Towards an artificial intelligence-based agent for characterising the organisation of primes
- Authors: Oyetunji, Nicole Armlade
- Date: 2024-04-04
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/435389 , vital:73153
- Description: Machine learning has experienced significant growth in recent decades, driven by advancements in computational power and data storage. One of the applications of machine learning is in the field of number theory. Prime numbers hold significant importance in mathematics and its applications, for example in cryptography, owing to their distinct properties. Therefore, it is crucial to efficiently obtain the complete list of primes below a given threshold, with low relatively computational cost. This study extensively explores a deterministic scheme, proposed by Hawing and Okouma (2016), that is centered around Consecutive Composite Odd Numbers, showing the link between these numbers and prime numbers by examining their internal structure. The main objective of this dissertation is to develop two main artificial intelligence agents capable of learning and recognizing patterns within a list of consecutive composite odd numbers. To achieve this, the mathematical foundations of the deterministic scheme are used to generate a dataset of consecutive composite odd numbers. This dataset is further transformed into a dataset of differences to simplify the prediction problem. A literature review is conducted which encompasses research from the domains of machine learning and deep learning. Two main machine learning algorithms are implemented along with their variations, Long Short-Term Memory Networks and Error Correction Neural Networks. These models are trained independently on two separate but related datasets, the dataset of consecutive composite odd numbers and the dataset of differences between those numbers. The evaluation of these models includes relevant metrics, for example, Root Mean Square Error, Mean Absolute Percentage Error, Theil U coefficient, and Directional Accuracy. Through a comparative analysis, the study identifies the top-performing 3 models, with a particular emphasis on accuracy and computational efficiency. The results indicate that the LSTM model, when trained on difference data and coupled with exponential smoothing, displays superior performance as the most accurate model overall. It achieves a RMSE of 0.08, which significantly outperforms the dataset’s standard deviation of 0.42. This model exceeds the performance of basic estimator models, implying that a data-driven approach utilizing machine learning techniques can provide valuable insights in the field of number theory. The second best model, the ECNN trained on difference data combined with exponential smoothing, achieves an RMSE of 0.28. However, it is worth mentioning that this model is the most computationally efficient, being 32 times faster than the LSTM model. , Thesis (MSc) -- Faculty of Science, Mathematics, 2024
- Full Text:
- Date Issued: 2024-04-04
- Authors: Oyetunji, Nicole Armlade
- Date: 2024-04-04
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/435389 , vital:73153
- Description: Machine learning has experienced significant growth in recent decades, driven by advancements in computational power and data storage. One of the applications of machine learning is in the field of number theory. Prime numbers hold significant importance in mathematics and its applications, for example in cryptography, owing to their distinct properties. Therefore, it is crucial to efficiently obtain the complete list of primes below a given threshold, with low relatively computational cost. This study extensively explores a deterministic scheme, proposed by Hawing and Okouma (2016), that is centered around Consecutive Composite Odd Numbers, showing the link between these numbers and prime numbers by examining their internal structure. The main objective of this dissertation is to develop two main artificial intelligence agents capable of learning and recognizing patterns within a list of consecutive composite odd numbers. To achieve this, the mathematical foundations of the deterministic scheme are used to generate a dataset of consecutive composite odd numbers. This dataset is further transformed into a dataset of differences to simplify the prediction problem. A literature review is conducted which encompasses research from the domains of machine learning and deep learning. Two main machine learning algorithms are implemented along with their variations, Long Short-Term Memory Networks and Error Correction Neural Networks. These models are trained independently on two separate but related datasets, the dataset of consecutive composite odd numbers and the dataset of differences between those numbers. The evaluation of these models includes relevant metrics, for example, Root Mean Square Error, Mean Absolute Percentage Error, Theil U coefficient, and Directional Accuracy. Through a comparative analysis, the study identifies the top-performing 3 models, with a particular emphasis on accuracy and computational efficiency. The results indicate that the LSTM model, when trained on difference data and coupled with exponential smoothing, displays superior performance as the most accurate model overall. It achieves a RMSE of 0.08, which significantly outperforms the dataset’s standard deviation of 0.42. This model exceeds the performance of basic estimator models, implying that a data-driven approach utilizing machine learning techniques can provide valuable insights in the field of number theory. The second best model, the ECNN trained on difference data combined with exponential smoothing, achieves an RMSE of 0.28. However, it is worth mentioning that this model is the most computationally efficient, being 32 times faster than the LSTM model. , Thesis (MSc) -- Faculty of Science, Mathematics, 2024
