Asymmetric

This paper estimates the dynamics of adjustment to long run purchasing power parity (PPP) using data for 18 mayor bilateral US dollar exchange rates, over the post-Bretton Woods period, in a non-linear framework. We use new unit root and cointegration tests that do not assume a specific non-linear adjustment process. Using a first-order Fourier approximation, we find evidence of non-linear mean reversion in deviations from both absolute and relative PPP. This first-order Fourier approximation allows us to capture many features of the nonlinear decay detected in the data. Our results are consistent with theoretical arguments on international goods markets arbitrage under transaction costs as well as with an emerging strand of empirical literature. In this sense, this paper contributes towards forming a consensus on the presence of nonzero transaction costs across a broad range of countries.

The boxplot method (Exploratory Data Analysis, Addison-Wesley, Reading, MA, 1977) is a graphically-based method of identifying outliers which is appealing not only in its simplicity but also because it does not use the extreme potential outliers in computing a measure of dispersion. The inner and outer fences are deÿned in terms of the hinges (or fourths), and therefore are not distorted by a few extreme values. Such distortion could lead to failing to detect some outliers, a problem known as "masking".

Throughout our life, long-lived somatic stem cells (SSC) regenerate adult tissues both during homeostatic processes and repair after injury. The role of aberrant regulation of SSC has also recently gained prominence in the field of cancer research. Following malignant transformation, so termed cancer stem cells (CSC), endowed with the same properties as SSC (i.e. the ability to both self-renew and generate differentiated progenitors), play a major part in tumor initiation, therapy resistance and ultimately relapse. The same signaling pathways involved in regulating SSC maintenance are involved in the regulation of CSC. CSC exist in a wide array of tumor types, including leukemias, and brain, breast, prostate and colon tumors. Consequently, one of the key goals in cancer research over the past decade has been to develop therapeutic strategies to safely eliminate the CSC population without damaging the endogenous SSC population. A major hurdle to this goal lies in the identification o...

The physics, technology, and modeling of complementary asymmetric MOSFETs are reviewed and illustrated with statistically representative silicon data from a recent manufacturing implementation, in which the transistors for the secondary power supply voltage are offered in asymmetric and symmetric constructions. The in-depth analysis of the device physics of asymmetric transistors provides new insights into their physical operation and into the operation of transistors using halo implants in general. The variability, matching, and noise implications of using halo implants are also analyzed, concluding that both asymmetric and symmetric devices need to be offered for uncompromised circuit design. The challenges associated with the compact modeling the asymmetric transistors are also reviewed and illustrated. The preferred manufacturing implementation uses retrograde wells with no dopant fillers at the surface, while avoiding the drain-to-source punch-through by source-side-only halo implants. In addition to the known switching speed and maximum voltage gain advantages of the asymmetric transistors, this particular device architecture offers superior hot-carrier reliability and transistor design flexibility. The availability of retrograde wells enables construction of high-reliability complementary extended-drain MOSFETs for a third higher power supply voltage.

Recently, advances in time-varying quantile modeling have proven effective in financial Value-at-Risk forecasting. Some well-known dynamic conditional autoregressive quantile models are generalized to a fully nonlinear family. The Bayesian solution to the general ...

Asymmetric supercapacitors (ASCs) have played a leading role in realizing energy storage devices with high energy and power densities. While both anode and cathode materials are important for high performance ASCs, more research effort has been devoted to developing cathode materials because the energy source of an ASC is mostly attributed to the cathode. However, the development of anode materials is essential in order to achieve high power density as well as stable long-term cycle life of ASCs. In this study, functionalized graphene aerogel (GA) decorated with palladium (Pd) nanoparticles is used as an efficient ASC anode material. The high surface area (328 m 2 g À 1) and low electrical resistivity (50 times lower than one without Pd) of the GA composite grants a high specific capacitance (175.8 F g À 1 at 5 mV s À 1), excllent rate capability (48.3% retention after a 10 fold increase of scan rate), and remarkable reversibility. ASCs assembled from manganese dioxide (cathode) and GA composite (anode) show stable extended cell voltage, fast charge-discharge capability, excellent cycle stability (89.6% retention after 3000 cycles), and high energy and power densities (average of

We explore the idea of using vision-based hand tracking over a constrained tabletop surface area to perform multifinger and whole-hand gestural interactions with large displays from a distance. We develop bimanual techniques to support a variety of asymmetric and symmetric interactions, including fast targeting and navigation to all parts of a large display from the comfort of a desk and chair, as well as techniques that exploit the ability of the vision-based hand tracking system to provide multi-finger identification and full 2D hand segmentation. We also posit a design that allows for handling multiple concurrent users.

