Abstract: We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a “law of large numbers for random partitions,” a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting search-cost can be split at an explicit deterministic threshold into one random variable in equilibrium, and a second one related to the initial ordering of the list. Our results ensure the stability of the limiting search-cost under general perturbations of the request probabilities. We provide the description of the limiting transient behavior in several examples where only the stationary regime is known, and discuss the range of validity of our scaling limit.

Abstract: Massive production and disposal of petrochemical derived plastics represent relevant environmental problems. Polyhydroxyalkanoates (PHA) are a renewable alternative that can even be produced from wastes. The production of PHA from acetate using mixed microbial cultures was studied. The effect of two key operational conditions was evaluated, i.e., substrate concentration and cycle length. The effects of these factors on several responses were studied using a surface response methodology. Several reactors were operated under selected conditions for at least 10 solids retention times to ensure stable operation. Results show that conditions providing higher PHA content involve lower biomass productivities. This has a great impact on biomass production costs. Results suggest then that PHA content alone may not be a reasonable criterion for determining optimal conditions for PHB production. If production costs need to be reduced, conditions that provide a lower PHA content in the selection reactor, but a higher biomass productivity may be of interest.

Abstract: The price of anarchy has become a standard measure of the efficiency of equilibria in games. Most of the literature in this area has focused on establishing worst-case bounds for specific classes of games, such as routing games or more general congestion games. Recently, the price of anarchy in routing games has been studied as a function of the traffic demand, providing asymptotic results in light and heavy traffic. The aim of this paper is to study the price of anarchy in nonatomic routing games in the intermediate region of the demand. To achieve this goal, we begin by establishing some smoothness properties of Wardrop equilibria and social optima for general smooth costs. In the case of affine costs we show that the equilibrium is piecewise linear, with break points at the demand levels at which the set of active paths changes. We prove that the number of such break points is finite, although it can be exponential in the size of the network. Exploiting a scaling law between the equilibrium and the social optimum, we derive a similar behavior for the optimal flows. We then prove that in any interval between break points the price of anarchy is smooth and it is either monotone (decreasing or increasing) over the full interval, or it decreases up to a certain minimum point in the interior of the interval and increases afterwards. We deduce that for affine costs the maximum of the price of anarchy can only occur at the break points. For general costs we provide counterexamples showing that the set of break points is not always finite.

Abstract: We propose a generic mechanism for allocating the benefits and costs that result from the development of international transmission interconnections under a cooperative agreement. The mechanism is based on a planning model that considers generation investments as a response to transmission developments, and the Shapley Value from cooperative game theory. This method provides a unique allocation of benefits and costs considering each country's average incremental contribution to the cooperative agreement. The allocation satisfies an axiomatic definition of fairness. We demonstrate our results for three planned transmission interconnections in the North Sea and show that the proposed mechanism can be used as a basis for defining a set of Power Purchase Agreements among countries. This achieves the desired final distribution of economic benefits and costs from transmission interconnections as countries trade power over time. We also show that, in this case, the proposed allocation is stable.

Abstract: With the growing use of quantum-dot cellular automata (QCA) nanotechnology, digital circuits designed at the Nanoscale have a number of advantages over CMOS devices, including the lower utilization of power, increased processing speed of the circuit, and higher density. There are several flip flop designs proposed in the literature with their realization in the QCA technology. However, the majority of these designs suffer from large cell counts, large area utilization, and latency, which leads to the high cost of the circuits. To address this, this work performed a literature survey of the D flip flop (DFF) designs and complex sequential circuits that can be designed from it. A new design of D flip flop was proposed in this work and to assess the performance of the proposed QCA design, an in-depth comparison with existing designs was performed. Further, sequential circuits such as parallel-in-parallel-out (PIPO) and serial-in-parallel-out (SIPO) shift registers were designed using the flip flop design that was put forward. A comprehensive evaluation of the energy dissipation of all presented fundamental flip-flop circuits and other sequential circuits was also performed using the QCAPro tool, and their energy dissipation maps were also obtained. The suggested designs showed lower power dissipation and were cost-efficient, making them suitable for designing higher-power circuits.

Abstract: A nano-scale quantum-dot cellular automaton (QCA) is one of the most promising replacements for CMOS technology. Despite the potential advantages of this technology, QCA circuits are frequently plagued by numerous forms of manufacturing faults (such as a missing cell, extra cell, displacement cell, and rotated cell), making them prone to failure. As a result, in QCA technology, the design of reversible circuits has received much attention. Reversible circuits are resistant to many kinds of faults due to their inherent properties and have the possibility of data reversibility, which is important. Therefore, this research proposes a new reversible gate, followed by a new 3 x 3 reversible gate. The proposed structure does not need rotated cells and only uses one layer, increasing the design's manufacturability. QCADesigner-E and the Euler method on coherence vector (w/energy) are employed to simulate the proposed structure. The 3 x 3 reversible circuit consists of 21 cells that take up just 0.046 mu m(2). Compared to the existing QCA-based single-layer reversible circuit, the proposed reversible circuit minimizes cell count, area, and delay. Furthermore, the energy consumption is studied, confirming the optimal energy consumption pattern in the proposed circuit. The proposed reversible 3 x 3 circuit dissipates average energy of 1.36 (eV) and overall energy of 1.49 (eV). Finally, the quantum cost for implementing the reversible circuits indicates a lower value than that of all the other examined circuits.

Abstract: In very large-scale integration (VLSI) circuits, a partial of energy lost leads to information loss in irreversible computing because, in conventional combinatorial circuits, each bit of information generates heat and power consumption, thus resulting in energy dissipation. When information is lost in conventional circuits, it will not be recoverable, as a result, the circuits are provided based on the reversible logic and according to reversible gates for data retrieval. Since comparators are one of the basic building blocks in digital logic design, in which they compare two numbers, the aim of this research is to design a 1-bit comparator building block based on reversible logic and implement it in the QCA with the minimum cell consumption, less occupied area, and lower latency, as well as to design it in a single layer. The proposed 1-bit reversible comparator is denser, cost-effective, and more efficient in quantum cost, power dissipation, and the main QCA parameters than that of previous works.