Dynamics of neural cryptography

Synchronization of neural networks has been used for novel public channel protocols in cryptography. In the case of tree parity machines the dynamics of both bidirectional synchronization and unidirectional learning is driven by attractive and repulsive stochastic forces. Thus it can be described well by a random walk model for the overlap between participating neural networks. For that purpose transition probabilities and scaling laws for the step sizes are derived analytically. Both these calculations as well as numerical simulations show that bidirectional interaction leads to full synchronization on average. In contrast, successful learning is only possible by means of fluctuations. Consequently, synchronization is much faster than learning, which is essential for the security of the neural key-exchange protocol. However, this qualitative difference between bidirectional and unidirectional interaction vanishes if tree parity machines with more than three hidden units are used, so that those neural networks are not suitable for neural cryptography. In addition, the effective number of keys which can be generated by the neural key-exchange protocol is calculated using the entropy of the weight distribution. As this quantity increases exponentially with the system size, brute-force attacks on neural cryptography can easily be made unfeasible.Comment: 9 pages, 15 figures; typos correcte

Genetic attack on neural cryptography

Different scaling properties for the complexity of bidirectional synchronization and unidirectional learning are essential for the security of neural cryptography. Incrementing the synaptic depth of the networks increases the synchronization time only polynomially, but the success of the geometric attack is reduced exponentially and it clearly fails in the limit of infinite synaptic depth. This method is improved by adding a genetic algorithm, which selects the fittest neural networks. The probability of a successful genetic attack is calculated for different model parameters using numerical simulations. The results show that scaling laws observed in the case of other attacks hold for the improved algorithm, too. The number of networks needed for an effective attack grows exponentially with increasing synaptic depth. In addition, finite-size effects caused by Hebbian and anti-Hebbian learning are analyzed. These learning rules converge to the random walk rule if the synaptic depth is small compared to the square root of the system size.Comment: 8 pages, 12 figures; section 5 amended, typos correcte

Glycerol confined in zeolitic imidazolate frameworks: The temperature-dependent cooperativity length scale of glassy freezing

In the present work, we employ broadband dielectric spectroscopy to study the molecular dynamics of the prototypical glass former glycerol confined in two microporous zeolitic imidazolate frameworks (ZIF-8 and ZIF-11) with well-defined pore diameters of 1.16 and 1.46 nm, respectively. The spectra reveal information on the modified alpha relaxation of the confined supercooled liquid, whose temperature dependence exhibits clear deviations from the typical super-Arrhenius temperature dependence of the bulk material, depending on temperature and pore size. This allows assigning well-defined cooperativity length scales of molecular motion to certain temperatures above the glass transition. We relate these and previous results on glycerol confined in other host systems to the temperature-dependent length scale deduced from nonlinear dielectric measurements. The combined experimental data can be consistently described by a critical divergence of this correlation length as expected within theoretical approaches assuming that the glass transition is due to an underlying phase transition.Comment: 14 pages, 5 figures + Supplemental Material (4 pages, 6 figures). Final version as accepted for publicatio

How do random Fibonacci sequences grow?

We study two kinds of random Fibonacci sequences defined by $F_1=F_2=1$ and for $n\ge 1$, $F_{n+2} = F_{n+1} \pm F_{n}$ (linear case) or $F_{n+2} = |F_{n+1} \pm F_{n}|$ (non-linear case), where each sign is independent and either + with probability $p$ or - with probability $1-p$ ($0<p\le 1$). Our main result is that the exponential growth of $F_n$ for $0<p\le 1$ (linear case) or for $1/3\le p\le 1$ (non-linear case) is almost surely given by $$\int_0^\infty \log x d\nu_\alpha (x),$$ where $\alpha$ is an explicit function of $p$ depending on the case we consider, and $\nu_\alpha$ is an explicit probability distribution on \RR_+ defined inductively on Stern-Brocot intervals. In the non-linear case, the largest Lyapunov exponent is not an analytic function of $p$, since we prove that it is equal to zero for $0<p\le1/3$. We also give some results about the variations of the largest Lyapunov exponent, and provide a formula for its derivative

Development of fidelity of delivery and enactment measures for interventions in communication disorders

