The power of choice in growing trees

The “power of choice” has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of random tree growth. In our models each new node has k randomly chosen contacts, where k > 1 is a constant. It then attaches to whichever one of these contacts is most desirable in some sense, such as its distance from the root or its degree. Even when the new node has just two choices, i.e., when k = 2, the resulting tree can be very different from a random graph or tree. For instance, if the new node attaches to the contact which is closest to the root of the tree, the distribution of depths changes from Poisson to a traveling wave solution. If the new node attaches to the contact with the smallest degree, the degree distribution is closer to uniform than in a random graph, so that with high probability there are no nodes in the tree with degree greater than O(log log N). Finally, if the new node attaches to the contact with the largest degree, we find that the degree distribution is a power law with exponent -1 up to degrees roughly equal to k, with an exponential cutoff beyond that; thus, in this case, we need k ≫ 1 to see a power law over a wide range of degrees.     

Memory effect in dielectric relaxation I

Dielectric relaxation theory is formulated taking into account the effect of inertia and the memory effect. With the use of the damping theoretical expansion formula, a rigorous equation for the probability density is derived and solved exactly in terms of the Jacobi theta function. Dielectric absorption, dispersion and fluctuation of the dipole moment are determined. For higher frequencies (i.e. short time behavior), deviation from the Debye result is found and the relevance to experiments is discussed.     

Memory effect on the glass transition in vulcanized rubber

The memory effect upon glassification is studied in the glass-to-rubber transition of vulcanized rubber with the strain as a controlling parameter. A phenomenological model is proposed, taking the history of the temperature and the strain into account, by which the experimental results are interpreted. The data and the model demonstrate that the glassy state memorizes the time course of strain upon glassification, not as a single parameter but as the history itself. The data also show that the effect of irreversible deformation in the glassy state is beyond the scope of the present model.     

Memory effect and multifractality of cross-correlations in financial markets

We introduce an instantaneous and an average instantaneous cross-correlation function to detect the temporal cross-correlations between individual stocks based on the daily data of the United States and the Chinese stock markets. The memory effect of the instantaneous cross-correlations is investigated by applying the detrended fluctuation analysis (DFA), where the DFA exponents can be partly explained by the correlation function from the common sense. Long-range memory is observed for the average instantaneous cross-correlations, and persists up to a month magnitude of timescale for the United States stock market and half a month magnitude of timescale for the Chinese stock market. In addition, multifractal nature is investigated by a multifractal detrended fluctuation analysis.     

Memory effect evaluation based on transmission matrix calculation

The memory effect is a type of auto correlation observed in linear systems, which is widely used to control scattered light through thin scattering layers.We show that there exists a strong correlation among the optimized phase distributions of adjacent focal points in focusing through scattering media.The numeric simulation and experiment indicate that within the memory effect, the phase difference between the two adjacent focal points shows an optical phase fringe pattern, and the closer the adjacent focal points are, the wider the fringe pattern will be, corresponding to the tilting of a plane wave phase added onto the acquired optical phase distribution at the focal point.This effect can be utilized for achieving optimal phase distributions of focal point scanning without optical phase evaluation via the experiment, which has great potential application in imaging through the scattering medium.     

Cavitation in trees

Sap is transported under tension (i.e. negative pressure) in trees, according to the tension-cohesion theory. Since water is physically instable under negative pressure, a risk of cavitation is possible. Techniques have been developed during the past two decennia to study cavitation in trees. Trees appear remarkably immune to cavitation events. Cavities form only when extreme water stresses occur or when sap freezes. Nucleation is heterogeneous in trees, presumably caused by the aspiration of air bubbles through conduit walls. Threshold xylem pressures for cavitation vary greatly between species, in concordance with the great functional and ecological diversity of trees. To cite this article: H. Cochard, C. R. Physique 7 (2006).     

Memory recall in arousing situations – an emotional von Restorff effect?

Background  

Previous research has demonstrated a relationship between memory recall and P300 amplitude in list learning tasks, but the variables mediating this P300-recall relationship are not well understood. In the present study, subjects were required to recall items from lists consisting of 12 words, which were presented in front of pictures taken from the IAPS collection. One word per list is made distinct either by font color or by a highly arousing background IAPS picture. This isolation procedure was first used by von Restorff. Brain potentials were recorded during list presentation.     

Memory effect and redistribution of cavitation nuclei in a thin liquid layer

Temporal evolution and spatial distribution of acoustic cavitation structures in a thin liquid layer were investigated experimentally with high-speed photography. The inception and disappearance processes of cavitation bubble cloud revealed that the metastable cavitaton structures formed in the thin liquid layer caused a long-term “memory effect”. A factor which weakens the memory effect was identified. The distribution of cavitation nuclei was investigated by changing the temporal decay of the memory effect.     

