Regular and almost universal hashing: an efficient implementation

Random hashing can provide guarantees regarding the performance of data structures such as hash tables---even in an adversarial setting. Many existing families of hash functions are universal: given two data objects, the probability that they have the same hash value is low given that we pick hash functions at random. However, universality fails to ensure that all hash functions are well behaved. We further require regularity: when picking data objects at random they should have a low probability of having the same hash value, for any fixed hash function. We present the efficient implementation of a family of non-cryptographic hash functions (PM+) offering good running times, good memory usage as well as distinguishing theoretical guarantees: almost universality and component-wise regularity. On a variety of platforms, our implementations are comparable to the state of the art in performance. On recent Intel processors, PM+ achieves a speed of 4.7 bytes per cycle for 32-bit outputs and 3.3 bytes per cycle for 64-bit outputs. We review vectorization through SIMD instructions (e.g., AVX2) and optimizations for superscalar execution.Comment: accepted for publication in Software: Practice and Experience in September 201

Multiscale Approach for the Optimization of Ketones Production From Carboxylic Acids by the Decarboxylative Ketonization Reaction

A historical perspective on the advancement of the decarboxylative ketonization catalysis research and development in industry and in academia is given with the focus on the past twenty years. Reviewed topics cover results of the most recent computational modeling and isotopic labeling studies, fine details of the reaction mechanism, experimental evidence for the existence of hidden degenerate reactions, explanation of the reaction rate inhibition, and reversibility of the reaction course. For this reaction, characterized strictly as acid-base catalysis, the origin of the misconception about the requirement for metal oxide catalysts being reducible and oxidizable is explained. Technology solutions for the selectivity improvement, as well as factors affecting catalyst stability are discussed. The review is prepared with the goal to help with the scaling up decarboxylative ketonization reaction for existing production of industrial ketones and for any bio fuels upgrading processes in the future

Cross-Selectivity in the Catalytic Ketonization of Carboxylic Acids

A mixture of acetic and 2-methylpropanoic (isobutyric) acids representing non-branched and branched acids, respectively, was catalytically converted to a mixture of ketones in a set of statistically designed experiments (DOE). The selectivity toward the cross-ketonization product was analyzed depending on (a) temperature within 300–450 °C range, (b) molar fraction of each acid in the mixture, from 10% to 90%, and (c) liquid hourly space velocity (LHSV) within 2–12 h−1, and compared against the selectivity toward two symmetrical ketones. Six metal oxide catalysts were tested and ranked on their ability to yield the cross-product as opposed to the self-condensation product. The catalysts were based on either the anatase form of titania or monoclinic form of zirconia and treated with either KOH or K2HPO4. The titania catalyst treated by KOH outperformed all other catalysts by providing the cross-selectivity above the statistically expected binomial distribution. The criterion for having a high cross-selectivity in the decarboxylative ketonization is formulated mathematically as the separation of roles of two acids, one being a more active enolic component, and the other being the preferred carbonyl component. According to the suggested criterion, the less branched acetic acid reacts as both the preferred carbonyl and enolic component with untreated catalysts. Therefore, untreated catalysts promote selective formation of the symmetrical ketone, acetone, thereby decreasing the selectivity to the cross-ketone. After alkaline treatment, both the anatase form of titania and monoclinic form of zirconia increase the isobutyric acid participation as the carbonyl component. Acetic acid remains as the preferred enolic component with all treated catalysts, thus increasing the selectivity toward the cross-product in the ketonization of a mixture of carboxylic acids. The condition for achieving a high cross-selectivity by polarizing roles of the two reactants can be extended to other types of cross-condensations

Equilibrium in the Catalytic Condensation of Carboxylic Acids with Methyl Ketones to 1,3-Diketones and the Origin of the Reketonization Effect

Acetone is the expected ketone product of an acetic acid decarboxylative ketonization reaction with metal oxide catalysts used in the industrial production of ketones and for biofuel upgrade. Decarboxylative cross-ketonization of a mixture of acetic and isobutyric acids yields highly valued unsymmetrical methyl isopropyl ketone (MIPK) along with two less valuable symmetrical ketones, acetone and diisopropyl ketone (DIPK). We describe a side reaction of isobutyric acid with acetone yielding the cross-ketone MIPK with monoclinic zirconia and anatase titania catalysts in the absence of acetic acid. We call it a reketonization reaction because acetone is deconstructed and used for the construction of MIPK. Isotopic labeling of the isobutyric acid’s carboxyl group shows that it is the exclusive supplier of the carbonyl group of MIPK, while acetone provides only methyl group for MIPK construction. More branched ketones, MIPK or DIPK, are less reactive in their reketonization with carboxylic acids. The proposed mechanism of reketonization supported by density functional theory (DFT) computations starts with acetone enolization and proceeds via its condensation with surface isobutyrate to a β-diketone similar to β-keto acid formation in the decarboxylative ketonization of acids. Decomposition of unsymmetrical β-diketones with water (or methanol) by the retrocondensation reaction under the same conditions over metal oxides yields two pairs of ketones and acids (or esters in the case of methanol) and proceeds much faster compared to their formation. The major direction yields thermodynamically more stable products—more substituted ketones. DFT calculations predict even a larger fraction of the thermodynamically preferred pair of products. The difference is explained by some degree of a kinetic control in the opposite direction. Reketonization has lower reaction rates compared to regular ketonization. Still, a high extent of reketonization occurs unnoticeably during the decarboxylative ketonization of acetic acid as the result of the acetone reaction with acetic acid. This degenerate reaction is the major cause of the inhibition by acetone of its own rate of formation from acetic acid at high conversions

