Exact solutions to the modified Korteweg-de Vries equation

A formula for certain exact solutions to the modified Korteweg-de Vries (mKdV) equation is obtained via the inverse scattering transform method. The kernel of the relevant Marchenko integral equation is written with the help of matrix exponentials as $$\Omega(x+y;t)=Ce^{-(x+y)A}e^{8A^3 t}B,$$ where the real matrix triplet $(A,B,C)$ consists of a constant $p\times p$ matrix $A$ with eigenvalues having positive real parts, a constant $p\times 1$ matrix $B$, and a constant $1\times p$ matrix $C$ for a positive integer $p$. Using separation of variables, the Marchenko integral equation is explicitly solved yielding exact solutions to the mKdV equation. These solutions are constructed in terms of the unique solution $P$ to the Sylvester equation $AP+PA=BC$ or in terms of the unique solutions $Q$ and $N$ to the respective Lyapunov equations $A^\dagger Q+QA=C^\dagger C$ and $AN+NA^\dagger=BB^\dagger$, where the $\dagger$ denotes the matrix conjugate transpose. Two interesting examples are provided.Comment: 15 pages, 1 figur

Molecular dynamics simulation of an activated transfer reaction in zeolites

The activated transfer of a light particle between two heavier species in the micropores of silicalite and ZK4 zeolites has been studied through molecular dynamics (MD) simulations. A three-body potential controls the exchange of the light particle between the heavier ones; an effective barrier of a few kBT separates the two stable regions corresponding to symmetric "reactant" and "product" species. Harmonic forces always retain the reactants at favorable distances so that in principle only the energetic requirement must be fulfilled for the transfer to occur. The rate constant for the process (obtained from a correlation analysis of equilibrium MD trajectories) decreases by more than one order of magnitude when the barrier height is increased from 2kBT to 5kBT following an Arrhenius-type behavior. The transfer rates are always lower in ZK4. When the reaction is studied in a liquid solvent the calculated rate constants are closer to those obtained in silicalite. Since with this model the diffusive approach of the reactants is almost irrelevant on the reactive dynamics, only the different ability of each environment to transfer the appropriate energy amount to the reactants and then promote the barrier passage could be invoked to explain the observed behavior. We found that structural, rather than energetic, effects are mainly involved on this point. The lower efficiency of ZK4 seems to arise from the frequent trapping of the reactive complex in the narrow ZK4 windows in which the transfer is forbidden and from the weaker interaction of the reactive complex with the host framework compared to silicalite

Diffusion and vibrational relaxation of a diatomic molecule in the pore network of a pure silica zeolite: a molecular dynamics study

The vibrational relaxation and the diffusion of diatomic molecules in the zeolite silicalite have been studied through molecular dynamics simulations in the microcanonical statistical ensemble. The adopted model accounts for the vibrations of the framework and sorbed atoms using a harmonic potential for the silicalite and a Morse potential for the diatomic molecule. The results show that the framework favors the relaxation of diatomics oscillating at frequencies near to its characteristic vibrational frequencies, leading in such cases to lower relaxation times and to an increasing in the energy exchanged per collision. The diffusion of a two-site oscillating molecule representing ethane has been also investigated; the diffusion coefficient and the heat of adsorption agree very well with the experimental data. Arrhenius parameters for the diffusion have been calculated, and some insights into the diffusion mechanism have been obtained from log–log plots and by inspection of the distribution of the ethane molecules in the silicalite channels. Therefore the simplified model adopted seems to adequately describe the diffusive motion and the guest–host energy exchanges, and it could be useful in order to study simple bimolecular reactions in zeolites

