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Phone: 819-822-9600 ext. 2740 Email: madjid.allili@ubishops.ca ## Research

## Publications

### Computational Topology

### Image Processing

### Dynamical Systems

My research activities are in the areas of computational topology and imaging science. In the domain of computational topology, my research objectives are to develop efficient algorithms for

- the computation of topological invariants and structures such as the homologies and cohomologies of spaces and maps, and
- the computation, the characterization, and the representation of critical points and critical regions in scalar and vector fields by means of Morse theory and Conely index theory.

Topological invariants such as homology have been used recently in a wide variety of applications in domains such as dynamical systems, and image processing and recognition. In dynamics, typical problems are translated into problems in topology where invariants such as the Conley index are computed using homology algorithms. In digital image analysis, topological invariants are useful in shape description, indexation, and classification. Scalar and vector fields are used to represent data in different applications areas like geographic information systems and the charaterization of the critical points of the data constitutes a fundamental technique for the study of the important features of the data and its visualization. Other areas of applications include computer graphics, computer aided-design (CAD) and electrical engineering to name but a few. The necessity of improved algorithms for the computation of the structures mentioned above appears evident as new applications of computational topology arise in research for very large data sets. Although several algorithms and software packages have been developed for this purpose, there is still a lot of room for improvement as processing very large data sets is often very time and memory-consuming.

I currently supervise (and co-supervise with colleagues from the Université de Sherbrooke) a group of MSc and Ph.D. students working on these problems and on other problems directly related to computer vision such as shape description and recognition and segmentation using deformable models techniques. I am interested in expanding my research team and I welcome new students interested in working on these issues. I provide for my students an exciting research environment with lab facilities at Bishop’s University and at Université de Sherbrooke where I am a member of two research groups

- The Imaging and Vision Group – MOIVRE (MOdélisation en Imagerie, Vision et RÉseaux de neurones), and
- The Computational Topology Group – GRTC (Groupe de recherche en topologie computationnelle).

- M. Allili, D. Corriveau, S. Derivière, and T. Kaczynski. Detecting Critical Regions in Multidimensional Data Sets via the Conley Index Approach. Submitted (2008, 30 pages) .
- M. Allili, D. Corriveau, S. Derivière, T. Kaczynski and A. Trahan. Discrete dynamical system framework for the topological study of lattice height data. Journal of Math. Imaging and Vision 28 (2) (2007), pp. 99-111.
- M. Allili, T. Kaczynski. Geometric construction of a coboundary of a cycle. Journal of Discrete and Computational Geometry 25 (2001), pp. 125-140.
- M. Allili, T. Kaczynski. An Algorithmic approach to the construction of homomorphisms induced by maps in homology. Journal of Transactions of the American Mathematical Society 352 (2000) , pp. 2261-2281.
- M. Allili. Une approche algorithmique pour le calcul de l’homologie de fonctions continues. Ph.D. Thesis, Université de Sherbrooke, 1999.