The Middle Proterozoic Mount Isa Basin, of the Mount Isa terrane, hosts several large Pb-Zn-Ag deposits and is arguably one of the richest mineral provinces in the world. The deformed remnants of this basin extend from the eastern margin of the Leichhardt River Fault Trough through to the Murphy Tectonic Ridge in the far north of the terrane. The Mount Isa Basin initially evolved in response to NW-SE-directed extension during the Mount Isa Rift Event. This event began before ¾1708 Ma and had ceased by ¾1653 Ma. A sag basin continued to evolve thereafter until ¾1595 Ma. Regional analysis of the highest level cover rocks of the Mount Isa Basin reveals a notable difference in the locus of syn-rift sedimentation, syn-rift magmatism, and post-rift subsidence. Although crustal extension was widespread across the Mount Isa Basin, tectonic subsidence was focussed along the ¾N-S-oriented Mount Isa Rift. Approximately 3-5 km of fluvial to shallow marine clastic sediments were deposited into isolated rift basins. Bimodal volcanism and emplacement of shallow level plutons occurred along the western and northwestern margins of the Mount Isa Rift. Magmatic provinces mark the locus of significant subcrustal lithospheric thinning, asthenospheric upwelling, and mafic underplating. Within these magmatic provinces the syn-rift sequences are fewer and thinner (750-2000 m) and were dominantly deposited in subaerial environments, suggesting a relatively stable uplift and subsidence history. The position of maximum subcrustal lithospheric extension is determined by the position of greatest post-rift subsidence. This occurred beneath the northern Mount Isa terrane where the thickest post-rift sequences are preserved and the depositional history is more protracted. We propose that the evolution of the Mount Isa Basin is a consequence of asymmetric extension of the Middle Proterozoic lithosphere.

This paper introduces and tests Bid Function Equilibria (BFE) in the British spot market for electricity. BFE extend von der Fehr and Harbord's (1993) multi-unit auction model of wholesale electricity markets by allowing firms to have heterogeneous costs for different generating units. Pure-strategy equilibria in BFE predict asymmetric bidding by producers: a single firm (the "price-setter") bids strategically while other firms ("non-price-setters") bid their costs. We test for asymmetries in firms' bid functions in the British spot market between 1993 and 1995 and find strong empirical support for the theory. We conclude that BFE have important implications for the design and governance of electricity markets.

Recebido em 31/7/02; aceito em 27/11/02 CATALYTIC ASYMMETRIC ALDOL REACTIONS: This review describes the use of catalytic asymmetric aldol reactions of silyl enol ethers and silyl (thio)ketene acetals with aldehydes (the Mukaiyama aldol reaction) in order to illustrate its synthetic utility. A variety of Lewis acid and basic reagents were employed for catalytic aldol reactions with high diastereo-and enantioselectivities. The origins of the selectivity of these reactions are discussed and some representative examples of their application in the synthesis of natural products are presented. New developments in chiral heterobimettalic lanthanoid catalysis and enantioselective aldol reactions in aqueous media are also included.

Behavioral economics (BE) examines the implications for decision-making when actors suffer from biases documented in the psychological literature. This article considers how such biases affect regulatory decisions. The article posits a simple model of a regulator who serves as an agent to a political overseer. The regulator chooses a policy that accounts for the rewards she receives from the political overseer-whose optimal policy is assumed to maximize short-run outputs that garner political support, rather than long-term welfare outcomes-and the weight the regulator puts on the optimal long run policy. Flawed heuristics and myopia are likely to lead regulators to adopt policies closer to the preferences of political overseers than they would otherwise. The incentive structure for regulators is likely to reward those who adopt politically expedient policies, either intentionally (due to a desire to please the political overseer) or accidentally (due to bounded rationality). The article urges that careful thought be given to calls for greater state intervention, especially when those calls seek to correct firm biases. The article proposes measures that focus rewards to regulators on outcomes rather than outputs as a way to help ameliorate regulatory biases. Cooper and Kovacic completed part of this paper while at the Federal Trade Commission. The views expressed are ours alone and do not necessarily represent those of the Federal Trade Commission or any other individual commissioner.

