Complementation, Local Complementation, and Switching in Binary Matroids

In 2004, Ehrenfeucht, Harju, and Rozenberg showed that any graph on a vertex set $V$ can be obtained from a complete graph on $V$ via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local complementation. The last operation involves taking the complement in the neighbourhood of a vertex. In this paper, we consider natural generalizations of these operations for binary matroids and explore their behaviour. We characterize all binary matroids obtainable from the binary projective geometry of rank $r$ under the operations of complementation and switching. Moreover, we show that not all binary matroids of rank at most $r$ can be obtained from a projective geometry of rank $r$ via a sequence of the three generalized operations. We introduce a fourth operation and show that, with this additional operation, we are able to obtain all binary matroids.Comment: Fixed an error in the proof of Theorem 5.3. Adv. in Appl. Math. (2020

Cographs and 1-sums

A graph that can be generated from $K_1$ using joins and 0-sums is called a cograph. We define a sesquicograph to be a graph that can be generated from $K_1$ using joins, 0-sums, and 1-sums. We show that, like cographs, sesquicographs are closed under induced minors. Cographs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We obtain an analogue of this result for sesquicographs, that is, we find those non-sesquicographs for which every proper induced subgraph is a sesquicograph

Characterizations of Certain Classes of Graphs and Matroids

``If a theorem about graphs can be expressed in terms of edges and cycles only, it probably exemplifies a more general theorem about matroids. Most of my work draws inspiration from this assertion, made by Tutte in 1979. In 2004, Ehrenfeucht, Harju and Rozenberg proved that all graphs can be constructed from complete graphs via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local complementation. In Chapter 2, we consider the binary matroid analogue of each of these graph operations. We prove that the analogue of the result of Ehrenfeucht et. al. does not hold for binary matroids. However, we introduce a fourth operation that does enable the construction of all binary matroids from projective geometries. A graph in which every connected induced subgraph has a disconnected complement is called a cograph. Such graphs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. In Chapter 3, we define a 2-cograph to be a graph in which the complement of every 2-connected induced subgraph is not 2-connected. The class of 2-cographs is closed under induced minors. We characterize the class of non-2-cographs for which every proper induced minor is a 2-cograph. We further find the finitely many members of this class whose complements are also induced-minor-minimal non-2-cographs. Chapter 4 introduces binary comatroids, a matroid analogue of cographs. We identify all binary non-comatroids for which every proper flat is a binary comatroid. In addition, we extend our results to ternary matroids

Exploiting the Genetic Diversity of Wild Ancestors and Relatives of Wheat for its Improvement

Wheat is the third most staple food worldwide but current 1% annual improvement in the wheat production is insufficient to meet the growing demands in future. The narrow genetic base of wheat limits continuous improvement in wheat productivity and tolerance to biotic and abiotic stresses under changing climate. Wild ancestors and relatives of wheat hold a potential in widening the genetic pool of wheat and enhance its resilience to biotic and abiotic stresses. This study was focused towards characterizing the genetic diversity in wild relatives of wheat for disease resistance and efficient association with diazotrophs. In the first study, we evaluated a mini core set of Triticum turgidum subsp. (tetraploid wheat, AABB) for resistance to Fusarium head blight (FHB), leaf rust and tan spot. Three, six, and nine accessions showed resistance response to Fusarium head blight (FHB), leaf rust and tan spot respectively. These germplasm resources could be further exploited in wheat breeding. In the second study, in addition to tetraploid wheat, diploid and hexaploid germplasm of both wild and adapted species were evaluated for efficient association with diazotrophic bacteria by analyzing the N content. We observed significant differences for 15N content among different species, represented as average σ15N. Lower σ15N indicates a higher possibility of biologically fixed nitrogen (BNF). Wild accessions both in diploid (T. boeticum, AmAm, σ15N = 20.85) and tetraploid species (T. turgidum subsp. dicoccoides, AABB, σ15N = 16.44) showed significantly better associations with diazotrophs as compared to domesticated species (T. monococcum, AmAm, σ15N = 26.67) and modern hexaploid varieties (T. aestivum, AABBDD, σ15N =31.74). Our study shows that the wild species hold a promise in identification and characterization of efficient association with diazotrophic bacteria and this interaction can be recovered in modern cultivars of wheat to enhance the performance of wheat in marginal soils. In the final study, we analyzed the genetic diversity in the global collection (178 accessions) of rye using 4,037 high-quality SNPs and developed of a mini core set of 32 accessions of rye that represents more than 95 % of the allelic diversity (PIC = 0.25) of our collection (PIC = 0.26). Genome-wide association study (GWAS) was performed on 160 accessions (Secale cereale subsp. cereale) with 4,037 high-quality SNPs to identify genomic regions conferring tan spot resistance. Nearly 32%, 27%, 24%, and 17% accessions showed resistant, moderately resistant, moderately susceptible and susceptible reaction to Pyrenophora tritici-repentis race 5 (PTR race 5) respectively. Two QTLs conferring resistance to tan spot (PTR race 5) were identified (p= \u3c 0.001) using mixed linear model (GAPIT) on chromosomes 5R and 2R. The QTLs QTs-sdsu-5R and QTs-sdsu-2R explained 13.11% and 11.62 % of the variation. In conclusion, wild relatives and ancestors of wheat hold a potential for wheat improvement especially for tolerance to abiotic and biotic factors

