Note on the neurobiophysical interpretation of imitative behavior

Simple reaction and discrimination reaction, under the influence of imitation, are considered for the situation in which the stimulus or the stimuli vary slowly with time. The result is analogous to hysteresis under certain conditions. The calculations are facilitated by the solution of

$$x = \int_{ - \infty }^{a + \beta x} {g\left( \xi \right)d} \xi ,$$     

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

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

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

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

Biologische reisestudien in südamerika.

Ohne ZusammenfassungAufzeichnungen vom ersten Standlager Lapango der vom Autor geleiteten Deutschen Chacoexpedition, etwa südl. Breite und westl. Länge, September 1925.     

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

     

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

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

Simultaneous nonlinear equations of growth

The simultaneous equations

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

Statistical distribution of impedance elements in biological systems

Electric impedance measurements on systems consisting of nonuniform elements (e.g. nerve bundles, cell suspensions, imperfect dielectrics)_can be interpreted if the impedance characteristics of the individuals and their impedance distribution are known. Conversely, given the observed overall impedance,z(p), the impedance distribution of the individuals is not uniquely determined in both phase angle and static capacitance. If all individual phase angles are equal, the distribution,D(τ), is the solution of Stieltjes' integral equation

$$F[z(p)] = \int_0^\infty {\frac{{D(\tau )d\tau }}{{1 + p\tau }}} ,$$     

Construction of population growth equations in the presence of viability constraints

A mathematical method based on the G-projection of differential inclusions is used to construct dynamical models of population biology. We suppose that the system under study, not being limited by resources, may be described by a control system

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.

     

On a three–dimensional model for the description of the passive characteristics of skeletal muscle tissue

In this work, a three–dimensional model was developed to describe the passive mechanical behaviour of anisotropic skeletal muscle tissue. To validate the model, orientation–dependent axial (\(0^\circ\), \(45^\circ\), \(90^\circ\)) and semi–confined compression experiments (mode I, II, III) were performed on soleus muscle tissue from rabbits. In the latter experiments, specimen deformation is prescribed in the loading direction and prevented in an additional spatial direction, fibre compression at \(0^\circ\) (mode I), fibre elongation at \(90^\circ\) (mode II) and a neutral state of the fibres at \(90^\circ\) where their length is kept constant (mode III). Overall, the model can adequately describe the mechanical behaviour with a relatively small number of model parameters. The stiffest tissue response during orientation–dependent axial compression (\(-\,7.7\,\pm \,1.3\) kPa) occurs when the fibres are oriented perpendicular to the loading direction (\(90^\circ\)) and are thus stretched during loading. Semi–confined compression experiments yielded the stiffest tissue (\(-\,36.7\,\pm \,11.2\) kPa) in mode II when the muscle fibres are stretched. The extensive data set collected in this study allows to study the different error measures depending on the deformation state or the combination of deformation states.

     

Can the positive aromatic ring be as ��-electron donor in ��-halogen bond? A MP2 theoretical investigation on the unusual ��-halogen bond interaction between three-membered ring \left( {\hbox{BNN}} \right)_3^{+} and X1X2 (X1, X2?=?F, Cl, Br)

The unusual ??-halogen bond interactions are investigated between $ \left( {\hbox{BNN}} \right)_3^{+} $ and X1X2 (X1, X2?=?F, Cl, Br) employing MP2 at 6-311?+?G(2d) and aug-cc-pVDZ levels according to the ??CP (counterpoise) corrected potential energy surface (PES)?? method. The order of the ??-halogen bond interactions and stabilities of the complexes are obtained to be $ \left( {\hbox{BNN}} \right)_3^{+} \ldots {{\hbox{F}}_2} < \left( {\hbox{BNN}} \right)_3^{+} \ldots {\hbox{ClF < }}\left( {\hbox{BNN}} \right)_3^{+} \ldots {\hbox{C}}{{\hbox{l}}_2} < \left( {\hbox{BNN}} \right)_3^{+} \ldots {\hbox{BrCl}}\quad { < }\quad \left( {\hbox{BNN}} \right)_3^{+} \ldots {\hbox{B}}{{\hbox{r}}_2}\quad { < }\quad \left( {\hbox{BNN}} \right)_3^{+} \ldots {\hbox{BrF}}{.} $ at MP2/aug-cc-pVDZ level. The analyses of the Mulliken charge transfer, natural bond orbital (NBO), atoms in molecules (AIM) theory and electron density shifts reveal that the nature of the ??-halogen bond interaction in the complexes of ClF, BrF and BrCl might partly be charge transfer from the delocalized ??-HOMO orbital of $ \left( {\hbox{BNN}} \right)_3^{+} $ to X1X2. This result suggests that the positive aromatic ring $ \left( {\hbox{BNN}} \right)_3^{+} $ might act as a ??-electron donor to form the ??-halogen bond.