Effetto della memantina su modelli animali di disturbi dell'umore

AIM: Mood disorders are one of the leading causes of morbidity, disability and premature mortality contributing for about 50% of the non-fatal burden of mental disorders. Bipolar disorder (BD) has a lifetime prevalence of approximately 1.0% for BD-I, 1.1% for BD-II and 2.4% for BD-NOS. Eighty-three percent of BD cases are classified as “seriously severe” and 17.1% as “moderately severe”. Long-term prophylactic treatment of BD aimed at preventing recurrences of the various phases is a leading clinical and research challenge for contemporary psychiatry. Dopaminergic behavioural supersensitivity induced by chronic treatment with antidepressants might be involved both in the antidepressant action and in the mechanisms underlying antidepressant treatment-related mania (antidepressant-induced mood switch and possibly, rapid cycling bipolar disorder). The stimulation of NMDA receptors is required for the development of dopamine receptor sensitization induced by antidepressants. Indeed, the administration of MK-801, a selective non-competitive NMDA receptor blocker, completely prevents the dopamine receptor sensitization induced by imipramine and by electroconvulsive shock. These observations strongly suggest that the non-competitive blockade of NMDA receptors should result in an anti-manic and mood stabilizing action, and that it should also be effective in the treatment of the disorders resistant to currently used antimanic and mood stabilizers. Memantine is a non-competitve NMDA receptor antagonist, she has been on the market in since 1982 for the treatment of Parkinsonism, before its approval in 2002 and 2004 by EMEA and FDA for the treatment of moderate to severe Alzheimer's Disease. Although its actual efficacy on the AD patient's quality of life has proven to be moderate, several pre-marketing and post marketing studies have demonstrated the excellent safety and tolerability profile of the drug. Moreover, the drug has been used off-label in a number of neurological and psychiatric conditions, including depression, with conflicting and inconclusive results. To further clarify the farmacology of memantine, I studied hers effect in animal models of in mood disorders. METHOD: Male and Female rats treated with memantine in animal model of: • dopaminergic behavioural supersensitivity • bipolard disorders by chronic antidepressant • stress • catatonia by haloperidol • tardive dyskinesia by cronic haloperidol RESULTS: The results show that memantine, at variance with antidepressant treatments (including drugs, electroconvulsive schock, REM-sleep deprivation), fails to induce dopaminergic behavioural supersensitivity. Therefore has not an antidepressant action. Memantine prevents not only, as observed with MK-801, the sensitization of dopamine receptors induced by chronic imipramine (mania), but also the ensuing desensitization of those receptors and the associated depressive-like behavior. Thus stabilizes the course of the manic-depressive illness Furthermore, memantine prevents stress, catatonia and tardive dyskinesia. This observation is consistent with the results of clinical studies suggesting that memantine has not an antidepressant action but an antimanic and mood-stabilizing effect.</br

"Two-step" model of molecular diffusion in silicalite

The influence of the particle "memory" on long-range diffusion in the channel network of silicalite is taken into account by considering pairs of subsequent steps between the channel intersections. It is shown that in this case the correlation rule between the principal elements of the diffusion tensor has to be modified by including an additional term, which takes account of the deviation of molecular propagation from complete randomness. The obtained relations are discussed in terms of molecular dynamics simulations of ethane in silicalite

Adversarial Detection of Flash Malware: Limitations and Open Issues

During the past four years, Flash malware has become one of the most insidious threats to detect, with almost 600 critical vulnerabilities targeting Adobe Flash disclosed in the wild. Research has shown that machine learning can be successfully used to detect Flash malware by leveraging static analysis to extract information from the structure of the file or its bytecode. However, the robustness of Flash malware detectors against well-crafted evasion attempts - also known as adversarial examples - has never been investigated. In this paper, we propose a security evaluation of a novel, representative Flash detector that embeds a combination of the prominent, static features employed by state-of-the-art tools. In particular, we discuss how to craft adversarial Flash malware examples, showing that it suffices to manipulate the corresponding source malware samples slightly to evade detection. We then empirically demonstrate that popular defense techniques proposed to mitigate evasion attempts, including re-training on adversarial examples, may not always be sufficient to ensure robustness. We argue that this occurs when the feature vectors extracted from adversarial examples become indistinguishable from those of benign data, meaning that the given feature representation is intrinsically vulnerable. In this respect, we are the first to formally define and quantitatively characterize this vulnerability, highlighting when an attack can be countered by solely improving the security of the learning algorithm, or when it requires also considering additional features. We conclude the paper by suggesting alternative research directions to improve the security of learning-based Flash malware detectors

Symmetries for exact solutions to the nonlinear Schr\"odinger equation

A certain symmetry is exploited in expressing exact solutions to the focusing nonlinear Schr\"odinger equation in terms of a triplet of constant matrices. Consequently, for any number of bound states with any number of multiplicities the corresponding soliton solutions are explicitly written in a compact form in terms of a matrix triplet. Conversely, from such a soliton solution the corresponding transmission coefficients, bound-state poles, bound-state norming constants and Jost solutions for the associated Zakharov-Shabat system are evaluated explicitly. It is also shown that these results hold for the matrix nonlinear Schr\"odinger equation of any matrix size