- Full Text:
- Date Issued: 2024-04-04
Taxonomic revision of the Natal mountain catfish, Amphilius natalensis (Siluriformes, Amphiliidae) in southern Africa
- Mazungula, Daniel Nkosinathi
- Authors: Mazungula, Daniel Nkosinathi
- Date: 2020
- Subjects: Uncatalogued
- Language: English
- Type: thesis , text , Masters , MSc
- Identifier: http://hdl.handle.net/10962/164490 , vital:41123
- Description: Thesis (MSc)--Rhodes University, Department of Ichthyology and Fisheries Science, 2020
- Full Text:
- Date Issued: 2020
- Authors: Mazungula, Daniel Nkosinathi
- Date: 2020
- Subjects: Uncatalogued
- Language: English
- Type: thesis , text , Masters , MSc
- Identifier: http://hdl.handle.net/10962/164490 , vital:41123
- Description: Thesis (MSc)--Rhodes University, Department of Ichthyology and Fisheries Science, 2020
- Full Text:
- Date Issued: 2020
Human FN1 is regulated by the heat-shock response
- Authors: Dhanani, Karim Colin Hassan
- Date: 2015
- Subjects: Uncatalogued
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/193487 , vital:45336
- Description: Heat shock protein 90 (Hsp90) and heat shock factors (HSFs) are known to be involved in the epigenetic regulation of several fundamental oncogenic genes. Fibronectin (FN) is an extracellular matrix (ECM) glycoprotein which plays key roles in cell adhesion and migration. Hsp90 binds directly to FN and Hsp90 inhibition has been shown to regulate FN protein levels and matrix formation. Where inhibition of Hsp90 with a C-terminal inhibitor (novobiocin) induced the loss of FN matrix, treatment with an N-terminal inhibitor (geldanamycin) increased FN matrix levels. GA treatment induced a strong dose and time dependent increase in FN1 promoter activity and increased total FN mRNA respectively. By contrast, NOV showed no increase in the promoter activity and no change in the expression of FN mRNA. As GA is known to induce the stress response, we investigated the relationship between the cell stress machinery and the transcriptional regulation of FN. Three putative heat shock elements (HSEs) were identified in the FN1 promoter. The loss of two of the three identified putative HSEs resulted in a loss in the basal transcriptional activity of the FN1 promoter in our reporter model. This was in addition to the loss of the induction of transcriptional activity with GA treatment observed with the full-length promoter. Binding of HSF1 to one of the putative HSEs, which was identified as potentially functional from the truncation analysis, was confirmed using ChIP. The occupancy of this HSE by HSF1 was shown to increase with GA treatment. These data support the hypothesis that FN1 is a functional HSF1 target gene. The 5' promoter regions of seven additional ECM protein encoding genes were analysed and mRNA levels were detected by quantitative RT-PCR upon treatment with GA. Collagen 4 _2 and laminin _3 mRNA were found to increase in the presence of GA, whereas collagen 4 _3 and osteopontin showed no change. Similarly to FN1, these data indicate that a subset of ECM genes may be under the regulation of the HSF1 mediated heat-shock response. This may have implications for our understanding of ECM dynamics in cancer, where the clinical application of Hsp90 inhibitors is intended. Additionally, our data provide a poten- tial underpinning for the role of the HSF1 mediated heat-shock response in several fibrotic and metabolic stress related pathologies. , Thesis (PhD) -- Faculty of Science, Biochemistry and Microbiology, 2015
- Full Text:
- Date Issued: 2015
- Authors: Dhanani, Karim Colin Hassan
- Date: 2015
- Subjects: Uncatalogued
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/193487 , vital:45336
- Description: Heat shock protein 90 (Hsp90) and heat shock factors (HSFs) are known to be involved in the epigenetic regulation of several fundamental oncogenic genes. Fibronectin (FN) is an extracellular matrix (ECM) glycoprotein which plays key roles in cell adhesion and migration. Hsp90 binds directly to FN and Hsp90 inhibition has been shown to regulate FN protein levels and matrix formation. Where inhibition of Hsp90 with a C-terminal inhibitor (novobiocin) induced the loss of FN matrix, treatment with an N-terminal inhibitor (geldanamycin) increased FN matrix levels. GA treatment induced a strong dose and time dependent increase in FN1 promoter activity and increased total FN mRNA respectively. By contrast, NOV showed no increase in the promoter activity and no change in the expression of FN mRNA. As GA is known to induce the stress response, we investigated the relationship between the cell stress machinery and the transcriptional regulation of FN. Three putative heat shock elements (HSEs) were identified in the FN1 promoter. The loss of two of the three identified putative HSEs resulted in a loss in the basal transcriptional activity of the FN1 promoter in our reporter model. This was in addition to the loss of the induction of transcriptional activity with GA treatment observed with the full-length promoter. Binding of HSF1 to one of the putative HSEs, which was identified as potentially functional from the truncation analysis, was confirmed using ChIP. The occupancy of this HSE by HSF1 was shown to increase with