Bose-Einstein condensation in random directed networks

We consider the phenomenon of Bose-Einstein condensation in a random growing directed net- work. The network grows by the addition of vertices and edges. At each time step the network gains a vertex with probabilty p and an edge with probability 1 − p. The new vertex has a fitness (a, b) with probability f(a, b). A vertex with fitness (a, b), in-degree i and out-degree j gains a new incoming edge with rate a(i + 1) and an outgoing edge with rate b(j + 1). The Bose-Einstein condensation occurs as a function of fitness distribution f(a, b)

Average Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the post-jump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach.Comment: 34 page

External quality measurements reveal internal processes

With the present developments in CA technology it becomes possible to fine tune the storage conditions to the specific needs of the product. This generates the need to know the exact quality conditions of the product before storage starts. By measuring the initial quality we can determine these conditions optimally. At present the most likely candidates to assess the initial quality with fast and non-destructive measurements are colour, chlorophyll fluorescence, and maybe NIR spectroscopy. Two examples are presented where initial colour measurements on all products in a batch can be shown to be indicative for the keeping quality of that batch. The first example focuses on how initial colour measurements using a 3CCD video camera can be utilised to predict the keeping quality of a batch of cucumbers where colour itself is regarded as the most important quality attribute. The second example focuses on how colour measurements can be used to predict the keeping quality of a batch of strawberries where the ability to suppress a Botrytis cinerea infection is the most important quality attribute. Furthermore, attention is given to the use of modulated chlorophyll fluorescence imaging as a possible initial quality indicator for rose leafy stem cuttings. The level of inhomogeneity in the quantum yield of photochmistry od PSII of leaves of rose cuttings may be an indictor of the capability of the cutting to recover from severance, and to form roots and generate regrowt

The temporal changes of the pulsational periods of the pre-white dwarf PG 1159-035

PG 1159-035, a pre-white dwarf with T=140000 K, is the prototype of the PG1159 spectroscopic class and the DOV pulsating class. Changes in the star cause variations in its oscillation periods. The measurement of temporal change in the oscillation periods, dP/dt, allows us to estimate directly rates of stellar evolutionary changes, such as the cooling rate and the envelope contraction rate, providing a way to test and refine evolutionary models for pre-white dwarf pulsating stars. We measured 27 pulsation modes period changes. The periods varied at rates of between 1 and 100 ms/yr, and several can be directly measured with a relative standard uncertainty below 10%. For the 516.0 s mode (the highest in amplitude) in particular, not only the value of dP/dt can be measured directly with a relative standard uncertainty of 2%, but the second order period change, d(dP/dt)/dt, can also be calculated reliably. By using the (O-C) method we refined the dP/dt and estimated the d(dP/dt)/dt for six other pulsation periods. As a first application, we calculated the change in the PG 1559-035 rotation period, dP_rot/dt = -2.13*10^{-6} s/s, the envelope contraction rate dR/dt = -2.2*10^{-13} solar radius/s, and the cooling rante dT/dt = -1.42*10^{-3} K/s.Comment: 8 pages; 2 figures; 2 tables; appendix with 2 table

Stability of a two-sublattice spin-glass model

We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from antiferromagnetic to spin glass state. The eigenvalues associated with replica-symmetric perturbations are in general complex. The natural generalization of the usual stability condition is to require the real part of these eigenvalues to be positive. The necessary and sufficient conditions for all the roots of the secular equation to have positive real parts is given by the Hurwitz criterion. The generalized stability condition allows a consistent analysis of the phase diagram within the replica-symmetric approximation.Comment: 21 pages, 5 figure