Fluorous chemistry has been in the focus of research interests since the end of the last century.... more Fluorous chemistry has been in the focus of research interests since the end of the last century. One of the most important contributions in the field was the article Facile Catalyst Separation Without Water: Fluorous Biphase Hydroformylation of Olef ins by Istvań T. Horvath and Joźsef Rabai. It has had great impact on academic chemical research. According to Web of Science (downloaded on 31 January 2017), in more than two decades, 2384 researchers have cited this work in 1077 scientific documents. In the present paper, we illustrate and analyze the co-authorship network determined by these citing documents. We studied the statistical features of these publications, as well as the macro-and micro-characteristics of the network using standard social network analysis techniques. We also interpret the results from a chemical point of view.
Two-dimensional chirality problems in mathematics can be studied by so-called lattice animals or ... more Two-dimensional chirality problems in mathematics can be studied by so-called lattice animals or 2D animals. Generalizing this idea for 3D problems we consider in the three-dimensional space R3 a Cartesian grid of the first octant consisting of n3 small unit cubic cells and define there solid animals or 3D animals. The simplest approach is to say that a 2D (or 3D) animal is chiral or achiral. One could assume that there is no other possibility. On the other hand a few scientists recognized that it is possible to measure the degree of chirality. For example F. Harary, R. W. Robinson, P. G. Mezey, A. I. Kitaigorodski, K. Mislow, J. Siegel, G. Gilat, D. Avnir, and A. Y. Meyer have made important contributions to this field. In this paper we provide a solution for quantification of the problem of chirality for 2D and 3D objects using graphs.
Fluorous chemistry has been in the focus of research interests since the end of the last century.... more Fluorous chemistry has been in the focus of research interests since the end of the last century. One of the most important contributions in the field was the article Facile Catalyst Separation Without Water: Fluorous Biphase Hydroformylation of Olef ins by Istvań T. Horvath and Joźsef Rabai. It has had great impact on academic chemical research. According to Web of Science (downloaded on 31 January 2017), in more than two decades, 2384 researchers have cited this work in 1077 scientific documents. In the present paper, we illustrate and analyze the co-authorship network determined by these citing documents. We studied the statistical features of these publications, as well as the macro-and micro-characteristics of the network using standard social network analysis techniques. We also interpret the results from a chemical point of view.
In this paper we intend to summarize the most important mathematical statistical methods which pl... more In this paper we intend to summarize the most important mathematical statistical methods which play a basic role in water quality control. In the first section we will use a random variable model and it will be shown how to observe the changing of water quality by testing homogeneity. In the second section we will compare the means of the random variables. A few new idea will be introduced in the third and fourth sections based on stochastic process models.
In this paper it is intended to apply the inequality 82 -9 - > P(I~I > IXil) -4x ~ 1 1- to ... more In this paper it is intended to apply the inequality 82 -9 - > P(I~I > IXil) -4x ~ 1 1- to test the examined probability variable C has a distribution function F(x).
Asymmetric autocatalysis (Soai reaction) was reported 20 years ago. Since then, this discovery ha... more Asymmetric autocatalysis (Soai reaction) was reported 20 years ago. Since then, this discovery has had an exceptional influence on several branches of natural sciences. In the present paper citations to this milestone article—556 publications of 908 scientists from Google Scholar’s database—are analyzed by graph theoretical and statistical tools. The results enable localization of the most active research groups, their priorities and the identification of the distribution of scientific disciplines influenced by the Soai reaction.
Long-armed multifunctional organosilicon molecules display self-replicating and self-perfecting b... more Long-armed multifunctional organosilicon molecules display self-replicating and self-perfecting behavior in asymmetric autocatalysis (Soai reaction). Two representatives of this class were studied by statistical methods aiming at determination of probabilities of natural abundance chiral isotopomers. The results, reported here, show an astonishing richness of possibilities of the formation of chiral isotopically substituted derivatives. This feature could serve as a model for the evolution of biological chirality in prebiotic and early biotic stereochemistry.