Nanostructural Al 1050 sheets were produced using a novel method of asymmetric cryorolling under ratios of upper and down rolling velocities (RUDV) of 1.1, 1.2, 1.3, and 1.4. Sheets were rolled to about 0.17 mm from 1.5 mm. Both the strength and ductility of Al 1050 sheets increase with RUDVs. Tensile strength of Al sheets with the RUDV 1.4 is larger 22.3% of that for RUDV 1.1, which is 196 MPa. The TEM observations show the grain size is 360 nm when the RUDV is 1.1, and 211 nm for RUDV 1.4.

A series of new highly efficient chiral aliphatic–aromatic diamine catalysts have been designed and successfully applied to the asymmetric Michael addition of cyclohexanone with nitroolefins under solvent-free conditions without any acidic additives. The desired adducts were obtained in high yields with excellent enantio- and diastereoselectivities of syn products (up to >99% ee, >99:1 dr). Chirality 2010. © 2010 Wiley-Liss, Inc

statement is important in many ways. First, it states that there are many aspects or domains in a person's life; thus, a person's well-being is expected to be related to her situation in all these aspects of life. Second, it recognises that economists usually deal with just one aspect of a person's life; hence, it is impossible to understand a person's well-being from an economic perspective alone. Third, it also recognises that economics, as a discipline, is an academic construct 1 that studies only one aspect of a person's life. Hicks' comment refers to economics, but it could also apply to any other of the social sciences, such as psychology, sociology, anthropology, and political science.

A new, fluorous-tagged chiral auxiliary has been developed for the asymmetric, SmI 2-mediated coupling of aldehydes and a,b-unsaturated esters. g-Butyrolactones are obtained in moderate to good isolated yield and in high enantiomeric excess. The fluorous tag allows the auxiliary to be conveniently recovered by fluorous solid-phase extraction (FSPE) and reused.

Orthogonally protected chiral β-hydroxy-γ-amino acids can be accessed in >100 g quantities from readily available starting materials and reagents in three to four steps. These chiral synthons contain two adjacent stereocenters along with suitably protected functional groups (O-TBS, N-Boc) for downstream reactivity. Implementation of two existing aldol technologies allows rapid access to all possible stereoisomers of 1. The guiding principles during reaction optimization were reaction scalability and operational efficiency. Conversion of the amino acids to a variety of chiral building blocks in one to two steps demonstrates their synthetic utility.

The size effect on the mechanism of fracture in ultrafine grained sheets is an unsolved problem in microforming. This paper describes a tensile test carried out to study the fracture behavior and the shear fracture angles of both rolled and aged ultrafine grained aluminum 6061 sheets produced by asymmetric cryorolling. A scanning electron microscope was used to observe the fracture surface. The finite element method was used to simulate the tensile test using the uncoupled Cockcroft-Latham and Tresca criteria and the coupled Gurson-Tvergaard-Needleman damage criterion. It was found that the shear fracture angle decreases gradually from 90 to 64 with an increasing number of passes. The results of simulations using the Gurson-Tvergaard-Needleman criterion show trends similar to the experimental ones. The paper also presents a discussion on the fracture mechanism and the size effect during the tensile test.

Several chiral and unsymmetrical tridentate [NNP]-type ligands with sp 2-N and sp 3-N were synthesized from monosulfonamide of (1R, 2R)-1,2-diaminocyclohexane and 2-(diphenylphosphino)benzaldehyde. Their ruthenium(II) complexes have been used in the enantioselective asymmetric hydrogen transfer reduction of acetophenone in 2-propanol with selectivities in the range 14-99% e.e. The good enantioselectivity with the ligands with sp 2-N and sp 3-N is believed to be due to formation of hexacoordinated complexes with a 2:1 ligand to metal ratio.

This paper estimates the long memory volatility model for 16 agricultural commodity futures returns from different futures markets, namely corn, oats, soybeans, soybean meal, soybean oil, wheat, live cattle, cattle feeder, pork, cocoa, coffee, cotton, orange juice, Kansas City wheat, rubber, and palm oil. The class of fractional GARCH models, namely the FIGARCH model of , FIEGACH model of , and FIAPARCH model of Tse (1998), are modelled and compared with the GARCH model of Bollerslev (1986), EGARCH model of Nelson (1991), and APARCH model of Ding et al. (1993). The estimated d parameters, indicating long-term dependence, suggest that fractional integration is found in most of agricultural commodity futures returns series. In addition, the FIGARCH (1,d,1) and FIEGARCH(1,d,1) models are found to outperform their GARCH(1,1) and EGARCH(1,1) counterparts.

