Simultaneous nonlinear equations of growth

The simultaneous equations

$$\begin{gathered} \frac{{dx}}{{dt}} = \frac{{a_x }}{{k_x }}[k_x - x - f_x (y)] x \hfill \\ \frac{{dy}}{{dt}} = \frac{{a_y }}{{k_y }}[k_y - y - f_y (x)] y \hfill \\ \end{gathered}$$     

The basic flow equations of electrophysiology in the presence of chemical reactions: I. Development of the equations

Starting from the basic flux equation, it is possible to obtain an integral form relating the current componentsI _i at an arbitrary pointr ₂ to the distribution of mobilities and concentrationsc _i, potential forces\(\bar \mu \), and chemical productivityp _i without any restrictive assumptions such as constant mobilities, constant field, steady state, or electrical neutrality. The equation is

$$\begin{gathered} I_i (r_2 ) = G_i (r_2 )\left[ {\Delta \bar \mu _i - \int_{r_1 }^{r_2 } {z_i } FA\left( {p_i - dc_i /dt} \right)\left( {\frac{1}{{G_i (r)}}} \right)dr} \right]; \hfill \\ G_i (r) = 1/\int_{r_1 }^r {\frac{{dr}}{{z_i^2 F^2 c_i u_i }}.} \hfill \\ \end{gathered} $$     

Kinetics of ultrafiltration hemodialysis

The expressions of Wolfet al. (1951) and Renkin (1956) for the kinetics of artificial kidneys are generalized to include the effects of filtration. IfB is the bath volume,b the relevant volume of distribution,f the filtration rate,t the time, andA ₀,B ₀,b ₀ representA, B, andb at timet=0, then the plasma concentrationA is given by

$$\frac{A}{{A_0 }} = \frac{{B_0 }}{{B_0 + b_0 }}e^{ - \frac{{\left( {B_0 + b_0 } \right)}}{{B_0 }}\frac{{D_f }}{{b_0 }}K\left( {ft} \right)t} + \frac{{b_0 }}{{B_0 + b_0 }}$$     

Weber's theory of the kernleiter

The potential distribution about a kernleiter is determined according to Weber's method. It is shown that the distribution reduces to the solution of a telegrapher's equation when the volume of the external medium is small. The velocity of propagation as a function of the external volume is determined approximately. This involves the solution of the equation

$$\frac{{\left[ {Y_0 (k\xi )} \right]^\prime }}{{\left[ {J_0 (k\xi )} \right]^\prime }} = \frac{{\left[ {\xi ^{ - a} Y_0 (\xi )} \right]^\prime }}{{\left[ {\xi ^{ - a} J_0 (\xi )} \right]^\prime }}$$     

Biological similarity relative to allometric quantities

It is an empirical finding that an allometric quantity with dimensional exponents α, β and γ relative to mass, length, and time, respectively, has a value for its allometric exponentb satisfying the relation

$$\tfrac{1}{3}(3\alpha + \beta + {\gamma \mathord{\left/ {\vphantom {\gamma 2}} \right. \kern-\nulldelimiterspace} 2}) \leqslant b \leqslant \tfrac{1}{3}(3\alpha + \beta + \gamma ).$$

A theoretical derivation is given of this double inequality using only the fact of constant density and the plausible assumption that metabolic rate is a dominant allometric quantity.

     

Correlation of body temperature and of respiration rate of swine with environmental temperature

Correlation analyses were carried out to determine relation of body temperature and respiration rate of three breeds of swine to the environmental temperature. Coefficients of regression were determined for a prediction equation of the form:

$$\begin{array}{*{20}c} {y = a + b_1 x_1 + b_2 x_2 + b_3 x_3 + b_4 x_4 + b_5 x_5 } \\ {where,y = body temperature} \\ {\begin{array}{*{20}c} {x_1 = respiration rate} \\ {x_2 = body weight} \\ {\begin{array}{*{20}c} {x_3 = sex} \\ {x_4 = environmental temperature} \\ {x_5 = x_1 x_4 } \\ \end{array} } \\ \end{array} } \\ \end{array}$$     

Présence dans une population congolaise deMus (Leggada) triton Th. de femelles hétérozygotes pour une délétion caractérisée par la suppression du bras court de l'un des chromosomes X métacentriques

