Nature plays with dice – terrorists do not: Allocating resources to counter strategic versus probabilistic risks

Probabilistic uncertainty is caused by “chance”, whereas strategic uncertainty is caused by an adverse interested party. Using linear impact functions, the problems of allocating a limited resource to defend sites that face either probabilistic risk or strategic risk are formulated as optimization problems that are solved explicitly. The resulting optimal policies differ – under probabilistic risk, the optimal policy is to focus the investment of resources on priority sites where they yield the highest impact, while under strategic risk, the best policy is to spread the resources so as to decrease the potential damage level of the most vulnerable site(s). Neither solution coincides with the commonly practiced proportionality allocation scheme.     

Exact Analytical Solution of the Telegraphic Warren and Root Model

We exactly solved a Warren and Root-like model that considers telegraphic fluid flow, a constant hydraulic head at the bottomhole, and an infinite Euclidean reservoir with radial flux. Complex integrals on the Bromwich contour are used to obtain the exact solutions of the hydraulic head and flux. Given that the behavior of the propagation of the hydraulic head has a discontinuous front, this system is appropriate for evaluating numerical methods that have difficulties with discontinuities. To this end, the results from the Stehfest method and Iseger method are analyzed.     

Shotgun assembly of random jigsaw puzzles

We consider the shotgun assembly problem for a random jigsaw puzzle, introduced by Mossel and Ross (2015). Their model consists of a puzzle—an n×n grid, where each vertex is viewed as a center of a piece. Each of the four edges adjacent to a vertex is assigned one of q colors (corresponding to “jigs,” or cut shapes) uniformly at random. Unique assembly refers to there being only one puzzle (the original one) that is consistent with the collection of individual pieces. We show that for any ε>0, if q ≥ n^1+ε, then unique assembly holds with high probability. The proof uses an algorithm that assembles the puzzle in time n^Θ(1/ε).22     

Incentive compatibility for the stable matching model with an entrance criterion

A case study of matching students with dormitory-groups at the Technion lead recently to the study of a variant of the stable matching model with a “qualifying criterion” for the inclusion of a student among those getting an assignment. A notion of stability was introduced for the model and a (student-courting) algorithm which finds a matching that satisfied this criterion and has desired properties was described. Here, we show that students cannot benefit from misrepresenting preferences in an extension of the model that allows dormitory-groups to have different preferences over students and allows these preferences to be incomplete.     

Hyperviscosity, Galerkin truncation, and bottlenecks in turbulence

It is shown that the use of a high power alpha of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid conservative dynamics with a finite range of spatial Fourier modes. Those at large wave numbers thermalize, whereas modes at small wave numbers obey ordinary viscous dynamics [C. Cichowlas et al., Phys. Rev. Lett. 95, 264502 (2005)10.1103/Phys. Rev. Lett. 95.264502]. The energy bottleneck observed for finite alpha may be interpreted as incomplete thermalization. Artifacts arising from models with alpha>1 are discussed.     

Single-component magnetic conductors based on Mo3S7 trinuclear clusters with outer dithiolate ligands

A trinuclear cluster complex containing the Mo(3)S(7) central unit coordinated to dithiolate ligands, in particular the organic dmit (1,3-dithia-2-thione-4,5-dithiolate) anion, has been used to prepare a single-component molecular conductor formed by the threefold symmetry magnetic building block Mo(3)S(7)(dmit)(3) (1). The [Mo(3)S(7)(dmit)(3)](2)(-) ([1](2)(-)) diamagnetic anion forms dimers by interaction between the electrophilic cluster axial sulfur atoms and the sulfur atoms of the outer dithiolate ligand. Additional contacts between adjacent dmit ligands result in chain formation. The two-electron oxidation of [1](2)(-) yields to a three-dimensional molecular solid formed by neutral Mo(3)S(7)(dmit)(3) (1) units with partially filled molecular orbitals, which exhibits sizable intermolecular electronic interactions together with a significant electron delocalization. It also contains large open channels. The interactions responsible for the conducting properties have been identified using a first-principle DFT approach and the calculated electronic structure has allowed us to model the magnetic behavior of the material with two competing antiferromagnetic interactions to produce a spin-frustrated extended network. The potential of this Mo(3)S(7) cluster complex to be modified together with the capability of filling the open channels with doping species paves the way to an entirely new set of molecular conductors and/or magnets.     

Engineering space-variant inhomogeneous media for polarization control

Novel devices for converting a linear polarization state to radial or azimuthal polarization states are realized by use of space-variant inhomogeneous media on a subwavelength scale. The two designs presented use form birefringence to locally transform the polarization state. The devices are fabricated in a GaAs substrate for operation in the far-infrared wavelength range. The experimental characterization is in good agreement with the designs, demonstrating high conversion efficiency.     

Inhomogenous dielectric metamaterials with space-variant polarizability

We experimentally demonstrate for the first time the focusing of optical beams within an inhomogeneous dielectric metamaterial with space-variant polarizability, implemented by etching subwavelength structures into a Silicon slab. Light focusing is obtained by creating an artificial slab material with graded refractive index profile. The local refractive index within the slab is modulated by controlling the duty cycle of the subwavelength structures. The demonstrated metamaterial based component can be integrated with various other building blocks towards the realization of devices and systems in free space optics on a chip configuration.     

β-Caryophyllene: A Therapeutic Alternative for Intestinal Barrier Dysfunction Caused by Obesity

Obesity is an excessive accumulation of fat that exacerbates the metabolic and inflammatory processes. Studies associate these processes with conditions and dysregulation in the intestinal tract, increased concentrations of lipopolysaccharides (LPSs) in the blood, differences in the abundance of intestinal microbiota, and the production of secondary metabolites such as short-chain fatty acids. β-Caryophyllene (BCP) is a natural sesquiterpene with anti-inflammatory properties and with the potential purpose of fighting metabolic diseases. A diet-induced obesity model was performed in 16-week-old C57BL/6 mice administered with BCP [50 mg/kg]. A reduction in the expression of Claudin-1 was observed in the group with a high-fat diet (HFD), which was caused by the administration of BCP; besides BCP, the phyla Akkermansia and Bacteroidetes decreased between the groups with a standard diet (STD) vs. HFD. Nevertheless, the use of BCP in the STD increased the expression of these phyla with respect to fatty acids; a similar effect was observed, in the HFD group that had a decreasing concentration that was restored with the use of BCP. The levels of endotoxemia and serum leptin increased in the HFD group, while in the HFD + BCP group, similar values were found to those of the STD group, attributing the ability to reduce these in conditions of obesity.     

Unexpected role of O-2 "protecting" groups of glycosyl donors in mediating regioselective glycosidation

Glycosidation of several vicinal diols reveals that exquisite regioselectivity can be achieved by using 2-O-benzoyl n-pentenyl glycoside donors and/or their cyclic 1,2-ortho ester counterparts. The regioselective preferences for both are the same, although ratios and yields may differ. In stark contrast, glycosidation of the diols with the corresponding 2-O-benzylated donors gives poor, if any, regioselectivity.