Smallest Root Research Articles

Foreign Currency Prognostication: Diverse Tests for Germany

This paper uses a large variety of different models and examines the predictive performance of these exchange rate models by applying parametric and non-parametric techniques. For forecasting, we will choose that predictor with the smallest root mean square forecast error (RMSE). The results show that the better models are in equations (3), (10), (17), and (18), although none gives a perfect forecast. At the end, error correction versions of the models will be fit so that plausible long-run elasticities can be imposed on the fundamental variables of each model.

Foreign Currency Forecasts: A Combination Analysis

This paper uses a large variety of different models and examines the predictive performance of these exchange rate models by applying parametric and non-parametric techniques. For forecasting, we will choose that predictor with the smallest root mean square forecast error (RMSE). The results show that the better model is equation (34), but none of them gives a perfect forecast. At the end, error correction versions of the models will be fit so that plausible long-run elasticities can be imposed on the fundamental variables of each model.

On the Second Least Distance Eigenvalue of a Graph

Let $G$ be a connected graph on $n$ vertices, and let $D(G)$ be the distance matrix of $G$. Let $\partial_1(G)\ge\partial_2(G)\ge\cdots\ge\partial_n(G)$ denote the eigenvalues of $D(G)$. In this paper, the connected graphs with @n􀀀1(G) at least the smallest root of $x^3=3x^2-11x-6 = 0$ are determined. Additionally, some non-isomorphic distance cospectral graphs are given.

Predictive models of cytotoxicity as mediated by exposure to chemicals or drugs

Predicting cytotoxicity is a challenging task because of the complex biological mechanisms behind it. Cytotoxicity due to toxin – biologically produced poison – is known to play a substantial role in a disease process. Two objectives in this research are to derive robust general predictive cytotoxicity models to minimize unnecessary toxicity. The first objective is to build accurate predictive statistical models for cytotoxicity data based on lymphoblastoid cell lines obtained from in vitro studies. This could be an important step for accomplishing a goal in biomedecial/biophamarceutical research, by obtaining the best medical outcomes by minimizing toxicity in regard to a person’s genetic profile. The second objective is to build predictive models to predict population-level cytotoxicity for unknown compounds based on chemical structural features. These two objectives were accomplished by a proposed variable selection process, the random forests, and the least absolute shrinkage and selection operator method. We achieved an excellent prediction result with the random forests algorithm using SNP markers from the proposed approach, having the smallest root mean squared error among the teams which participated in the DREAM Toxicogenetics Challenge. Since chemical compounds for drugs have great influence on human health, the predictive statistical models for these objectives could be helpful to government agencies in relevant decision-making.

Moment and IV Selection Approaches: A Comparative Simulation Study

We compare three moment selection approaches, followed by post-selection estimation strategies. The first is adaptive least absolute shrinkage and selection operator (ALASSO) of Zou (2006), recently extended by Liao (2013) to possibly invalid moments in GMM. In this method, we select the valid instruments with ALASSO. The second method is based on the J test, as in Andrews and Lu (2001). The third one is using a Continuous Updating Objective (CUE) function. This last approach is based on Hong et al. (2003), who propose a penalized generalized empirical likelihood-based function to pick up valid moments. They use empirical likelihood, and exponential tilting in their simulations. However, the J-test-based approach of Andrews and Lu (2001) provides generally better moment selection results than the empirical likelihood and exponential tilting as can be seen in Hong et al. (2003). In this article, we examine penalized CUE as a third way of selecting valid moments.Following a determination of valid moments, we run unpenalized generalized method of moments (GMM) and CUE and model averaging technique of Okui (2011) to see which one has better postselection estimator performance for structural parameters. The simulations are aimed at the following questions: Which moment selection criterion can better select the valid ones and eliminate the invalid ones? Given the chosen instruments in the first stage, which strategy delivers the best finite sample performance?We find that the ALASSO in the model selection stage, coupled with either unpenalized GMM or moment averaging of Okui delivers generally the smallest root mean square error (RMSE) for the second stage coefficient estimators.