A sample of 12Mus (Leggada) triton Th. from the region of Bukavu (Democratic Republic of Congo) contains 5 ♂♂ and 7 ♀♀. 2N=32. All the autosomes are acrocentric. The sex-chromosomes of the ♂ are of the typeX—Y, theX beeing a big submetacentric (I.C.=0,4). Three ♀♀ possess two metacentricX, as expected. By four ♀♀, there is only one typicalX whose partner is acrocentric and as long as the long arm of a normalX. ThisX must have been arisen through the deletion of the short arm and is calledX _ddc. The statistical analysis of the sample is compatible with this pattern:

$$\begin{array}{*{20}c} { \circ \circ } \\ { + + } \\ \end{array} \begin{array}{*{20}c} {X---X = 4/9} \\ {X---X_{dc} = 4/9} \\ {X_{dc} ---X_{dc} = 1/9} \\ \end{array} \begin{array}{*{20}c} { \nearrow \nearrow } \\ { \circ \circ } \\ \end{array} \begin{array}{*{20}c} {X---Y = 2/3} \\ {X_{dc} ---Y = 1/3} \\ \end{array} $$     

Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis

An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:

$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$     

Contribution to the genetics of the serum β-lipoproteins in man

A study was made of the genetic behaviour of the factors Ag(x) and Ag(y) of the β-lipoproteins of human serum. It was found that these factors are controlled by a single pair of autosomal codominant genes with complete penetrance at birth. The gene frequencies were:

$$\begin{gathered} Milan . . . . Ag^x = 0,23 Ag^y = 0,77 \hfill \\ Berne . . . . Ag^x = 0,24 Ag^y = 0,76. \hfill \\ \end{gathered}$$     

Interaction-induced electric (hyper)polarizability in the dihydrogen–neon pair: basis set and electron correlation effects

We investigated the interaction (hyper)polarizability of neon–dihydrogen pairs by performing high-level ab initio calculations with atom/molecule-specific, purpose-oriented Gaussian basis sets. We obtained interaction-induced electric properties at the SCF, MP2, and CCSD levels of theory. At the CCSD level, for the T-shaped configuration, around the respective potential minimum of 6.437 a₀, the interaction-induced mean first hyperpolarizability varies for 5?<? R/a₀?<?10 as

$$ \left[{\overline{\beta}}_{\mathrm{int}}(R)\hbox{-} {\overline{\beta}}_{\mathrm{int}}\left({R}_{\mathrm{e}}\right)\right]/{e}^3{a_0}^3{E_{\mathrm{h}}}^{-2}=-0.91\left(R\hbox{-} {R}_{\mathrm{e}}\right)+0.50{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^2\hbox{--} 0.13{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^3+0.01{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^4. $$

Again, at the CCSD level, but for the L-shaped configuration around the respective potential minimum of 6.572 a₀, this property varies for 5?<? R/a₀?<?10 as

$$ \left[{\overline{\beta}}_{\mathrm{int}}(R)\hbox{-} {\overline{\beta}}_{\mathrm{int}}\left({R}_{\mathrm{e}}\right)\right]/{e}^3{a_0}^3{E_{\mathrm{h}}}^{-2}=-1.33\left(R\hbox{-} {R}_{\mathrm{e}}\right)+0.75{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^2-0.20{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^3+0.02{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^4. $$

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Graphical Abstract Interaction-induced mean dipole polarizability (\( \overline{a} \)) for the T-shaped configuration of H₂–Ne calculated at the SCF, MP2, and CCSD levels of theory

     

Patterns of tooth size variability in the dentition of primates

Published data on tooth size in 48 species of non-human primates have been analyzed to determine patterns of variability in the primate dentition. Average coefficients of variation calculated for all species, with males and females combined, are greatest for teeth in the canine region. Incisors tend to be somewhat less variable, and cheek teeth are the least variable. Removing the effect of sexual dimorphism, by pooling coefficients of variation calculated for males and females separately, reduces canine variability but does not alter the basic pattern. Ontogenetic development and position in functional fields have been advanced to explain patterns of variability in the dentition, but neither of these appears to correlate well with patterns documented here. We tentatively suggest another explanation. Variability is inversely proportional to occlusal complexity of the teeth. This suggests that occlusal complexity places an important constraint on relative variability within the dentition. Even when the intensity of natural selection is equal at all tooth positions, teeth with complex occlusal patterns must still be less variable than those with simple occlusion in order to function equally well. Hence variability itself cannot be used to estimate the relative intensity of selection. Low variability of the central cheek teeth ( \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm M}\frac{1}{1} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm M}\frac{2}{2} $\end{document}) makes them uniquely important for estimating body size in small samples, and for distinguishing closely related species in the fossil record.     

E-waste projection using life-span and population statistics

Purpose

E-waste is the most rapidly growing problem throughout the world, which has serious future concerns over its management and recycling. This article proposes a simple approach for future e-waste projection which can be obtained by using life-span data of various electronic items along with incorporation of population statistics.

Methods

For this purpose, 7-year sales data of electronic items were collected, which is then used to generate various mathematical equations. These mathematical relations are then modified by incorporating life-span and population data.

