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.     

Superfilters, Ramsey theory, and van der Waerden's Theorem

Superfilters are generalizations of ultrafilters, and capture the underlying concept in Ramsey-theoretic theorems such as van der Waerden's Theorem. We establish several properties of superfilters, which generalize both Ramsey's Theorem and its variants for ultrafilters on the natural numbers. We use them to confirm a conjecture of Kočinac and Di Maio, which is a generalization of a Ramsey-theoretic result of Scheepers, concerning selections from open covers. Following Bergelson and Hindman's 1989 Theorem, we present a new simultaneous generalization of the theorems of Ramsey, van der Waerden, Schur, Folkman–Rado–Sanders, Rado, and others, where the colored sets can be much smaller than the full set of natural numbers.     

Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology

This paper addresses the problem of scheduling activities in projects with stochastic activity durations. The aim is to determine for each activity a gate—a time before it the activity cannot begin. Setting these gates is analogous to setting inventory levels in the news vendor problem. The resources required for each activity are scheduled to arrive according to its gate. Since activities’ durations are stochastic, the start and finish time of each activity is uncertain. This fact may lead to one of two outcomes: (1) an activity is ready to start its processing as all its predecessors have finished, but it cannot start because the resources required for it were scheduled to arrive at a later time. (2) The resources required for the activity have arrived and are ready to be used but the activity is not ready to start because of precedence constraints. In the first case we will incur a “holding” cost while in the second case, we will incur a “shortage” cost. Our objective is to set gates so as to minimize the sum of the expected holding and shortage costs. We employ the Cross-Entropy method to solve the problem. The paper describes the implementation of the method, compares its results to various heuristic methods and provides some insights towards actual applications.     

Noise-induced linewidth in frequency combs

Frequency combs generated by trains of pulses emitted from mode-locked lasers are analyzed when the center time and phase of the pulses undergo noise-induced random walk, which broadens the comb lines. Asymptotic analysis and computation reveal that, when the standard deviation of the center-time jitter of the nth pulse scales as n(p/2) where p is a jitter exponent, the linewidth of the kth comb line scales as k(2/p). The linear-dispersionless (p=1) and pure-soliton (p=3) dynamics in lasers are derived as special cases of this time-frequency duality relation. In addition, the linewidth induced by phase jitter decreases with power P(out), as (P(out))(-1/p).     

Economically relevant preferences for all observed epsilon

The common investment decision rules, Markowitz’s Mean-Variance (MV) rule and the non-parametric Stochastic Dominance (SD) rules, suffer from one severe drawback: there are pairs of prospects where experimentally 100% of the subjects choose one prospect, yet these rules are unable to rank the two prospects—a paradoxical result. Thus, the set of all preferences corresponding to these decision rules is too large, because it contains theoretical preferences that are not encountered in practice. Based on 400 subjects’ choices we define the economically relevant set of preference and the corresponding new decision rules, which avoid the paradoxical results. The results are very robust and are almost unaffected by the magnitude of the outcomes and the structure of the prospects under consideration.     

Lattice Shrinkage by Incorporation of Recombinant Starmaker-Like Protein within Bioinspired Calcium Carbonate Crystals

The biological mediation of mineral formation (biomineralization) is realized through diverse organic macromolecules that guide this process in a spatial and temporal manner. Although the role of these molecules in biomineralization is being gradually revealed, the molecular basis of their regulatory function is still poorly understood. In this study, the incorporation and distribution of the model intrinsically disordered starmaker-like (Stm-l) protein, which is active in fish otoliths biomineralization, within calcium carbonate crystals, is revealed. Stm-l promotes crystal nucleation and anisotropic tailoring of crystal morphology. Intracrystalline incorporation of Stm-l protein unexpectedly results in shrinkage (and not expansion, as commonly described in biomineral and bioinspired crystals) of the crystal lattice volume, which is described herein, for the first time, for bioinspired mineralization. A ring pattern was observed in crystals grown for 48 h; this was composed of a protein-enriched region flanked by protein-depleted regions. It can be explained as a result of the Ostwald-like ripening process and intrinsic properties of Stm-l, and bears some analogy to the daily growth layers of the otolith.     

Can Special Relativity Be Derived from Galilean Mechanics Alone?

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.     

Growth, microhardness, dielectric and photoconductivity characterization of a highly polarizable NLO material: Sodium p-nitrophenolate dihydrate (NO2-C6H4-ONa.2H2O)

Sodium p-nitrophenolate dihydrate (NPNa.2H₂O) is a highly polarisable non linear optical material. It has a d_eff about 1.45 times than that of potassium titanyl phosphate. Single crystals of (NPNa.2H₂O) have been grown successfully by slow solvent evaporation having water and methanol as solvent. The structure of the crystal is verified by single X-ray analysis. Optical absorption shows that the crystal is highly transparent between 1500 and 300 nm. Microhardness of the crystal is found to increases with increase in load and the hardness number is found to be high for methanol grown crystal as compared to the water grown crystal. Electrical conductivity as evaluated from the cole-cole plot is found to be 1.26 × 10⁻⁵ mho m⁻¹. The dielectric constant of the crystal is low and independent at higher frequencies. The crystal has prominent photoconduction in the presence of trap energy levels formed by the Na⁺ ions. The SHG efficiency of the crystal is studied by performing Kurtz powder test and the results of scanning electron microscope analysis indicate that the major part of the crystal surface is free from inclusion and dislocation.     

Microscopic flow measurements with optically trapped microprobes

The use of optical tweezers to measure micrometer-resolution velocity fields in fluid flow is demonstrated as an extension of a scanning confocal viscosity microscope. This demonstration is achieved by detection of the motion of an optically trapped microsphere in an oscillating laser trap. The technique is validated by comparison with an independent video-based measurement and applied to obtain a two-dimensional map of the flow past a microscopic wedge. Since the velocity is measured simultaneously with the trap relaxation time, the technique requires no fluid-dependent calibration and is independent of the trap stiffness and the particle size.