- R. Dedic, M. Allili. Adaptive Topology Preserving Deformable Model. Submitted (2008, 16 pages).
- R. Dedic, M. Allili, R. Lecomte, A. Benchakroun. Segmentation of Cardiac Images by the Force Field Driven Speed Term . Accepted in Proceedings of CVISP 2008, Prague, Czech Republic July 25-27, 2008.
- R. Dedic, M. Allili, R. Lecomte, A. Benchakroun. Segmentation of Cardiac Images by the Force Field Driven Speed Term . Accepted in Proceedings of 2008 Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC 2008), Dresden, Germany, October 19-25, 2008.
- D. Li, M. Allili. A Digital Topology-based Method for the Topological Filtering of a Reconstructed Surface . Submitted (2008, 13 pages).
- M. Allili, D. Corriveau. Topological Analysis of Shapes Using Morse Theory. Computer Vision and Image Understanding 105 (2007), pp. 188-199.
- R. Dedic, M. Allili. Intelligent topology preserving geometric deformable model. Proceedings of the 2nd International Conference on Computer Vision Theory and Applications VISAPP(1) (2007), pp 322-327.
- R. Dedic, M. Allili. Complete boundary detection of textured objects via deformable models. Proc. SPIE-IS&T Electronic Imaging , Vision Geometry XV, Vol. 6499 (2007), 64990H.
- S. Derdar, M. Allili, Djemel Ziou. Topological feature extraction using algebraic topology. Proc. SPIE-IS&T Electronic Imaging, Vision Geometry XV, Vol. 6499 (2007), 64990G.
- R. Dedic, M. Allili. A Deformable Model for Complete Boundary Detection. Proceedings of IEEE International Symposium on Industrial Electronics ISIE 2006, pp. 685-690.
- M. Allili, D. Corriveau. Descripteur topologique pour les formes basé sur la théorie de Morse. Proceedings of Congrès Reconnaissance des Formes et Intelligence Artificielle, RFIA 2006. Tours, France, January 2006.
- S. Derdar, M. Allili, D. Ziou. Image matching using algebraic topology. Proc. SPIE-IS&T Electronic Imaging , Vision Geometry XIV, Vol. 6066 (2006), 6066-21.
- M. Allili, B. Yang, L. Bentabet. A deformable model with topology analysis and adaptive clustering for boundary detection. Proc. SPIE-IS&T Electronic Imaging , Vision Geometry XIV, Vol. 6066 (2006), 6066-01.
- D. Corriveau, M. Allili, D. Ziou. Morse Connections Graph for Shape Representation. Proceedings Advanced Concepts for Intelligent Vision Systems ACIVS 2005, Lecture Notes in Computer Science 3708 Springer 2005, pp. 219-226.
- B. Yang, M. Allili. Geometric Deformable Models with Topology Analysis for Shape Modeling. Proceedings of Fifth IASTED International Conference VIIP 2005 (track: 480-253), pp. 660-665.
- M. Allili, D. Corriveau, D. Ziou. Efficient Topological Descriptor for Shape Representation. Proceedings of SPIE, Image Processing: Algorithms and Systems IV, vol. 5672, 2005, pp. 287-296.
- M. Allili, D. Corriveau, D. Ziou. Morse Homology Descriptors for Shape Characterization. International Conference on Pattern Recognition (ICPR 2004), vol. 4, 2004, pp 27-30.
- M.-F. Auclair-Fortier, D. Ziou, M. Allili. Global computational algebraic topology approach for diffusion. Proc. SPIE Int. Soc. Opt. Eng., vol. 5299, 357, 2004, pp. 357-368.
- D. Ziou, M. Allili. Image Modeling: new perspective for image processing and computer vision. Proc. SPIE Int. Soc. Opt. Eng., vol. 5299, 123, 2004, pp. 123-133.
- M. Allili, D. Ziou. Computational Homology Approach for Topology Descriptors and Shape Representation. Proceedings of International Conference on Image and Signal Processing (ICISP’2003), vol. 2, 2003, pp. 508-516.
- M.-F. Auclair-Fortier, D. Ziou, M. Allili. A Global CAT Approach for Graylevel Diffusion. 7th IEEE International Symposium on Signal Processing and its Applications (ISSPA 2003), vol. 1, 2003, pp. 453-456.
- M.-F. Auclair-Fortier, P. Poulin, D. Ziou, M. Allili. A Computational Algebraic Topology Approach for Diffusion Process. Proceedings of 3rd Workshop on Physics in Signal and Image Processing (PSIP 2003), 2003, pp. 77-80.
- D. Ziou, M. Allili. Generating Cubical Complexes from Image Data and Computation of the Euler Number. Journal of Pattern Recognition, 35-12, 2002, pp. 2833-2839.
- M.-F. Auclair-Fortier, P. Poulin, D. Ziou, M. Allili. A Computational Algebraic Topology Model for the Deformation of Curves . Proceedings of 2nd International Workshop on Articulated Motion and Deformable Objects (AMDO 2002), vol. 2492, 2002, pp. 56-67.
- P. Poulin, M.-F. Auclair-Fortier, D. Ziou, M. Allili. A Physics Based Model for the Deformation of Curves: A Computational Algebraic Topology Approach. Joint International Symposium on GeoSpatial Theory, Processing and Applications Symposium of the ISPRS Commission IV, WG5, 2002.
- M.-F. Auclair-Fortier, P. Poulin, D. Ziou, M. Allili. A Computational Algebraic Topology Approach for Optical Flow . International Conference on Pattern Recognition (ICPR 2002), vol. 1, 2002, pp. 347-355.
- M. Allili, D. Ziou. Topological Feature Extraction in Binary Images. 6th IEEE International Symposium on Signal Processing and its Applications (ISSPA 2001), vol. 2, 2001, pp. 651-654.
- M. Allili, K. Mischaikow, A. Tannenbaum. Cubical Homology and the Topological Classification of 2D and 3D Imagery. IEEE International Conference on Image Processing (ICIP 2001), v 2, 2001, pp. 173-176.

- M. Allili, S. Day, O. Junge, and K. Mischaikow. A Rigorous Numerical Method for the Global Analysis of Infinite Dimensional Discrete Dynamical Systems. Preliminary Report, 2001.
- M. Allili, T. Kaczynski. Stability of Index Pairs for Multivalued Flows. Nonlinear Analysis, Vol. 30:7 (1997), pp. 4113-4122.
- M. Allili, T. Kaczynski. Stability of Index Pairs for Flows. Proceedings of the Conference “Topological Methods in Differential Equations and Dynamical Systems” (Krakow, Przegorzaly, 1996), Univ. Iagel. Acta Math. No. 36 (1998), pp. 173-175.