The Effect of Feedback Frequency on Performance in Applied Behavior Analysis: a Field Study.

Occupational safety continues to be a major social concern in spite of the attention which it has received over the years. While unsafe acts and behaviors have been major contributors to accidents, the attention paid to increasing safety by changing human behavior has only been sporadic. This study used an applied behavior analysis package of training, goal setting, and feedback as a behavioral approach to improving safety in an industrial setting. In addition, the effects of changing the frequency of feedback on safe behavior performance were investigated. All the employees in a plant engaged in the manufacture and repair of heat exchangers, were put through various phases of the above mentioned applied behavior analysis package. Safe behavior performance of the employees was monitored over the ten month duration of the study through behavioral observation and measurement. A variation and extension of the basic reversal (A-B-A) design was used to assess the effect of varying the frequency of feedback along with the other inverventions, namely, training and goal setting. Statistical analyses were performed through the autoregressive integrated moving average (ARIMA) analysis suitable for such time series data, analysis of variance (ANOVA), and comparison of means through Duncan\u27s multiple range test and Tukey\u27s method for pairwise comparison of means. Based on the results obtained, the following conclusions were arrived at: (1) It is possible to improve performance through a combination of training, goal setting, and feedback as a package of applied behavior analysis. (2) Providing feedback can help improve performance over and above the level achieved with only training and goal setting. (3) It may not be necessary for feedback to be as frequent as possible to sustain a given, desired level of performance. It is possible to sustain a desired level of performance with some optimum feedback frequency which may be less than the most frequent possible. (4) A behavioral approach to safety can complement a conventional, environmental approach in sustaining and enhancing the safety level in an organization

Strategic human resource managament in Malaysian hotels: formulation and implementation challenges

This research explores the challenges faced by hotels in Malaysia, in formulating and implementing strategic human resource management (SHRM). The study addresses the lack of empirical research into SHRM in Malaysian hotels at a time of rapid growth in the Malaysian tourism industry. Building on current debates regarding strategic HRM, including SHRM and business strategy integration, and the role of HR as a strategic partner, this research explores the relationship between human resource management and business strategies, and the challenges of HRM strategy realisation. The thesis has a particular focus on Recruitment and Selection, and Training and Development, as these two functions lie at the heart of how businesses access and develop the critical skills required to implement SHRM initiatives. The study is conducted from a constructivist ontological stance coupled with an interpretivist epistemology. A set of three semi-structured interviews, involving the Chief Executive Officer, HR professional and line manager, were conducted in five leading hotels. Three additional interviews were conducted to gain feedback on the study’s topic from individuals with HR and/or hotel industry expertise. Data were analysed using a priori and data driven coding following King’s (2004) template analysis method. This research reveals challenges in formulating and implementing strategic HRM exist within Malaysian hotels from three analytical levels, namely, organisational, industry and societal. The challenges include the readiness of HR as a strategic partner, the absence of clearly-defined HR-related key performance indicators, labour scarcity, and government policies relating to labour and education. Although this exploratory research may not be generalisable to all Malaysian hotels, its insights into SHRM challenges may be transferable to other similar hotels and resorts. Discussion of the practical implications of the study’s results highlight the actions recommended as necessary for the three target audiences, namely, Hotel Managers (which include CEOs/General Managers, HR professionals and line managers), the Malaysian Association of Hotels, and the Government, to improve professional practice pertaining to strategic human resource management in Malaysian hotels

Comparative Analysis of Energy Efficient Clustering Protocol in Wireless Sensor Networks

The clustering based protocols are the best for the heterogeneous wireless sensor networks because they perform the work on divide and conquer rule. In this study, the mainly focus is on the cluster head selection using tabu search in energy efficient clustering protocol. Due to limited energy in sensor nodes, the networkis not stable. For this, many protocols has been proposed so far to improve the energy efficiency .This paper presents the comparative analysis of REAC-IN protocol with Tabu based REAC-IN protocol in terms of alive nodes, energy variance and data received to the sink in bytes. The simulation results show that tabu based REAC-IN protocol performs better instead of REAC-IN protoco