Memory effect in MIS structures with amorphous silicon nanoparticles embedded in ultra thin SiOx matrix

Metal/${\mathrm{SiO}}_2$/a-Si-${\mathrm{SiO}}_x$/c-Si structures containing amorphous silicon nanoparticles (a-Si NPs) embedded in ultra thin ${\mathrm{SiO}}_x$ matrix are fabricated by thermal evaporation of ${\mathrm{SiO}}_x$ and sputtering of ${\mathrm{SiO}}_2$ layers followed by thermal annealing at $700{}^{\circ }\mathrm{C}$. A memory effect, due to charging of a-Si NPs in ${\mathrm{SiO}}_x$, is observed. The processes of NP charging and discharging are accomplished by applying pulses with alternative polarities. The observed shift of the flat band voltage of the high-frequency C–V curve caused by a voltage pulse of $-15\mathrm{V}$ having duration of 1 s is more than 3 V. In addition, the structures show good retention characteristics which make them promising for application in non-volatile memory devices.     

Memory effect in the triglycine sulphate crystal polarized not parallel to the ferroelectric axis

The experimental results concerning the electric susceptibility χ₂₂ of the triglycine sulphate (TGS) crystal polarized not parallel to the ferroelectric axis at different temperatures have been shown. The process of partial rejuvenation in the ferroelectric phase has been presented. It has been found that the temperature changes of the slope correspond to step-wise changes of a pyroelectric coefficient p=dP/dT (P=P₂, P₃), where P₂ and P₃ are the longitudinal and transverse polarizations, respectively. An interpretation of temperature dependences of P₂ and P₃ as well as χ₂₂ of the triglycine sulphate ferroelectric previously exposed to a prolonged transverse electric field has been proposed. It has been concluded that the number of elementary cells containing molecules in metastable states depends on temperature in such a way that some kind of memory effect can be observed.     

Conical defects in growing sheets

A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle phi(e) at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if phi(e)0. We construct these states in the regime where bending dominates and determine their energies and how stress is distributed in them. For each state a critical value of phi(e) is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has twofold symmetry.     

Memory effect of pentacene field-effect transistors with embedded monolayer of semiconductor colloidal nano-dots

We demonstrate memory effect of pentacene-based field-effect transistors (FETs) in which CdSe/ZnS colloidal nano-dots (NDs) are embedded. The colloidal NDs were dispersed in chloroform, and spread over a water surface to form monolayer of NDs. Then, they were transferred onto a 30-nm-thick poly(methyl methacrylate) (PMMA) surface by horizontal lifting method, and a 30-nm-thick pentacene film was deposited as an active layer to fabricate FETs. The threshold voltage (V_th) was shifted by ∼10 V after a writing voltage of 70–100 V was applied to the gate electrode of the memory-FETs. On the other hand, such a large shift of V_th was not observed for reference pentacene-FETs without NDs. We consider that the large shift of V_th is due to electrons trapped in the NDs at the interface of pentacene and PMMA layers.     

Remerging Feigenbaum trees in dynamical systems

Finite sequences of remerging period-doubling bifurcations have been recently observed in a variety of physically interesting dynamical systems. We show here that such remerging Feigenbaum trees are quite common in models with more than one parameter and discuss a number of criteria under which they are generally observed. These criteria are applied to simple mappings as well as the conservative Duffing's equation where the formation of a primary “bubble” is seen to lead to higher-order bubbles and hence to remerging Feigenbaum sequences. In the case of Duffing's equation, we follow the development of one such sequence, with the aid of the variation of the winding number along a symmetry axis of the problem.     

Mutation accumulation in growing asexual lineages

The stochastic loss of entire classes of individuals bearing the fewest number of mutations-a process known as Muller's ratchet-is studied in asexual populations growing unconstrained from a single founder. In the neutral regime, where mutations have zero effect on fitness, we derive a recursion equation for the probability distribution of the minimum number of mutations carried by individuals in the least-loaded class, and obtain an explicit condition for the halting of the ratchet. Next, we consider the case of deleterious mutations, and show that weak selection can actually accelerate the ratchet beyond that achieved for the neutral regime. This effect is transitory, however, as our results suggest that even weak purifying selection will eventually lead to the complete cessation of the ratchet. These results may have important implications for problems in biology and the medical sciences.     

Modeling wealth distribution in growing markets

We introduce an auto-regressive model which captures the growing nature of realistic markets. In our model agents do not trade with other agents, they interact indirectly only through a market. Change of their wealth depends, linearly on how much they invest, and stochastically on how much they gain from the noisy market. The average wealth of the market could be fixed or growing. We show that in a market where investment capacity of agents differ, average wealth of agents generically follow the Pareto-law. In few cases, the individual distribution of wealth of every agentcould also be obtained exactly. We also show that the underlying dynamics of other well studied kinetic models of markets can be mapped to the dynamics of our auto-regressive model.     

Mirror nodes in growing random networks

In this article, we consider mirror nodes, which are widely used to reduce local burden, and present two models that are practical for the Internet and probably some other networks. One model introduces an upper limit to the number of links that a node can have, beyond which the node will share the total links with a newly introduced one. Similarly, in the second model, if the number of links exceeds a limit, a new node will be introduced. Unlike the first model, the new node shares with the old one the chance of receiving new links but not the existing links. These models are analytically treated, and from the degree distribution, we can see that the number of nodes with medium links (half the upper limit) increases at the expense of the loss of highly connected nodes. By reducing the burden, this may improve the robustness of the networks.