Effects of soil bulk density on sessile oak Quercus petraea Liebl. seedlings

This article presents the results of laboratory examinations concerning the effects of soil bulk density on the growth of sessile oak Quercus petraea Liebl. seedlings. The soil for the study was collected from a nursery plot and then compacted into PCV pots in eight different bulk density levels ranging from 0.81 to 1.32 g cm−3. Oak seedlings were cultivated in controlled conditions for 76 days after sowing. The growth and mass parameters of particular seedlings together with the parameters of the assimilation apparatus and roots were measured, taking into account the share of various diameter roots in the root system. For the purpose of the experiment, 120 acorns were sowed, of which 73 seedlings were cultured. An analysis of the growth of the sessile oak seedlings revealed that a change in soil density significantly affected root system development, total height of seedlings and dry mass. It was observed that the dry mass of the root system as well as the area and length of the roots decreased with an increase in soil density. Root system reduction was noted, the size of which determines the proper development of the tree and ensures its stability. Besides a decrease in the root system, an increase in soil compaction also resulted in a reduction in the number of roots of a specified diameter. The first to be affected were the smallest roots, i.e., those with diameters up to 0.2 mm, which are responsible for the uptake of mineral components. It was confirmed that even a slight increase in soil compaction might negatively result in the growth of young seedlings, impeding root system development.

Development of Indoor Air Pollution Concentration Prediction by Geospatial Analysis

People living near busy roads are potentially exposed to traffic-induced air pollutants. The pollutants may intrude into the indoor environment, causing health risks to the occupants. Prediction of pollutant exposure therefore is of great importance for impact assessment and policy making related to environmentally sustainable transport. This study involved the selection of spatial interpolation methods that can be used for prediction of indoor air quality based on outdoor pollutant mapping without indoor measurement data. The research was undertaken in the densely populated area of Karees, Bandung, Indonesia. The air pollutant NO 2 was monitored in this area as a preliminary study. Nitrogen dioxide concentrations were measured by passive diffusion tube. Outdoor NO 2 concentrations were measured at 94 locations, consisting of 30 roadside and 64 outdoor locations. Residential indoor NO 2 concentrations were measured at 64 locations. To obtain a spatially continuous air quality map, the spatial interpolation methods of inverse distance weighting (IDW) and Kriging were applied. Selection of interpolation method was done based on the smallest root mean square error (RMSE) and standard deviation (SD). The most appropriate interpolation method for outdoor NO 2 concentration mapping was Kriging with an SD value of 5.45 µg/m 3 and an RMSE value of 5.45 µg/m 3 , while for indoor NO 2 concentration mapping the IDW was best fitted with an RMSE value of 5.92 µg/m 3 and an SD value of 5.92 µg/m 3 .

Critical evaluation of anharmonic corrections to the equilibrium isotope effect for methyl cation transfer from vacuum to dielectric continuum

Harmonic and anharmonic vibrational frequencies are computed for isotopologues of methyl cation in vacuum and in apolarised continuum model (PCM) dielectric continuum (ϵ = 80) within Gaussian09. Comparison of results in vacuum for two methods (B3LYP and second-order Møller–Plesset perturbation theory) and three basis sets (6-31+G(d), cc-aug-PVDZ, cc-aug-PVQZ) with published anharmonic frequencies obtained from an accurate vibrational configuration interaction (VCI) method shows the smallest root mean square error in the frequencies from B3LYP/6-31+G(d) with anharmonic corrections. Using this method to calculate isotopic partition function ratios (IPFRs) for all six pairs of CH3+, CH2D+, CHD2+ and CD3+ gives better results for anharmonic frequencies than for unscaled harmonic frequencies, but scaled harmonic frequencies give even better results for less cost. The scaling factor is simply the ratio of the sum of the anharmonic VCI frequencies to the sum of the harmonic B3LYP/6-31+G(d) frequencies, which corresponds to the dominance of zero-point energy changes in determining the IPFRs. Both the scaled and unscaled harmonic frequencies provide reasonable estimates for the equilibrium isotope effects (EIEs) upon transfer of methyl cation from vacuum to PCM ‘water’, but the anharmonic PCM calculations give erratic results. The use of scaled B3LYP/6-31+G(d) harmonic frequencies is recommended for the estimations of EIEs rather than expensive anharmonic corrections.

Mineral nutrition plants in function of stabile sugar beet production

The study presents results of a three year research on sugar beet yield and technological value of root in the conditions of increased mineral fertilizers. Research was carried out on chernozem in the climatic conditions of South Banat. Subject of studies were four varieties (Chiara, Irina, Laetitia and Severina) and ten variants mineral nutrition of plants with different amounts and ratios of NPK fertilizers. The results are shown root traits that have the most important role in the creation of yield (average root weight, digestion, root yield and crystal sugar yield). The results obtained were compared by years of research. The variation caused by changing weather conditions, are determined by the coefficient of variation. The study results showed that proper mineral nutrition of plants and variety characteristics significantly affect the stability productive traits of sugar beet. The yield of crystal sugar in the overall average was the highest in the variant with 50 kg ha-1 of nitrogen, phosphorus and potassium. Variety Chiara had the biggest roots and the highest root yield, but the slightest digestion. The best production results were obtained variety Severina. This variety had the smallest roots, but had the largest digestion. Therefore, the biggest crystal sugar yield was achieved by Severina variety and the lowest coefficient of variation according to years of investigation.

