The Computational Complexity of the Game of Set and its Theoretical Applications

The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and establish interesting connections with other classical computational problems. Specifically, we first show that a natural generalization of the problem of finding a single Set, parameterized by the size of the sought Set is W-hard; our reduction applies also to a natural parameterization of Perfect Multi-Dimensional Matching, a result which may be of independent interest. Second, we observe that a version of the game where one seeks to find the largest possible number of disjoint Sets from a given set of cards is a special case of 3-Set Packing; we establish that this restriction remains NP-complete. Similarly, the version where one seeks to find the smallest number of disjoint Sets that overlap all possible Sets is shown to be NP-complete, through a close connection to the Independent Edge Dominating Set problem. Finally, we study a 2-player version of the game, for which we show a close connection to Arc Kayles, as well as fixed-parameter tractability when parameterized by the number of rounds played

Evaluation of cystatin C for the detection of chronic kidney disease in cats

BackgroundSerum cystatin C (sCysC) and urinary cystatin C (uCysC) are potential biomarkers for early detection of chronic kidney disease (CKD) in cats. An in-depth clinical validation is required. ObjectivesTo evaluate CysC as a marker for CKD in cats and to compare assay performance of the turbidimetric assay (PETIA) with the previously validated nephelometric assay (PENIA). AnimalsNinety cats were included: 49 CKD and 41 healthy cats. MethodsSerum CysC and uCysC concentrations were prospectively evaluated in cats with CKD and healthy cats. Based on plasma exo-iohexol clearance test (PexICT), sCysC was evaluated to distinguish normal, borderline, and low GFR. Sensitivity and specificity to detect PexICT<1.7mL/min/kg were calculated. Serum CysC results of PENIA and PETIA were correlated with GFR. Statistical analysis was performed using general linear modeling. ResultsCats with CKD had significantly higher meanSD sCysC (1.4 +/- 0.5mg/L) (P<.001) and uCysC/urinary creatinine (uCr) (291 +/- 411mg/mol) (P<.001) compared to healthy cats (sCysC 1.0 +/- 0.3 and uCysC/uCr 0.32 +/- 0.97). UCysC was detected in 35/49 CKD cats. R-2 values between GFR and sCysC or sCr were 0.39 and 0.71, respectively (sCysC or sCr=+GFR+epsilon). Sensitivity and specificity were 22 and 100% for sCysC and 83 and 93% for sCr. Serum CysC could not distinguish healthy from CKD cats, nor normal from borderline or low GFR, in contrast with sCr. ConclusionSerum CysC is not a reliable marker of reduced GFR in cats and uCysC could not be detected in all CKD cats

Covering Problems for Partial Words and for Indeterminate Strings

We consider the problem of computing a shortest solid cover of an indeterminate string. An indeterminate string may contain non-solid symbols, each of which specifies a subset of the alphabet that could be present at the corresponding position. We also consider covering partial words, which are a special case of indeterminate strings where each non-solid symbol is a don't care symbol. We prove that indeterminate string covering problem and partial word covering problem are NP-complete for binary alphabet and show that both problems are fixed-parameter tractable with respect to $k$, the number of non-solid symbols. For the indeterminate string covering problem we obtain a $2^{O(k \log k)} + n k^{O(1)}$-time algorithm. For the partial word covering problem we obtain a $2^{O(\sqrt{k}\log k)} + nk^{O(1)}$-time algorithm. We prove that, unless the Exponential Time Hypothesis is false, no $2^{o(\sqrt{k})} n^{O(1)}$-time solution exists for either problem, which shows that our algorithm for this case is close to optimal. We also present an algorithm for both problems which is feasible in practice.Comment: full version (simplified and corrected); preliminary version appeared at ISAAC 2014; 14 pages, 4 figure

