and 72.2% (N=365) had overweight/obese BMI. Hypertension prevalence (age-standardized) was 50.4% (n=257). Psychological distress was independently associated with hypertension (aOR 2.14, 95% CI 1.23, 3.73). Age &gt;50 years (aOR 2.75, 95% CI 1.42, 5.31), obese BMI (aOR 2.36, 95% CI 1.41, 3.94), and tobacco use at hazardous level (World Health Organization ASSIST score 4-26) (aOR 2.88, 95% CI 1.38, 6.02) were also significantly associated with hypertension. Upon sex-stratification, similar results were seen among women. We found a high prevalence of hypertension in a predominately female urban slum population in India. Hypertension was associated with stress. Public health programs for hypertension prevention in low-income populations should screen for and address stress in addition to traditional risk factors.