JSONYA/FN: Functional Computation in JSON

Functional programming has a lot to offer to the developers of global Internet-centric applications, but is often applicable only to a small part of the system or requires major architectural changes. The data model used for functional computation is often simply considered a consequence of the chosen programming style, although inappropriate choice of such model can make integration with imperative parts much harder. In this paper we do the opposite: we start from a data model based on JSON and then derive the functional approach from it. We outline the identified principles and present Jsonya/fn — a low-level functional language that is defined in and operates with the selected data model. We use several Jsonya/fn implementations and the architecture of a recently developed application to show that our approach can improve interoperability and can achieve additional reuse of representations and operations at relatively low cost. ACM Computing Classification System (1998): D.3.2, D.3.4.

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

On Optimal Quadratic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant via Symbolic Computation

ACM Computing Classification System (1998): G.1.1, G.1.2.

The Methodology of the Subsistence Minimum Calculation for Developing Countries and its Computation on the Georgian Example

This article shows the social importance of subsistence minimum in Georgia. The methodology of its calculation is also shown. We propose ways of improving the calculation of subsistence minimum in Georgia and how to extend it for other developing countries. The weights of food and non-food expenditures in the subsistence minimum baskets are essential in these calculations. Daily consumption value of the minimum food basket has been calculated too. The average consumer expenditures on food supply and the other expenditures to the share are considered in dynamics. Our methodology of the subsistence minimum calculation is applied for the case of Georgia. However, it can be used for similar purposes based on data from other developing countries, where social stability is achieved, and social inequalities are to be actualized. ACM Computing Classification System (1998): H.5.3, J.1, J.4, G.3.

Exact Solutions of Nonlocal Pluriparabolic Problems

MSC 2010: 44A35, 44A40

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherWe adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Convex and exact games with non-transferable utility

We generalize exactness to games with non-transferable utility (NTU). A game is exact if for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We consider ve generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be uni¯ed under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another.

Secure routing and trust computation in multihop infrastructureless networks

Today's wireless networks rely mostly on infrastructural support for their operation. With the concept of ubiquitous computing growing more popular, research on infrastructureless networks have been rapidly growing. However, such types of networks face serious security challenges when deployed. This dissertation focuses on designing a secure routing solution and trust modeling for these infrastructureless networks. ^ The dissertation presents a trusted routing protocol that is capable of finding a secure end-to-end route in the presence of malicious nodes acting either independently or in collusion, The solution protects the network from active internal attacks, known to be the most severe types of attacks in an ad hoc application. Route discovery is based on trust levels of the nodes, which need to be dynamically computed to reflect the malicious behavior in the network. As such, we have developed a trust computational model in conjunction with the secure routing protocol that analyzes the different malicious behavior and quantifies them in the model itself. Our work is the first step towards protecting an ad hoc network from colluding internal attack. To demonstrate the feasibility of the approach, extensive simulation has been carried out to evaluate the protocol efficiency and scalability with both network size and mobility. ^ This research has laid the foundation for developing a variety of techniques that will permit people to justifiably trust the use of ad hoc networks to perform critical functions, as well as to process sensitive information without depending on any infrastructural support and hence will enhance the use of ad hoc applications in both military and civilian domains. ^

The Effectiveness of an Intervention Package on Math Computation

Abstract: Four second-grade students participated in a B-A-B withdrawal single-subject design experiment. The intervention package implemented consisted of three components: self-monitoring, performance feedback, and reinforcers. Participants completed math probes across phases. Accuracy and productivity was recorded and calculated. Results demonstrated the intervention package improved accuracy and productivity for all participants.

Seawater carbonate chemistry and processes during experiments with phytoplankton Emiliania huxleyi (strain Bergen 2005), 2010

The response of the coccolithophore Emiliania huxleyi to rising CO2 concentrations is well documented for acclimated cultures where cells are exposed to the CO2 treatments for several generations prior to the experiment. The exact number of generations required for acclimation to CO2-induced changes in seawater carbonate chemistry, however, is unknown. Here we show that Emiliania huxleyi's short-term response (26 h) after cultures (grown at 500 µatm) were abruptly exposed to changed CO2 concentrations (~190, 410, 800 and 1500 ?atm) is similar to that obtained with acclimated cultures under comparable conditions in earlier studies. Most importantly, from the lower CO2 levels (190 and 410 ?atm) to 750 and 1500 µatm calcification decreased and organic carbon fixation increased within the first 8 to 14 h after exposing the cultures to changes in carbonate chemistry. This suggests that Emiliania huxleyi rapidly alters the rates of essential metabolical processes in response to changes in seawater carbonate chemistry, establishing a new physiological "state" (acclimation) within a matter of hours. If this relatively rapid response applies to other phytoplankton species, it may simplify interpretation of studies with natural communities (e.g. mesocosm studies and ship-board incubations), where often it is not feasible to allow for a pre-conditioning phase before starting experimental incubations.