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The structure, antioxidant and neuroprotective properties of lithium comenate (lithium 5-hydroxy-4-oxo-4H-pyran-2-carboxylate) were studied. Lithium comenate was obtained by reacting comenic acid (H 2 Com) with lithium hydroxide in an aqueous solution. The structure of lithium comenate was confirmed via thermal analysis, mass spectrometry, IR, NMR and UV spectroscopy. The crystal structure was studied in detail via X-ray diffraction. The compound crystallized in a non-centrosymmetric space group of symmetry of the orthorhombic system Pna2 1 in the form of a hydrate, with three water molecules entering the first coordination sphere of the cation Li + and one molecule forming a second environment through non-valent contacts. The gross formula of the complex compound was established [Li(HCom)(H 2 O) 3 ]·H 2 O. It has been established that lithium comenate has a pronounced neuroprotective activity under the excitotoxic effect of glutamate, increasing the survival rate of cultured rat cerebellar neurons more than two-fold. It has also been found that the pre-stress use of lithium comenate at doses of 1 and 2 mg/kg has an antioxidant effect, which is manifested in a decrease in oxidative damage to the brain tissues of mice subjected to immobilization stress. Based on the data available in the literature, we believe that the high neuroprotective and antioxidant efficacy of lithium comenate is a consequence of the mutual potentiation of the pharmacological effects of lithium and comenic acid.

The crystal structure and the biological activity of a new coordination compound of magnesium ions with comenic acid, magnesium comenate, was characterized and studied. Quantitative and qualitative analysis of the compound was investigated in detail using elemental X-ray fluorescent analysis, thermal analysis, IR-Fourier spectrometry, UV spectroscopy, NMR spectroscopy, and X-ray diffraction analysis. Based on experimental analytical data, the empirical formula of magnesium comenate [Mg(HCom) 2 (H 2 O) 6 ]·2H 2 O was established. This complex compound crystallizes with eight water molecules, six of which are the hydration shell of the Mg 2+ cation, and two more molecules bind the [Mg(H 2 O) 6 ] 2+ aquacation with ionized ligand molecules by intermolecular hydrogen bonds. The packing of molecules in the crystal lattice is stabilized by a branched system of hydrogen bonds with the participation of solvate water molecules and oxygen atoms of various functional groups of ionized ligand molecules. With regard to the biological activity of magnesium comenate, a neuroprotective, stress-protective, and antioxidant effect was established in in vitro and in vivo models. In in vitro experiments, magnesium comenate protected cerebellar neurons from the toxic effects of glutamate and contributed to the preservation of neurite growth parameters under oxidative stress caused by hydrogen peroxide. In animal studies, magnesium comenate had a stress-protective and antioxidant effect in models of immobilization-cold stress. Oral administration of magnesium comenate at a dose of 2 mg/kg of animal body weight for 3 days before stress exposure and for 3 days during the stress period led to a decrease in oxidative damage and normalization of the antioxidant system of brain tissues against the background of induced stress. The obtained results indicate the advisability of further studies of magnesium comenate as a compound potentially applicable in medicine for the pharmacological correction of conditions associated with oxidative and excitotoxic damage to nerve cells.

We study the recognition capabilities of the Hopfield model with auxiliary hidden layers, which emerge naturally upon a Hubbard-Stratonovich transformation. We show that the recognition capabilities of such a model at zero temperature outperform those of the original Hopfield model, due to a substantial increase of the storage capacity and the lack of a naturally defined basin of attraction. The modified model does not fall abruptly into the regime of complete confusion when memory load exceeds a sharp threshold. This latter circumstance, together with an increase of the storage capacity, renders such a modified Hopfield model a promising candidate for further research, with possible diverse applications.

We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size L like ∼Llnln(L). In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a δ peak in the thermodynamic limit L→∞. While previously a lack of self-averaging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.

We discuss the non-self-averaging phenomena in the critical point of weakly disordered Ising ferromagnet. In terms of the renormalized replica Ginzburg-Landau Hamiltonian in dimensions D<4, we derive an explicit expression for the probability distribution function (PDF) of the critical free-energy fluctuations. In particular, using known fixed-point values for the renormalized coupling parameters, we obtain the universal curve for such PDF in the dimension D=3. It is demonstrated that this function is strongly asymmetric: its left tail is much slower than the right one.

We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the X and the Y directions. In the stationary regime the system is described by a nontrivial particle position distribution, P(x,y), which we determine explicitly. We show that this distribution corresponds to a nonequilibrium stationary state, characterized by the presence of space-dependent particle currents which exhibit a nonzero rotor. Theoretical results are confirmed by the numerical simulations.