Ivan Slapnicar - Academia.edu (original) (raw)

Papers by Ivan Slapnicar

IEEE Access, 2023

In the paper ''MLCM: Multi-Label Confusion Matrix'' a method for computing the confusion matrix f... more In the paper ''MLCM: Multi-Label Confusion Matrix'' a method for computing the confusion matrix for the multi-label classification problem is proposed. Although the authors state that there is no similar work on computing confusion matrix for multi-label classification problems, we point out that the method for computing a multi-label confusion matrix was previously proposed in the paper ''Multi-Label Classifier Performance Evaluation with Confusion Matrix'' by Krstinić et al. We will show that both methods are based on the same set of assumptions and scenarios for instances of true and predicted labels, while there are differences in computing the contribution of classification errors to the confusion matrix between these two approaches.

arXiv (Cornell University), May 29, 2014

We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is... more We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with high relative accuracy in O(n) operations. The algorithm is based on a shift-and-invert approach. Only a single element of the inverse of the shifted matrix eventually needs to be computed with double the working precision. Each eigenvalue and the corresponding eigenvector can be computed separately, which makes the algorithm adaptable for parallel computing. Our results extend to the complex Hermitian case. The algorithm is similar to the algorithm for solving the eigenvalue problem for real symmetric arrowhead matrices from:

arXiv (Cornell University), Apr 6, 2011

We analyze the spectra of generalized Fibonacci and Fibonacci-like operators in Banach space l 1.... more We analyze the spectra of generalized Fibonacci and Fibonacci-like operators in Banach space l 1. Some of the results have application in population dynamics.

Glasnik Matematicki, Dec 1, 2000

We give a bound for the perturbations of invariant subspaces of a non-singular Hermitian matrix H... more We give a bound for the perturbations of invariant subspaces of a non-singular Hermitian matrix H under relative additive perturbations of H. Such perturbations include the case when the elements of H are known up to some relative tolerance. Our bound is, in appropriate cases, sharper than the classical bounds, and it generalizes some of the recent relative perturbation results.

Zbirka je namijenjena studentima tehnickih i prirodnih znanosti. Zbirka sadrži 152 rijesena zadat... more Zbirka je namijenjena studentima tehnickih i prirodnih znanosti. Zbirka sadrži 152 rijesena zadatka i poglavlja Osnove matematike, Linearna algebra, Vektorska algebra i analiticka geometrija, Funkcije realne varijable, Derivacije i primjene te Nizovi i redovi. Slican sadržaj nalazi se u vecini istoimenih kolegija koji se predaju na tehnickim i prirodoslovnim fakultetima. Zbirka prati gradivo i nacin izlaganja udžbenika Sveucilista u Splitu: I. Slapnicar, Matematika 1, Sveuciliste u Splitu, FESB, Split, 2002. Rjesenja zadataka se, radi lakseg pracenja i razumijevanja, referenciraju na odgovarajuce djelove udžbenika. Pored potpuno rijesenih zadataka, zbirka sadrži i 166 zadataka za vježbu s rjesenjima te DA/NE kviz s ukupno 600 pitanja.

The Distorted Born Iterative (DBI) method is used for ultrasound tomography in order to localize ... more The Distorted Born Iterative (DBI) method is used for ultrasound tomography in order to localize and identify malignant breast tissues. This approach begins with the Born approximation to generate an initial prediction of the scattering function. Then, iteratively solves the forward problem for the total field and the inhomogeneous Green’s function, and the inverse problem for the scattering function. The drawback of this method is that the associated inverse scattering problem is ill-posed. We are proposing the Truncated General Singular Value Decomposition (TGSVD) approach as a regularization method for the ill posed inverse problem Xy = b in DBI and comparing it to the well known Truncated Singular Value Decomposition (TSVD). The TGSVD employs generalized SVD (GSVD) of matrix pair (X,L) and is neglecting the smallest, contaminated with noise, generalized singular values, while regularization matrix L (we used the first order derivative operator) is responsible for smoothing the solution. This results in better image quality. We compared the performances of these two methods on simulated phantom and proved that TGSVD produces lower relative error and better reconstructed image.