GA treatment. These data support the hypothesis that FN1 is a functional HSF1 target gene. The 5' promoter regions of seven additional ECM protein encoding genes were analysed and mRNA levels were detected by quantitative RT-PCR upon treatment with GA. Collagen 4 _2 and laminin _3 mRNA were found to increase in the presence of GA, whereas collagen 4 _3 and osteopontin showed no change. Similarly to FN1, these data indicate that a subset of ECM genes may be under the regulation of the HSF1 mediated heat-shock response. This may have implications for our understanding of ECM dynamics in cancer, where the clinical application of Hsp90 inhibitors is intended. Additionally, our data provide a poten- tial underpinning for the role of the HSF1 mediated heat-shock response in several fibrotic and metabolic stress related pathologies. , Thesis (PhD) -- Faculty of Science, Biochemistry and Microbiology, 2015
- Full Text:
- Date Issued: 2015
Tectonic and structural aspects at the Otjihase Mine, Matchless Belt, Namibia: A Systematic Review
- Authors: Hartmann, K
- Date: 1995-04
- Subjects: Uncatalogued
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/190232 , vital:44976
- Description: The Otjihase pyritic massive sulphide deposit occurs within a 10km thick metasedimentary sequence of the Kuiseb Formation. The Kuiseb metasediments were deposited within the Khomas Trough, which forms the southernmost rift of the intracontinental arm of the Damara orogen. Amphibolite units of the Matchless member at Otjihase have a MORB-type geochemical character and occur within the Kuiseb schists, about 200m above the ore zone. The Otjihase mine is the largest of many Besshi-type deposits that occur in close proximity to the Matchless amphibolites. A depositional environment in a rift, slightly more advanced than the present-day Red Sea is envisaged. The five parallel, ruler-shaped, mineralised shoots at Otjihase occur on the same stratigraphic level. They have a plunge of approximately 6° to the west and a dip of approximately 16° to the northwest. The largest and best mineralised, is the northernmost shoot (the Main Shoot) which is ±250m wide, up to 12m thick and has a known length of 7,5km. The large length/breadth ratio is ascribed to the original setting along faults and thickening of the ore zone during thrusting. Intense ductile deformation has affected the ore bodies, with isoclinal refolding, boudinaging, duplexes of more competent bands and smearing of the schists. Squeezing and remobilisation of the sulphides into the schistosity and low pressure pods has taken place. Successive folding and thrusting during the D2 deformational event resulted in the dominant structural style. Fold axes of drag folds plot onto a great circle in stereographic projection, indicating the formation of sheath folds. The axial planar cleavages of competent layers is steeper than the S(0,1) foliation and suggests a structural right way-up. The presence of chloritic alteration above the ore shoots, is suggestive of footwall alteration indicating that the sequence was overturned during the D1 deformational event. Ore zone lithologies include stringery-, massive- and semi-massive sulphides, mineralised magnetite- quartzites and disseminated sulphide mineralisation within quartz-biotite-chlorite schists. Chalcopyrite is the main economic mineral and mainly occurs as matrix to pyrite and in coarse-grained pods. Lithological and metal zoning within the Main Shoot is distinct and is an indication that the macroscopic shape of the orebody is largely unaffected by later ductile deformation. North-south trending normal faults of the Windhoek Graben have disrupted the continuity of the ore shoots. In section, the faults appear to have a listric shape. The major faults have pronounced scissor movements and as a result the dips of the blocks within fault zones are affected. , Thesis (MSc) -- Faculty of Science, Exploration Geology, 2021
- Full Text:
- Date Issued: 1995-04
- Authors: Hartmann, K
- Date: 1995-04
- Subjects: Uncatalogued
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/190232 , vital:44976
- Description: The Otjihase pyritic massive sulphide deposit occurs within a 10km thick metasedimentary sequence of the Kuiseb Formation. The Kuiseb metasediments were deposited within the Khomas Trough, which forms the southernmost rift of the intracontinental arm of the Damara orogen. Amphibolite units of the Matchless member at Otjihase have a MORB-type geochemical character and occur within the Kuiseb schists, about 200m above the ore zone. The Otjihase mine is the largest of many Besshi-type deposits that occur in close proximity to the Matchless amphibolites. A depositional environment in a rift, slightly more advanced than the present-day Red Sea is envisaged. The five parallel, ruler-shaped, mineralised shoots at Otjihase occur on the same stratigraphic level. They have a plunge of approximately 6° to the west and a dip of approximately 16° to the northwest. The largest and best mineralised, is the northernmost shoot (the Main Shoot) which is ±250m wide, up to 12m thick and has a known length of 7,5km. The large length/breadth ratio is ascribed to the original setting along faults and thickening of the ore zone during thrusting. Intense ductile deformation has affected the ore bodies, with isoclinal refolding, boudinaging, duplexes of more competent bands and smearing of the schists. Squeezing and remobilisation of the sulphides into the schistosity and low pressure pods has taken place. Successive folding and