Statistical modeling of ground motion relations for seismic hazard analysis

We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area-equivalence; wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual variance and hazard. Beside this, we discuss important aspects of classical approaches and discover discrepancies with the state of the art of stochastics and statistics (model selection and significance, test of distribution assumptions, extreme value statistics). We criticize especially the assumption of logarithmic normally distributed residuals of maxima like the peak ground acceleration (PGA). The natural distribution of its individual random component (equivalent to exp(epsilon_0) of Joyner and Boore 1993) is the generalized extreme value. We show by numerical researches that the actual distribution can be hidden and a wrong distribution assumption can influence the PSHA negatively as the negligence of area equivalence does. Finally, we suggest an estimation concept for GMRs of PSHA with a regression-free variance estimation of the individual random component. We demonstrate the advantages of event-specific GMRs by analyzing data sets from the PEER strong motion database and estimate event-specific GMRs. Therein, the majority of the best models base on an anisotropic point source approach. The residual variance of logarithmized PGA is significantly smaller than in previous models. We validate the estimations for the event with the largest sample by empirical area functions. etc

ZnO based thermopower wave sources

Exothermic chemical reactions of nitrocellulose are coupled onto thermoelectric zinc oxide (ZnO) layers to generate self-propagating thermopower waves resulting in highly oscillatory voltage output of the order of 500 mV. The peak specific power obtained from ZnO based sources is approximately 0.5 kW kg-1

High-dose etoposide with granulocyte colony-stimulating factor for mobilization of peripheral blood progenitor cells: efficacy and toxicity at three dose levels.

High-dose etoposide (2.0-2.4 g m(-2)) with granulocyte colony-stimulating factor (G-CSF) is an effective strategy to mobilize peripheral blood progenitor cells (PBPCs), although in some patients this is associated with significant toxicity. Sixty-three patients with malignancy were enrolled into this non-randomized sequential study. The majority (55/63, 87%) had received at least two prior regimens of chemotherapy, and seven patients had previously failed to mobilize following high-dose cyclophosphamide with G-CSF. Consecutive patient groups received etoposide at three dose levels [2.0 g m(-2) (n = 22), 1.8 g m(-2) (n = 20) and 1.6 g m(-2) (n = 21)] followed by daily G-CSF. Subsequent leukaphereses were assayed for CD34+ cell content, with a target total collection of 2.0 x 10(6) CD34+ cells kg(-1). Toxicity was assessed by the development of significant mucositis, the requirement for parenteral antibiotics or blood component support and rehospitalization incidence. Ten patients (16%) had less than the minimum target yield collected. Median collections in the three groups were 4.7 (2 g m(-2)), 5.7 (1.8 g m(-2)) and 6.5 (1.6 g m(-2)) x 10(6) CD34+ cells kg(-1). Five of the seven patients who had previously failed cyclophosphamide mobilization achieved more than the target yield. Rehospitalization incidence was significantly lower in patients receiving 1.6 g m(-2) etoposide than in those receiving 2.0 g m(-2) (P = 0.03). These data suggest that high-dose etoposide with G-CSF is an efficient mobilization regimen in the majority of heavily pretreated patients, including those who have previously failed on high-dose cyclophosphamide with G-CSF. An etoposide dose of 1.6 g m(-2) appears to be as effective as higher doses but less toxic

Consistent Anisotropic Repulsions for Simple Molecules

We extract atom-atom potentials from the effective spherical potentials that suc cessfully model Hugoniot experiments on molecular fluids, e.g., $O_2$ and $N_2$. In the case of $O_2$ the resulting potentials compare very well with the atom-atom potentials used in studies of solid-state propertie s, while for $N_2$ they are considerably softer at short distances. Ground state (T=0K) and room temperatu re calculations performed with the new $N-N$ potential resolve the previous discrepancy between experimental and theoretical results.Comment: RevTeX, 5 figure

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings

Verifying a Computational Method for Predicting Extreme Ground Motion

Large earthquakes strike infrequently and close-in recordings are uncommon. This situation makes it difficult to predict the ground motion very close to earthquake-generating faults, if the prediction is to be based on readily available observations. A solution might be to cover the Earth with seismic instruments so that one could rely on the data from previous events to predict future shaking. However, even in the case of complete seismic data coverage for hundreds of years, there would still be one type of earthquake that would be difficult to predict: those very rare earthquakes that produce very large ground motion