A Torsion Problem of a Prismatic Rod Composed of Two Orthotropic Materials

A rod composed of two different prismatic rods built-up with rectilinear orthotropic materials is studied. Composite parts of the prismatic rods are connected entirely by their common surface. The anisotropy axis is perpendicular to the cross-section plane. The problem has been solved in Cartesian coordinate system. The functions of stresses are presented by the sums of solutions corresponding to positive eigenvalues of homogeneous boundary problems and partial solutions of inhomogeneous boundary problems. From condition of existence of the non-trivial solution of the homogeneous boundary problem an equation in respect to eigenvalues is derived of which roots are real and different. If there are roots in (0; 1) interval, then the stresses tend to infinity at the vertex of the cross-section of the composite rod have a feature with the order equal to where - is the smallest root in the interval (0, 1).

Artificial neural network for forecasting rainfall pattern in Prince Edward Island, Canada

The forecast performance of alternative artificial neural network (ANN) models was studied to compare their forecast accuracy to the fractionally integrated autoregressive moving average model using monthly rainfall data for the Canadian province of Prince Edward Island (PEI). A multilayer feed-forward back-propagation ANN algorithm is implemented to evaluate the forecast accuracy and to analyse the statistical characteristics of the ANN model for original data and for data pre-processed with moving average and exponential smoothing transformations. The prediction performance of these models is compared to that of a seasonal autoregressive fractionally integrated moving average time series model. The statistical results show that the ANN model with exponential smoothing of the data has the smallest root mean square error and the highest correlation coefficient and thus, outperforms the alternative models investigated in this study.

Soft Sensing of the Lysozyme Mycelium Bacteria Concentration Based on SUKF Algorithm

In order to measure lysozyme biomass activity concentration accurately and in real-time in the fermentation process of marine biological enzyme preparation, soft sensing with the nonlinear state-estimation based on SUKF has been used, the method uses KF framework, embedded in SUT. In fact the fermentation bacteria is lysozyme, which is fermented in a fermenter of KRH-100L according to process requirements. The statistical properties of variables through the nonlinear transformation has been calculated and the degradation effects of aggregation of high-dimensional and nonlinear fermentation model would be effectively settled in sample. By using σ-point set with symmetric sampling strategy, the mean points increased, according to the fermentation of priori information of each dimension mean. By using cross-validation method to select model parameters, compared with the support vector machine SVM with RBFNN algorithm, the experimental results show that the smallest root mean square statistical error of training and testing in soft Sensing with SUKF reduced by 2% or so.

On the limit points of the smallest eigenvalues of regular graphs

In this paper, we give infinitely many examples of (non-isomorphic) connected $k$-regular graphs with smallest eigenvalue in half open interval $[-1-\sqrt2, -2)$ and also infinitely many examples of (non-isomorphic) connected $k$-regular graphs with smallest eigenvalue in half open interval $[\alpha_1, -1-\sqrt2)$ where $\alpha_1$ is the smallest root$(\approx -2.4812)$ of the polynomial $x^3+2x^2-2x-2$. From these results, we determine the largest and second largest limit points of smallest eigenvalues of regular graphs less than -2. Moreover we determine the supremum of the smallest eigenvalue among all connected 3-regular graphs with smallest eigenvalue less than -2 and we give the unique graph with this supremum value as its smallest eigenvalue.

Operational Prediction of Groundwater Fluctuation in South Florida using Sequence Based Markovian Stochastic Model

