Optimization by ant algorithms: possible roles for an individual ant

In most ant algorithms, the role of each ant is to build a solution in a constructive way, basing each decision on the greedy force and the trails. However, different roles are possible for each individual ant, ranging from a negligible help in the decision process to a refined local search heuristic. In this paper, the importance of the role assigned to each ant is discussed. Three general ant methodologies are presented. Comparative results are analyzed for the well-known graph coloring problem.     

On SA, CA, and GA numbers

Gronwall’s function G is defined for n>1 by $G(n)=\frac{\sigma(n)}{n \log\log n}$ where σ(n) is the sum of the divisors of n. We call an integer N>1 a GA1 number if N is composite and G(N)≥G(N/p) for all prime factors p of N. We say that N is a GA2 number if G(N)≥G(aN) for all multiples aN of N. In (Caveney et al. Integers 11:A33, 2011), we used Robin’s and Gronwall’s theorems on G to prove that the Riemann Hypothesis (RH) is true if and only if 4 is the only number that is both GA1 and GA2. In the present paper, we study GA1 numbers and GA2 numbers separately. We compare them with superabundant (SA) and colossally abundant (CA) numbers (first studied by Ramanujan). We give algorithms for computing GA1 numbers; the smallest one with more than two prime factors is 183783600, while the smallest odd one is 1058462574572984015114271643676625. We find nineteen GA2 numbers ≤5040, and prove that a GA2 number N>5040 exists if and only if RH is false, in which case N is even and >10⁸⁵⁷⁶.     

Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals

We consider a classical system of n charged particles in an external confining potential in any dimension d ≥ 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter is of order n^?1 (mean‐field scaling). By a suitable splitting of the Hamiltonian, we extract the next‐to‐leading‐order term in the ground state energy beyond the mean‐field limit. We show that this next order term, which characterizes the fluctuations of the system, is governed by a new “renormalized energy” functional providing a way to compute the total Coulomb energy of a jellium (i.e., an infinite set of point charges screened by a uniform neutralizing background) in any dimension. The renormalization that cuts out the infinite part of the energy is achieved by smearing out the point charges at a small scale, as in Onsager's lemma. We obtain consequences for the statistical mechanics of the Coulomb gas: next‐to‐leading‐order asymptotic expansion of the free energy or partition function, characterizations of the Gibbs measures, estimates on the local charge fluctuations, and factorization estimates for reduced densities. This extends results of Sandier and Serfaty to dimension higher than 2 by an alternative approach. © 2016 Wiley Periodicals, Inc.     

基于耦合道Gamow壳模型计算17O和17F的能谱以及16O(p,p)反应的微分散射截面

利用耦合道Gamow壳模型计算了17O和17F的低激发能谱以及16O(p,p)反应的低能弹性散射截面。结果表明,17O和17F中非束缚共振态能级的核子发射宽度的计算需要合理地考虑连续态耦合效应。计算得到的17O和17F的低激发能谱以及16O(p,p)反应的低能弹性散射激发函数都与实验数据吻合较好。这说明基于现实核力的计算可更好地描述16O(p,p)反应的低能弹性散射截面。     

Critical reflexivity in financial markets: a Hawkes process analysis

We model the arrival of mid-price changes in the E-mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a decay exponent close to ?1.15 at short times, less than ≈ 10³ s, and crosses over to a second power-law regime with a larger decay exponent ≈–1.45 for longer times scales in the range [10³ ,10⁶ ] seconds. More importantly, we find that the Hawkes kernel integrates to unity independently of the analysed period, from 1998 to 2011. This suggests that markets are and have always been close to criticality, challenging a recent study which indicates that reflexivity (endogeneity) has increased in recent years as a result of increased automation of trading. However, we note that the scale over which market events are correlated has decreased steadily over time with the emergence of higher frequency trading.     

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937–940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix’s radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.     

Superefficient drift estimation on the Wiener space

In the framework of a nonparametric functional estimation for the drift of a Brownian motion $X_t$ we construct Stein type estimators of the form $X_t+D_t\log F$ which are superefficient when $\sqrt{F}$ is a superharmonic functional on the Wiener space for the Malliavin derivative D. To cite this article: N. Privault, A. Réveillac, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

A Class of Integrable Non-QRT Mappings and Their Deautonomisation

We study classes of mappings which do not belong to the QRT family. We obtain several integrable non-autonomous forms of these mappings extending previous results where only linearisable cases were found. Using our recently introduced method of singularity confinement with full deautonomisation, we analyse a mapping which, while non-integrable, does possess confined singularities and show that our method makes it possible to obtain the exact value of its algebraic entropy.     

Direct measurement of the flow field around swimming microorganisms

Swimming microorganisms create flows that influence their mutual interactions and modify the rheology of their suspensions. While extensively studied theoretically, these flows have not been measured in detail around any freely-swimming microorganism. We report such measurements for the microphytes Volvox carteri and Chlamydomonas reinhardtii. The minute (～0.3%) density excess of V. carteri over water leads to a strongly dominant Stokeslet contribution, with the widely-assumed stresslet flow only a correction to the subleading source dipole term. This implies that suspensions of V. carteri have features similar to suspensions of sedimenting particles. The flow in the region around C. reinhardtii where significant hydrodynamic interaction is likely to occur differs qualitatively from a puller stresslet, and can be described by a simple three-Stokeslet model.