title: Regularisation of neural networks by enforcing Lipschitz continuity

authors: Gouk, Henry

subjects: Science & Technology

abstract: We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant—for multiple p-norms—of a feed forward neural network composed of commonly used layer types. Our technique is then used to formulate training a neural network with a bounded Lipschitz constant as a constrained optimisation problem that can be solved using projected stochastic gradient methods. Our evaluation study shows that the performance of the resulting models exceeds that of models trained with other common regularisers. We also provide evidence that the hyperparameters are intuitive to tune, demonstrate how the choice of norm for computing the Lipschitz constant impacts the resulting model, and show that the performance gains provided by our method are particularly noticeable when only a small amount of training data is available.

text: Regularisation of neural networks by enforcing Lipschitz continuity We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant—for multiple p-norms—of a feed forward neural network composed of commonly used layer types. Our technique is then used to formulate training a neural network with a bounded Lipschitz constant as a constrained optimisation problem that can be solved using projected stochastic gradient methods. Our evaluation study shows that the performance of the resulting models exceeds that of models trained with other common regularisers. We also provide evidence that the hyperparameters are intuitive to tune, demonstrate how the choice of norm for computing the Lipschitz constant impacts the resulting model, and show that the performance gains provided by our method are particularly noticeable when only a small amount of training data is available.

year: 2020

title: Exploring the role of binding surface in enzymatic ligation of modified and synthetic substrates

authors: Dutta, Aakashdeep

subjects: XNA

abstract: Deoxyribonucleic acid (DNA) ligases are essential enzymes that catalyze the formation of phosphodiester bonds to repair nicks in DNA during replication and repair processes. Their ability to ligate synthetic non-canonical nucleic acids (NCNAs), such as unnatural base pairs (UBPs) and backbone-modified DNA/RNA, has significant implications for synthetic biology, biotechnology, and therapeutic applications. This study aimed to evaluate the activity of various DNA ligases on UBP and backbone-modified DNA/RNA substrates, optimize ligation conditions, and explore the relationship between ligase structure and substrate preference.

The study focused on three main objectives: (1) establishing baseline ligation activity for UBP and backbone-modified substrates across multiple ligases, (2) investigating the impact of ligase binding domain size on substrate preference, and (3) optimizing ligation conditions to enhance enzyme activity. A panel of ligases, including Human DNA ligase I, Escherichia coli ligase A, Neisseria gonorrhoeae ligase A, and several ATP-dependent ligases (Lig 3, Lig 4, Lig 5, Lig 12, Lig 15), were tested on substrates containing UBPs (P-Z and S-B systems) and backbone modifications (phosphorothioate (PPT) and 2’-Methoxyethoxy (MOE) RNA).

Results revealed that ligases exhibited varying levels of activity depending on the substrate type and modification position. H-Lig I and Lig 4 demonstrated the highest ligation activity on UBP substrates, particularly those with modifications at the 5’ end of the nick. In contrast, substrates with UBPs on both ends of the nick were poorly tolerated. Gel shift assays confirmed that low ligation activity was not due to binding failure but rather steric hindrance during the adenyl group transfer step. For backbone-modified substrates, Lig 3 and Lig 5 emerged as the most effective, with PPT modifications being better tolerated than MOE modifications. The addition of 10% polyethylene glycol (PEG) 3350 as a crowding agent significantly improved ligation efficiency, particularly for MOE substrates, but inhibited the activity of larger ligases like Lig 12 and H-Lig I.

In conclusion, this study provides valuable insights into the activity of DNA ligases on non-canonical substrates, highlighting the importance of ligase structure and reaction conditions in determining ligation efficiency. The findings contribute to the growing toolbox of synthetic biology and pave the way for further exploration of ligase-substrate interactions, enzyme engineering, and the development of novel biotechnological applications.

text: Exploring the role of binding surface in enzymatic ligation of modified and synthetic substrates Deoxyribonucleic acid (DNA) ligases are essential enzymes that catalyze the formation of phosphodiester bonds to repair nicks in DNA during replication and repair processes. Their ability to ligate synthetic non-canonical nucleic acids (NCNAs), such as unnatural base pairs (UBPs) and backbone-modified DNA/RNA, has significant implications for synthetic biology, biotechnology, and therapeutic applications. This study aimed to evaluate the activity of various DNA ligases on UBP and backbone-modified DNA/RNA substrates, optimize ligation conditions, and explore the relationship between ligase structure and substrate preference.

The study focused on three main objectives: (1) establishing baseline ligation activity for UBP and backbone-modified substrates across multiple ligases, (2) investigating the impact of ligase binding domain size on substrate preference, and (3) optimizing ligation conditions to enhance enzyme activity. A panel of ligases, including Human DNA ligase I, Escherichia coli ligase A, Neisseria gonorrhoeae ligase A, and several ATP-dependent ligases (Lig 3, Lig 4, Lig 5, Lig 12, Lig 15), were tested on substrates containing UBPs (P-Z and S-B systems) and backbone modifications (phosphorothioate (PPT) and 2’-Methoxyethoxy (MOE) RNA).

