Gröbner Bases over Galois Rings with an Application to Decoding Alternant Codes

We develop a theory of Gröbner bases over Galois rings, following the usual formulation for Gröbner bases over finite fields. Our treatment includes a division algorithm, a characterization of Gröbner bases, and an extension of Buchberger’s algorithm. One application is towards the problem of decoding alternant codes over Galois rings. To this end we consider the module M =  {(a, b) :aS ≡ b  mod x^r} of all solutions to the so-called key equation for alternant codes, where S is a syndrome polynomial. In decoding, a particular solution (Σ, Ω)  ∈ M is sought satisfying certain conditions, and such a solution can be found in a Gröbner basis of M. Applying techniques introduced in the first part of this paper, we give an algorithm which returns the required solution.     

Mason: morphological simplification

The traditional rounding and filleting morphological filters are biased. Hence, as r grows, the rounding R_r (S) of S shrinks and the filleting F_r (S) grows. A shape S is r-regular when R_r (S) = F_r (S) = S. The combinations F_r (R_r (S)) and R_r (F_r (S)) produce nearly r-regular shapes, but retain a bias: F_r (R_r (S)) is usually smaller than S and R_r (F_r (S)) is larger. To overcome this bias, we propose a new filter, called Mason. The r-mortar M_r (S) of S is F_r (S)–R_r (S), and the stability of a point P with respect to S is the smallest value of r for which P belongs to M_r (S). Stability provides important information about the shape’s imbedding that cannot be obtained through traditional topological or differential analysis tools. F_r (R_r (S)) and R_r (F_r (S)) only affect space in M_r (S). For each maximally connected component of M_r (S), Mason performs either F_r (R_r (S)) or R_r (F_r (S)), choosing the combination that alters the smallest portion of that component. Hence, Mason acts symmetrically on the shape and on its complement. Its output is guaranteed to have a smaller symmetric difference with the original shape than that of either combination F_r (R_r (S)) or R_r (F_r (S)). Many previously proposed shape simplification algorithms were focused on reducing the combinatorial storage or processing costs of a shape at the expense of the smoothness and regularity or altered the shape in regular portions that did not exhibit any high frequency complexity. Mason is the first shape simplification operator that is independent of the particular representation and offers the advantage of preserving portions of the boundary of S that are regular at the desired scale.     

Algorithmic complexity bounds on future prediction errors

We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor M from the true distribution μ by the algorithmic complexity of μ. Here we assume that we are at a time t > 1 and have already observed x = x₁ ⋯ x_t. We bound the future prediction performance on x_t+1x_t+2 ⋯ by a new variant of algorithmic complexity of μ given x, plus the complexity of the randomness deficiency of x. The new complexity is monotone in its condition in the sense that this complexity can only decrease if the condition is prolonged. We also briefly discuss potential generalizations to Bayesian model classes and to classification problems.     

Irregular Primes and Cyclotomic Invariants to 12 Million

Computations of irregular primes and associated cyclotomic invariants were extended to all primes up to 12 million using multisectioning/convolution methods and a novel approach which originated in the study of Stickelberger codes Shokrollahi (1996). The latter idea reduces the problem to that of finding zeros of a polynomial overF_pof degree  <  (p −  1) / 2 among the quadratic nonresidues mod p. Use of fast polynomial gcd-algorithms gives anO (p log²p loglog p)-algorithm for this task. A more efficient algorithm, with comparable asymptotic running time, can be obtained by using Schönhage–Strassen integer multiplication techniques and fast multiple polynomial evaluation algorithms; this approach is particularly efficient when run on primes p for whichp −  1 has small prime factors. We also give some improvements on previous implementations for verifying the Kummer–Vandiver conjecture and for computing the cyclotomic invariants of a prime.     

Bounds for the Roots of Lacunary Polynomials

A polynomial P(X)  = X^d + a_d − 1X^d − 1 + ⋯ is called lacunary when a_d − 1 =  0. We give bounds for the roots of such polynomials with complex coefficients. These bounds are much smaller than for general polynomials.     

