Separating sets of strings by finding matching patterns is almost always hard

© 2017 Elsevier B.V. We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in understanding the complexity of genetic algorithms. We show that the basic problem of finding a small set of patterns that match one set of strings but do not match any string in a second set is difficult (NP-complete, W[2]-hard when parameterized by the size of the pattern set, and APX-hard). We then perform a detailed parameterized analysis of the problem, separating tractable and intractable variants. In particular we show that parameterizing by the size of pattern set and the number of strings, and the size of the alphabet and the number of strings give FPT results, amongst others

Recreation GPS as a Low-Cost Alternative for Introductory Courses in Natural Resources

The Global Positioning System (GPS) has proven reliable for collecting spatial data for integration into a computer-based Geographic Information System (GIS). However, high cost often prohibits the purchase of individual GPS units for each student in a class. Recent advances in technology coupled with decreasing prices have made recreational GPS a low-cost alternative for introductory courses in Natural Resource Management. These units utilize 12-channel receivers, range in price from $115 to$500, and exhibit a point-location accuracy within 14 meters 95% of the time (6.2m - 66% of the time). Although recreational units lack the capacity for differential correction through postprocessing, the addition of real-time differential correction can improve accuracy to less than 9 meters 95% of the time in areas where free differential correction signals are obtainable (4.2m - 66% of the time). Several free computer programs are available for retrieving data from a recreational GPS directly into a GIS. Still others exist as stand-alone software that allows image registration for GPS data overlay. Thus, it is now feasible for students to purchase their own GPS unit for use in introductory classes, in advanced courses, in their research, or in any endeavor requiring spatial data collection for computer-based mapping

Recreation GPS as a low-cost alternative for introductory courses in natural reaources

The Global Positioning System (GPS) has proven reliable for collecting spatial data for integration into a computer-based Geographic Information System (GIS). However, high cost often prohibits the purchase of individual GPS units for each student in a class. Recent advances in technology coupled with decreasing prices have made recreational GPS a low-cost alternative for introductory courses in Natural Resource Management. These units utilize 12-channel receivers, range in price from $115 to$500, and exhibit a point-location accuracy within 14 meters 95% of the time (6.2m - 66% of the time). Although recreational units lack the capacity for differential correction through postprocessing, the addition of real-time differential correction can improve accuracy to less than 9 meters 95% of the time in areas where free differential correction signals are obtainable (4.2m - 66% of the time). Several free computer programs are available for retrieving data from a recreational GPS directly into a GIS. Still others exist as stand-alone software that allows image registration for GPS data overlay. Thus, it is now feasible for students to purchase their own GPS unit for use in introductory classes, in advanced courses, in their research, or in any endeavor requiring spatial data collection for computer-based mapping

Selective gold and palladium adsorption from standard aqueous solutions

The intensive exploitation of resources on a global level has led to a progressive depletion of mineral reserves, which were proved to be insufficient to meet the high demand for high-technological devices. On the other hand, the continuous production of Waste from Electrical and Electronic Equipment (WEEE) is causing serious environmental problems, due to the complex composition of WEEE, which makes the recycling and reuse particularly challenging. The average metal content of WEEE is estimated to be around 30% and varies depending on the manufacturing period and brand of production. It contains base metals and precious metals, such as gold and palladium. The remaining 70% of WEEEs is composed of plastics, resins, and glassy materials. The recovery of metals from WEEEs is characterized by two main processes well represented by the literature: Pyrometallurgy and hydrometallurgy. Both of them require the pre-treatment of WEEEs, such as dismantling and magnetic separation of plastics. In this work, the selective adsorption of precious metals has been attempted, using copper, gold, and palladium aqueous solutions and mixtures of them. A screening on different adsorbent materials such as granular activated carbons and polymers, either as pellets or foams, has been performed. Among these, PolyEther Block Amide (PEBA) was elected as the most performing adsorbent in terms of gold selectivity over copper. Spent PEBA has been then characterized using scanning electron microscope, coupled with energy dispersive spectroscopy, demonstrating the predominant presence of gold in most analyzed sites, either in the pellet or foam form

Selective leaching of precious metals from electrical and electronic equipment through hydrometallurgical methods

The rapid human evolution has improved the quality of our lives through the use of technology. This not only resulted in increased raw materials extraction but also in the production of a worrying amount of electronic wastes. Indeed, in 2019 worldwide production of Electronic and Electric Equipment Waste (WEEE) was worth 50 million tons, causing several disadvantages such as the reduced space in landfills and massive shipping to countries with less restrictive regulations. On the other side, the billionaire electrical devices market is causing a significant increase in Precious Metals (PM) demand. Nowadays, the economic importance of PMs is as high as their supply risk. The answer to this problem consists of finding selective methods to extract and raffinate precious metals from disposed WEEE. On average, WEEEs contain around 30 % of plastics, 30 % ceramics, and 40 % metals; among these only around 0.1 % is characterized by PMs, such as gold, silver, rhodium, platinum, and palladium. The separation of PMs from other non-precious components is generally obtained using pyrometallurgy, which consists of fusing the wastes at temperatures up to 1500 ÷ 1700 °C. However, this method produces toxic gaseous byproducts and implies high energy costs. A possible alternative is given by hydrometallurgical processes, consisting of leaching the WEEE with solutions containing acids and oxidants at temperatures lower than 100°C. One of the main issues of the hydrometallurgical process is to leach copper and other non-precious base-metals selectively while keeping PMs in the solid-state. In this work, we report preliminary results of equilibrium and kinetic leaching tests in a well-stirred batch reactor, aimed at the optimization of the main operating parameters of a hydrometallurgical process for selective leaching of copper and other base-metals from Wasted Printed Circuit Boards (WPCBs). In particular, experiments have been carried out at different HCl and NaCl concentrations of the leaching solutions, exploring also the effect of temperature variation (20, 50, and 70 °C)

