Parallel Exhaustive Search without Coordination

We analyze parallel algorithms in the context of exhaustive search over totally ordered sets. Imagine an infinite list of "boxes", with a "treasure" hidden in one of them, where the boxes' order reflects the importance of finding the treasure in a given box. At each time step, a search protocol executed by a searcher has the ability to peek into one box, and see whether the treasure is present or not. By equally dividing the workload between them, $k$ searchers can find the treasure $k$ times faster than one searcher. However, this straightforward strategy is very sensitive to failures (e.g., crashes of processors), and overcoming this issue seems to require a large amount of communication. We therefore address the question of designing parallel search algorithms maximizing their speed-up and maintaining high levels of robustness, while minimizing the amount of resources for coordination. Based on the observation that algorithms that avoid communication are inherently robust, we analyze the best running time performance of non-coordinating algorithms. Specifically, we devise non-coordinating algorithms that achieve a speed-up of $9/8$ for two searchers, a speed-up of $4/3$ for three searchers, and in general, a speed-up of $\frac{k}{4}(1+1/k)^2$ for any $k\geq 1$ searchers. Thus, asymptotically, the speed-up is only four times worse compared to the case of full-coordination, and our algorithms are surprisingly simple and hence applicable. Moreover, these bounds are tight in a strong sense as no non-coordinating search algorithm can achieve better speed-ups. Overall, we highlight that, in faulty contexts in which coordination between the searchers is technically difficult to implement, intrusive with respect to privacy, and/or costly in term of resources, it might well be worth giving up on coordination, and simply run our non-coordinating exhaustive search algorithms

Harnack type estimates and Hölder continuity for non-negative solutions to certain sub-critically singular parabolic partial differential equations

A two-parameter family of Harnack type inequalities for non-negative solutions of a class of singular, quasilinear, homogeneous parabolic equations is established, and it is shown that such estimates imply the Hoelder continuity of solutions. These classes of singular equations include p-Laplacean type equation in the sub-critical range 1<p\le\frac2N/(N+1) and equations of the porous medium type in the sub-critical range 0<m\le(N-2)_+/N

Local regularity for parabolic nonlocal operators

Weak solutions to parabolic integro-differential operators of order $\alpha \in (\alpha_0, 2)$ are studied. Local a priori estimates of H\"older norms and a weak Harnack inequality are proved. These results are robust with respect to $\alpha \nearrow 2$. In this sense, the presentation is an extension of Moser's result in 1971.Comment: 31 pages, 3 figure

Well-posedness for a class of nonlinear degenerate parabolic equations

In this paper we obtain well-posedness for a class of semilinear weakly degenerate reaction-diffusion systems with Robin boundary conditions. This result is obtained through a Gagliardo-Nirenberg interpolation inequality and some embedding results for weighted Sobolev spaces

Riesz potentials and nonlinear parabolic equations

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear cas

Selective Aerobic Oxidation of 5-Hydroxymethylfurfural to 2,5-Diformylfuran or 2-Formyl-5-furancarboxylic Acid in Water by using MgO⋅CeO2 Mixed Oxides as Catalysts

Mixed oxides based on MgO⋅CeO2 were used as efficient catalysts in the aerobic oxidation of 5-hydroxymethylfurfural (5-HMF) to afford, with very high selectivity, either 2,5-diformylfuran (DFF, 99 %) or 2-formyl-5-furancarboxylic acid (FFCA, 90 %), depending on the reaction conditions. 5-Hydroxymethyl-2-furancarboxylic acid (HMFCA, 57–90 %) was formed only at low concentration of 5-HMF (&lt;0.03 m) or in presence of external bases. The conversion of 5-HMF ranged from a few percent to 99 %, according to the reaction conditions. The oxidation was performed in water, with O2 as oxidant, without any additives. The surface characterization of the catalysts gave important information about their acid–base properties, which drive the selectivity of the reaction towards DFF. FFCA was formed from DFF at longer reaction times. Catalysts were studied by XPS and XRD before and after catalytic runs to identify the reason why they undergo reversible deactivation. XRD showed that MgO is hydrated to Mg(OH)2, which, even if not leached out, changes the basic properties of the catalyst that becomes less active after some time. Calcination of the recovered catalyst allows recovery of its initial activity. The catalyst is thus recoverable (&gt;99 %) and reusable. The use of mixed oxides allows tuning of the basicity of the catalysts, avoiding the need for external bases for efficient and selective conversion of 5-HMF and waste formation, resulting in an environmentally friendly, sustainable process

Comparative life cycle assessment study on environmental impact of oil production from micro-algae and terrestrial oilseed crops

In this study the LCA methodology is applied in order to satisfy two goals: i) to evaluate the hot spots in site-specific production chain of biodiesel from terrestrial and micro-algae feedstock; ii) to compare quantitatively, utilizing primary data, the impacts of the first generation in respect to the third generation bio-fuels. Results show that micro-algae are neither competitive yet with traditional oil crops nor with fossil fuel. The use of renewable technologies as photovoltaics and biogas self production might increase the competitiveness of micro-algae oil. Further investigations are however necessary to optimize their production chain and to increase the added value of co-products