The ecosystem of South Florida is characterized by a vast wetland system, karst surficial hydrogeology, and extended coastal boundary. The ecosystem is poised under risks of: ecological failure due to increased fragmentation by urbanization; groundwater flow disruption because of sinkhole formation; and intrusion of oceanic water with decreasing water table head because of drought or over pumping. It was found important to synthesize the spatiotemporal state of the groundwater hydrology and also develop a forecasting model to support the intensive management and monitoring in place. In this study, an objective was set to develop a stochastic sequence model capable of forecasting groundwater levels on a monthly span at a daily time scale. The groundwater level simulation was conceptualized as a sequence of daily fluctuating states of magnitudes and patterns that has a defined probability of occurrence. The model setup involved representation of daily fluctuation magnitudes in ten states and pattern changes in three states. The sequential occurrence of states of magnitudes and patterns at each time step was used for estimation of the transitional probabilities and employed in a hidden Markov model frame work for ensemble generation and estimation of posterior probabilities. A realization was chosen based on the highest maximum likelihood ratio of 90% and smallest root mean square error of 0.05–0.12 m against the historical data. A monthly forecasting at daily time step was done dynamically incorporating observed data at each time step and revising prior and posterior probability estimation in the hidden Markov model formulation. A case study was conducted at three well sites, which are situated at three different hydrogeologic settings. The model not only reproduced annual groundwater fluctuation patterns but also forecasted preceding monthly fluctuations at maximum likelihood ratio above 90% and root mean square error below 0.15 m. A further study was recommended first to analyze break point parametric estimation for seasonal analysis, and secondly to integrate the approach in other hydrological models for the purpose of synthetic groundwater fluctuation generation.

C:N ratios and carbon distribution profile across rooting zones in oilseed and pulse crops

Knowledge on the C : N ratio of crop residues is of great importance for modelling carbon (C) and nitrogen (N) dynamics of agricultural systems. This study determined (i) the C : N ratios in the seed, straw, and roots of selected broadleaf crops and (ii) the root C and N distribution in the 0–100 cm rooting zone. Three oilseed (Brassica napus canola, Brassica juncea mustard, Linum usitatissimum flax), three pulse crops (Cicer arietinum chickpea, Pisum sativum dry pea, Lens culinaris lentil), and spring wheat (Triticum aestivum L.) were grown under field conditions with low- (rainfall only) and high-water (rainfall plus irrigation) availability. Root C mass decreased substantially with rooting depth, with ~58% of root C mass in the top 20 cm of the soil, 78% in the top 40 cm, and 94% in the top 60 cm. Significant differences in root C mass between crop species occurred in the top 20 cm with canola, mustard, and wheat allocating 66% of their root C total, compared with 55% for dry pea, lentil, and flax, and 41% for chickpea. Root N mass followed a similar response to root C. Seed C : N ratios ranged between 6 and 17, whereas straw C : N ranged between 14 and 55, and root C : N between 17 and 75. Under low-water conditions, canola and mustard had a straw C : N of 33, lower than that of flax (38) and wheat (41). Under higher-water availability, however, mustard and wheat had straw C : N ratios at 55, greater than canola, mustard and flax (47). Three pulses had an average straw C : N ratio of 17, significantly lower than 41 for the oilseeds and 32 for wheat. On average, canola, mustard and wheat had greater root C : N ratios (44) than chickpea (33) and lentil (29), with dry pea having a smallest root C : N ratio (18). Root C : N ratios did not change with soil depth. These detailed measurements on the vertical distribution of root C and N as well as C : N ratios for various crops will assist in improving estimates of inputs for C and N cycling studies.

On the location of roots of non-reciprocal integer polynomials

Let P be a polynomial of degree d with integer coefficients such that P(0) ≠ 0. Assuming that P has no reciprocal factors we obtain a lower bound on the modulus of the smallest root of P in terms of its degree d, its Mahler measure M(P) and the number of roots of P lying outside the unit circle, say, k. We derive from this that all d roots of P must lie in the annulus R 0 }\,(12M(\alpha)^2 \log M(\alpha))^{-d}}$$. Some lower bounds on the moduli of the conjugates of a Pisot number are also given. In particular, it is shown that if α is a cubic Pisot number, then the disc |z| ≤ α −1 + 0.1999α −2 contains no conjugates of α. Here the constant 0.1999 cannot be replaced by the constant 0.2. We also show that if α is a Pisot number of degree at least 4 and α′ is its conjugate, then |α α′ − 1| > (19α 2)−1.

Quantitative Precipitation Estimation over Ocean Using Bayesian Approach from Microwave Observations during the Typhoon Season

We have developed a new Bayesian approach to retrieve oceanic rain rate from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), with an emphasis on typhoon cases in the West Pacific. Retrieved rain rates are validated with measurements of rain gauges located on Japanese islands. To demonstrate improvement, retrievals are also compared with those from the TRMM/Precipitation Radar (PR), the Goddard Profiling Algorithm (GPROF), and a multi-channel linear regression statistical method (MLRS). We have found that qualitatively, all methods retrieved similar horizontal distributions in terms of locations of eyes and rain bands of typhoons. Quantitatively, our new Bayesian retrievals have the best linearity and the smallest root mean square (RMS) error against rain gauge data for 16 typhoon overpasses in 2004. The correlation coefficient and RMS of our retrievals are 0.95 and ~2 mm hr-1, respectively. In particular, at heavy rain rates, our Bayesian retrievals outperform those retrieved from GPROF and MLRS. Overall, the new Bayesian approach accurately retrieves surface rain rate for typhoon cases. Accurate rain rate estimates from this method can be assimilated in models to improve forecast and prevent potential damages in Taiwan during typhoon seasons.