thrusting during the D2 deformational event resulted in the dominant structural style. Fold axes of drag folds plot onto a great circle in stereographic projection, indicating the formation of sheath folds. The axial planar cleavages of competent layers is steeper than the S(0,1) foliation and suggests a structural right way-up. The presence of chloritic alteration above the ore shoots, is suggestive of footwall alteration indicating that the sequence was overturned during the D1 deformational event. Ore zone lithologies include stringery-, massive- and semi-massive sulphides, mineralised magnetite- quartzites and disseminated sulphide mineralisation within quartz-biotite-chlorite schists. Chalcopyrite is the main economic mineral and mainly occurs as matrix to pyrite and in coarse-grained pods. Lithological and metal zoning within the Main Shoot is distinct and is an indication that the macroscopic shape of the orebody is largely unaffected by later ductile deformation. North-south trending normal faults of the Windhoek Graben have disrupted the continuity of the ore shoots. In section, the faults appear to have a listric shape. The major faults have pronounced scissor movements and as a result the dips of the blocks within fault zones are affected. , Thesis (MSc) -- Faculty of Science, Exploration Geology, 2021
- Full Text:
- Date Issued: 1995-04
A phenomenological investigation of the beginning therapist's experience of the first session of psychotherapy with the first patient
- Authors: Allen, Jennifer Ann
- Date: 1987
- Subjects: Uncatalogued
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/193129 , vital:45301
- Description: The aim of this project is to come to an understanding of how the situation of the first session of psychotherapy with the first patient is lived by the beginning therapist and what meaning this situation holds for him. The writer's interest in this phenomenon grew out of her own experience of this situation as a clinical Masters coursework student, an experience which was of important to the writer and meaningful still as a therapist in training. In dialogue with experienced therapists the importance of this situation was again made apparant. It was the opinion of these therapists that although for some the details of this experience had become dulled by time, what remained meaningful to them was that this experience was seen as the beginning of a project which remains important to them - they identified this situation as an important moment in the history of their development as psychotherapists. In the hope that the literature pertaining to psychotherapy would throw some light on this situation, the writer turned to a number of sources in this area to discover that no literature available to her elucidated this situation in a holistic manner. This led the writer to go back to the beginning therapists themselves so that they may speak for themselves of their experience of this situation. A phenomenological method of enquiry is implemented in this study as it renders the subject matter accessible to investigation, and allows it to reveal itself as it essentially is. This project is then an attempt to come to a general description of the beginning therapist's experience of the first session of psychotherapy with the first patient and thus to articulate the structure of the beginning therapist's lived situation (world) in this context. , Thesis (MA) -- Faculty of Humanities, Psychology, 1987
- Full Text:
- Date Issued: 1987
- Authors: Allen, Jennifer Ann
- Date: 1987
- Subjects: Uncatalogued
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/193129 , vital:45301
- Description: The aim of this project is to come to an understanding of how the situation of the first session of psychotherapy with the first patient is lived by the beginning therapist and what meaning this situation holds for him. The writer's interest in this phenomenon grew out of her own experience of this situation as a clinical Masters coursework student, an experience which was of important to the writer and meaningful still as a therapist in training. In dialogue with experienced therapists the importance of this situation was again made apparant. It was the opinion of these therapists that although for some the details of this experience had become dulled by time, what remained meaningful to them was that this experience was seen as the beginning of a project which remains important to them - they identified this situation as an important moment in the history of their development as psychotherapists. In the hope that the literature pertaining to psychotherapy would throw some light on this situation, the writer turned to a number of sources in this area to discover that no literature available to her elucidated this situation in a holistic manner. This led the writer to go back to the beginning therapists themselves so that they may speak for themselves of their experience of this situation. A phenomenological method of enquiry is implemented in this study as it renders the subject matter accessible to investigation, and allows it to reveal itself as it essentially is. This project is then an attempt to come to a general description of the beginning therapist's experience of the first session of psychotherapy with the first patient and thus to articulate the structure of the beginning therapist's lived situation (world) in this context. , Thesis (MA) -- Faculty of Humanities, Psychology, 1987
- Full Text:
- Date Issued: 1987
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