Special opportunities for conserving cultural and biological diversity: The co-occurrence of Indigenous languages and UNESCO Natural World Heritage Sites

Recent research indicates that speakers of Indigenous languages often live in or near United Nations Educational, Scientific, and Cultural Organization (UNESCO) Natural World Heritage Sites (WHSs). Because language is a key index of cultural diversity, examining global patterns of co-occurrence between languages and these sites provides a means of identifying opportunities to conserve both culture and nature, especially where languages, WHSs, or both are recognized as endangered. This paper summarizes instances when Indigenous languages share at least part of their geographic extent with Natural WHSs. We consider how this co-occurrence introduces the potential to co­ordinate conservation of nature and sociocultural systems at these localities, particularly with respect to the recently issued UNESCO policy on engaging Indigenous people and the forthcoming International Year of Indigenous Languages. The paper concludes by discussing how the presence of Indigenous people at UNESCO Natural WHSs introduces important opportunities for co-management that enable resident Indigenous people to help conserve their language and culture along with the natural settings where they occur. We discuss briefly the example of Australia as a nation exploring opportunities for employing and strengthening such coordinated conservation efforts

Polymer translocation through a nanopore - a showcase of anomalous diffusion

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one dimensional {\em anomalous} diffusion process in terms of reaction coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown to be governed by an universal exponent $\alpha = 2/(2\nu+2-\gamma_1)$ whose value is nearly the same in two- and three-dimensions. The process is described by a {\em fractional} diffusion equation which is solved exactly in the interval $0 <s < N$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments: $$, and $- < s(t)>^2$ which provide full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo (MC) simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev.

Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equations

It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct consequence, a specialized form of the Ito formula is derived. When a standard Brownian motion is the original semimartingale, classical Ito stochastic differential equations driven by the Brownian motion with drift extend to a larger class of stochastic differential equations involving a time-change with continuous paths. A form of the general solution of linear equations in this new class is established, followed by consideration of some examples analogous to the classical equations. Through these examples, each coefficient of the stochastic differential equations in the new class is given meaning. The new feature is the coexistence of a usual drift term along with a term related to the time-change.Comment: 27 pages; typos correcte

Fractional Fokker-Planck dynamics: Numerical algorithm and simulations

Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying CTRW. An efficient numerical algorithm is developed which is applicable for an arbitrary potential. This algorithm is then applied to investigate the fractional current and the corresponding nonlinear mobility in different washboard potentials. Normal and fractional diffusion are compared through their time evolution of the probability density in state space. Moreover, we discuss the stationary probability density of the fractional current values.Comment: 10 pages, 9 figure

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.Comment: 7 pages, 5 figures, 1 table. Presented at the Conference on Computing in Economics and Finance in Montreal, 14-16 June 2007; at the conference "Modelling anomalous diffusion and relaxation" in Jerusalem, 23-28 March 2008; et

Conformal symmetry in non-local field theories

We have shown that a particular class of non-local free field theory has conformal symmetry in arbitrary dimensions. Using the local field theory counterpart of this class, we have found the Noether currents and Ward identities of the translation, rotation and scale symmetries. The operator product expansion of the energy-momentum tensor with quasi-primary fields is also investigated.Comment: 15 pages, V2 (Some references added) V3(published version

Fractional diffusion in periodic potentials

Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two quadratures. This theoretical result is corroborated by numerical simulations for different shapes of the periodic potential. Normal and fractional spreading processes are contrasted via their time evolution of the corresponding probability densities in state space. While there are distinct differences occurring at small evolution times, a re-scaling of time yields a mutual matching between the long-time behaviors of normal and fractional diffusion

Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations

We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, can not be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity of the solutions of the proposed equations and establish the relation to the Continuous Time Random Walk theory. We show that the distributed order time fractional diffusion equation describes the sub-diffusion random process which is subordinated to the Wiener process and whose diffusion exponent diminishes in time (retarding sub-diffusion) leading to superslow diffusion, for which the square displacement grows logarithmically in time. We also demonstrate that the distributed order space fractional diffusion equation describes super-diffusion phenomena when the diffusion exponent grows in time (accelerating super-diffusion).Comment: 11 pages, LaTe

Proceedings of the North Aleutian Basin information status and research planning meeting.

The North Aleutian Basin Planning Area of the Minerals Management Service (MMS) is a large geographic area with significant ecological and natural resources. The Basin includes most of the southeastern part of the Bering Sea continental shelf including all of Bristol Bay. The area supports important habitat for a wide variety of species and globally significant habitat for birds and marine mammals including federally listed species. Villages and communities of the Alaska Peninsula and other areas bordering or near the Basin rely on its natural resources (especially commercial and subsistence fishing) for much of their sustenance and livelihood. The offshore area of the North Aleutian Basin is considered to have important hydrocarbon reserves, especially natural gas. In 2006, the MMS released a draft proposed program, Outer Continental Shelf Oil and Gas Leasing Program, 2007-2012 and an accompanying draft programmatic environmental impact statement (EIS). The draft proposed program identified two lease sales proposed in the North Aleutian Basin in 2010 and 2012, subject to restrictions. The area proposed for leasing in the Basin was restricted to the Sale 92 Area in the southwestern portion. Additional EISs will be needed to evaluate the potential effects of specific lease actions, exploration activities, and development and production plans in the Basin. A full range of updated multidisciplinary scientific information will be needed to address oceanography, fate and effects of oil spills, marine ecosystems, fish, fisheries, birds, marine mammals, socioeconomics, and subsistence in the Basin. Scientific staff at Argonne National Laboratory (Argonne) were contracted to assist the MMS Alaska Outer Continental Shelf (OCS) Region in identifying and prioritizing information needs related to the North Aleutian Basin and potential future oil and gas leasing and development activities. The overall approach focused on three related but separate tasks: (1) identification and gathering of relevant literature; (2) synthesis and summary of the literature; and (3) identification and prioritization of information needs. To assist in gathering this information, MMS convened the North Aleutian Basin Information Status and Research Planning Meeting, held in Anchorage, Alaska, from November 28 through December 1, 2006; this report presents a summary of that meeting. The meeting was the primary method used to gather input from stakeholders and identify information needs and priorities for future inventory, monitoring, and research related to potential leasing and oil and gas developments in the North Aleutian Basin

Open system approach to the internal dynamics of a model multilevel molecule

A model multilevel molecule described by two sets of rotational internal energy levels of different parity and degenerate ground states, coupled by a constant interaction, is considered, by assuming that the random collisions in a gas of identical molecules, provoke transitions between adjacent energy levels of the same parity. The prescriptions of the continuous time quantum random walk are applied to the single molecule, interpreted as an open quantum system, and the master equation driving its internal dynamics is built for a general distribution of the waiting times between two consecutive collisions. The coherence terms and the populations of the energy levels relax to the asymptotics with inverse power laws for relevant classes of non-Poissonian distributions of the collision times. The stable asymptotic equilibrium configuration is independent of the distribution. The long time dynamics may be hindered by increasing the tail of the distribution density. This effect may be interpreted as the appearance of the quantum Zeno effect over long time scales