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Papers by Tadeusz Krasinski
Results in Mathematics, Jun 18, 2018
arXiv (Cornell University), Mar 14, 2021
arXiv (Cornell University), Sep 27, 2011
Fundamenta Informaticae, 2013
Illinois Journal of Mathematics, Jul 1, 2002
arXiv (Cornell University), Feb 16, 1998
arXiv (Cornell University), Nov 24, 2011
arXiv (Cornell University), Sep 27, 2011
In this paper we discuss various possibilities of using DNA to information processing. We describ... more In this paper we discuss various possibilities of using DNA to information processing. We describe some practical implementations and theoretical models of computation built on DNA.
Fundamenta Informaticae, 2013
Illinois Journal of Mathematics, 2002
Genetics and molecular biology
The development of conventional, silicon-based computers has several limitations, including some ... more The development of conventional, silicon-based computers has several limitations, including some related to the Heisenberg uncertainty principle and the von Neumann "bottleneck". Biomolecular computers based on DNA and proteins are largely free of these disadvantages and, along with quantum computers, are reasonable alternatives to their conventional counterparts in some applications. The idea of a DNA computer proposed by Ehud Shapiro's group at the Weizmann Institute of Science was developed using one restriction enzyme as hardware and DNA fragments (the transition molecules) as software and input/output signals. This computer represented a two-state two-symbol finite automaton that was subsequently extended by using two restriction enzymes. In this paper, we propose the idea of a multistate biomolecular computer with multiple commercially available restriction enzymes as hardware. Additionally, an algorithmic method for the construction of transition molecules in th...
Zeitschrift für Naturforschung C, 2017
Great advances in biotechnology have allowed the construction of a computer from DNA. One of the ... more Great advances in biotechnology have allowed the construction of a computer from DNA. One of the proposed solutions is a biomolecular finite automaton, a simple two-state DNA computer without memory, which was presented by Ehud Shapiro’s group at the Weizmann Institute of Science. The main problem with this computer, in which biomolecules carry out logical operations, is its complexity – increasing the number of states of biomolecular automata. In this study, we constructed (in laboratory conditions) a six-state DNA computer that uses two endonucleases (e.g. AcuI and BbvI) and a ligase. We have presented a detailed experimental verification of its feasibility. We described the effect of the number of states, the length of input data, and the nondeterminism on the computing process. We also tested different automata (with three, four, and six states) running on various accepted input words of different lengths such as ab, aab, aaab, ababa, and of an unaccepted word ba. Moreover, this...
. An estimation of the exponent of separation at infinity of algebraic sets is given. As a coroll... more . An estimation of the exponent of separation at infinity of algebraic sets is given. As a corollary a sharp extension of Koll`ar's results on the / Lojasiewicz exponent of polynomial mappings is obtained. 1. Introduction. Let F = (F 1 ; :::; Fm ) : C n ! C m , n ? 2 be a polynomial mapping such that F \Gamma1 (0) is finite. Denote d i := deg F i for i = 1; : : : ; m, and assume that d 1 ? : : : ? dm . One of the most interesting characteristic of F is the / Lojasiewicz exponent at infinity i.e. the greatest exponent s 2 R such that jF (z)j ? Cjzj s ; for some C ? 0 and sufficiently large jzj. Denote it by L1 (F ). It characterizes the properness of F (see [H]), and gives criteria for polynomial mapping to be an automorphism ([P 1 ], for n = m = 2), and for polynomial of two variables to be a component of a polynomial automorphism ([CK 2 ], [CK 3 ]). There are also strong connections of L1 (F ) with the problem of effective Nulstellensatz [Br], [K] [BY]. 1991 Mathematics Subj...
Lecture Notes in Mathematics, 1983
In this paper examples and applications of the semi-norms on homology groups of complex manifolds... more In this paper examples and applications of the semi-norms on homology groups of complex manifolds, introduced in [4], are given.
Lecture Notes in Mathematics, 1983
In this paper there has been given a constructive proof of the equivalence of the parametric and ... more In this paper there has been given a constructive proof of the equivalence of the parametric and algebraic multiplicities of an isolated zero of a holomorphic mapping.