Approximate Solutions of Polynomial Equations

In this paper, we introduce “approximate solutions" to solve the following problem: given a polynomial F(x, y) over Q, where x represents an n -tuple of variables, can we find all the polynomials G(x) such that F(x, G(x)) is identically equal to a constant c in Q ? We have the following: let F(x, y) be a polynomial over Q and the degree of y in F(x, y) be n. Either there is a unique polynomial g(x)  ∈ Q [ x ], with its constant term equal to 0, such that F(x, y)  = ∑_j = 0ⁿc_j(y − g(x))^jfor some rational numbers c_j, hence, F(x, g(x)  + a)  ∈ Q for all a ∈ Q, or there are at most t distinct polynomials g₁(x),⋯ , g_t(x), t ≤ n, such that F(x, g_i(x))  ∈ Q for 1  ≤ i ≤ t. Suppose that F(x, y) is a polynomial of two variables. The polynomial g(x) for the first case, or g₁(x),⋯ , g_t(x) for the second case, are approximate solutions of F(x, y), respectively. There is also a polynomial time algorithm to find all of these approximate solutions. We then use Kronecker’s substitution to solve the case of F(x, y).     

On identifying codes that are robust against edge changes

Assume that G = (V, E) is an undirected graph, and C ⊆ V. For every v ∈ V, denote I_r(G; v) = {u ∈ C: d(u,v) ≤ r}, where d(u,v) denotes the number of edges on any shortest path from u to v in G. If all the sets I_r(G; v) for v ∈ V are pairwise different, and none of them is the empty set, the code C is called r-identifying. The motivation for identifying codes comes, for instance, from finding faulty processors in multiprocessor systems or from location detection in emergency sensor networks. The underlying architecture is modelled by a graph. We study various types of identifying codes that are robust against six natural changes in the graph; known or unknown edge deletions, additions or both. Our focus is on the radius r = 1. We show that in the infinite square grid the optimal density of a 1-identifying code that is robust against one unknown edge deletion is 1/2 and the optimal density of a 1-identifying code that is robust against one unknown edge addition equals 3/4 in the infinite hexagonal mesh. Moreover, although it is shown that all six problems are in general different, we prove that in the binary hypercube there are cases where five of the six problems coincide.     

Generalized Strong Pseudoprime Tests and Applications

We describe probabilistic primality tests applicable to integers whose prime factors are all congruent to 1 mod r where r is a positive integer;r =  2 is the Miller–Rabin test. We show that if ν rounds of our test do not find n ≠  =  (r +  1)²composite, then n is prime with probability of error less than (2 r) ^− ν. Applications are given, first to provide a probabilistic primality test applicable to all integers, and second, to give a test for values of cyclotomic polynomials.     

Spectral and chemical analysis of tropical forests: Scaling from leaf to canopy levels

Variation in the foliar chemistry of humid tropical forests is poorly understood, and airborne imaging spectroscopy could provide useful information at leaf and canopy scales. However, variation in canopy structure affects our ability to estimate foliar properties from airborne spectrometer data, yet these structural affects remain poorly quantified. Using leaf spectral (400–2500 nm) and chemical data collected from 162 Australian tropical forest species, along with partial least squares (PLS) analysis and canopy radiative transfer modeling, we determined the strength of the relationship between canopy reflectance and foliar properties under conditions of varying canopy structure.At the leaf level, chlorophylls, carotenoids and specific leaf area (SLA) were highly correlated with leaf spectral reflectance (r = 0.90–0.91). Foliar nutrients and water were also well represented by the leaf spectra (r = 0.79–0.85). When the leaf spectra were incorporated into the canopy radiative transfer simulations with an idealistic leaf area index (LAI) = 5.0, correlations between canopy reflectance spectra and leaf properties increased in strength by 4–18%. The effects of random LAI (= 3.0–6.5) variation on the retrieval of leaf properties remained minimal, particularly for pigments and SLA (r = 0.92–0.93). In contrast, correlations between leaf nitrogen (N) and canopy reflectance estimates decreased from r = 0.87 at constant LAI = 5 to r = 0.65 with randomly varying LAI = 3.0–6.5. Progressive increases in the structural variability among simulated tree crowns had relatively little effect on pigment, SLA and water predictions. However, N and phosphorus (P) were more sensitive to canopy structural variability. Our modeling results suggest that multiple leaf chemicals and SLA can be estimated from leaf and canopy reflectance spectroscopy, and that the high-LAI canopies found in tropical forests enhance the signal via multiple scattering. Finally, the two factors we found to most negatively impact leaf chemical predictions from canopy reflectance were variation in LAI and viewing geometry, which can be managed with new airborne technologies and analytical methods.     