The palladium-catalysed asymmetric methoxycarbonylation of styrene has been investigated for the first time using phosphetanes as chiral ligands and showed good catalytic activity, excellent regioselectivity to the branched product and enantioselectivity up to 29%.

The effect of electronic factors, solvent composition, identity of the chiral bidentate, and olefin structure on the yields and enantioselectivities of the asymmetric chlorohydrin synthesis were investigated. Electronic effects on the chlorohydrin reaction were tested by oxidation of phenyl allyl ether p -substituted by H, Cl, CH 3 O and CN. All species gave same similar yields and enantioselectivities indicating that electronic effects are not important. Varying the solvent composition of the THF Á/H 2 O mixtures indicated that the optimal solvent mixture contains more than 85% THF. Variation of added [Cl ( ] indicated that the added chloride had to be greater than 0.2 M for high yields and %ee's. Under ideal conditions the enantioselectivities of the chlorohydrins from the phenyl allyl ethers were more than 90%ee. Vinylacetic acid, methyl acrylate and trans -cinnamaldehyde were unreactive under the usual reaction conditions while 2-hydroxy-3-butene and allyl acetate give lower %ee's than did the phenyl allyl ethers. Styrene and amethylstyrene gives comparable rates of reactions but the %ee's were lower with the latter. (2,6-Diisopropyl)phenyl allyl ether and 2hydroxy-3-butene give high %ee's indicating that steric hindrance was not a major factor. All of the chiral bridging ligands tested gave satisfactory results except for DACH. A strange case was BZOX which did not give any induction at all. Structural studies showed the ligands are not large enough to bridge both Pd(II) in the bimetallic catalyst so one Pd(II) contained both ligand groups of the bidentate ligand and was thus unreactive. The other Pd(II) of the dimer was reactive but did not contain any chiral ligands to induce optical activity. #

The bond strength in bimetallic materials is an important material characteristic. In this study, 0.1-mm thick bimetallic foils (AA1050/AA6061) were produced using one pass of accumulative roll bonding followed by three passes of asymmetric rolling (AR). The AR passes were carried out at roll speed ratios of 1.0, 1.1, 1.2, 1.3, and 1.4 separately. Finite element simulation was used to model the deformation of the bimetallic foils for the various experimental conditions. Particular attention was focused on the bonding of the interface between AA1050 and AA6061 layers in the simulation. The optimization of the roll speed ratio was obtained for improvement of the bond strength of the interface of AA1050/AA6061 bimetallic foils during AR process. In the simulation, the mean equivalent strain at the interface zone between the AA1050 and AA6061 layers was seen to reach a peak value at a roll speed ratio of about 1.2 to 1.3, which also corresponded to a high quality bond at the interface as observed experimentally.

 This paper presents requirements, detailed analysis, and operation of six converter types used with 3phase 6/4 switched reluctance motor (SRM). These converters are R-dump, C-dump, C-dump with freewheeling transistor, asymmetric, series, and parallel type.

A key feature of the 2007-2008 …nancial crisis is that for some classes of securities trade has ceased. And where trade does occur, it appears that market prices are well below what one might believe to be the intrinsic value for that class of security. This seems to be especially true for those securities where the payo¤ streams are particularly complex (for example, CDOs). One explanation for this is that information about these securities'intrinsic values is asymmetric, with the current holders having better information than potential buyers. We show how the resulting adverse selection problem can help explain why more complex securities trade at signi…cant discounts to their intrinsic values or do not trade at all. To examine whether asymmetric information alone would su¢ ce to shut down portions of the asset-backed securities (ABS) market, we append a simple "workhorse"model for pricing securities under asymmetric information into a Monte Carlo simulation that generates hypothetical securities backed by residential mortgages. We conduct a type of "stress test" on the ABS by making the distribution of payo¤s to the underlying loans worse, and …nd that the intrinsic values of the securities further down the securitization chain become dispersed in such a way that the market for them may shut down under asymmetric information. We then consider the role for government intervention, and compare the e¤ectiveness of di¤erent policies that aim to unclog these markets.

