The use of ideas of Information Theory for studying "language" and intelligence in ants

In this review we integrate results of long term experimental study on ant "language" and intelligence which were fully based on fundamental ideas of Information Theory, such as the Shannon entropy, the Kolmogorov complexity, and the Shannon's equation connecting the length of a message ($l$) and its frequency $(p)$, i.e. $l = - \log p$ for rational communication systems. This approach, new for studying biological communication systems, enabled us to obtain the following important results on ants' communication and intelligence: i) to reveal "distant homing" in ants, that is, their ability to transfer information about remote events; ii) to estimate the rate of information transmission; iii) to reveal that ants are able to grasp regularities and to use them for "compression" of information; iv) to reveal that ants are able to transfer to each other the information about the number of objects; v) to discover that ants can add and subtract small numbers. The obtained results show that Information Theory is not only wonderful mathematical theory, but many its results may be considered as Nature laws

Real-space Manifestations of Bottlenecks in Turbulence Spectra

An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature of oscillations in the real-space velocity, which are explained by boundary-layer-expansion techniques. Pseudospectral simulations are used to show that such oscillations occur in velocity correlation functions in one- and three-dimensional hyperviscous hydrodynamical equations that display genuine turbulence.Comment: 5 pages, 2 figure

Observation of Lasing Mediated by Collective Atomic Recoil

We observe the buildup of a frequency-shifted reverse light field in a unidirectionally pumped high-$Q$ optical ring cavity serving as a dipole trap for cold atoms. This effect is enhanced and a steady state is reached, if via an optical molasses an additional friction force is applied to the atoms. We observe the displacement of the atoms accelerated by momentum transfer in the backscattering process and interpret our observations in terms of the collective atomic recoil laser. Numerical simulations are in good agreement with the experimental results.Comment: 4 pages, 3 figure

Slow dynamics in a turbulent von K\'arm\'an swirling flow

We present an experimental study of a turbulent von K\'arm\'an flow produced in a cylindrical container using two propellers. The mean flow is stationary up to $Re = 10^4$, where a bifurcation takes place. The new regime breaks some symmetries of the problem, and is time-dependent. The axisymmetry is broken by the presence of equatorial vortices with a precession movement, being the velocity of the vortices proportional to the Reynolds number. The reflection symmetry through the equatorial plane is broken, and the shear layer of the mean flow appears displaced from the equator. These two facts appear simultaneously. In the exact counterrotating case, a bistable regime appears between both mirrored solutions and spontaneous reversals of the azimuthal velocity are registered. This evolution can be explained using a three-well potential model with additive noise. A regime of forced periodic response is observed when a very weak input signal is applied.Comment: Improved model, additional results and figures, accepted in PR

Why the P600 is not just a P300: The role of the basal ganglia

One of the important issues in event-related brain potential research is whether the language-related P600 and the P300 oddball effect are distinct components or not. We addressed this question by testing 14 aphasic patients, half of them with lesions including the basal ganglia and half of them with temporo-parietal lesions, in both an auditory oddball task and an experiment with auditory presented verb inflection violations. Whereas both patient groups displayed a clear P300 effect in the oddball experiment, only the group with temporo-parietal lesions showed a P600 in the language experiment. These data indicate that the basal ganglia seem to play a crucial role in the modulation of the P600, but not of the P300 component

Syntactic language processing: ERP lesion data on the role of the basal ganglia

The role of the basal ganglia in syntactic language processing was investigated with event-related brain potentials in fourteen neurologically impaired patients. Seven of these patients had basal ganglia lesions while 7 other patients primarily had lesions of the left temporo-parietal region excluding the basal ganglia. All patients listened to sentences that were either correct or included a verb argument structure violation. In previous experiments this type of violation elicited a biphasic pattern of an N400-P600 complex in young healthy participants. While the N400 may result from incorrect semantic-thematic role assignment, the P600 reflects the fact that verb information does not license the syntactic structure at present. Results of the patient experiment revealed a double dissociation: patients with left temporo-parietal lesions only show a P600, whereas patients with lesions of the basal ganglia showed no P600, but a negativity with extended duration that resembled an N400. The latter pattern not only confirms previous reports that the basal ganglia modulate the P600 but extends these results by showing that the N400 as a late semantic-thematic integration process appears partially modulated by the basal ganglia

Conditional regularity of solutions of the three dimensional Navier-Stokes equations and implications for intermittency

Two unusual time-integral conditional regularity results are presented for the three-dimensional Navier-Stokes equations. The ideas are based on $L^{2m}$-norms of the vorticity, denoted by $\Omega_{m}(t)$, and particularly on $D_{m} = \Omega_{m}^{\alpha_{m}}$, where $\alpha_{m} = 2m/(4m-3)$ for $m\geq 1$. The first result, more appropriate for the unforced case, can be stated simply : if there exists an $1\leq m < \infty$ for which the integral condition is satisfied ($Z_{m}=D_{m+1}/D_{m}$) $$\int_{0}^{t}\ln (\frac{1 + Z_{m}}{c_{4,m}}) d\tau \geq 0$$ then no singularity can occur on $[0, t]$. The constant $c_{4,m} \searrow 2$ for large $m$. Secondly, for the forced case, by imposing a critical \textit{lower} bound on $\int_{0}^{t}D_{m} d\tau$, no singularity can occur in $D_{m}(t)$ for \textit{large} initial data. Movement across this critical lower bound shows how solutions can behave intermittently, in analogy with a relaxation oscillator. Potential singularities that drive $\int_{0}^{t}D_{m} d\tau$ over this critical value can be ruled out whereas other types cannot.Comment: A frequency was missing in the definition of D_{m} in (I5) v3. 11 pages, 1 figur

Kinetic theory of age-structured stochastic birth-death processes

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution

Identification of the honey bee swarming process by analysing the time course of hive vibrations

Honey bees live in groups of approximately 40,000 individuals and go through their reproductive cycle by the swarming process, during which the old queen leaves the nest with numerous workers and drones to form a new colony. In the spring time, many clues can be seen in the hive, which sometimes demonstrate the proximity to swarming, such as the presence of more or less mature queen cells. In spite of this the actual date and time of swarming cannot be predicted accurately, as we still need to better understand this important physiological event. Here we show that, by means of a simple transducer secured to the outside wall of a hive, a set of statistically independent instantaneous vibration signals of honey bees can be identified and monitored in time using a fully automated and non-invasive method. The amplitudes of the independent signals form a multi-dimensional time-varying vector which was logged continuously for eight months. We found that combined with specifically tailored weighting factors, this vector provides a signature highly specific to the swarming process and its build up in time, thereby shedding new light on it and allowing its prediction several days in advance. The output of our monitoring method could be used to provide other signatures highly specific to other physiological processes in honey bees, and applied to better understand health issues recently encountered by pollinators