Medical Imaging 2018: Ultrasonic Imaging and Tomography, 2018

The distorted Born iterative method (DBI) is used to solve the inverse scattering problem in the ... more The distorted Born iterative method (DBI) is used to solve the inverse scattering problem in the ultrasound tomography with the objective of determining a scattering function that is related to the acoustical properties of the region of interest (ROI) from the disturbed waves measured by transducers outside the ROI. Since the method is iterative, we use Born approximation for the first estimate of the scattering function. The main problem with the DBI is that the linear system of the inverse scattering equations is ill-posed. To deal with that, we use two different algorithms and compare the relative errors and execution times. The first one is Truncated Total Least Squares (TTLS). The second one is Regularized Total Least Squares method (RTLS-Newton) where the parameters for regularization were found by solving a nonlinear system with Newton method. We simulated the data for the DBI method in a way that leads to the overdetermined system. The advantage of RTLS-Newton is that the computation of singular value decomposition for a matrix is avoided, so it is faster than TTLS, but it still solves the similar minimization problem. For the exact scattering function we used Modified Shepp-Logan phantom. For finding the Born approximation, RTLS-Newton is 10 times faster than TTLS. In addition, the relative error in L2-norm is smaller using RTLS-Newton than TTLS after 10 iterations of the DBI method and it takes less time.

Handbook of Linear Algebra, 2006

arXiv (Cornell University), Dec 21, 2022

Fast multiplication, determinants, and inverses of arrowhead and diagonal-plus-rank-one matrices ... more Fast multiplication, determinants, and inverses of arrowhead and diagonal-plus-rank-one matrices over associative fields N. Jakovčević Stor, I. Slapničar • Fast O(n) formulas. • Matrix elements are real or complex numbers, quaternions, or block matrices. • Same formulas for all types of matrix entries.

2022 IEEE International Ultrasonics Symposium (IUS)

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

SIAM Journal on Matrix Analysis and Applications

arXiv: Populations and Evolution, 2020

Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are l... more Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are larger prime numbers, like 13 or 17, to bamboos whose periods are large multiples of small primes, like 40 or even 120. The periodicity is caused by interaction of species, be it a predator-prey relationship, symbiosis, commensialism, or competition exclusion principle. We propose a simple mathematical model which explains and models all those principles, including listed extremel cases. This, rather universal, qualitative model is based on the concept of a local fitness function, where a randomly chosen new period is selected if the value of the global fitness function of the species increases. Arithmetically speaking, the different observed interactions are related to only four principles: given a couple of integer periods either (1) their greatest common divisor is one, (2) one of the periods is prime, (3) both periods are equal, or (4) one period is an integer multiple of the other.

arXiv: Populations and Evolution, 2020

Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are l... more Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are larger prime numbers, like 13 or 17, to bamboos whose periods are large multiples of small primes, like 40 or even 120. The periodicity is caused by interaction of species, be it a predator-prey relationship, symbiosis, commensialism, or competition exclusion principle. We propose a simple mathematical model which explains and models all those principles, including listed extremel cases. This, rather universal, qualitative model is based on the concept of a local fitness function, where a randomly chosen new period is selected if the value of the global fitness function of the species increases. Arithmetically speaking, the different observed interactions are related to only four principles: given a couple of integer periods either (1) their greatest common divisor is one, (2) one of the periods is prime, (3) both periods are equal, or (4) one period is an integer multiple of the other.

We formulate the quadratic eigenvalue problem underlying the mathematical model of a linear vibra... more We formulate the quadratic eigenvalue problem underlying the mathematical model of a linear vibrational system as an eigenvalue problem of a diagonal-plus-low-rank matrix A. The eigenvector matrix of A has a Cauchy-like structure. Optimal viscosities are those for which trace(X) is minimal, where X is the solution of the Lyapunov equation AX+XA^*=GG^*. Here G is a low-rank matrix which depends on the eigenfrequencies that need to be damped. After initial eigenvalue decomposition of linearized problem which requires O(n^3) operations, our algorithm computes optimal viscosities for each choice of external dampers in O(n^2) operations, provided that the number of dampers is small. Hence, the subsequent optimization is order of magnitude faster than in the standard approach which solves Lyapunov equation in each step, thus requiring O(n^3) operations. Our algorithm is based on O(n^2) eigensolver for complex symmetric diagonal-plus-rank-one matrices and fast O(n^2) multiplication of link...