FTIR and NMR spectroscopy and ab initio calculations were applied to understand the nature of enantioselection in the hydrogenation of the heteroaromatic ring in furan-and benzofurancarboxylic acids over cinchonidine-modified Pd. Most probably, cinchonidine adsorbs on Pd, via its quinoline moiety, approximately parallel to the surface, and the protonated quinuclidine N atom and the OH function of the alkaloid form a cyclic complex with the deprotonated acid dimer (2:1 acid:cinchonidine). The acid dimer adsorbs via the electron-rich furan ring and the carboxylate groups close to parallel to the Pd surface; the furan O atom points toward the OH function of cinchonidine. In this position, hydrogen uptake from the Pd surface results in the (S)-enantiomer as the major product. Another cyclic complex (1:1) involving cinchonidine and only one acid molecule is also feasible in solution, but this rigid structure is thermodynamically less favored, and it may be difficult to fulfill the geometric constraints imposed by adsorption on the metal surface.  2004 Elsevier Inc. All rights reserved.

The platinum-catalyzed enantioselective hydrogenation of ethyl pyruvate (EP) has been studied in a continuous fixed-bed reactor working under trickle bed conditions. The alumina-supported platinum catalyst was chirally modified by continuous dosing of small amounts of cinchonidine (CD) to the reactor feed containing EP and hydrogen dissolved in acetic acid. A parametric sensitivity study, including CD/EP ratio, hydrogen pressure, temperature, solvent/EP ratio and total liquid feed rate indicated significant dependence of reaction rate and enantiomeric excess (ee) on these parameters. Optimization using the Box Wilson method with hydrogenation rate as objective function and ee > 90% as boundary condition afforded a site-time-yield, expressed as average turnover frequency (TOF), of 84 000 h −1 . The space-time-yield was found to be approximately one order of magnitude higher than that achieved in a batch reactor (autoclave) under otherwise similar conditions. These findings indicate that the continuous fixed-bed reactor operation may provide an interesting opportunity for process intensification of this type of asymmetric catalytic hydrogenations.

A bimetallic palladium(II) complex containing a triketone ligand and a bridging diphosphine ligand oxidizes olefins in acetic acid to allylic acetates by a direct air oxidation, which does not require intermediate redox systems. When the diphosphine is chiral, an asymmetric reaction occurs which gives enantioselectivities between 52 and 78% for cyclic olefins.

The reaction of (AE)-1,6-Bisoximo[4.4]nonane 1 (prepared quantitatively from the reaction of hydroxylamine hydrochloride and (AE)-spiro[4.4]-1,6-nonanedione) with cyclopalladated compounds ½Pdðo-C 6 H 4 CHðRÞNMe 2 Þ-l-Cl 2 (R@H, Me) in the presence of KPF 6 yields monocationic dimeric complexes of the type ½Pdðo-C 6 H 4 CHðRÞNMe 2 Þ-ðl-1Þ-l-ClPF 6 containing the bisoxime bridging two palladium centers. The structures of the oxime ligand 1 and the dimeric palladium complex (R@H) 2 were determined by means of X-ray diffraction analysis. Ó

The objective of this work is to obtain estimations of the amplification factors α and δ used for torsion design of buildings, from experiments. For this study, simple one-storey torsionally unbalanced (TU) steel models were considered. Models consisted of a deck ...

An inverted pendulum with asymmetric elastic restraints (e.g. a one-sided spring), when subjected to harmonic vertical base excitation, on linearizing trigonometric terms, is governed by an asymmetric Mathieu equation. This system is parametrically forced and strongly nonlinear (linearization for small motions is not possible). However, solutions are scaleable: if x(t) is a solution, then so is ax(t) for any real aO0. We numerically study the stability regions in the parameter plane of this system for a fixed degree of asymmetry in the elastic restraints. A Lyapunov-like exponent is defined and numerically evaluated to find these regions of stable and unstable behaviour. These numerics indicate that there are infinitely many possibilities of instabilities in this system that are missing in the usual or symmetric Mathieu equation. We find numerically that there are periodic solutions at the boundaries of stable regions in the parameter plane, analogous to the symmetric Mathieu equation. We compute and plot several of these solution branches, which provide a relatively simpler means of computing the stability transition curves of this system. We prove theoretically that such periodic solutions must exist on all stability boundaries. Our theoretical results apply to the asymmetric Hill's equation, of which the pendulum system is a special case. We demonstrate this with numerical studies of a more general asymmetric Mathieu equation.