Assessment of grape yield and composition using the reflectance based Water Index in Mediterranean rainfed vineyards

In rainfed vineyards water deficits play a major role in determining berry yield and composition. Therefore, reliable indicators of vine water status might be of great value for the optimization of grape yield and quality. In the present study the feasibility of using hyperspectral reflectance indices related to plant biophysical properties at predicting berry yield and quality attributes in rainfed vineyards is assessed. The study was conducted on Vitis vinifera cv. Chardonnay in commercial vineyards in the D.O. Penedès region (Catalonia, Spain) over two consecutive years (2007–2008). Field measurements of fractional intercepted Photosynthetic Active Radiation (fIPAR), canopy reflectance, predawn water potential (Ψ_p) and the canopy to air temperature difference at midday (ΔT_midday) were conducted at the stage of veraison. Yield, Total Soluble Solids (TSS), Titratable Acidity (TA) and the ratio TSS/TA (maturation index, IMAD) were determined at harvest. Contrasted water availability among vineyards prompted considerable variation in berry yield and quality attributes. Across years, higher yield was accompanied by higher TA (r = 0.59, p < 0.01) and lower IMAD (r = ? 0.63, p < 0.01) while no significant relationship was observed between yield and TSS. Yield was related to canopy vigor (fIPAR) in a variable extend: in 2007, yield was positively related to fIPAR (r = 0.71, p < 0.05) while yield was found to decrease along with increasing fIPAR in 2008 (r = ? 0.62, p < 0.05). Contrastingly, NDVI provided consistent estimates of yield across years (r = 0.57, p < 0.05). These results suggest that NDVI might be more appropriate to characterize the effects of varying water availability on yield than fIPAR. In addition, yield was found to be related to ΔT_midday (r = ? 0.63 and r = ? 0.66, in 2007 and 2008, respectively). Accordingly, the Water Index (WI), an indicator of vine water status, provided robust estimates of yield across years (r = 0.61, p < 0.01). The strength of the correlation between NDVI and WI vs. yield suggests that yield was influenced by changes in both leaf area (intercepted light) and photosynthesis (stomatal aperture) in a variable extent according to the timing and severity of water deficits in the years of study. Berry quality attributes did not show significant relationships against fIPAR but were related to ΔT_midday. Accordingly, NDVI did not show significant correlation with berry quality attributes, while WI was found to be consistently related to TA (r = 0.70, p < 0.01) and IMAD (r = ? 0.71, p < 0.01) across years. The results obtained suggest that the WI might provide reliable estimates of berry quality attributes in vineyards experiencing moderate to severe water deficits with potential application in precision viticulture activities such as selective harvesting according to grape quality attributes as well as for ripening assessment.     

A genetic algorithm approach for multi-product multi-period continuous review inventory models

This paper formulates an approach for multi-product multi-period (Q, r) inventory models that calculates the optimal order quantity and optimal reorder point under the constraints of shelf life, budget, storage capacity, and “extra number of products” promotions according to the ordered quantity. Detailed literature reviews conducted in both fields have uncovered no other study proposing such a multi-product (Q, r) policy that also has a multi-period aspect and which takes all the aforementioned constraints into consideration. A real case study of a pharmaceutical distributor in Turkey dealing with large quantities of perishable products, for whom the demand structure varies from product to product and shows deterministic and variable characteristics, is presented and an easily-applicable (Q, r) model for distributors operating in this manner proposed. First, the problem is modeled as an integer linear programming (ILP) model. Next, a genetic algorithm (GA) solution approach with an embedded local search is proposed to solve larger scale problems. The results indicate that the proposed approach yields high-quality solutions within reasonable computation times.     

A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: Validation

Accurate assessment of phytoplankton chlorophyll-a (chla) concentrations in turbid waters by means of remote sensing is challenging due to the optical complexity of case 2 waters. We have applied a recently developed model of the form [R_rs^? 1(λ₁) ? R_rs^? 1(λ₂)] × R_rs(λ₃) where R_rs(λ_i) is the remote-sensing reflectance at the wavelength λ_i, for the estimation of chla concentrations in turbid waters. The objectives of this paper are (a) to validate the three-band model as well as its special case, the two-band model R_rs^? 1(λ₁) × R_rs(λ₃), using datasets collected over a considerable range of optical properties, trophic status, and geographical locations in turbid lakes, reservoirs, estuaries, and coastal waters, and (b) to evaluate the extent to which the three-band model could be applied to the Medium Resolution Imaging Spectrometer (MERIS) and two-band model could be applied to the Moderate Resolution Imaging Spectroradiometer (MODIS) to estimate chla in turbid waters.The three-band model was calibrated and validated using three MERIS spectral bands (660–670 nm, 703.75–713.75 nm, and 750?757.5 nm), and the 2-band model was tested using two MODIS spectral bands (λ₁ = 662–672, λ₃ = 743–753 nm). We assessed the accuracy of chla prediction in four independent datasets without re-parameterization (adjustment of the coefficients) after initial calibration elsewhere. Although the validation data set contained widely variable chla (1.2 to 236 mg m^? 3), Secchi disk depth (0.18 to 4.1 m), and turbidity (1.3 to 78 NTU), chla predicted by the three-band algorithm was strongly correlated with observed chla (r² > 0.96), with a precision of 32% and average bias across data sets of ? 4.9% to 11%. Chla predicted by the two-band algorithm was also closely correlated with observed chla (r² > 0.92); however, the precision declined to 57%, and average bias across the data sets was 18% to 50.3%. These findings imply that, provided that an atmospheric correction scheme for the red and NIR bands is available, the extensive database of MERIS and MODIS imagery could be used for quantitative monitoring of chla in turbid waters.     