IEEE Access, 2023

In the paper ''MLCM: Multi-Label Confusion Matrix'' a method for computing the confusion matrix f... more In the paper ''MLCM: Multi-Label Confusion Matrix'' a method for computing the confusion matrix for the multi-label classification problem is proposed. Although the authors state that there is no similar work on computing confusion matrix for multi-label classification problems, we point out that the method for computing a multi-label confusion matrix was previously proposed in the paper ''Multi-Label Classifier Performance Evaluation with Confusion Matrix'' by Krstinić et al. We will show that both methods are based on the same set of assumptions and scenarios for instances of true and predicted labels, while there are differences in computing the contribution of classification errors to the confusion matrix between these two approaches.

arXiv (Cornell University), May 29, 2014

We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is... more We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with high relative accuracy in O(n) operations. The algorithm is based on a shift-and-invert approach. Only a single element of the inverse of the shifted matrix eventually needs to be computed with double the working precision. Each eigenvalue and the corresponding eigenvector can be computed separately, which makes the algorithm adaptable for parallel computing. Our results extend to the complex Hermitian case. The algorithm is similar to the algorithm for solving the eigenvalue problem for real symmetric arrowhead matrices from:

arXiv (Cornell University), Apr 6, 2011

We analyze the spectra of generalized Fibonacci and Fibonacci-like operators in Banach space l 1.... more We analyze the spectra of generalized Fibonacci and Fibonacci-like operators in Banach space l 1. Some of the results have application in population dynamics.

Glasnik Matematicki, Dec 1, 2000

We give a bound for the perturbations of invariant subspaces of a non-singular Hermitian matrix H... more We give a bound for the perturbations of invariant subspaces of a non-singular Hermitian matrix H under relative additive perturbations of H. Such perturbations include the case when the elements of H are known up to some relative tolerance. Our bound is, in appropriate cases, sharper than the classical bounds, and it generalizes some of the recent relative perturbation results.

Zbirka je namijenjena studentima tehnickih i prirodnih znanosti. Zbirka sadrži 152 rijesena zadat... more Zbirka je namijenjena studentima tehnickih i prirodnih znanosti. Zbirka sadrži 152 rijesena zadatka i poglavlja Osnove matematike, Linearna algebra, Vektorska algebra i analiticka geometrija, Funkcije realne varijable, Derivacije i primjene te Nizovi i redovi. Slican sadržaj nalazi se u vecini istoimenih kolegija koji se predaju na tehnickim i prirodoslovnim fakultetima. Zbirka prati gradivo i nacin izlaganja udžbenika Sveucilista u Splitu: I. Slapnicar, Matematika 1, Sveuciliste u Splitu, FESB, Split, 2002. Rjesenja zadataka se, radi lakseg pracenja i razumijevanja, referenciraju na odgovarajuce djelove udžbenika. Pored potpuno rijesenih zadataka, zbirka sadrži i 166 zadataka za vježbu s rjesenjima te DA/NE kviz s ukupno 600 pitanja.

The Distorted Born Iterative (DBI) method is used for ultrasound tomography in order to localize ... more The Distorted Born Iterative (DBI) method is used for ultrasound tomography in order to localize and identify malignant breast tissues. This approach begins with the Born approximation to generate an initial prediction of the scattering function. Then, iteratively solves the forward problem for the total field and the inhomogeneous Green’s function, and the inverse problem for the scattering function. The drawback of this method is that the associated inverse scattering problem is ill-posed. We are proposing the Truncated General Singular Value Decomposition (TGSVD) approach as a regularization method for the ill posed inverse problem Xy = b in DBI and comparing it to the well known Truncated Singular Value Decomposition (TSVD). The TGSVD employs generalized SVD (GSVD) of matrix pair (X,L) and is neglecting the smallest, contaminated with noise, generalized singular values, while regularization matrix L (we used the first order derivative operator) is responsible for smoothing the solution. This results in better image quality. We compared the performances of these two methods on simulated phantom and proved that TGSVD produces lower relative error and better reconstructed image.