2014 Sixth World Congress on Nature and Biologically Inspired Computing (NaBIC 2014), 2014
A major challenge in DNA computing area is to design autonomous and programmable biomolecular dev... more A major challenge in DNA computing area is to design autonomous and programmable biomolecular devices built on DNA. The significant achievement in the field of DNA nanodevices was a laboratory implementation of the 2-state biomolecular finite automaton based on one restriction enzyme FokI [3]. Although this practical implementation represents a proof of concept for autonomous computing with DNA molecules, it has a limited computational power. The restriction enzyme FokI enables construction an automata with at most 3-states. We propose to use several restriction enzymes (instead of one) which act autonomously in a test tube to construct more powerful finite state machines. It enables to build any finite nondeterministic automata or even push-down automata. The autonomous operation of the automaton is based on alternating cleavages of DNA molecules by several restriction enzymes. We illustrate this new idea by presenting a laboratory implementation of a particular case of finite automata. In this experiment two restriction endonucleases act autonomously on DNA in one test tube. This approach may be used (in the future) to build nanomachines, even push-down automata (made of DNA molecules) which may be applied in medicine, pharmacy or biotechnology.
SpringerReference
Biocomputers can be an alternative for traditional "silicon-based" computers, which con... more Biocomputers can be an alternative for traditional "silicon-based" computers, which continuous development may be limited due to further miniaturization (imposed by the Heisenberg Uncertainty Principle) and increasing the amount of information between the central processing unit and the main memory (von Neuman bottleneck). The idea of DNA computing came true for the first time in 1994, when Adleman solved the Hamiltonian Path Problem using short DNA oligomers and DNA ligase. In the early 2000s a series of biocomputer models was presented with a seminal work of Shapiro and his colleguas who presented molecular 2 state finite automaton, in which the restriction enzyme, FokI, constituted hardware and short DNA oligomers were software as well as input/output signals. DNA molecules provided also energy for this machine. DNA computing can be exploited in many applications, from study on the gene expression pattern to diagnosis and therapy of cancer. The idea of DNA computing is still in progress in research both in vitro and in vivo and at least promising results of these research allow to have a hope for a breakthrough in the computer science.
Results in Mathematics, Jun 18, 2018
arXiv (Cornell University), Mar 14, 2021
arXiv (Cornell University), Sep 27, 2011
Fundamenta Informaticae, 2013
Illinois Journal of Mathematics, Jul 1, 2002
arXiv (Cornell University), Feb 16, 1998
arXiv (Cornell University), Nov 24, 2011
arXiv (Cornell University), Sep 27, 2011
In this paper we discuss various possibilities of using DNA to information processing. We describ... more In this paper we discuss various possibilities of using DNA to information processing. We describe some practical implementations and theoretical models of computation built on DNA.
Fundamenta Informaticae, 2013
Illinois Journal of Mathematics, 2002
Genetics and molecular biology
The development of conventional, silicon-based computers has several limitations, including some ... more The development of conventional, silicon-based computers has several limitations, including some related to the Heisenberg uncertainty principle and the von Neumann "bottleneck". Biomolecular computers based on DNA and proteins are largely free of these disadvantages and, along with quantum computers, are reasonable alternatives to their conventional counterparts in some applications. The idea of a DNA computer proposed by Ehud Shapiro's group at the Weizmann Institute of Science was developed using one restriction enzyme as hardware and DNA fragments (the transition molecules) as software and input/output signals. This computer represented a two-state two-symbol finite automaton that was subsequently extended by using two restriction enzymes. In this paper, we propose the idea of a multistate biomolecular computer with multiple commercially available restriction enzymes as hardware. Additionally, an algorithmic method for the construction of transition molecules in th...
Zeitschrift für Naturforschung C, 2017
Great advances in biotechnology have allowed the construction of a computer from DNA. One of the ... more Great advances in biotechnology have allowed the construction of a computer from DNA. One of the proposed solutions is a biomolecular finite automaton, a simple two-state DNA computer without memory, which was presented by Ehud Shapiro’s group at the Weizmann Institute of Science. The main problem with this computer, in which biomolecules carry out logical operations, is its complexity – increasing the number of states of biomolecular automata. In this study, we constructed (in laboratory conditions) a six-state DNA computer that uses two endonucleases (e.g. AcuI and BbvI) and a ligase. We have presented a detailed experimental verification of its feasibility. We described the effect of the number of states, the length of input data, and the nondeterminism on the computing process. We also tested different automata (with three, four, and six states) running on various accepted input words of different lengths such as ab, aab, aaab, ababa, and of an unaccepted word ba. Moreover, this...