Heritability of shoot die-back and root biomass in sixteen Pterocarpus angolensis (Fabaceae) half-sib families from Malawi, Namibia and Zambia

The experiment was conducted to ascertain narrow-sense heritability (h 2) and the family-within-provenance variation in shoot die-back, taproot length and root biomass of half-sib Pterocarpus angolensis families from Malawi, Namibia and Zambia. Provenances differed significantly in shoot die-back for both shoot die-back seasons. A within provenance family effect was not significant in the first shoot die-back season but was significant in the second shoot die-back season. An increase in proportion of seedlings dying back, to 91%, for a Malawi family was observed in the second shoot die-back season. Provenance and within provenance family effects may be due to latitudinal differences between the provenances. The h 2 of shoot die-back was 0.07 (SE = 0.07) in the first shoot die-back season and 0.42 (SE = 0.27) in the second shoot die-back season. Narrow-sense heritability for root biomass was 0.81 (SE = 0.45). The h 2 for the second die-back season and root biomass suggest the traits are heritable. Random selection of individual families for assessing shoot die-back is important since this trait is only restricted to seedlings and saplings and not mature trees. Within provenance family effects for root biomass were significant, indicating differences between families. Two families from the most northerly provenances of Phalombe and Skull Rock in Malawi were significantly different from other southern families. Non-significant phenotypic correlation between shoot die-back and root biomass shows that shoot die-back is not likely to be determined by root size nor taproot depth. Although a non-significant negative phenotypic correlation (–0.15) between the second shoot die-back season and root biomass was obtained, a family from Malawi that had the highest mean shoot die-back in the second shoot die-back season had the smallest root biomass. Half-sib families with post shoot die-back growth potential, in the first shoot die-back season, are likely to have a better chance of post shoot die-back growth later.

Combined effects of partial root drying and patchy fertilizer placement on nutrient acquisition and growth of oilseed rape

Partial rootzone drying (PRD) is widely investigated as an effective irrigation technique, resulting in higher water use efficiency and yield for plants growing under mild water deficit. Nutrition is another important factor affecting plant yield, but nutrient acquisition has only rarely been considered in conjunction with PRD. Here we investigate the interaction between water and fertilizer supply in a pot experiment with oilseed rape (Brassica napus L.). Eight treatments were set up for the experiment, a factorial combination of four watering regimes (100% control watering at both sides of the plants; 50% control watering at both sides of the plants; 50% fixed watering applied only to one side of the plants; 50% alternate watering applied alternately to both sides of the plant) and two fertilizer placement levels (uniform over the entire pot, and patchy supplied to one side). For the 50% watering treatments, the total amount of water supplied to the plants was the same, only the pattern of application differed between treatments. Also the total fertilizer applied was the same for all treatments. Oilseed rape roots foraged effectively for water and nutrients resulting in relatively small differences in nutrient uptake and above-ground growth among the water-deficit treatments. Placing fertilizer at one side of the plants increased nutrient uptake, but there were differences between the water treatments and interactions with water uptake. Alternate watering resulted in the highest growth, as a result of the largest nitrogen and phosphorus uptake with the smallest root investment among the three water deficit treatments. Fixed watering resulted in poorest performance when fertilizer was uniformly spread throughout the pot, because the plants were unable to acquire the nutrients on the dry side. Our results show that PRD can be well combined with patchy fertilizer supply, but that reduced nutrient uptake may be expected when nutrients are supplied in parts of the soil volume that remain too dry.

On the Brieskorn [formula omitted]-module of an isolated hypersurface singularity

For a germ g of holomorphic function with an isolated singularity at the origin of C n we show that there is a pole for the meromorphic continuation of the distribution 1 Γ ( λ ) . | g | 2 λ g ¯ − n at λ = − n − α where α is the smallest root in its class modulo Z of the reduced Bernstein–Sato polynomial of g. This rather ‘unexpected’ result is a consequence of the fact that the self-duality of the Brieskorn ( a , b ) -module E g associated to g exchanges the biggest simple pole sub- ( a , b ) -module of E g with the saturation of E g by b −1 a . To cite this article: D. Barlet, C. R. Acad. Sci. Paris, Ser. I 343 (2006).