Fedor Duzhin - Academia.edu (original) (raw)

Papers by Fedor Duzhin

Big data and cognitive computing, Jul 5, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Uspehi matematičeskih nauk, 1998

ICERI proceedings, Nov 1, 2019

Education Sciences, Jan 10, 2018

Course instructors need to assess the efficacy of their teaching methods, but experiments in educ... more Course instructors need to assess the efficacy of their teaching methods, but experiments in education are seldom politically, administratively, or ethically feasible. Quasi-experimental tools, on the other hand, are often problematic, as they are typically too complicated to be of widespread use to educators and may suffer from selection bias occurring due to confounding variables such as students' prior knowledge. We developed a machine learning algorithm that accounts for students' prior knowledge. Our algorithm is based on symbolic regression that uses non-experimental data on previous scores collected by the university as input. It can predict 60-70 percent of variation in students' exam scores. Applying our algorithm to evaluate the impact of teaching methods in an ordinary differential equations class, we found that clickers were a more effective teaching strategy as compared to traditional handwritten homework; however, online homework with immediate feedback was found to be even more effective than clickers. The novelty of our findings is in the method (machine learning-based analysis of non-experimental data) and in the fact that we compare the effectiveness of clickers and handwritten homework in teaching undergraduate mathematics. Evaluating the methods used in a calculus class, we found that active team work seemed to be more beneficial for students than individual work. Our algorithm has been integrated into an app that we are sharing with the educational community, so it can be used by practitioners without advanced methodological training.

International Journal of Mobile Learning and Organisation, 2023

COVID-19 and remote learning have accelerated online collaboration. Capturing online collaboratio... more COVID-19 and remote learning have accelerated online collaboration. Capturing online collaboration in terms of quantitative and qualitative description of students' interaction to achieve learning outcomes remains a challenge. We introduce a framework for describing and visualising students' interactions in WhatsApp group chat. We present five studies (N = 123, N = 64, N = 106, N = 55, N = 46) in courses taken by mathematics and business students. We found that mathematics students wrote more messages and shorter messages than business students. We also found that average number of words per message correlated with the project mark positively in mathematics but negatively in business courses. We suggest a way to visualise a WhatsApp chat as a network and tested the hypothesis that the centralisation coefficient of this network correlated negatively with the project score. The hypothesis was not confirmed. Implications and suggestions for further study are presented.

Journal of Mathematical Sciences, Oct 1, 2006

Dalton Transactions, 2017

Complex [Cp*Ru(NCMe)3][PF6], 1a, has been identified as a cis-to-trans isomerization catalyst of ... more Complex [Cp*Ru(NCMe)3][PF6], 1a, has been identified as a cis-to-trans isomerization catalyst of various non-conjugated cis-polyalkenes under exceptional kinetic control as no alkene conjugation was observed.

arXiv (Cornell University), Apr 6, 2019

The "free rider" problem has long plagued pedagogies based on collaborative learning. The most co... more The "free rider" problem has long plagued pedagogies based on collaborative learning. The most common solution to the free rider problem is peer evaluation. As well other existing methods of peer evaluation include self-evaluation-and hence are prone to grade inflation or, as we show here, are inaccurate in that they do not fairly reward the most hard working student. Another common concern with existing methods of peer evaluation is that students often do not have the necessary skills to evaluate the work of their peers objectively. In this paper, we introduce a new mechanism for peer evaluation that does not rely on self-evaluation, and yet remains accurate, i.e., if all students are completely truthful in their evaluations, then the output of our mechanism becomes an objective truth. At the same time, our mechanism integrates the instructor's judgment with respect to the credibility of students' evaluations. For example, the instructor gives scores to students for writing credible reviews and, in turn, subsequent students' evaluations are weighted according to these instructor scores.

The theory of generic smooth closed plane curves initiated by Vladimir Arnold is a beautiful fusi... more The theory of generic smooth closed plane curves initiated by Vladimir Arnold is a beautiful fusion of topology, combinatorics, and analysis. The theory remains fairly undeveloped. We review existing methods to describe generic smooth closed plane curves combinatorially, introduce a new one, and give an algorithm for efficient computation of Arnold's invariants. Our results provide a good source of future research projects that involve computer experiments with plane curves. The reader is not required to have background in topology and even undergraduate students with basic knowledge of differential geometry and graph theory will easily understand our paper.

arXiv (Cornell University), Apr 11, 2006

We consider the most general case when the billiard ball reflects from an arbitrary submanifold o... more We consider the most general case when the billiard ball reflects from an arbitrary submanifold of a Euclidean space. We prove Morse inequalities in this situation and apply them to find a lower estimate for the number of closed billiard trajectories of any prime period in terms of Betti numbers of the given manifold.

arXiv (Cornell University), Dec 18, 2001

In this paper the problem of estimating the number of periodical billiard trajectories is conside... more In this paper the problem of estimating the number of periodical billiard trajectories is considered. The main result is the theorem on Morse theory for periodical billiard trajectories.

