Stochastic tunneling across fitness valleys can give rise to a logarithmic long-term fitness trajectory

Adaptation, where a population evolves increasing fitness in a fixed environment, is typically thought of as a hill-climbing process on a fitness landscape. With a finite genome, such a process eventually leads the population to a fitness peak, at which point fitness can no longer increase through individual beneficial mutations. Instead, the ruggedness of typical landscapes due to epistasis between genes or DNA sites suggests that the accumulation of multiple mutations (via a process known as stochastic tunneling) can allow a population to continue increasing in fitness. However, it is not clear how such a phenomenon would affect long-term fitness evolution. By using a spin-glass type model for the fitness function that takes into account microscopic epistasis, we find that hopping between metastable states can mechanistically and robustly give rise to a slow, logarithmic average fitness trajectory.

Strain-induced modulations of electronic structure and electron–phonon coupling in dense H3S

External stress is an effective tool to modulate the Fermi surface topology, logarithmic average frequency, and electron–phonon coupling parameter of dense H3S and thus has a sensitive and considerable effect to the superconducting critical temperature.

ON BINARY CORRELATIONS OF MULTIPLICATIVE FUNCTIONS

We study logarithmically averaged binary correlations of bounded multiplicative functions $g_{1}$ and $g_{2}$. A breakthrough on these correlations was made by Tao, who showed that the correlation average is negligibly small whenever $g_{1}$ or $g_{2}$ does not pretend to be any twisted Dirichlet character, in the sense of the pretentious distance for multiplicative functions. We consider a wider class of real-valued multiplicative functions $g_{j}$, namely those that are uniformly distributed in arithmetic progressions to fixed moduli. Under this assumption, we obtain a discorrelation estimate, showing that the correlation of $g_{1}$ and $g_{2}$ is asymptotic to the product of their mean values. We derive several applications, first showing that the numbers of large prime factors of $n$ and $n+1$ are independent of each other with respect to logarithmic density. Secondly, we prove a logarithmic version of the conjecture of Erdős and Pomerance on two consecutive smooth numbers. Thirdly, we show that if $Q$ is cube-free and belongs to the Burgess regime $Q\leqslant x^{4-\unicode[STIX]{x1D700}}$, the logarithmic average around $x$ of the real character $\unicode[STIX]{x1D712}\hspace{0.6em}({\rm mod}\hspace{0.2em}Q)$ over the values of a reducible quadratic polynomial is small.

Findings from measurements of noise levels in indoor and outdoor environments in an expanding urban area: a case of Tirana

The increasing human population and the increasing number of vehicles in Tirana, Albania, emerges the need for extensive measurements of noise levels. The 831 measurements of noise levels were taken in Tirana in November 2015 for education purposes. Measurements were collected in eight locations in indoor like a classroom in a school building environment, a library and a healthcare facility and in outdoor environments like five crossroads. Noise levels were then compared with domestic and World Health Organization (WHO) standards. The logarithmic average of noise levels and the maximum value of noise level measured for the period of measurement (LAFmax) were interpolated using Interpolated Noise Levels for Observer Points in ArcGIS producing noise level maps for crossroads. The logarithmic average of noise levels and LAFmax measurements were respectively above domestic and WHO standards in 96% and 100% of outdoor environment and indoor environment locations. Interpolated values of logarithmic average of noise levels and LAFmax for five crossroads were above domestic and WHO standards indicating noise levels in road traffic could remain high. A yearly acoustic measurement for vehicles should be implemented. Participatory measurements of noise levels in quite indoor environments can be used to increase the awareness of inhabitants in Tirana.

On the functional complexity of a two-dimensional interval search problem

We suggest a modification of the Bentley-Maurer algorithm which solves a twodimensional interval search problem. This modification allows us to decrease the initially logarithmic average search time to constant, retaining the logarithmic worst-case search time. This algorithm depends on a parameter whose change results in variation of the needed memory from Ϭ(k

STATISTICAL COMPARISON OF LOGARITHMIC-AVERAGE, 3-OUT-OF-4, AND 3-OUT-OF-5 METHODS FOR GRADING MILK BY PLATE COUNTS

Analyses of 469 series of plate counts from milksheds in almost every region of the country showed clearly that the 3-out-of-4 method of grading bacterial quality of milk by plate counts is considerably more stringent than the log-average method. In practice a 3-out-of-5 rule yields about the same proportion of violations and degradings as the log-average: These findings held for a grade limit of 100,000 as well as 200,000 colonies per ml. Wide, roughly periodic fluctuations in plate counts were often observed, but did not appear to be related to season of the year.