Channel-Supermodular Entropies: Order Theory and an Application to Query Anonymization

This work introduces channel-supermodular entropies, a subset of quasi-concave entropies. Channel-supermodularity is a property shared by some of the most commonly used entropies in the literature, including Arimoto–Rényi conditional entropies (which include Shannon and min-entropy as special cases), k-tries entropies, and guessing entropy. Based on channel-supermodularity, new preorders for channels that strictly include degradedness and inclusion (or Shannon ordering) are defined, and these preorders are shown to provide a sufficient condition for the more-capable and capacity ordering, not only for Shannon entropy but also regarding analogous concepts for other entropy measures. The theory developed is then applied in the context of query anonymization. We introduce a greedy algorithm based on channel-supermodularity for query anonymization and prove its optimality, in terms of information leakage, for all symmetric channel-supermodular entropies.     

Water as the Key to Proto‐Aragonite Amorphous CaCO3

Temperature and pH value can affect the short‐range order of proto‐structured and additive‐free amorphous calcium carbonates (ACCs). Whereas a distinct change occurs in proto‐vaterite (pv) ACC above 45 °C at pH 9.80, proto‐calcite (pc) ACC (pH 8.75) is unaffected within the investigated range of temperatures (7–65 °C). IR and NMR spectroscopic studies together with EXAFS analysis showed that the temperature‐induced change is related to the formation of proto‐aragonite (pa) ACC. The data strongly suggest that the binding of water molecules induces dipole moments across the carbonate ions in pa‐ACC as in aragonite, where the dipole moments are due to the symmetry of the crystal structure. Altogether, a (pseudo‐)phase diagram of the CaCO₃ polyamorphism in which water plays a key role can be formulated based on variables of state, such as the temperature, and solution parameters, such as the pH value.     

Efficient and Eco‐friendly Syntheses of 1,5‐Benzothiazepines and 1,5‐Benzodiazepines Catalyzed by [Hmim][NO3] under Mild Conditions

This article presents a synthetic method and reaction mechanism of the 1,5‐benzothiazepines and 1,5‐benzodiazepines derivatives. In this research, 36 thiazepines and diazepines (mostly new) with a new method have been prepared and their structures have been characterized by spectroscopic methods. Crystal structures of a new thiazepine and diazepine (seven‐membered rings) have also been determined and compared with thiazine (six‐membered ring). In this method, N‐methylimidazolium nitrate [Hmim][NO₃] has been used as a catalyst that acts as an environmental friendly system.     

Intramolecular interactions in nitroamines studied by 1H, 13C, 15N and 17O NMR spectral and quantum chemical methods

¹H, ¹³C, ¹⁵N and ¹⁷O NMR chemical shifts are used for the characterization of the intramolecular interactions in several nitramines of the Me₂N-G-NO₂ type. The charge of lone electron pair of the amino group in N,N-dimethylnitramine, N,N-dimethyl-2-nitroethenamine, N,N-dimethyl-p-nitroaniline, 4-nitro-β-dimethylaminostyrene, 4-N,N-dimethylamino-β-nitrostyrene, 4-(N,N-dimethylamino)-4′-nitrobiphenyl, and 4-(N,N-dimethylamino)-4′-nitrostilbene is transferred not only to the nitro oxygens, but also to the vinylene and benzene carbons of the G spacer and to N-methyl carbons as well. Decreased nuclear shielding is found to be qualitatively related to the decreased atomic charge around a nucleus. This finding was further verified and quantified by comparison of the NMR data with those obtained by ab initio quantum chemical calculations. ¹⁷O NMR chemical shift changes seem to be more significant when the interacting NMe₂ and NO₂ groups are separated by a short spacer. On the other hand, ¹⁵N NMR chemical shifts suggest that a decrease of the charge at the amino nitrogen is not related to the length of the spacer alone. A lack of the linear dependence between the ¹⁷O_nitro and ¹⁵N_amino chemical shifts suggests that the charge lost by the amino nitrogen was only partially gained by the oxygens in the nitro group. The increased shieldings of the aryl carbons in 4-(N,N-dimethylamino)-4′-nitrobiphenyl indicate that atoms of the p,p-biphenylene spacer also gain some charge originating from the amino nitrogen. ³ J _H,H spin–spin coupling constant shows that among different vinylene compounds, the charge transfer to the nitro group is practically effective only in N,N-dimethyl-2-nitroethenamine where the bond between the vinylene carbons is significantly of low order by character. The calculated Natural Population Analysis (NPA) data confirms that except the nitro oxygens, other atoms that receive the negative charge lost by NMe₂ in the compounds studied are the aryl and N-methyl carbons.