Results revealed that ligases exhibited varying levels of activity depending on the substrate type and modification position. H-Lig I and Lig 4 demonstrated the highest ligation activity on UBP substrates, particularly those with modifications at the 5’ end of the nick. In contrast, substrates with UBPs on both ends of the nick were poorly tolerated. Gel shift assays confirmed that low ligation activity was not due to binding failure but rather steric hindrance during the adenyl group transfer step. For backbone-modified substrates, Lig 3 and Lig 5 emerged as the most effective, with PPT modifications being better tolerated than MOE modifications. The addition of 10% polyethylene glycol (PEG) 3350 as a crowding agent significantly improved ligation efficiency, particularly for MOE substrates, but inhibited the activity of larger ligases like Lig 12 and H-Lig I.

In conclusion, this study provides valuable insights into the activity of DNA ligases on non-canonical substrates, highlighting the importance of ligase structure and reaction conditions in determining ligation efficiency. The findings contribute to the growing toolbox of synthetic biology and pave the way for further exploration of ligase-substrate interactions, enzyme engineering, and the development of novel biotechnological applications.

year: 2025

title: Tā Pikitia Hei Āwhina Kōrero  Collaborative Drawing and Storying

authors: Kururangi, Aorere Helen Mary

subjects: collaborative drawing and storying

abstract: Creating a Māori medium context for beginning learners of te reo Māori to converse in genuine dialogue, was a real challenge for our mainstream bilingual unit. This study involved six Year 3-5 primary school students working in two groups of three. The bilingual unit is in a contributing school in an urban setting.

The teacher, a second language learner herself, found students seldom initiated any spontaneous Māori dialogue and tended to respond only to questions or formal teacher initiated direction. So the project sought to develop and explore the approach Tā Pikitia hei āwhina kōrero or Collaborative Drawing and Storying, to improve Children's Oral Language Acquisition in Māori, using a socially responsive approach (Glynn, Wearmouth,  Berryman, 2006)
 
This method encouraged students to initiate, respond and share their own learning in a social and interactive community of learners. The method also allowed students the freedom to generate conversations about their own interests, ideas and background experiences without teacher intervention or direction. The only requirement was me kōrero Māori i nga wā katoa (speak Māori all the time). A collaborative picture was created as each group of students quickly illustrated their ideas on a large piece of paper.

 Each student was pre tested and post tested using the Aromatawai Reo A Waha  - Kia Tere Tonu  (Berryman  Langdon, 2001).This test assessed each student's Māori vocabulary knowledge and their ability to speak spontaneously about a familiar item. The daily conversations created by each student group involved Tā Pikitia hei āwhina  kōrero was recorded on tape, then transcribed verbatim each day to assess changes over time. 

 Student ownership of the learning and their positive participation resulted in improved language outcomes. At the end of the ten week period there were encouraging gains in the post test, Aromatawai Reo A Waha - Kīanga or spontaneous phrases students were able to generate. Furthermore an improved ability to focus on an oral task, and improved engagement by the students were unexpected positive outcomes of this easy to implement activity.

text: Tā Pikitia Hei Āwhina Kōrero  Collaborative Drawing and Storying Creating a Māori medium context for beginning learners of te reo Māori to converse in genuine dialogue, was a real challenge for our mainstream bilingual unit. This study involved six Year 3-5 primary school students working in two groups of three. The bilingual unit is in a contributing school in an urban setting.

The teacher, a second language learner herself, found students seldom initiated any spontaneous Māori dialogue and tended to respond only to questions or formal teacher initiated direction. So the project sought to develop and explore the approach Tā Pikitia hei āwhina kōrero or Collaborative Drawing and Storying, to improve Children's Oral Language Acquisition in Māori, using a socially responsive approach (Glynn, Wearmouth,  Berryman, 2006)
 
This method encouraged students to initiate, respond and share their own learning in a social and interactive community of learners. The method also allowed students the freedom to generate conversations about their own interests, ideas and background experiences without teacher intervention or direction. The only requirement was me kōrero Māori i nga wā katoa (speak Māori all the time). A collaborative picture was created as each group of students quickly illustrated their ideas on a large piece of paper.

 Each student was pre tested and post tested using the Aromatawai Reo A Waha  - Kia Tere Tonu  (Berryman  Langdon, 2001).This test assessed each student's Māori vocabulary knowledge and their ability to speak spontaneously about a familiar item. The daily conversations created by each student group involved Tā Pikitia hei āwhina  kōrero was recorded on tape, then transcribed verbatim each day to assess changes over time. 

 Student ownership of the learning and their positive participation resulted in improved language outcomes. At the end of the ten week period there were encouraging gains in the post test, Aromatawai Reo A Waha - Kīanga or spontaneous phrases students were able to generate. Furthermore an improved ability to focus on an oral task, and improved engagement by the students were unexpected positive outcomes of this easy to implement activity.

year: 2008