Entropy-driven cutoff phenomena

In this paper we present, in the context of Diaconis' paradigm, a general method to detect the cutoff phenomenon. We use this method to prove cutoff in a variety of models, some already known and others not yet appeared in literature, including a chain which is non-reversible w.r.t. its stationary measure. All the given examples clearly indicate that a drift towards the opportune quantiles of the stationary measure could be held responsible for this phenomenon. In the case of birth- and-death chains this mechanism is fairly well understood; our work is an effort to generalize this picture to more general systems, such as systems having stationary measure spread over the whole state space or systems in which the study of the cutoff may not be reduced to a one-dimensional problem. In those situations the drift may be looked for by means of a suitable partitioning of the state space into classes; using a statistical mechanics language it is then possible to set up a kind of energy-entropy competition between the weight and the size of the classes. Under the lens of this partitioning one can focus the mentioned drift and prove cutoff with relative ease.Comment: 40 pages, 1 figur

Rapid Accurate Calculation of the s-Wave Scattering Length

Transformation of the conventional radial Schr\"odinger equation defined on the interval $\,r\in[0,\infty)$ into an equivalent form defined on the finite domain $\,y(r)\in [a,b]\,$ allows the s-wave scattering length $a_s$ to be exactly expressed in terms of a logarithmic derivative of the transformed wave function $\phi(y)$ at the outer boundary point $y=b$, which corresponds to $r=\infty$. In particular, for an arbitrary interaction potential that dies off as fast as $1/r^n$ for $n\geq 4$, the modified wave function $\phi(y)$ obtained by using the two-parameter mapping function $r(y;\bar{r},\beta) = \bar{r}[1+\frac{1}{\beta}\tan(\pi y/2)]$ has no singularities, and $$a_s=\bar{r}[1+\frac{2}{\pi\beta}\frac{1}{\phi(1)}\frac{d\phi(1)}{dy}].$$ For a well bound potential with equilibrium distance $r_e$, the optimal mapping parameters are $\,\bar{r}\approx r_e\,$ and $\,\beta\approx \frac{n}{2}-1$. An outward integration procedure based on Johnson's log-derivative algorithm [B.R.\ Johnson, J.\ Comp.\ Phys., \textbf{13}, 445 (1973)] combined with a Richardson extrapolation procedure is shown to readily yield high precision $a_s$-values both for model Lennard-Jones ($2n,n$) potentials and for realistic published potentials for the Xe--e$^-$, Cs_2(a\,^3\Sigma_u^+) and $^{3,4}$He_2(X\,^1\Sigma_g^+) systems. Use of this same transformed Schr{\"o}dinger equation was previously shown [V.V. Meshkov et al., Phys.\ Rev.\ A, {\bf 78}, 052510 (2008)] to ensure the efficient calculation of all bound levels supported by a potential, including those lying extremely close to dissociation.Comment: 12 pages, 9 figures, to appear in J. Chem. Phy

Collisionless Shock Acceleration of protons in a plasma slab produced in a gas jet by the collision of two laser-driven hydrodynamic shockwaves

We recently proposed a new technique of plasma tailoring by laser-driven hydrodynamic shockwaves generated on both sides of a gas jet [J.-R. Marqu\`es et al., Phys. Plasmas 28, 023103 (2021)]. In the continuation of this numerical work, we studied experimentally the influence of the tailoring on proton acceleration driven by a high-intensity picosecond-laser, in three cases: without tailoring, by tailoring only the entrance side of the ps-laser, or both sides of the gas jet. Without tailoring the acceleration is transverse to the laser axis, with a low-energy exponential spectrum, produced by Coulomb explosion. When the front side of the gas jet is tailored, a forward acceleration appears, that is significantly enhanced when both the front and back sides of the plasma are tailored. This forward acceleration produces higher energy protons, with a peaked spectrum, and is in good agreement with the mechanism of Collisionless Shock Acceleration (CSA). The spatio-temporal evolution of the plasma profile was characterized by optical shadowgraphy of a probe beam. The refraction and absorption of this beam was simulated by post-processing 3D hydrodynamic simulations of the plasma tailoring. Comparison with the experimental results allowed to estimate the thickness and near-critical density of the plasma slab produced by tailoring both sides of the gas jet. These parameters are in good agreement with those required for CSA