Results and discussion

By comparing sales data with their life-span (average) and population statistics, future e-waste can be quantified both in terms of specified area under investigation and proposed estimation area. The following equation is thus proposed: E - waste In terms of quantity = m Waste projection year ? Life - span ? Initial data collection year + C × Population of estimation area Population of study area $$ \begin{array}{c}\mathrm{E}-\mathrm{waste}\;\\ {}\left(\mathrm{In}\ \mathrm{terms}\ \mathrm{of}\ \mathrm{quantity}\right)=\left[m\left\{\mathrm{Waste}\;\mathrm{projection}\;\mathrm{year}-\mathrm{Life}-\mathrm{span}\right\}-\mathrm{Initial}\ \mathrm{data}\ \mathrm{collection}\ \mathrm{year}+C\right]\times \frac{\mathrm{Population}\ \mathrm{of}\ \mathrm{estimation}\ \mathrm{area}}{\mathrm{Population}\ \mathrm{of}\ \mathrm{study}\ \mathrm{area}\ }\end{array} $$ Where m and C can be obtained from plotting year-wise sales data over Excel sheet.

Conclusions

Local as well as global projection of future e-waste can be possible with the help of final equation.     

Proposal for a scoring of the quality of the banding of chromosomes

Summary We propose an objective scoring of the quality of the banding of mitoses based on the number of bands (B), the length (L), and the width (W) of chromosome 7 in metaphase as used in the formula . When no figure shows the quality of mitoses from which a breakpoint is described, this scoring could give information about it. It could be applied in cytogenetic cancer studies as well as for preparations with high resolution banding.     

An improved Four-Russians method and sparsified Four-Russians algorithm for RNA folding

Background

The basic RNA secondary structure prediction problem or single sequence folding problem (SSF) was solved 35 years ago by a now well-known \(O(n^3)\)-time dynamic programming method. Recently three methodologies—Valiant, Four-Russians, and Sparsification—have been applied to speedup RNA secondary structure prediction. The sparsification method exploits two properties of the input: the number of subsequence Z with the endpoints belonging to the optimal folding set and the maximum number base-pairs L. These sparsity properties satisfy \(0 \le L \le n / 2\) and \(n \le Z \le n^2 / 2\), and the method reduces the algorithmic running time to O(LZ). While the Four-Russians method utilizes tabling partial results.

Results

In this paper, we explore three different algorithmic speedups. We first expand the reformulate the single sequence folding Four-Russians \(\Theta \left(\frac{n^3}{\log ^2 n}\right)\)-time algorithm, to utilize an on-demand lookup table. Second, we create a framework that combines the fastest Sparsification and new fastest on-demand Four-Russians methods. This combined method has worst-case running time of \(O(\tilde{L}\tilde{Z})\), where \(\frac{{L}}{\log n} \le \tilde{L}\le min\left({L},\frac{n}{\log n}\right)\) and \(\frac{{Z}}{\log n}\le \tilde{Z} \le min\left({Z},\frac{n^2}{\log n}\right)\). Third we update the Four-Russians formulation to achieve an on-demand \(O( n^2/ \log ^2n )\)-time parallel algorithm. This then leads to an asymptotic speedup of \(O(\tilde{L}\tilde{Z_j})\) where \(\frac{{Z_j}}{\log n}\le \tilde{Z_j} \le min\left({Z_j},\frac{n}{\log n}\right)\) and \(Z_j\) the number of subsequence with the endpoint j belonging to the optimal folding set.

Conclusions

The on-demand formulation not only removes all extraneous computation and allows us to incorporate more realistic scoring schemes, but leads us to take advantage of the sparsity properties. Through asymptotic analysis and empirical testing on the base-pair maximization variant and a more biologically informative scoring scheme, we show that this Sparse Four-Russians framework is able to achieve a speedup on every problem instance, that is asymptotically never worse, and empirically better than achieved by the minimum of the two methods alone.

     

Sampling bias in estimating Design II variance components with S1 families

Summary The use of several S₁ individuals to represent an S₀ individual permits the use of a Design II mating scheme for plants with only one pistillate flower per plant. Estimates of additive (V _A ) and dominance (V _D ) variance from this mating scheme will be biased upwards, when a small number (10) of individuals of each S₁ line are used. This bias can be computed, and the additive and dominance estimates can be corrected. Of particular interest is the observation that the additive genetic variance contributes to bias in estimates of V _D . When S₀ plants are non inbred and their selfedprogeny (S₁ lines) are used to represent them in developing families for use in the Design II, where m₁ is the number of individuals used to represent an S₁ line in developing half sib-families and m₂ is the number of individuals used to represent the S₁ line in making up full sib-families. For example, in a 3×3 Design II, with about 10 individuals used to represent each S₁ line in each cross, m₂ = 10 and m₁ = 30. When m₁ = m₂ = 1, and Joint contribution from Department of Agronomy, University of Nebraska 68583, and the S. S. Cameron Laboratory, Werribee, Victoria 3030, Australia. Published as paper No. 7395, Journal Series     