Medical Imaging 2018: Ultrasonic Imaging and Tomography, 2018

The distorted Born iterative method (DBI) is used to solve the inverse scattering problem in the ... more The distorted Born iterative method (DBI) is used to solve the inverse scattering problem in the ultrasound tomography with the objective of determining a scattering function that is related to the acoustical properties of the region of interest (ROI) from the disturbed waves measured by transducers outside the ROI. Since the method is iterative, we use Born approximation for the first estimate of the scattering function. The main problem with the DBI is that the linear system of the inverse scattering equations is ill-posed. To deal with that, we use two different algorithms and compare the relative errors and execution times. The first one is Truncated Total Least Squares (TTLS). The second one is Regularized Total Least Squares method (RTLS-Newton) where the parameters for regularization were found by solving a nonlinear system with Newton method. We simulated the data for the DBI method in a way that leads to the overdetermined system. The advantage of RTLS-Newton is that the computation of singular value decomposition for a matrix is avoided, so it is faster than TTLS, but it still solves the similar minimization problem. For the exact scattering function we used Modified Shepp-Logan phantom. For finding the Born approximation, RTLS-Newton is 10 times faster than TTLS. In addition, the relative error in L2-norm is smaller using RTLS-Newton than TTLS after 10 iterations of the DBI method and it takes less time.

Handbook of Linear Algebra, 2006

arXiv (Cornell University), Dec 21, 2022

Fast multiplication, determinants, and inverses of arrowhead and diagonal-plus-rank-one matrices ... more Fast multiplication, determinants, and inverses of arrowhead and diagonal-plus-rank-one matrices over associative fields N. Jakovčević Stor, I. Slapničar • Fast O(n) formulas. • Matrix elements are real or complex numbers, quaternions, or block matrices. • Same formulas for all types of matrix entries.

2022 IEEE International Ultrasonics Symposium (IUS)

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

SIAM Journal on Matrix Analysis and Applications

arXiv: Populations and Evolution, 2020

Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are l... more Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are larger prime numbers, like 13 or 17, to bamboos whose periods are large multiples of small primes, like 40 or even 120. The periodicity is caused by interaction of species, be it a predator-prey relationship, symbiosis, commensialism, or competition exclusion principle. We propose a simple mathematical model which explains and models all those principles, including listed extremel cases. This, rather universal, qualitative model is based on the concept of a local fitness function, where a randomly chosen new period is selected if the value of the global fitness function of the species increases. Arithmetically speaking, the different observed interactions are related to only four principles: given a couple of integer periods either (1) their greatest common divisor is one, (2) one of the periods is prime, (3) both periods are equal, or (4) one period is an integer multiple of the other.

arXiv: Populations and Evolution, 2020

Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are l... more Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are larger prime numbers, like 13 or 17, to bamboos whose periods are large multiples of small primes, like 40 or even 120. The periodicity is caused by interaction of species, be it a predator-prey relationship, symbiosis, commensialism, or competition exclusion principle. We propose a simple mathematical model which explains and models all those principles, including listed extremel cases. This, rather universal, qualitative model is based on the concept of a local fitness function, where a randomly chosen new period is selected if the value of the global fitness function of the species increases. Arithmetically speaking, the different observed interactions are related to only four principles: given a couple of integer periods either (1) their greatest common divisor is one, (2) one of the periods is prime, (3) both periods are equal, or (4) one period is an integer multiple of the other.

We formulate the quadratic eigenvalue problem underlying the mathematical model of a linear vibra... more We formulate the quadratic eigenvalue problem underlying the mathematical model of a linear vibrational system as an eigenvalue problem of a diagonal-plus-low-rank matrix A. The eigenvector matrix of A has a Cauchy-like structure. Optimal viscosities are those for which trace(X) is minimal, where X is the solution of the Lyapunov equation AX+XA^*=GG^*. Here G is a low-rank matrix which depends on the eigenfrequencies that need to be damped. After initial eigenvalue decomposition of linearized problem which requires O(n^3) operations, our algorithm computes optimal viscosities for each choice of external dampers in O(n^2) operations, provided that the number of dampers is small. Hence, the subsequent optimization is order of magnitude faster than in the standard approach which solves Lyapunov equation in each step, thus requiring O(n^3) operations. Our algorithm is based on O(n^2) eigensolver for complex symmetric diagonal-plus-rank-one matrices and fast O(n^2) multiplication of link...