Internet use and verbal aggression: The moderating role of parents and peers

This research investigated the influence of parent–adolescent communication quality, as perceived by the adolescents, on the relationship between adolescents’ Internet use and verbal aggression. Adolescents (N = 363, age range 10–16, M_T1 = 12.84, SD = 1.93) were examined twice with a six-month delay. Controlling for social support in general terms, moderated regression analyses showed that Internet-related communication quality with parents determined whether Internet use is associated with an increase or a decrease in adolescents’ verbal aggression scores over time. A three way interaction indicated that high Internet-related communication quality with peers can have disadvantageous effects if the communication quality with parents is low. Implications on resources and risk factors related to the effects of Internet use are discussed.     

Factors responsible for the aggregation behavior of hydrophobic polyelectrolyte PEA in aqueous solution studied by molecular dynamics simulations

Self-association (i.e. interchain aggregation) behavior of atactic poly(ethacrylic acid) PEA in dilute aqueous solution as function of degree-of-neutralization by Na⁺ counter-ions (i.e. charge fraction f) was investigated by molecular dynamics simulations. Aggregation is found to occur in the range 0 ≤ f ≤0.7 in agreement with experimental results compared at specified polymer concentration C_p = 0.36 mol/l in dilute solution. The macromolecular solution was characterized and analysed for radius-of-gyration, torsion angle distribution, inter and intra-molecular hydrogen bonds, radial distribution functions of intermolecular and inter-atomic pairs, inter-chain contacts and solvation enthalpy. The PEA chains form aggregate through attractive inter-chain interaction via hydrogen bonding, in the range f < 0.7, in agreement with experimental observation. The numbers of inter-chain contacts decreases with f. A critical structural transition occurs at f = 0.7, observed via simulations for the first time, in R_g as well as inter-chain H-bonds. The inter-chain distance increases with f due to repulsive interactions between COO− groups on the chains. PEA-PEA electrostatic interactions dominant solvation enthalpy. The PEA solvation enthalpy becomes increasingly favorable with increase in f. The transition enthalpy change, in going from uncharged (acid) state to fully charged state (f = 1) is unfavorable towards aggregate formation.     

Hands-free administration of subjective workload scales: Acceptability in a surgical training environment

IntroductionSubjective workload measures are usually administered in a visual–manual format, either electronically or by paper and pencil. However, vocal responses to spoken queries may sometimes be preferable, for example when experimental manipulations require continuous manual responding or when participants have certain sensory/motor impairments. In the present study, we evaluated the acceptability of the hands-free administration of two subjective workload questionnaires – the NASA Task Load Index (NASA-TLX) and the Multiple Resources Questionnaire (MRQ) – in a surgical training environment where manual responding is often constrained.MethodSixty-four undergraduates performed fifteen 90-s trials of laparoscopic training tasks (five replications of 3 tasks – cannulation, ring transfer, and rope manipulation). Half of the participants provided workload ratings using a traditional paper-and-pencil version of the NASA-TLX and MRQ; the remainder used a vocal (hands-free) version of the questionnaires. A follow-up experiment extended the evaluation of the hands-free version to actual medical students in a Minimally Invasive Surgery (MIS) training facility.ResultsThe NASA-TLX was scored in 2 ways – (1) the traditional procedure using participant-specific weights to combine its 6 subscales, and (2) a simplified procedure – the NASA Raw Task Load Index (NASA-RTLX) – using the unweighted mean of the subscale scores. Comparison of the scores obtained from the hands-free and written administration conditions yielded coefficients of equivalence of r = 0.85 (NASA-TLX) and r = 0.81 (NASA-RTLX). Equivalence estimates for the individual subscales ranged from r = 0.78 (“mental demand”) to r = 0.31 (“effort”). Both administration formats and scoring methods were equally sensitive to task and repetition effects. For the MRQ, the coefficient of equivalence for the hands-free and written versions was r = 0.96 when tested on undergraduates. However, the sensitivity of the hands-free MRQ to task demands (η_partial² = 0.138) was substantially less than that for the written version (η_partial² = 0.252). This potential shortcoming of the hands-free MRQ did not seem to generalize to medical students who showed robust task effects when using the hands-free MRQ (η_partial² = 0.396). A detailed analysis of the MRQ subscales also revealed differences that may be attributable to a “spillover” effect in which participants’ judgments about the demands of completing the questionnaires contaminated their judgments about the primary surgical training tasks.ConclusionVocal versions of the NASA-TLX are acceptable alternatives to standard written formats when researchers wish to obtain global workload estimates. However, care should be used when interpreting the individual subscales if the object is to make comparisons between studies or conditions that use different administration modalities. For the MRQ, the vocal version was less sensitive to experimental manipulations than its written counterpart; however, when medical students rather than undergraduates used the vocal version, the instrument’s sensitivity increased well beyond that obtained with any other combination of administration modality and instrument in this study. Thus, the vocal version of the MRQ may be an acceptable workload assessment technique for selected populations, and it may even be a suitable substitute for the NASA-TLX.     