Prognose des Stoffhaushaltes von Staugewässern mit Hilfe kontinuierlicher und semikontinuierlicher biologischer Modelle. II. Prüfung der Prognosegenauigkeit. Prediction of the Balance of Matter in Storage Reservoirs by Means of Continuous or Semicontinuous Biological Models. II. Reliability of the Prediction Method

The phosphate removal in small, completely mixed storage reservoirs (preimpoundment basins) mainly is a function of the production of biomass by the phytoplankton. The knowledge of the critical detention time of the water is the most important premise to the prediction. The critical detention time t̄ is computed from the equation: \documentclass{article}\pagestyle{empty}\begin{document}$ \overline t _c = \frac{1}{{\mu ^* - 0,1}} $\end{document} and the growth rate μ* at a given combination of the light intensity J, temperature T and phosphate concentration P is computed from: \documentclass{article}\pagestyle{empty}\begin{document}$ \mu ^* = \frac{{\mu T \cdot \mu J \cdot \mu P}}{{\mu \max ^2 }}\mu \max \cdot \frac{P}{{K_p + P}}\frac{J}{{K_j + J}}\frac{T}{{T_{opt} }}, $\end{document} (μmax = maximum possible growth rate of the dominant species; K_p, K_j and T_opt are constants computed from batch cultures). The quotient \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\bar t_{act.} }}{{\bar t_c }}(\bar t_{act.} = {\rm actual detention time in the water body)} $\end{document} enables prediction of the phosphate removal. A comparison of the predicted results from semicontinuous cultures and from the preimpoundment basin of the Weida reservoir revealed a satisfactory degree of conformity.     

Response to various shock loadings of the constant recycle-sludge-concentration activated-sludge process

The stability of the model of a completely mixed activated-sludge process holding the recycle sludge concentration, X_R, as a system constant subjected to pH, temperature, potassium cyanide, and phenol shock loading was investigated. Soft-drink bottling wastewater was used and maintained at 1000 mg/liter chemical oxygen demand (COD). The hydraulic ratio and recycle sludge concentration were maintained at 0.3 and 7000 mg/liter, respectively. An initial dilution rate of ¼ hr^?1 was maintained for pH and temperature shock loading, with ¼ and ? hr^?1 for KCN shock loading and ¼, ?, and \documentclass{article}\pagestyle{empty}\begin{document}$\frac{1}{16}$\end{document} hr^?1 for phenol shock loading. It was found that the present system could handle pH shock loading as low as 4.0 and as high as 10.4 without any serious disruption of biological solid concentration and filtrate COD. At pH 4.0 shock loading, filamentous organisms were predominant. Temperature shock loading could be handled from 23 to 36°C without any leakage of effluent filtrate COD. At 46°C temperature shock, a 14 hr period was required to recuperate to the new steady state and provided only 85% of COD removal efficiency. For KCN (50 mg/liger) and phenol (85 mg/liter) shock loading, the dilution rates should be lower than \documentclass{article}\pagestyle{empty}\begin{document}$\frac{1}{16}$\end{document} hr^?1 in order to shorten the transient period and improve the effluent quality. Biological kinetic constants included cell yield value, maximum growth rate, and the saturation constant, which was varied with the qualitative shock applied.     

Structure determination of the disialylated poly-(N-acetyllactosamine)-containingO-linked carbohydrate chains of equine chorionic gonadotropin

The disialylated poly-(N-acetyllactosamine)-containingO-linked oligosaccharide alditols, released by alkaline borohydride treatment of the enzymicallyN-deglycosylated β-subunit of equine chorionic chonadotropin, were purified by fast protein liquid chromatography (FPLC) on Mono Q and analysed by fast ion bombardment mass spectrometry (FAB-MS) and¹H-NMR spectroscopy. The identified oligosaccharide alditols have the following structure: $$\begin{gathered} Neu5Ac\alpha 2 - 3\left[ {Gal\beta 1 - 4GlcNAc\beta 1 - 3} \right]_{0 - 4} Gal\beta 1 - 4GlcNAc\beta 1 - 6 \hfill \\ \begin{array}{*{20}c} { \backslash } \\ { GalNAc - ol} \\ { /} \\ {Neu5Ac\alpha 2 - 3Gal\beta 1 - 3} \\ \end{array} \hfill \\ \end{gathered}$$