Contact Information and full bio

CVContact Information and full bio

Phone: 819-822-9600 ext. 2363 Email: francois.huard@ubishops.ca ## Research

### Representation Theory of Finite Dimensional Algebras

#### Partners

#### Student involvement

#### Links

## Publications

Dr. Huard’s current research focuses on the finitistic dimension conjecture.

The finitistic dimension conjecture was first publicized by Bass in 1960. For an artin algebra A we define the finitistic dimension dimension of A to be fin.dim. A =sup {pd M such that M is a finitely generated right A-module and pd M is finite} where pd M denotes the projective dimension of M. Bass conjectured that for A as above, fin.dim. A is always finite. Since then, this conjecture has been verified for few classes of algebras. Our long term objectives are thus to better understand the finitistic dimension of an algebra, and to provide the community with new tools to study this invariant. We also want to determine new classes of algebras with finite finitistic dimension. This is of significant importance since the more diverse algebras that can be found for which the conjecture holds, the greater the chance that a general proof of the conjecture will occur. In order to achieve these goals, we study the finitistic dimension from three different perspectives. The first is through the relative homology theory developed by Auslander and Solberg. The second approach is through modules of infinite projective dimension. Finally, we study it from the point of view of stratifying systems.

Dr. Huard is a member of the Bishop’s-Sherbrooke research group in representation theory of algebras which consists of five professors and around 15 graduate students.

He is also a member of the Groud d’algèbre et théorie de nombre de l’ISM

(Institut des Sciences Mathématiques).

Dr. Huard is working with undergraduate students from Bishop’s University and graduate students from Université de Sherbrooke. Each year the research group gives summer research grants to undergraduate students interested in pursuing research in algebra. Since 2006, Dr. Huard organizes a mathematics camp held every two year at Bishop’s University. The 25 best CEGEP mathematics students from Québec, selected following a provincial examination, are invited to attend this unique 10 day event where the focus is put on mathematics.

Huard, F. “Tilted gentle algebras.” /Comm. Algebra/ 26, 63-72.

Huard, F. and Liu, S. 1999. “Tilted special biserial algebras.” /J.Algebra/ 217, 679-700.

Huard, F. and Liu, S. 1999. “Tilted string algebras.” /J. Pure and Applied Algebra,/153 (2000) 151-164

Huard, F. 2000. “One-point extensions of quasi-tilted algebras by projectives.” /Comm. Algebra, /(29) (7) (2001) 3055-3060

Huard, F. 2001. “Tilted algebras having underlying graph Dn”, Ann. Sc. Math. Québec

Brewster, R., Dedic R. and Huard, F. 2005. “Edge coloured homomorphisms and the recognition of bound quivers” /Discrete Math/(297) (2005) 13-25

Huard, F., Lanzilotta M. and Mendoza O. 2007. “A new approach to the finitistic dimension” J. Algebra

Huard, F., Lanzilotta M. and Mendoza O. 2007. “Finitistic dimension through infinite projective dimension” Bulletin of the London Math. Soc.

WebsiteContact Information and full bio

Phone: 819-822-9600 ext. 2828 Email: trevor.jones@ubishops.ca ## Publications

G. M. L. Gladwell, **T. H. Jones**, and N. B. Willms, A Test Matrix for an Inverse Eigenvalue Problem, *Journal of Applied Mathematics*, vol. 2014, Article ID 515082, 6 pages, 2014. doi:10.1155/2014/515082

Trevor H. Jones, Heat Kernel for Open Manifolds, *Differential Geometry and its Applications*, 28 (2010), pp. 518-522

CVContact Information and full bio

Phone: 819-822-9600 ext. 2560 Email: paul.lin@ubishops.ca ## Research

Dr. Lin’s current research interest is about finding new characteristic properties for Hilbert space from normed linear spaces, with some applications. This is a classical question and essential in the sense that most beautiful and interesting theorems in Functional Analysis are based on Hilbert spaces. Let X be a normed linear space over the real line. One can characterize an inner product space by means of orthogonalities in X. James (1945) defined and studied two types of orthogonalities. By using relations among orthogonal vectors he was able to prove that in X if either orthogonality has homogeneity or additivity property, then X is an inner product space. In this article we first define a new notion of (a,b,c,d)-orthogonality in an infinite dimensional normed linear space, which is natural extension of the two orthogonalities by James. It is proved that X is an inner product space if and only if one orthogonality implies the other. Our unified approach is different from James’, Day’s (1947), Freese (1983), or many others. Some applications of our results regarding inner product spaces and related topics in normed spaces are given.