The main goal of this communication is to show the utility of empirical approaches combined with ... more The main goal of this communication is to show the utility of empirical approaches combined with mathematical methods in the research regarding the molecular basis of biological chirality. Preparative results (enantiomeric excesses, e.e.) obtained in asymmetric autocatalysis with (AAC) and without (AES) chiral additive were analyzed. Statistical calculations show, that AES (absolute enantioselective synthesis) experiments yield two independent groups of
Enantiomeric excesses obtained in absolute enantioselective synthesis by chiral autocatalysis (So... more Enantiomeric excesses obtained in absolute enantioselective synthesis by chiral autocatalysis (Soai-reaction) were statistically analyzed. Two sets of parallel experiments, which were performed under chemically different conditions, are available. One group contains 37, while the other contains 84 preparative results. The former group shows some interesting tendencies but does not give conclusive statistical results. The sample of 84 parallel experiments, providing 39 R- and 45 S-excesses have shown that these data represent two distinct, non-symmetric sets with different non-Gaussian distributions. Clear S preference was found.
Statistical distribution of enantiomeric excesses obtained by two sets of parallel experiments of... more Statistical distribution of enantiomeric excesses obtained by two sets of parallel experiments of absolute asymmetric synthesis by asymmetric autocatalysis was analyzed. It has been found that expe...
Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocat... more Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocatalysis. Therefore magnitude and eventual effects of isotopic chirality caused by natural abundance isotopic substitution (H, C, O, Zn) in the reagents of the Soai reaction were analyzed by combinatorics and probability calculations. Expectable enantiomeric excesses were calculated by the Pars-Mills equation. It has been found that the chiral isotopic species formed by substitution in the otherwise achiral reagents provide enantiomeric excess (e.e.) levels that are higher than the sensitivity threshold of the Soai autocatalysis towards chiral induction. Consequently, possible chiral induction exerted by these e.e. values should be taken into account in considerations regarding the molecular events and the mechanism of the chiral induction in the Soai reaction.
The main goal of the present review is to collect in a unified framework the deterministic and st... more The main goal of the present review is to collect in a unified framework the deterministic and stochastic models of emergence and amplification of chirality by mechanisms such as asymmetric autocatalysis and absolute asymmetric synthesis. Empirical approach and modeling have recently provided a good insight into these phenomena. Our groups in Italy and Hungary have a wide variety of expertise both in fields of experiments and modeling. In the last decade important results have been achieved, however, more experiments and more detailed deterministic and stochastic models are needed for a better understanding of details and significance of asymmetric autocatalysis and absolute asymmetric synthesis.
Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocat... more Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocatalysis. Therefore magnitude and eventual effects of isotopic chirality caused by natural abundance isotopic substitution (H, C, O, Zn) in the reagents of the Soai reaction were analyzed by combinatorics and probability calculations. Expectable enantiomeric excesses were calculated by the Pars-Mills equation. It has been found that the chiral isotopic species formed by substitution in the otherwise achiral reagents provide enantiomeric excess (e.e.) levels that are higher than the sensitivity threshold of the Soai autocatalysis towards chiral induction. Consequently, possible chiral induction exerted by these e.e. values should be taken into account in considerations regarding the molecular events and the mechanism of the chiral induction in the Soai reaction.
Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a... more Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a chiral compound from achiral precursor(s) by a chemical reaction, without enantiopure chiral additive and/or without applied asymmetric physical field. Only one well-characterized example of AAS is known today: the Soai-autocatalysis. In an attempt at clarification of the mechanism of this particular reaction we have undertaken empirical and stochastic analysis of several parallel AAS experiments. Our results show that the initial steps of the reaction might be controlled by simple normal distribution ("coin tossing") formalism. Advanced stages of the reaction, however, appear to be of a more complicated nature. Symmetric beta distribution formalism could not be brought into correspondence with the experimental observations. A bimodal beta distribution algorithm provided suitable agreement with the experimental data. The parameters of this bimodal beta function were determined by a Pólya-urn experiment (simulated by computer). Interestingly, parameters of the resulting bimodal beta function give a golden section ratio. These results show, that in this highly interesting autocatalysis two or even perhaps three catalytic cycles are cooperating. An attempt at constructing a "designed" Soai-type reaction system has also been made.
Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a... more Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a chiral compound from achiral precursor(s) by a chemical reaction, without enantiopure chiral additive and/or without applied asymmetric physical field. Only one well-characterized example of AAS is known today: the Soai-autocatalysis. In an attempt at clarification of the mechanism of this particular reaction we have undertaken empirical and stochastic analysis of several parallel AAS experiments. Our results show that the initial steps of the reaction might be controlled by simple normal distribution ("coin tossing") formalism. Advanced stages of the reaction, however, appear to be of a more complicated nature. Symmetric beta distribution formalism could not be brought into correspondence with the experimental observations. A bimodal beta distribution algorithm provided suitable agreement with the experimental data. The parameters of this bimodal beta function were determined...
Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a... more Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a chiral compound from achiral precursor(s) by a chemical reaction, without enantiopure chiral additive and/or without applied asymmetric physical field. Only one well-characterized example of AAS is known today: the Soai-autocatalysis. In an attempt at clarification of the mechanism of this particular reaction we have undertaken empirical and stochastic analysis of several parallel AAS experiments. Our results show that the initial steps of the reaction might be controlled by simple normal distribution ("coin tossing") formalism. Advanced stages of the reaction, however, appear to be of a more complicated nature. Symmetric beta distribution formalism could not be brought into correspondence with the experimental observations. A bimodal beta distribution algorithm provided suitable agreement with the experimental data. The parameters of this bimodal beta function were determined...
Fluorous chemistry has been in the focus of research interests since the end of the last century.... more Fluorous chemistry has been in the focus of research interests since the end of the last century. One of the most important contributions in the field was the article Facile Catalyst Separation Without Water: Fluorous Biphase Hydroformylation of Olef ins by Istvań T. Horvath and Joźsef Rabai. It has had great impact on academic chemical research. According to Web of Science (downloaded on 31 January 2017), in more than two decades, 2384 researchers have cited this work in 1077 scientific documents. In the present paper, we illustrate and analyze the co-authorship network determined by these citing documents. We studied the statistical features of these publications, as well as the macro-and micro-characteristics of the network using standard social network analysis techniques. We also interpret the results from a chemical point of view.
Two-dimensional chirality problems in mathematics can be studied by so-called lattice animals or ... more Two-dimensional chirality problems in mathematics can be studied by so-called lattice animals or 2D animals. Generalizing this idea for 3D problems we consider in the three-dimensional space R3 a Cartesian grid of the first octant consisting of n3 small unit cubic cells and define there solid animals or 3D animals. The simplest approach is to say that a 2D (or 3D) animal is chiral or achiral. One could assume that there is no other possibility. On the other hand a few scientists recognized that it is possible to measure the degree of chirality. For example F. Harary, R. W. Robinson, P. G. Mezey, A. I. Kitaigorodski, K. Mislow, J. Siegel, G. Gilat, D. Avnir, and A. Y. Meyer have made important contributions to this field. In this paper we provide a solution for quantification of the problem of chirality for 2D and 3D objects using graphs.
