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Improving the explainability of results from machine learning methods has become an important research goal. In this thesis, we have studied the problem of making clusters more interpretable using a recent approach by Davidson et al., and Sambaturu et al., based on succinct representations of clusters. Given a set of objects S, a partition of S (into clusters), and a universe T of descriptors such that each element in S is associated with a subset of descriptors, the goal is to find a representative set of descriptors for each cluster such that those sets are pairwise-disjoint and the total size of all the representatives is at most a given budget. Since this problem is NP-hard in general, Sambaturu et al. have developed a suite of approximation algorithms for the problem. We also show applications to explain clusters of genomic sequences that represent different threat levels / Master of Science / Improving the explainability of results from machine learning methods has become an important research goal. Clustering is a commonly used Machine Learning technique which is performed on a variety of datasets. In this thesis, we have studied the problem of making clusters more interpretable; and have tried to answer whether it is possible to explain clusters using a set of attributes which were not used while generating these clusters.

Adverse maternal events around the time of conception influence embryonic development. Thus, aberrations in the uterine environment during early pregnancy, such as those resulting from maternal metabolic or nutritional disruption, can alter gene expression in the developing embryo, leading to variations in its developmental trajectory. Dietary supplementation of long-chain omega-3 polyunsaturated fatty acids (LCPUFA), especially Docosahexaenoic acid (DHA) improves metabolic and reproductive health across species. The objective of this study was to evaluate the effects of peri-conceptual LCPUFA supplementation on endometrial gene expression, uterine health and embryonic gene expression in overweight horses. Thirteen non-lactating light horse mares (mean ± SEM age=13.56±0.11 yr; mean ± SEM BCS=7.07±0.21) were supplemented with concentrate (n=6) or an isocaloric diet containing 0.06 g/kg BW algae-derived omega-3 LCPUFA (n=7) beginning 60 d prior to sample collection. Four consecutive ovulatory cycles were monitored, and uterine endometrial samples were obtained 12 d post-ovulation in cycles 1, 3 and 4. Mares were bred and embryos were flushed 12 d post ovulation 2,3 and 4. Endometrial biopsies obtained from supplemented mares contained increased DHA and omega-3 fatty acids as a percent of total fat (P< 0.05). Endometrial biopsy scores were assigned to endometrial tissues and mares receiving the LCPUFA supplementation had improved scores during the first ovulatory period as compared to control animals (P=0.009). Candidate genes essential to inflammation, prostaglandin synthesis and embryonic development were evaluated by quantitative reverse transcriptase polymerase chain reaction. Data were log transformed and analyzed using the GLM procedure in SAS (v9.3). When examining the data independent of breeding and pregnancy status, endometrial obtained samples from LCPUFA supplemented mares contained reduced IL6 (P= 0.04) and TNFa (P=0.03) mRNA abundance and tended to have increased transcript abundance for Uterocalin (P= 0.09), SAA (P= 0.06) and IL10 (P= 0.06). Endometrial samples from mares fed LCPUFA pregnant in cycle 3 contained greater IL10 (P< 0.001), PTGFS (P=0.05), OXTR (P=0.05) and PLA2G3 mRNA (P= 0.009) and had a tendency for increased SAA (P= 0.08), PTGES (P=0.10) and SLCO2A1 (P=0.10) mRNA abundance. Supplemented mares bred but not pregnant at day 12 in cycle 3 had reduced expression of PTGER2 (P=0.001) and PTGS1 (P= <0.001) in endometrial samples. In embryos obtained post ovulatory cycle 3 and 4, relative transcript abundance of GATA4 and GATA6, markers of endoderm differentiation, along with GATA3 and ELF3, markers of trophectoderm differentiation were greater (P< 0.05) in embryos from LCPUFA supplemented mares (n=5), than controls (n=5). These results indicate that algae-derived LCPUFA supplementation during the peri-conceptual period alters the post-ovulatory uterine environment in the horse by modifying expression of genes related to inflammation and regulating prostaglandin synthesis. Additionally, embryos obtained from supplemented mares displayed differential gene expression related to embryonic lineage specification. / Ph. D.

SNCF is a large-sized railway transportation company that needs to be operated 365 days a year and 24 hours a day. In order to schedule a certain category of workers in train stations and selling points, rosters are designed to cover a cyclical demand. However, the highly combinatorial nature of the rostering problem makes it very difficult to solve manually, and experts spend a huge amount of time to derive implementable solutions that improve a number of preference criteria. This thesis presents two formulations based on mixed-integer programming to adress the cyclical rostering problem. The first one uses variables to express the nature of each day of the roster, whereas the second one uses patterns corresponding to feasible blocks of seven days and assigns them to each week of the roster. Different strategies relative to the management of some preference criteria are compared, some of them leading to significant reductions in computational times. Cuts are finally introduced to improve the bounds obtained by the linear relaxation of the mixed-integer programs. The impact of these cuts on computational times depends much on the problem. / Master of Science

Constructs for functional and logic programming can be smoothly integrated into an existing object-oriented language. We demonstrate this in the context of C++ (a statically-typed object-oriented language with effects and parametric polymorphism) via two libraries: FC++ and LC++. FC++ is a library for functional programming in C++; FC++ supports higher-order polymorphic functions, lazy lists, and a small lambda language; it also contains a large library of useful functions, datatypes, combinators, and monads. LC++ is a library for logic programming in C++; LC++ provides the same general functionality as Prolog, including the ability to return query results lazily (one at a time). Both libraries are embedded in C++ so that they share C++'s static type system, and the library interfaces provide straightforward ways for code from within one paradigm to ``call out' to another. Our work describes the techniques used to implement these libraries in C++ and shows that the resulting multiparadigm language has useful applications in real-world domains. We also describe how many of the implementation techniques can be generalized from C++ and applied to other programming languages to yield similar results.