Beyond the Death of Linear Response: 1/f optimal information transport

Non-ergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the ``death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating non-ergodic renewal processes, by taking as stimulus a similar non-ergodic process. The ideal condition of 1/f-noise corresponds to a singularity that is expected to be relevant in several experimental conditions.Comment: 4 pages, 2 figures, 1 table, in press on Phys. Rev. Let

Aging and Rejuvenation with Fractional Derivatives

We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index mu in the interval 2<mu <3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord, is given by ord=3-mu . A brand new system is characterized by the degree ord=mu -2. If the system is prepared at time -ta<0$ and the observation begins at time t=0, we derive the following scenario. For times 0<t<<ta the system is satisfactorily described by the fractional derivative with ord=3-mu . Upon time increase the system undergoes a rejuvenation process that in the time limit t>>ta yields ord=mu -2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.Comment: 11 pages, 4 figure

Primary cosmic ray spectrum in the 10 to the 12th power - 10 to the 16th power eV energy range from the NUSEX experiment

A primary cosmic ray spectrum was derived which fits both experimental multiple muon rates and the all-nucleon flux derived from the single muon intensities underground. In the frame of the interaction model developed by Gaisser, Elbert and Stanev, it is possible to reproduce NUSEX muon data with a primary composition in which the iron spectrum is only slightly flatter than the proton one. This result rules out the popular idea that the primary composition varies drastically with increasing energy, leading to the dominance of heavier nuclei at energies 10 to the 15th power to 10 to the 16th power eV

A New Baseline for Diadema antillarum, Echinometra viridis, E. lucunter, and Eucidaris tribuloides Populations Within the Cayos Cochinos MPA, Honduras

We investigated the density of 4 urchin species from 5 shallow reefs in the Cayos Cochinos Marine Protected Area in Honduras. Individual species density varied among reefs with total urchin density ranging from 3.2–7.9 individuals/m2. Echinometra viridis (Agassiz, 1863) was the numerically dominant species (2.29/m2) followed by E. lucunter (Linnaeus, 1758) (1.76/m2) with Eucidaris tribuloides (Lamarck 1816) representing the fewest individuals (0.42/m2). Our results indicated that density of Diadema antillarum (Philippi, 1845) differed significantly among reefs (0.4-1.3/m2, mean = 0.63/m2), but are three times greater than data collected 12 years after the mass mortality event of the 1980’s. Size frequency analysis of D. antillarum indicated that test diameter also differed significantly among reef sites while correlation analysis showed that D. antillarum density was negatively related to both coral and algal cover. Echinometra viridis density, however, was positively related to coral cover (p \u3c 0.05). When all urchins were combined, they showed a negative correlation with algal cover and a positive correlation with coral cover indicating a potential top-down effect within the reefs. While urchin densities remain relatively low compared to other sites in the Caribbean, the D. antillarum population appears to be recovering in this Honduran MPA. If overall grazer abundance continues to increase then they may limit macroalgae on reefs, thereby encouraging coral settlement

Fractional order hereditariness of knee human ligament and tendon

Anterior Cruciate Ligament (ACL) is one of the four major ligaments in the knee, playing a critical role in stabilizing the joint. ACL is highly susceptible to injury, overall during sport activities, often precipitating catastrophic long-term joint outcomes. The ideal replacement graft for a torn ACL would restore native anatomy and function to the knee. Most commonly used autograft and allograft, including patellar tendon (P) and hamstring tendon (H) graft, or bioengineered synthetic grafts, may substantially alter the biomechanics of the knee, permitting a return to only moderate physical activities [1]. Main issues are the sub-optimal graft properties [2] and a still incomplete biomechanics characterization [1]. The goal of the present work is to fully characterize and compare the viscoelastic behavior of the ACL and natural/artificial grafts in order to highlight the differences that should be overcome to achieve a successful biomechanical performance and an ideal graft design