Mandelic acid (1) and its derivatives and 1-naphthylglycolic acid (8) were used as modifiers for the asymmetric hydrogenation of ketopantolactone to pantolactone on supported Pt, Ru, and Rh catalysts. A systematic variation of the modifier structure showed that 8 was the best modifier, affording up to 28% ee on Pt; the other metals were barely efficient. The catalytic studies were completed with FTIR spectroscopic analysis of the modifier-modifier and modifier-substrate interactions in solution. Attenuated total reflection infrared spectroscopy was applied to study the adsorption of the α-hydroxy-carboxylic acid type modifiers on a Pt/Al 2 O 3 model catalyst in the presence of hydrogen. The study indicates that the modifiers are present on the metal surface as monomers with an internal hydrogen bond between the hydroxyl group and the carboxyl carbonyl group, and the phenyl or naphthalene rings are in a tilted position relative to the surface. The moderate enantioselection is attributed to a hydrogen bond interaction between the carboxylic OH group of the modifier and the carbonyl O atom of the substrate. The poor enantioselectivities attained in ketopantolactone hydrogenation may be explained by the overly weak adsorption of the modifiers on Pt and by the weakness of the O-H-O-type H bond between the substrate and the modifiers. It seems that the carboxyl group has a double role, allowing interaction with the substrate and the Pt surface.

The allylic substitution of (E)-1,3-diphenylallyl acetate (1a) with dimethyl malonate was investigated on Pd/Al 2 O 3 modified by (R)-and (S)-BINAP, (S,S)-Chiraphos, (R)-C 3 -Tunephos, and (R)-Solphos. Stable performance of Pd/Al 2 O 3 required its reduction in hydrogen before the allylic substitution reaction, which was carried out under Ar. The enantioselectivity of the Pd/Al 2 O 3 -BINAP system [58-60% ee to (S)-2] was independent of the reaction temperature (60 and 120 • C), and only 300 ppm BINAP related to 1a was required. According to UV-vis analysis, only a small fraction of BINAP was adsorbed on Pd/Al 2 O 3 . At 120 • C, full conversion and 94% chemoselectivity were achieved in 6 h. For comparison, analogous soluble Pd-BINAP complexes were poorly efficient and afforded low ee to the opposite enantiomer of the product at 60 • C or above. Electron microscopy could detect no restructuring of Pd in Pd/Al 2 O 3 during the reaction. Surprisingly, the addition of BINAP induced a significant rate acceleration (by a factor of almost 7 at 60 • C) and also improved the chemoselectivity of Pd/Al 2 O 3 . Among the diphosphine ligands tested, (R)-Solphos was the most effective (67% ee). An important advantage of the Pd/Al 2 O 3 -BINAP system is that it can transform not only the allyl acetate 1a, but also the corresponding allyl alcohol 1b without the application of any additive.

The aim of this study is to investigate whether market reacts asymmetrically to the issuance of selected sukuk structures (ijarah and musyarakah) in Malaysia for the period 2008-2011. The estimation periods in this study are from 2004-2006. Data are collected from the Securities Commission Malaysia (SC) and Bloomberg database. The study employs event study methodology using cumulative average abnormal return (CAAR) on symmetric and asymmetric events based on the reaction of the FTSE Kuala Lumpur Composite Index (FTSEKLCI) to the announcement of sukuk issuance. The results indicate positive, significant and both symmetric and asymmetric market reactions to sukuk issuance. Hence, market reacts positively and asymmetrically to the announcements of ijarah and musyarakah after the recent crisis. The findings would be useful to issuers, investors and decision-makers to ensure the stability of Islamic capital market and sustainable economic growth.

Small molecule asymmetric catalysts are often described as being "good" or "bad" but to date there has been no way of comparing catalyst efficiency quantitatively. We define a simple formula, Asymmetric Catalyst Efficiency (ACE), that allows for such a comparison. We propose that a catalyst is more efficient if fewer atoms are utilised to give a product in a required enantiomeric excess. We illustrate this concept by analysing several well-known asymmetric catalytic chemical reactions carried out in academic laboratories, and compare small molecule catalysts with enzymes. We conclude that ACE is a useful descriptor for the comparison of diverse catalytic systems. It is also noteworthy that, despite the relatively short period of investigation into small molecule catalysts, they are competitive with enzymes with regards to this measure of catalytic efficiency.

The importance of click chemistry is widely recognized. Among all the known click reactions, those involving tetrazines represent the fastest click reactions reported and are generating a great deal of interest. However, there is no efficient entry to asymmetric tetrazines and those with strong electron withdrawing groups, which limits the development of this field. Herein, we report a general and efficient entry to asymmetric tetrazines with strongly electron withdrawing groups.