Fluorous chemistry has been in the focus of research interests since the end of the last century.... more Fluorous chemistry has been in the focus of research interests since the end of the last century. One of the most important contributions in the field was the article Facile Catalyst Separation Without Water: Fluorous Biphase Hydroformylation of Olef ins by Istvań T. Horvath and Joźsef Rabai. It has had great impact on academic chemical research. According to Web of Science (downloaded on 31 January 2017), in more than two decades, 2384 researchers have cited this work in 1077 scientific documents. In the present paper, we illustrate and analyze the co-authorship network determined by these citing documents. We studied the statistical features of these publications, as well as the macro-and micro-characteristics of the network using standard social network analysis techniques. We also interpret the results from a chemical point of view.
In this paper we intend to summarize the most important mathematical statistical methods which pl... more In this paper we intend to summarize the most important mathematical statistical methods which play a basic role in water quality control. In the first section we will use a random variable model and it will be shown how to observe the changing of water quality by testing homogeneity. In the second section we will compare the means of the random variables. A few new idea will be introduced in the third and fourth sections based on stochastic process models.
In this paper it is intended to apply the inequality 82 -9 - > P(I~I > IXil) -4x ~ 1 1- to ... more In this paper it is intended to apply the inequality 82 -9 - > P(I~I > IXil) -4x ~ 1 1- to test the examined probability variable C has a distribution function F(x).
Asymmetric autocatalysis (Soai reaction) was reported 20 years ago. Since then, this discovery ha... more Asymmetric autocatalysis (Soai reaction) was reported 20 years ago. Since then, this discovery has had an exceptional influence on several branches of natural sciences. In the present paper citations to this milestone article—556 publications of 908 scientists from Google Scholar’s database—are analyzed by graph theoretical and statistical tools. The results enable localization of the most active research groups, their priorities and the identification of the distribution of scientific disciplines influenced by the Soai reaction.
Long-armed multifunctional organosilicon molecules display self-replicating and self-perfecting b... more Long-armed multifunctional organosilicon molecules display self-replicating and self-perfecting behavior in asymmetric autocatalysis (Soai reaction). Two representatives of this class were studied by statistical methods aiming at determination of probabilities of natural abundance chiral isotopomers. The results, reported here, show an astonishing richness of possibilities of the formation of chiral isotopically substituted derivatives. This feature could serve as a model for the evolution of biological chirality in prebiotic and early biotic stereochemistry.
The main goal of this communication is to show the utility of empirical approaches combined with ... more The main goal of this communication is to show the utility of empirical approaches combined with mathematical methods in the research regarding the molecular basis of biological chirality. Preparative results (enantiomeric excesses, e.e.) obtained in asymmetric autocatalysis with (AAC) and without (AES) chiral additive were analyzed. Statistical calculations show, that AES (absolute enantioselective synthesis) experiments yield two independent groups of
Enantiomeric excesses obtained in absolute enantioselective synthesis by chiral autocatalysis (So... more Enantiomeric excesses obtained in absolute enantioselective synthesis by chiral autocatalysis (Soai-reaction) were statistically analyzed. Two sets of parallel experiments, which were performed under chemically different conditions, are available. One group contains 37, while the other contains 84 preparative results. The former group shows some interesting tendencies but does not give conclusive statistical results. The sample of 84 parallel experiments, providing 39 R- and 45 S-excesses have shown that these data represent two distinct, non-symmetric sets with different non-Gaussian distributions. Clear S preference was found.
Statistical distribution of enantiomeric excesses obtained by two sets of parallel experiments of... more Statistical distribution of enantiomeric excesses obtained by two sets of parallel experiments of absolute asymmetric synthesis by asymmetric autocatalysis was analyzed. It has been found that expe...
Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocat... more Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocatalysis. Therefore magnitude and eventual effects of isotopic chirality caused by natural abundance isotopic substitution (H, C, O, Zn) in the reagents of the Soai reaction were analyzed by combinatorics and probability calculations. Expectable enantiomeric excesses were calculated by the Pars-Mills equation. It has been found that the chiral isotopic species formed by substitution in the otherwise achiral reagents provide enantiomeric excess (e.e.) levels that are higher than the sensitivity threshold of the Soai autocatalysis towards chiral induction. Consequently, possible chiral induction exerted by these e.e. values should be taken into account in considerations regarding the molecular events and the mechanism of the chiral induction in the Soai reaction.