. An estimation of the exponent of separation at infinity of algebraic sets is given. As a coroll... more . An estimation of the exponent of separation at infinity of algebraic sets is given. As a corollary a sharp extension of Koll`ar's results on the / Lojasiewicz exponent of polynomial mappings is obtained. 1. Introduction. Let F = (F 1 ; :::; Fm ) : C n ! C m , n ? 2 be a polynomial mapping such that F \Gamma1 (0) is finite. Denote d i := deg F i for i = 1; : : : ; m, and assume that d 1 ? : : : ? dm . One of the most interesting characteristic of F is the / Lojasiewicz exponent at infinity i.e. the greatest exponent s 2 R such that jF (z)j ? Cjzj s ; for some C ? 0 and sufficiently large jzj. Denote it by L1 (F ). It characterizes the properness of F (see [H]), and gives criteria for polynomial mapping to be an automorphism ([P 1 ], for n = m = 2), and for polynomial of two variables to be a component of a polynomial automorphism ([CK 2 ], [CK 3 ]). There are also strong connections of L1 (F ) with the problem of effective Nulstellensatz [Br], [K] [BY]. 1991 Mathematics Subj...
Lecture Notes in Mathematics, 1983
In this paper examples and applications of the semi-norms on homology groups of complex manifolds... more In this paper examples and applications of the semi-norms on homology groups of complex manifolds, introduced in [4], are given.
Lecture Notes in Mathematics, 1983
In this paper there has been given a constructive proof of the equivalence of the parametric and ... more In this paper there has been given a constructive proof of the equivalence of the parametric and algebraic multiplicities of an isolated zero of a holomorphic mapping.
2014 Sixth World Congress on Nature and Biologically Inspired Computing (NaBIC 2014), 2014
A major challenge in DNA computing area is to design autonomous and programmable biomolecular dev... more A major challenge in DNA computing area is to design autonomous and programmable biomolecular devices built on DNA. The significant achievement in the field of DNA nanodevices was a laboratory implementation of the 2-state biomolecular finite automaton based on one restriction enzyme FokI [3]. Although this practical implementation represents a proof of concept for autonomous computing with DNA molecules, it has a limited computational power. The restriction enzyme FokI enables construction an automata with at most 3-states. We propose to use several restriction enzymes (instead of one) which act autonomously in a test tube to construct more powerful finite state machines. It enables to build any finite nondeterministic automata or even push-down automata. The autonomous operation of the automaton is based on alternating cleavages of DNA molecules by several restriction enzymes. We illustrate this new idea by presenting a laboratory implementation of a particular case of finite automata. In this experiment two restriction endonucleases act autonomously on DNA in one test tube. This approach may be used (in the future) to build nanomachines, even push-down automata (made of DNA molecules) which may be applied in medicine, pharmacy or biotechnology.
SpringerReference
Biocomputers can be an alternative for traditional "silicon-based" computers, which con... more Biocomputers can be an alternative for traditional "silicon-based" computers, which continuous development may be limited due to further miniaturization (imposed by the Heisenberg Uncertainty Principle) and increasing the amount of information between the central processing unit and the main memory (von Neuman bottleneck). The idea of DNA computing came true for the first time in 1994, when Adleman solved the Hamiltonian Path Problem using short DNA oligomers and DNA ligase. In the early 2000s a series of biocomputer models was presented with a seminal work of Shapiro and his colleguas who presented molecular 2 state finite automaton, in which the restriction enzyme, FokI, constituted hardware and short DNA oligomers were software as well as input/output signals. DNA molecules provided also energy for this machine. DNA computing can be exploited in many applications, from study on the gene expression pattern to diagnosis and therapy of cancer. The idea of DNA computing is still in progress in research both in vitro and in vivo and at least promising results of these research allow to have a hope for a breakthrough in the computer science.