A series of diphosphines of the novel Walphos ligand family all based on a phenylferrocenylethyl backbone were synthesised in a four-step sequence. In the rhodium-or ruthenium-catalysed asymmetric hydrogenation of olefins and ketones enantioselectivities of up to 95% and 97%, respectively, were obtained. A 2-isopropylcinnamic acid derivative of industrial interest was hydrogenated in 95% ee and with turnover numbers of > 5000.Keywords: alkene reduction; asymmetric catalysis; asymmetric hydrogenation; ketone reduction; Pligands; rhodium; ruthenium Over a period of more than three decades homogenous enantioselective hydrogenation has been investigated extensively by numerous researchers in academia and industry, and is now being considered as a mature methodology for the production of enantiopure, bioactive ingredients and fine chemicals on an industrial scale.[1] The most efficient catalysts for the asymmetric hydrogenation of olefins, ketones or imines [2] are rhodium, ruthenium and iridium complexes of chiral diphosphine ligands. However, even though innumerable chiral diphosphines have been designed and investigated in the past, only a few out of more than thousands have been found suitable for industrial processes. Representative examples are biaryl-, phospholaneand ferrocenyl-based ligands like binap, duphos or josiphos type ferrocenes. [3] In our search for novel classes of diphosphines, we focused on the design of ligands that fulfil all relevant prerequisites particularly with regard to industrial applications: shortness and modularity of ligand synthesis that should allow an efficient fine tuning of catalysts× properties. In addition, such ligands should be readily accessible from enantiopure key intermediates. In this context, we have examined the potential of a new family with a novel phenylferrocenylethyl backbone that we named Walphos (1; Figure 1). The synthesis concept for this ligand family is straightforward: (i) the enantiomerically pure ligand framework ± an orthobromophenylferrocenylethylamine (3) ± is constructed from Ugi×s amine [4] and (ii) the final functional groups are implemented stepwise.[5] (Scheme 1) In this preliminary contribution, we report the synthesis of six representatives of the Walphos family with varying phosphino substituents R 1 and R 2 , together with first applications in the enantioselective hydrogenation.Starting from amine 2, six derivatives with electronrich and electron-withdrawing phosphino substituents R 1 and R 2 were prepared in a four-step sequence. In a Negishi coupling reaction [6] of (R c )-N,N-dimethyl-1-ferrocenylethylamine, (R c )-2, with 2-bromoiodobenzene the enantiomerically pure key intermediate (R c ,R p )-3 was built up. A subsequent lithiation of this bromide followed by trapping with the appropriate electrophile ±either chlorodiphenylphosphine or chlorobis(3,5-dimethyl-4-methoxyphenyl)phosphine ±result-ed in the formation of the corresponding aminophosphines. In order to prevent a ring closure reaction in the next step, the aminophosphin...

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We present ecient algorithmic methods to detect Hopf bifurcation xed points in chemical reaction networks with symbolic rate constants, thereby yielding information about the oscillatory behavior of the networks. Our methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of our methods then reduces the problem of determining the existence of Hopf bifurcation xed points to a rst-order formula over the ordered eld of the reals that can be solved using computational logic packages. The second method uses ideas from tropical geometry to formulate a more ecient method that is incomplete in theory but worked very well for the examples that we have attempted; we have shown it to be able to handle systems involving more than 20 species

Given a quantifier-free first-order formula over the theory of ordered fields, our aim is to find an equivalent first-order formula that is simpler. The notion of a formula being simpler will be specified. An overview is given over various methods combining elements of field theory, order theory, and logic. These methods do not require a Boolean normal form computation. They have been developed and implemented in reduce for simplifying intermediate and final results of automatic quantifier elimination by elimination sets. Their applicability is certainly not restricted to the area of quantifier elimination.

We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.Comment: Accepted into ISSAC 2017. This version has additional page showing all 11 CAD trees discussed in Section 2.1.

Symbolic methods to investigate Hopf bifurcation problems of vector fields arising in the context of algebraic biology have recently obtained renewed attention. However, the symbolic investigations have not been fully algorithmic but required a sequence of symbolic computations intervened with ad hoc insights and decisions made by a human. In this paper we discuss the use of algebraic and logical methods to reduce questions on the existence of Hopf bifurcations in parameterized polynomial vector fields to quantifier elimination problems over the reals combined with the use of the quantifier elimination over the reals and simplification techniques available in REDLOG. We can reconstruct most of the results given in the literature within a few seconds of computation time and extend the investigations on these systems to previously not analyzed related systems. Especially we discuss cases in which one suspects that no Hopf bifurcation fixed point exists for biologically relevant values of parameters and system variables. Here we focus on logical and algebraic techniques of finding subconditions being inconsistent with the hypothesis of the existence of Hopf bifurcation fixed points.

We present the application of real quantifier elimination to formal verification and synthesis of continuous and switched dynamical systems. Through a series of case studies, we show how first-order formulas over the reals arise when formally analyzing models of complex control systems. Existing off-the-shelf quantifier elimination procedures are not successful in eliminating quantifiers from many of our benchmarks. We therefore automatically combine three established software components: virtual subtitution based quantifier elimination in Reduce/Redlog, cylindrical algebraic decomposition implemented in Qepcad, and the simplifier Slfq implemented on top of Qepcad. We use this combination to successfully analyze various models of systems including adaptive cruise control in automobiles, adaptive flight control system, and the classical inverted pendulum problem studied in control theory.

The paper shows why and how an empirical study of fast-and-frugal heuristics can provide norms of good reasoning, and thus how (and how far) rationality can be naturalized. We explain the heuristics that humans often rely on in solving problems, for example, choosing investment strategies or apartments, placing bets in sports, or making library searches. We then show that heuristics can lead to judgments that are as accurate as or even more accurate than strategies that use more information and computation, including optimization methods. A standard way to defend the use of heuristics is by reference to accuracy-effort trade-offs. We take a different route, emphasizing ecological rationality (the relationship between cognitive heuristics and environment), and argue that in uncertain environments, more information and computation are not always better (the "less-can-be-more" doctrine). The resulting naturalism about rationality is thus normative because it not only describes what heuristics people use, but also in which specific environments one should rely on a heuristic in order to make better inferences. While we desist from claiming that the scope of ecological rationality is unlimited, we think it is of wide practical use.