Artificial neural network-based model for predicting VO2max from a submaximal exercise test

The goal of this study is to develop an accurate artificial neural network (ANN)-based model to predict maximal oxygen uptake (VO₂max) of fit adults from a single stage submaximal treadmill jogging test. Participants (81 males and 45 females), aged from 17 to 40 years, successfully completed a maximal graded exercise test (GXT) to determine VO₂max. The variables; gender, age, body mass, steady-state heart rate and jogging speed are used to build the ANN prediction model. Using 10-fold cross validation on the dataset, the average values of standard error of estimate (SEE), Pearson’s correlation coefficient (r) and multiple correlation coefficient (R) of the model are calculated as 1.80 ml kg^?1 min^?1, 0.95 and 0.93, respectively. Compared with the results of the other prediction models in literature that were developed using Multiple Linear Regression Analysis, the reported values of SEE, r and R in this study are considerably more accurate.     

Hyperspectral remote sensing of cyanobacteria in turbid productive water using optically active pigments,chlorophyll a and phycocyanin

Nuisance blue-green algal blooms contribute to aesthetic degradation of water resources by means of accelerated eutrophication, taste and odor problems, and the production of toxins that can have serious adverse human health effects. Current field-based methods for detecting blooms are costly and time consuming, delaying management decisions. Methods have been developed for estimating phycocyanin concentration, the accessory pigment unique to freshwater blue-green algae, in productive inland water. By employing the known optical properties of phycocyanin, researchers have evaluated the utility of field-collected spectral response patterns for determining concentrations of phycocyanin pigments and ultimately blue-green algal abundance. The purpose of this research was to evaluate field spectroscopy as a rapid cyanobacteria bloom assessment method. In-situ field reflectance spectra were collected at 54 sampling sites on two turbid reservoirs on September 6th and 7th in Indianapolis, Indiana using ASD Fieldspec (UV/VNIR) spectroradiometers. Surface water samples were analyzed for in-vitro pigment concentrations and other physical and chemical water quality parameters. Semi-empirical algorithms by Simis et al. [Simis, S., Peters, S., Gons, H. (2005). Remote sensing of the cyanobacterial pigment phycocyanin in turbid inland water. American Society of Limnology and Oceanography 50(11): 237–245] were applied to the field spectra to predict chlorophyll a and phycocyanin absorption at 665 nm and 620 nm, respectively. For estimation of phycocyanin concentration, a specific absorption coefficient of 0.0070 m² mg PC^-1 for phycocyanin at 620 nm, a_PC^?(620), was employed, yielding an r² value of 0.85 (n = 48, p < 0.0001), mean relative residual value of 0.51 (σ = 1.41) and root mean square error (RMSE) of 19.54 ppb. Results suggest this algorithm could be a robust model for estimating phycocyanin. Error is highest in water with phycocyanin concentrations of less than 10 ppb and where phycocyanin abundance is low relative to chlorophyll a. A strong correlation between measured phycocyanin concentrations and biovolume measurements of cyanobacteria was also observed (r = 0.89), while a weaker relationship (r = 0.66) resulted between chlorophyll a concentration and cyanobacterial biovolume.