Ab initio study of the mechanism of carboxylic acids cross-ketonization on monoclinic zirconia via condensation to beta-keto acids followed by decarboxylation

Catalytic mechanism of acetic and isobutyric acids mixture conversion into two symmetrical and one cross-ketone product on monoclinic zirconia (111) surface was extensively modeled by Density Functional Theory for periodic structures. Several options were evaluated for each mechanistic step by calculating their reaction rate constants. The best option for each kinetically relevant step was chosen by matching calculated rates of reaction with experimental values. Four zirconium surface atoms define each catalytic site. The most favorable pathway includes condensation between surface carboxylates, one of which is enolized through alpha-hydrogen abstraction by lattice oxygen. Condensation of gas phase molecules with the enolized carboxylate on surface is less attainable. The kinetic scheme considers all steps being reversible, except for decarboxylation. The equilibrium constant of the enolization step and the rate constant of the condensation step define the global reaction rate for non-bulky acetic acid. For bulky isobutyric acid, decarboxylation step is added to the kinetic scheme as kinetically significant, while hydrocarbonate departure may also compete with the decarboxylation. Electronic and steric effect of alkyl substituents on the decarboxylation step is disclosed. The cross-selectivity is controlled by both condensation and decarboxylation steps. None of the mechanistic steps require metal oxide to be reducible/oxidizable

Reversibility of the catalytic ketonization of carboxylic acids and of beta-keto acids decarboxylation

Decarboxylation of beta-keto acids in enzymatic and heterogeneous catalysis has been considered in the literature as an irreversible reaction due to a large positive entropy change. We report here experimental evidence for its reversibility in heterogeneous catalysis by solid metal oxide(s) surfaces. Ketones and carboxylic acids having 13C-labeled carbonyl group undergo 13C/12C exchange when heated in an autoclave in the presence of 12CO2 and ZrO2 catalyst. In the case of ketones, the carbonyl group exchange with CO2 serves as evidence for the reversibility of all steps of the catalytic mechanism of carboxylic acids ketonic decarboxylation, i.e. enolization, condensation, dehydration and decarboxylation

Catalytic Condensation of Ketones with Carboxylic Acids

It is found that use of acetone in place of acetic acid in the reaction with isobutyric acid is effective for the synthesis of the cross-ketonization product, methyl isopropyl ketone (MIPK). Rate of MIPK formation is of the same order of magnitude, but slightly lower for acetone compared to acetic acid under similar conditions (Fig. 1). The most active catalyst is KOH-treated titania. The second product of this reaction, DIPK, results from the ketonic decarboxylative condensation of isobutyric acid with itself. The 13C labeled carbonyl group from isobutyric acid is almost exclusively (within the detection error) transferred to the MIPK product (Scheme 2). In the reaction of acetic acid with a more branched ketone, DIPK, only a negligible amount of MIPK is produced with all studied catalysts. Based on the experimental data, the proposed mechanism most likely includes enolization of acetone, followed by its condensation as the nucleophile with isobutyric acid as the electrophile, and completed by the retro-condensation to MIPK (Scheme 2). The order of the enolic components activity, acetic acid ≥ isobutyric acid \u3e acetone \u3e\u3e DIPK, is generally consistent with the order of their adsorption energies on metal oxides. Low or non-branched ketones could be efficiently used in place of one of the acids in the cross-ketonization reaction. Because of the relatively high reaction rate, this process needs to be accounted for in the kinetic scheme of the decarboxylative ketonization

Statistical theory of the excited strip domain structure

A statistical theory of the strip domain structure excited in a bubble film by an oscillating magnetic field is developed. The theory is based on the consideration of the strip domain structure as a thermodynamic system characterized by the spectrum of domain walls oscillation and an effective temperature that is caused by an oscillating magnetic field and film nonuniformities. We found the thermodynamic characteristics of that domain structure and calculated its period as a function of the frequency and amplitude of an oscillating magnetic field.Comment: 6 pages, 3 figure