Journal of Knot Theory and Its Ramifications, Mar 1, 2021

Finding homotopy group of spheres is an old open problem in topology. Berrick et al. derive in [A... more Finding homotopy group of spheres is an old open problem in topology. Berrick et al. derive in [A. J. Berrick, F. Cohen, Y. L. Wong and J. Wu, Configurations, braids, and homotopy groups, J. Amer. Math. Soc. 19 (2006)] an exact sequence that relates Brunnian braids to homotopy groups of spheres. We give an interpretation of this exact sequence based on the combed form for braids over the sphere developed in [R. Gillette and J. V. Buskirk, The word problem and consequences for the braid groups and mapping class groups of the two-sphere, Trans. Amer. Math. Soc. 131 (1968) 277–296] with the aim of helping one to visualize the sequence and to do calculations based on it.

Journal of Knot Theory and Its Ramifications, Mar 1, 2014

Brunnian links and braids are those that become trivial upon removing any of the components. It i... more Brunnian links and braids are those that become trivial upon removing any of the components. It is well known that any link is the closure of some braid. However, a Brunnian link might not be the closure of any Brunnian braid. In this paper, we present two methods of constructing Brunnian links from Brunnian braids and show that our methods do result in Brunnian links that cannot be obtained as the closure of a Brunnian braid.

arXiv (Cornell University), Dec 18, 2001

International Journal of Mobile Learning and Organisation

Big Data and Cognitive Computing

Topological data analysis has recently found applications in various areas of science, such as co... more Topological data analysis has recently found applications in various areas of science, such as computer vision and understanding of protein folding. However, applications of topological data analysis to natural language processing remain under-researched. This study applies topological data analysis to a particular natural language processing task: fake news detection. We have found that deep learning models are more accurate in this task than topological data analysis. However, assembling a deep learning model with topological data analysis significantly improves the model’s accuracy if the available training set is very small.

Journal of Knot Theory and Its Ramifications, 2014

Brunnian links and braids are those that become trivial upon removing any of the components. It i... more Brunnian links and braids are those that become trivial upon removing any of the components. It is well known that any link is the closure of some braid. However, a Brunnian link might not be the closure of any Brunnian braid. In this paper, we present two methods of constructing Brunnian links from Brunnian braids and show that our methods do result in Brunnian links that cannot be obtained as the closure of a Brunnian braid.

Успехи математических наук, 1998

Eprint Arxiv Math 0604236, Apr 11, 2006

Big data and cognitive computing, Jul 5, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Uspehi matematičeskih nauk, 1998

ICERI proceedings, Nov 1, 2019

Education Sciences, Jan 10, 2018

Course instructors need to assess the efficacy of their teaching methods, but experiments in educ... more Course instructors need to assess the efficacy of their teaching methods, but experiments in education are seldom politically, administratively, or ethically feasible. Quasi-experimental tools, on the other hand, are often problematic, as they are typically too complicated to be of widespread use to educators and may suffer from selection bias occurring due to confounding variables such as students' prior knowledge. We developed a machine learning algorithm that accounts for students' prior knowledge. Our algorithm is based on symbolic regression that uses non-experimental data on previous scores collected by the university as input. It can predict 60-70 percent of variation in students' exam scores. Applying our algorithm to evaluate the impact of teaching methods in an ordinary differential equations class, we found that clickers were a more effective teaching strategy as compared to traditional handwritten homework; however, online homework with immediate feedback was found to be even more effective than clickers. The novelty of our findings is in the method (machine learning-based analysis of non-experimental data) and in the fact that we compare the effectiveness of clickers and handwritten homework in teaching undergraduate mathematics. Evaluating the methods used in a calculus class, we found that active team work seemed to be more beneficial for students than individual work. Our algorithm has been integrated into an app that we are sharing with the educational community, so it can be used by practitioners without advanced methodological training.

International Journal of Mobile Learning and Organisation, 2023

COVID-19 and remote learning have accelerated online collaboration. Capturing online collaboratio... more COVID-19 and remote learning have accelerated online collaboration. Capturing online collaboration in terms of quantitative and qualitative description of students' interaction to achieve learning outcomes remains a challenge. We introduce a framework for describing and visualising students' interactions in WhatsApp group chat. We present five studies (N = 123, N = 64, N = 106, N = 55, N = 46) in courses taken by mathematics and business students. We found that mathematics students wrote more messages and shorter messages than business students. We also found that average number of words per message correlated with the project mark positively in mathematics but negatively in business courses. We suggest a way to visualise a WhatsApp chat as a network and tested the hypothesis that the centralisation coefficient of this network correlated negatively with the project score. The hypothesis was not confirmed. Implications and suggestions for further study are presented.