OBJECTIVES: This study was part of a process evaluation for a single-blind, randomized controlled pilot study comparing Better Conversations with Primary Progressive Aphasia (BCPPA), an approach to communication partner training, with no speech and language therapy treatment. It was necessary to explore fidelity of delivery (delivery of intervention components) and intervention enactment (participants' use of intervention skills in the form of conversation behaviours comprising facilitators, that enhance the conversational flow, and barriers, that impeded the flow of conversation). This study aimed to: (1) Outline an adapted methodological process that uses video observation, to measure both fidelity of delivery and enactment. (2) Measure the extent to which the BCPPA pilot study was delivered as planned, and enacted. DESIGN: Observational methods were used alongside statistical analysis to explore the fidelity of intervention and enactment using video recordings obtained from the BCPPA pilot study. METHODS: A 5-step methodology, was developed to measure fidelity of delivery and enactment for the BCPPA study using video-recorded data. To identify delivery of intervention components, a random sample of eight video recorded and transcribed BCPPA intervention sessions was coded. To examine the enactment of conversation behaviours, 108 transcribed 10 -min-video recorded conversations were coded from 18 participants across the control and intervention group. RESULTS: Checklists and guidelines for measurement of fidelity of treatment delivery and coding spreadsheets and guidelines for measurement of enactment are presented. Local collaborators demonstrated 87.2% fidelity to the BCPPA protocol. Participants in the BCPPA treatment group increased their use of facilitator behaviours enacted in conversation from a mean of 13.5 pre-intervention to 14.2 post-intervention, whilst control group facilitators decreased from a mean of 15.5 to 14.4, over the same timescale. CONCLUSIONS: This study proposes a novel and robust methods, using video recorded intervention sessions and conversation samples, to measure both fidelity of intervention delivery and enactment. The learnings from this intervention are transferable to other communication interventions

Metal-Organic Frameworks in Germany: from Synthesis to Function

Metal-organic frameworks (MOFs) are constructed from a combination of inorganic and organic units to produce materials which display high porosity, among other unique and exciting properties. MOFs have shown promise in many wide-ranging applications, such as catalysis and gas separations. In this review, we highlight MOF research conducted by Germany-based research groups. Specifically, we feature approaches for the synthesis of new MOFs, high-throughput MOF production, advanced characterization methods and examples of advanced functions and properties

Root asymptotics of spectral polynomials for the Lame operator

The study of polynomial solutions to the classical Lam\'e equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schr\"odinger equation with finite gap potential given by the Weierstrass $\wp$-function on the real line. In this paper we establish several natural (and equivalent) formulas in terms of hypergeometric and elliptic type integrals for the density of the appropriately scaled asymptotic distribution of these eigenvalues when the integer-valued spectral parameter tends to infinity. We also show that this density satisfies a Heun differential equation with four singularities.Comment: final version, to appear in Commun. Math. Phys.; 13 pages, 3 figures, LaTeX2

Colonização de substrato artificial por macroinvertebrados límnicos, no delta do rio Jacuí (RS, Brasil).

Com a finalidade de avaliar a colonização de um substrato artificial por macroinvertebrados límnicos, foram realizados experimentos em duas estações de coleta no delta do rio Jacuí, em Porto Alegre (RS, Brasil): Canal do Jacuí (CJ) e Cais do Porto (PO). Os substratos foram constituídos de garrafa PET com uma malha interna de nylon. Os organismos que apresentaram os maiores valores de densidade média no substrato artificial exposto no CJ foram L. fortunei (8229,0ind.m-2), Chironomidae (188,9ind.m-2) e Heleobia piscium (39,6ind.m-2) e no PO, L. fortunei (3233,0ind.m-2), Chironomidae (288,9ind.m-2) e Oligochaeta (211,1ind.m-2). Trochospongilla paulula apresentou uma área de cobertura de bioincrustação de 0,016m2, equivalente a 31,1%, da superfície externa do substrato (PET). A esponja de água doce, Trochospongilla paulula, também cresceu sobre as valvas dos mexilhões (epizoísmo). Por meio do teste T de Student foram verificadas diferenças significativas (p=0,01) entre os valores de densidade média de Oligochaeta verificados no CJ (menor valor) e PO (maior valor). Também foram verificadas diferenças altamente significativas (p<0,0001) entre as áreas de bioincrustação de T. paulula verificados no CJ (maior valor) e PO (menor valor). Os valores de densidade média dos demais taxa nos substratos expostos no CJ e PO não diferiram estatisticamente. O substrato foi adequado para amostrar macroinvertebrados, sobretudo poríferos, grupo de difícil amostragem