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Examination seating optimization using graph coloring and combinatorial design
(ELSEVIER, 2026-05-12) Kibona, Isack E; January, Jeremiah,; Matimbwa, Hadija; Nchia, Edwin; Matungwa, William; Vuai, Said A.H
This paper presents an optimization approach for exam seating in universities with limited infrastructure, based on a mixed-course allocation model. Students in different courses share rooms while maintaining spatial separation to improve academic integrity. The model incorporates a theoretical probability of interaction, which decreases as the number of mixed courses in a room increases.
Using real data with 5175 students, the proposed model significantly improves upon the traditional method. Although the traditional approach required 35 rooms with a total capacity of 7269, the proposed model utilized only 12 large rooms, leaving 23 rooms unused and saving about 2475 seats. The unused space within the occupied rooms was minimal (approximately 29 seats), indicating near-optimal utilization.
The invigilation requirement was reduced from at least 70 to 36, achieving nearly 50% savings. Small-enrollment and carryover courses are efficiently integrated and sorted. The model is formulated using graph coloring and combinatorial optimization, supported by a simple allocation algorithm.
Photochromic and fluorescence switching behavior of triazole-functionalized fulgimides:
(ELSEVIER, 2026-05-11) Ally, Khamis Nassor; Tsere, Melkizedeck Hiiti; Vuai, Said Ali; Lameck, Azaria Stephano; Oztürk , Leyla; K¨ose , Mahmut
Integrating photochromism and fluorescence switching within a single molecular platform remains a central challenge in the development of light-regulated functional materials. Here, we report a structure-encoded design strategy based on the direct covalent incorporation of a 1,2,4-triazole unit into the imide framework of fulgimides, yielding three new photoresponsive molecules (4E–6E). Experimentally, all compounds exhibit photochromism based on the interconversion between open and closed forms. This is accompanied by large visible-range spectral contrast and reversible fluorescence ON/OFF switching under alternating UV and visible light. The open-ring forms are strongly emissive, while photoinduced cyclization produces systematic fluorescence quenching (20–40%) governed by intramolecular energy transfer to the conjugated closed-ring core. Density functional and time-dependent DFT calculations quantitatively reproduce the observed experimental absorption behavior and reveal pronounced π-delocalization and HOMO-LUMO gap narrowing upon ring closure, establishing clear structure–property relationships. Among the series, compound 6E shows the most favorable electronic and optical characteristics. These results identify triazole-imide coupling as a generalizable molecular engineering route for multifunctional organic photo-switches and advance their potential for optical memory, sensing, and adaptive photonic applications.
Quantifying the Public Health Effects of Vaccine Hesitancy and Delays in Screening Clinically Infected Patients: Insights From a COVID-19 Transmission Model
(IJMSO, 2025-05-14) Lolika, Paride O,; Mlyashimbi Helikumi,; Kenneth Sube,; Steady Mushayabasa
Motivated by the recent COVID-19 outbreak, we develop a time delay infectious disease
model that incorporates vaccination and screening of clinically infected patients and calibrate
it using Chinese data to understand the quantitative implications of vaccine hesitancy and
delay in the screening of clinically infected patients. Vaccine hesitancy refers to the denial or
delay in acceptance of vaccines despite their availability. Understanding the implications of
vaccine hesitancy is therefore essential for designing public health interventions. Analysis of
the model revealed that whenever R0 ≤ 1, there exists a globally asymptotically disease-free
equilibrium. However, whenever R0 > 1, there exists a unique endemic equilibrium which is
globally asymptotically stable. In addition, results also show that vaccine hesitancy and delay
in hospitalizing clinically infected patients have a stronger impact on the deaths toll and new
infections generated [1,2]. Vaccine hesitancy and delayed screening of clinically infected patients
lead to harmonic oscillations in deaths and new cases, which, however, die out over time. Our
findings underscore the importance of including vaccine hesitancy and delay in hospitalizing
clinically infected patients in the design of control strategies for infectious diseases
Examination Seating Optimization Using Graph Coloring and Combinatorial Design
(ELSEVIER, 2026) Kibona, Isack E.; January, Jeremiah; Matimbwa, Hadija; Nchia, Edwin; Matungwa, William; Vuai, Said A.H.
This paper presents an optimization approach for exam seating in universities with limited infrastructure,
based on a mixed-course allocation model. Students in different courses share rooms while maintaining spatial
separation to improve academic integrity. The model incorporates a theoretical probability of interaction,
which decreases as the number of mixed courses in a room increases.
Using real data with 5175 students, the proposed model significantly improves upon the traditional method.
Although the traditional approach required 35 rooms with a total capacity of 7269, the proposed model utilized
only 12 large rooms, leaving 23 rooms unused and saving about 2475 seats. The unused space within the
occupied rooms was minimal (approximately 29 seats), indicating near-optimal utilization.
The invigilation requirement was reduced from at least 70 to 36, achieving nearly 50% savings. Small-
enrollment and carryover courses are efficiently integrated and sorted. The model is formulated using graph
coloring and combinatorial optimization, supported by a simple allocation algorithm
Performance Dynamics of Batch Arrival Feedback Queue With General Second Optional Services, Server Breakdown and Standby Server
(AIMS, 2026) Pikkala, Vijaya L.; Kisakali, Justin; Gilaka, Anjalidevi; Qrewi, Hasan A.
This paper aims to analyze the steady state behavior of a bulk
input general service queue with second optional service, breakdowns, general
repair, and delay times. The server may experience random failures during the
first essential and second optional services, and we assume there is a delay be-
fore the server starts the repair process. The system is equipped with a standby
server, which provides service to the customers only when the main server is
under repair due to sudden failure or during the delay time for repair to start.
Moreover, the service times first essential service and second optional service,
delay times, and repair times have a general distribution, while the breakdown
times and standby service times follow an exponential distribution. The steady
state probabilities are computed using the probability generating function. Fi-
nally, numerical illustrations of performance measures are provided