The main goal of the present review is to collect in a unified framework the deterministic and st... more The main goal of the present review is to collect in a unified framework the deterministic and stochastic models of emergence and amplification of chirality by mechanisms such as asymmetric autocatalysis and absolute asymmetric synthesis. Empirical approach and modeling have recently provided a good insight into these phenomena. Our groups in Italy and Hungary have a wide variety of expertise both in fields of experiments and modeling. In the last decade important results have been achieved, however, more experiments and more detailed deterministic and stochastic models are needed for a better understanding of details and significance of asymmetric autocatalysis and absolute asymmetric synthesis.
Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocat... more Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocatalysis. Therefore magnitude and eventual effects of isotopic chirality caused by natural abundance isotopic substitution (H, C, O, Zn) in the reagents of the Soai reaction were analyzed by combinatorics and probability calculations. Expectable enantiomeric excesses were calculated by the Pars-Mills equation. It has been found that the chiral isotopic species formed by substitution in the otherwise achiral reagents provide enantiomeric excess (e.e.) levels that are higher than the sensitivity threshold of the Soai autocatalysis towards chiral induction. Consequently, possible chiral induction exerted by these e.e. values should be taken into account in considerations regarding the molecular events and the mechanism of the chiral induction in the Soai reaction.
Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a... more Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a chiral compound from achiral precursor(s) by a chemical reaction, without enantiopure chiral additive and/or without applied asymmetric physical field. Only one well-characterized example of AAS is known today: the Soai-autocatalysis. In an attempt at clarification of the mechanism of this particular reaction we have undertaken empirical and stochastic analysis of several parallel AAS experiments. Our results show that the initial steps of the reaction might be controlled by simple normal distribution ("coin tossing") formalism. Advanced stages of the reaction, however, appear to be of a more complicated nature. Symmetric beta distribution formalism could not be brought into correspondence with the experimental observations. A bimodal beta distribution algorithm provided suitable agreement with the experimental data. The parameters of this bimodal beta function were determined by a Pólya-urn experiment (simulated by computer). Interestingly, parameters of the resulting bimodal beta function give a golden section ratio. These results show, that in this highly interesting autocatalysis two or even perhaps three catalytic cycles are cooperating. An attempt at constructing a "designed" Soai-type reaction system has also been made.
Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a... more Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a chiral compound from achiral precursor(s) by a chemical reaction, without enantiopure chiral additive and/or without applied asymmetric physical field. Only one well-characterized example of AAS is known today: the Soai-autocatalysis. In an attempt at clarification of the mechanism of this particular reaction we have undertaken empirical and stochastic analysis of several parallel AAS experiments. Our results show that the initial steps of the reaction might be controlled by simple normal distribution ("coin tossing") formalism. Advanced stages of the reaction, however, appear to be of a more complicated nature. Symmetric beta distribution formalism could not be brought into correspondence with the experimental observations. A bimodal beta distribution algorithm provided suitable agreement with the experimental data. The parameters of this bimodal beta function were determined...
Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a... more Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a chiral compound from achiral precursor(s) by a chemical reaction, without enantiopure chiral additive and/or without applied asymmetric physical field. Only one well-characterized example of AAS is known today: the Soai-autocatalysis. In an attempt at clarification of the mechanism of this particular reaction we have undertaken empirical and stochastic analysis of several parallel AAS experiments. Our results show that the initial steps of the reaction might be controlled by simple normal distribution ("coin tossing") formalism. Advanced stages of the reaction, however, appear to be of a more complicated nature. Symmetric beta distribution formalism could not be brought into correspondence with the experimental observations. A bimodal beta distribution algorithm provided suitable agreement with the experimental data. The parameters of this bimodal beta function were determined...
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