Dr. Lin’s published research articles involve the following topics of Pure Mathematics:

- Operator Theory (Bounded linear transformations on Hilbert spaces).
- C*-algebra.
- Operator Inequalities on Hilbert spaces.
- Inner Product and 2-Inner Product spaces with applications.
- Functional Analysis, Banach spaces in particular.
- Numerical Ranges and Spectral Theory.

Coordinator of the Math-Stats help centerContact Information and full bio

Phone: 819-822-9600 ext. 2722 Email: scosha.merovitz@ubishops.ca

Coordinator of the Math-Stats help center

Dr. Smith holds a Ph.D. in Mathematics from *Université de Sherbrooke* and has been working as a contract faculty at Bishop's University since 2008. Over these 9 years, he has taught a wide variety of math courses, including the math business courses such as MAT 190, MAT 193, MAT 195, MAT 196 and MAT 197.…Contact Information and full bio

Email: david.smith@ubishops.ca ## Research

## Funding

## Publications

Dr. Smith holds a Ph.D. in Mathematics from *Université de Sherbrooke* and has been working as a contract faculty at Bishop’s University since 2008. Over these 9 years, he has taught a wide variety of math courses, including the math business courses such as MAT 190, MAT 193, MAT 195, MAT 196 and MAT 197. Since 2010, he is one of the co-organizor of the international Sherbrooke-Bishop’s annual Meeting in the Representation Theory of Algebra. He is also occasionally a referee for some scientific journals and has also been a reviewer for the important collection Mathematical Reviews. Currently, he also co-supervise three Ph.D. students in Mathematics, all based at *Université de Sherbrooke*.

His main interest research interest is Algebra, and more precisely Representation Theory of Algebras.

Since 2010, he holds an NSERC (Natural Sciences and Engineering Research Council of Canada) research grant: $150,000 over 8 years.

Since 2003, he has been the author or co-author of 12 published research papers.

**Published Papers**

1. I. Assem, G. Dupont, R. Schiffler and D. Smith, Friezes, strings and cluster variables, Glasg. Math. J. 54 (2012), no. 1, 27-60.

2. A. Buan, O. Iyama, I. Reiten and D. Smith, Mutation of cluster-tilting objects and potentials, Amer. J. Math., 133 (2011), no. 4, 835-887.

3. I. Assem, C. Reutenauer and D. Smith, Friezes, Adv. Math. 225 (2010), no. 6, 3134-3165.

4. J.C. Bustamante, J. Dionne and D. Smith, (Co)homology theories for oriented algebras, Comm. Algebra, 27 (2009), no.5, 1516-1544.

5. J. Dionne, M. Lanzilotta and D. Smith, Skew group algebras of piecewise hereditary algebras are piecewise hereditary, J. Pure Appl. Algebra, 213 (2009), 241-249.

6. D. Smith, On tilting modules over cluster-tilted algebras, Illinois J. Math. 52 (2008), no. 4, 1223-1247.

7. D. Smith, Almost laura algebras, J. Algebra, 319 (2008), no. 1, 432-456.

8. M. Lanzilotta and D. Smith, Laura algebras and quasi-directed components, Colloq. Math., 105 (2006), no. 2, 179-196.

9. J. Dionne and D. Smith, Articulations of algebras and their homological properties, J. Algebra Appl., 5 (2006), no. 3 1-15.

10. I. Assem, F. U. Coelho, M. Lanzilotta, D. Smith and S. Trepode, Algebras determined by their left and right parts. Algebraic structures and their representations, 13-47, Contemp. Math., 376, Amer. Math. Soc., Providence, RI, 2005.

11. D. Smith, On generalized standard Auslander-Reiten components having only finitely many non-directing modules, J. Algebra, 279 (2004), no. 2, 493-513.

12. J-C. Bustamante, J. Dionne and D. Smith, Ordonnés de chaînes et algèbres d’incidence, Ann. Sci. Math. Québec 27 (2003), no. 1, 1-11.

**Other publications**

13. D. Smith, Algèbres de type laura, algèbres de groupes gauches et groups de (co)homologie, Ph.D. Thesis (2006), Université de Sherbrooke.

14. D. Smith, Articulation d’algèbres et propriétés homologiques, Master Thesis (2003), Université de Sherbrooke.

Phone: 819-822-9600 ext. 2404 Email: brad.willms@ubishops.ca

**Chair of the Sports Studies program**

Dr. Willms is not only a mathematics professor; he is also passionate about sports. Dr. Willms serve as the academic advisor for Sports Studies students.