Journal of Mathematical Sciences, Oct 1, 2006

Dalton Transactions, 2017

Complex [Cp*Ru(NCMe)3][PF6], 1a, has been identified as a cis-to-trans isomerization catalyst of ... more Complex [Cp*Ru(NCMe)3][PF6], 1a, has been identified as a cis-to-trans isomerization catalyst of various non-conjugated cis-polyalkenes under exceptional kinetic control as no alkene conjugation was observed.

arXiv (Cornell University), Apr 6, 2019

The "free rider" problem has long plagued pedagogies based on collaborative learning. The most co... more The "free rider" problem has long plagued pedagogies based on collaborative learning. The most common solution to the free rider problem is peer evaluation. As well other existing methods of peer evaluation include self-evaluation-and hence are prone to grade inflation or, as we show here, are inaccurate in that they do not fairly reward the most hard working student. Another common concern with existing methods of peer evaluation is that students often do not have the necessary skills to evaluate the work of their peers objectively. In this paper, we introduce a new mechanism for peer evaluation that does not rely on self-evaluation, and yet remains accurate, i.e., if all students are completely truthful in their evaluations, then the output of our mechanism becomes an objective truth. At the same time, our mechanism integrates the instructor's judgment with respect to the credibility of students' evaluations. For example, the instructor gives scores to students for writing credible reviews and, in turn, subsequent students' evaluations are weighted according to these instructor scores.

The theory of generic smooth closed plane curves initiated by Vladimir Arnold is a beautiful fusi... more The theory of generic smooth closed plane curves initiated by Vladimir Arnold is a beautiful fusion of topology, combinatorics, and analysis. The theory remains fairly undeveloped. We review existing methods to describe generic smooth closed plane curves combinatorially, introduce a new one, and give an algorithm for efficient computation of Arnold's invariants. Our results provide a good source of future research projects that involve computer experiments with plane curves. The reader is not required to have background in topology and even undergraduate students with basic knowledge of differential geometry and graph theory will easily understand our paper.

arXiv (Cornell University), Apr 11, 2006

We consider the most general case when the billiard ball reflects from an arbitrary submanifold o... more We consider the most general case when the billiard ball reflects from an arbitrary submanifold of a Euclidean space. We prove Morse inequalities in this situation and apply them to find a lower estimate for the number of closed billiard trajectories of any prime period in terms of Betti numbers of the given manifold.

arXiv (Cornell University), Dec 18, 2001

In this paper the problem of estimating the number of periodical billiard trajectories is conside... more In this paper the problem of estimating the number of periodical billiard trajectories is considered. The main result is the theorem on Morse theory for periodical billiard trajectories.

Journal of Knot Theory and Its Ramifications, Mar 1, 2021

Finding homotopy group of spheres is an old open problem in topology. Berrick et al. derive in [A... more Finding homotopy group of spheres is an old open problem in topology. Berrick et al. derive in [A. J. Berrick, F. Cohen, Y. L. Wong and J. Wu, Configurations, braids, and homotopy groups, J. Amer. Math. Soc. 19 (2006)] an exact sequence that relates Brunnian braids to homotopy groups of spheres. We give an interpretation of this exact sequence based on the combed form for braids over the sphere developed in [R. Gillette and J. V. Buskirk, The word problem and consequences for the braid groups and mapping class groups of the two-sphere, Trans. Amer. Math. Soc. 131 (1968) 277–296] with the aim of helping one to visualize the sequence and to do calculations based on it.

Journal of Knot Theory and Its Ramifications, Mar 1, 2014

Brunnian links and braids are those that become trivial upon removing any of the components. It i... more Brunnian links and braids are those that become trivial upon removing any of the components. It is well known that any link is the closure of some braid. However, a Brunnian link might not be the closure of any Brunnian braid. In this paper, we present two methods of constructing Brunnian links from Brunnian braids and show that our methods do result in Brunnian links that cannot be obtained as the closure of a Brunnian braid.

arXiv (Cornell University), Dec 18, 2001

International Journal of Mobile Learning and Organisation

Big Data and Cognitive Computing

Topological data analysis has recently found applications in various areas of science, such as co... more Topological data analysis has recently found applications in various areas of science, such as computer vision and understanding of protein folding. However, applications of topological data analysis to natural language processing remain under-researched. This study applies topological data analysis to a particular natural language processing task: fake news detection. We have found that deep learning models are more accurate in this task than topological data analysis. However, assembling a deep learning model with topological data analysis significantly improves the model’s accuracy if the available training set is very small.

Journal of Knot Theory and Its Ramifications, 2014

Brunnian links and braids are those that become trivial upon removing any of the components. It i... more Brunnian links and braids are those that become trivial upon removing any of the components. It is well known that any link is the closure of some braid. However, a Brunnian link might not be the closure of any Brunnian braid. In this paper, we present two methods of constructing Brunnian links from Brunnian braids and show that our methods do result in Brunnian links that cannot be obtained as the closure of a Brunnian braid.

Успехи математических наук, 1998

Eprint Arxiv Math 0604236, Apr 11, 2006