Sharp load thresholds for cuckoo hashing

The paradigm of many choices has influenced significantly the design of efficient data structures and, most notably, hash tables. Cuckoo hashing is a technique that extends this concept. There, we are given a table with n locations, and we assume that each location can hold one item. Each item to be inserted chooses randomly k ≥ 2 locations and has to be placed in any one of them. How much load can cuckoo hashing handle before collisions prevent the successful assignment of the available items to the chosen locations? Practical evaluations and theoretical analysis of this method have shown that one can allocate a number of elements that is a large proportion of the size of the table, being very close to 1 even for small values of k such as 4 or 5. In this paper we show that there is a critical value for this proportion: with high probability, when the amount of available items is below this value, then these can be allocated successfully, but when it exceeds this value, the allocation becomes impossible. We give explicitly for each k ≥ 3 this critical value. This answers an open question posed by Mitzenmacher (ESA '09) and underpins theoretically the experimental results. Our proofs are based on the translation of the question into a hypergraph setting, and the study of the related typical properties of random k ‐uniform hypergraphs.© 2012 Wiley Periodicals, Inc. Random Struct., 2012     

Scattering of magnetic mirror trapped fast electrons by a shear Alfvén wave

Laboratory observations of enhanced loss of fast electrons trapped in a magnetic mirror geometry irradiated by shear Alfvén waves (SAW) are reported. A population of runaway electrons generated by second harmonic electron-cyclotron-resonance heating, as evidenced by the production of hard x rays with energy up to 3?MeV, is subjected to SAW launched with a rotating magnetic field antenna. It is observed that the SAW dramatically affect the trapped fast electrons and scatter them out of the magnetic mirror despite any obvious resonance. The results could have implications on the techniques of artificial reduction of energetic electrons in the inner radiation belt.     

“Breathing” in Adsorbate‐Responsive Metal Tetraphosphonate Hybrid Materials

Breathe easy : Reversible H₂O and NH₃ gas uptake by 2D calcium tetraphosphonates (see figure) is accompanied by framework structural changes similar to those previously reported for some carboxylate‐based hybrids. This breathing mechanism is accompanied by a volume increase of 55 %, while maintaining the topology and crystallinity of the material.

     

Analysis and finite element approximations for distributed optimal control problems for implicit parabolic equations

This work concerns analysis and error estimates for optimal control problems related to implicit parabolic equations. The minimization of the tracking functional subject to implicit parabolic equations is examined. Existence of an optimal solution is proved and an optimality system of equations is derived. Semi-discrete (in space) error estimates for the finite element approximations of the optimality system are presented. These estimates are symmetric and applicable for higher-order discretizations. Finally, fully-discrete error estimates of arbitrarily high-order are presented based on a discontinuous Galerkin (in time) and conforming (in space) scheme. Two examples related to the Lagrangian moving mesh Galerkin formulation for the convection-diffusion equation are described.     

Solving the multi-criteria time-dependent routing and scheduling problem in a multimodal fixed scheduled network

Multi-criteria routing and scheduling in a multimodal fixed scheduled network with time-dependent travel times involves the determination of the non-dominated itineraries (i.e., paths enhanced with scheduled departures) under the following constraints: (i) visiting a given set of intermediate stops in a specified sequence, and (ii) strict time windows on the origin, the destination and the intermediate stops. The objective of this paper is to present the formulation and algorithmic solution for the multi-criteria itinerary planning problem that takes into account the aforementioned features. The algorithmic approach proposed is based on the decomposition of the problem to a sequence of elementary itinerary sub-problems, solved by a dynamic programming algorithm. The computational performance of the algorithms on a set of large scale test problems indicates non-prohibitive time requirements and encourages its integration into travel planning decision support systems.     

Effect of Large Scale 3-D Structures on the Flow Around a Heated Cylinder at Low Reynolds Number

This work presents results of flow around a heated circular cylinder in mixed convection regime and demonstrates that Prandtl number and angle of attack of the incoming flow have a large influence on the characterisation of the flow transition from 2-D to 3-D. Previous studies show that heat transfer can enhance the formation of large 3-D structures in the wake of the cylinder for Reynolds numbers between 75 and 127 and a Richardson number larger than 0.35. This transitional mode is generally identified as “mode E”. In this work, we compare the results for water-based flow (large Prandtl number) with the ones for air-based flows (low Prandtl number). The comparison is carried out at two Reynolds numbers (100 and 150) and at a fixed Richardson number of 1. It shows that at the low Reynolds number of 100 the low Prandtl number flow does not enter into transition. This is caused by the impairment of the baroclinic vorticity production provoked by the spanwise temperature gradient. At low Prandtl number temperature gradients are less steep. For an air-based flow at Reynolds number 150, several Richardson numbers have been simulated. In this situation, the flow enters into transition and exhibits the characteristics of “mode E”, with the development of Λ-shaped structures in the near wake and mushroom-like structures in the far wake. It is also observed that the transition is delayed at Richardson number of 0.5. Simulations are also carried to investigate the effect of the angle of attack on the incoming flow on the development of large coherent structures. When the angle of attack is positive, the development of the wake tends to return to a more bi-dimensional configuration, where large scale coherent structures are impaired. In contrast, when the angle of attack is negative, large scale tri-dimensional structures dominate the flow in the wake, but with a very chaotic behaviour and the regular pattern of zero angle of attack is destroyed. The different behaviour of the flow with the variation of the angle of attack is also related to the baroclinic vorticity production, where new terms appear in the equations, leading to a positive effect of the vorticity production in case of a negative angle of attack and the opposite for a positive angle of attack.     

Regularized Laplacian determinants of self-similar fractals

We study the spectral zeta functions of the Laplacian on fractal sets which are locally self-similar fractafolds, in the sense of Strichartz. These functions are known to meromorphically extend to the entire complex plane, and the locations of their poles, sometimes referred to as complex dimensions, are of special interest. We give examples of locally self-similar sets such that their complex dimensions are not on the imaginary axis, which allows us to interpret their Laplacian determinant as the regularized product of their eigenvalues. We then investigate a connection between the logarithm of the determinant of the discrete graph Laplacian and the regularized one.     

Principles of demineralization: modern strategies for the isolation of organic frameworks. Part I. Common definitions and history

In contrast to biomineralization phenomena, that are among the most widely studied topics in modern material and earth science and biomedicine, much less is systematized on modern view of demineralization. Biomineralized structures and tissues are composites, containing a biologically produced organic matrix and nano- or microscale amorphous or crystalline minerals. Demineralization is the process of removing the inorganic part, or the biominerals, that takes place in nature via either physiological or pathological pathways in organisms. In vitro demineralization processes, used to obtain mechanistic information, consist in the isolation of the mineral phase of the composite biomaterials from the organic matrix. Physiological and pathological demineralization include, for example, bone resorption mediated by osteoclasts. Bioerosion, a more general term for the process of deterioration of the composite biomaterials represents chemical deterioration of the organic and mineral phase followed by biological attack of the composite by microorganisms and enzymes. Bioerosional organisms are represented by endolithic cyanobacteria, fungi, algae, plants, sponges, phoronids and polychaetes, mollusks, fish and echinoids.In the history of demineralization studies, the driving force was based on problems of human health, mostly dental caries. In this paper we summarize and integrate a number of events, discoveries, milestone papers and books on different aspect of demineralization during the last 400 years. Overall, demineralization is a rapidly growing and challenging aspect of various scientific disciplines such as astrobiology, paleoclimatology, geomedicine, archaeology, geobiology, dentistry, histology, biotechnology, and others to mention just a few.