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:

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

Sur l'espace topologique lié à une nouvelle théorie de l'apprentissage

There have been two contrasting doctrines concerning learning, more generally about acquisition of knowledge: empiricism and rationalism. The theory of learning in such a field as artificial intelligence seems to fall within the empiricist framework. On the hand, N. Chomsky and his followers have discussed, during the last decade, concerning learning, especially about language learning, from the rationalist point of view (Chomsky, 1965). The main feature in the rationalist approach toward a theory of learning lies in the speculation that in order to acquire knowledge it is indispensable for a learner to be endowed with “innate ideas”, and that “experience” in the external world are merely subsidiary types of information for the learner. If this is acceptable, we can inquire: Under what kind of innate ideas can the learner understand the structure of the external world? In our previous paper (Uesaka, Aizawa, Ebara, and Ozeki, 1973), we formalized this by introducing the mathematical notion of “learnability”, and gave a partial answer to the above inquiry. In this formalization we assumed that the set F of objects to be learned consists of mappings of N to itself, where N is the set of positive integers. Then, constructing a topological space (F, \(\mathcal{O}\) ) by an appropriate family \(\mathcal{O}\) of open sets, we observed that the notion of learnability can be well described in terms of topological properties of the learning space (F, \(\mathcal{O}\) ). Many problems must be solved, however, before we raise the theory to a complete model of the rationalist theory of learning. The topological study of the space (F, \(\mathcal{O}\) ) is, we believe, the first step toward this approach. In this context, we discuss the topological aspects of this space. Now we define \(\mathcal{O}\) as follows: By N ² we mean the direct product of two N's. Let s be a subset of N ². If, for any (x, y), (x′, y′) in s, x=x′ implies y=y′, then we say that s is single-valued. Let f ∈ F, If, for any (x, y) in s, y=f(x), then f is said to be on s, denoted as \(f\underline \supseteq s\) . Let \(\pi \left( s \right) = \left\{ {g;g \in F,g\underline \supseteq s} \right\}\) . A single-valued finite subset of N ² is called datum. Let D denote the family of all data. Let \(\mathcal{O}* = \left\{ \phi \right\} \cup \left\{ {\pi \left( d \right);d \in D} \right\}\) , and \(\mathcal{O}\) denote the family of all subsets of F, each of which is written as \(\mathop \cup \limits_\alpha W_{\alpha }\) , where W _α is in \(\mathcal{O}*\) . Then, it is easily seen that \(\mathcal{O}\) satisfies the axiom of the open system of a topological space. It is shown that the learning space (F, \(\mathcal{O}\) ) has the following properties:

1. It satisfies the first and the second countability axioms.
2. It is separable and is totally disconnected.
3. It is a Hausdorff space and, further, is regular and normal.
4. It is neither compact nor locally compact.
5. It is metrizable, or more precisely there exists a complete but not totally bounded metric space which is homeomorphic to learning space.
6. Any of its subspace can be embedded into its special subspace.

     

A kinetics model of abrin binding in a virus transformed lymphocyte cell culture

The second order nonlinear differential equation arises from a kinetics model of abrin binding in an Epstein-Barr virus-transformed lymphocyte culture. Some results on the dynamical behavior of this equation are given. These results are then discussed in relation to the known kinetics behavior of abrin in an EBV-lymphocyte cell culture.     

Orthogonal P-wave morphology is affected by intra-atrial pressures

Background

It has previously been shown that the morphology of the P-wave neither depends on atrial size in healthy subjects with physiologically enlarged atria nor on the physiological anatomical variation in transverse orientation of the left atrium. The present study aimed to investigate if different pressures in the left and right atrium are associated with different P-wave morphologies.

Methods

38 patients with isolated, increased left atrial pressure, 51 patients with isolated, increased right atrial pressure and 76 patients with biatrially increased pressure were studied. All had undergone right heart catheterization and had 12-lead electrocardiographic recordings, which were transformed into vectorcardiograms for detailed P-wave morphology analysis.

Results

Normal P-wave morphology (type 1) was more common in patients with isolated increased pressure in the right atrium while abnormal P-wave morphology (type 2) was more common in the groups with increased left atrial pressure (P = 0.032). Moreover, patients with increased left atrial pressure, either isolated or in conjunction with increased right atrial pressure, had significantly more often a P-wave morphology with a positive deflection in the sagittal plane (P = 0.004).

Conclusion

Isolated elevated right atrial pressure was associated with normal P-wave morphology while left-sided atrial pressure elevation, either isolated or in combination with right atrial pressure elevation, was associated with abnormal P-wave morphology.

     

Provenance variation and genetic parameters of Eucalyptus viminalis in Argentina

Genetic parameters for growth, stem straightness, pilodyn penetration, relative bark thickness and survival were estimated in a base-population of five open-pollinated provenance/progeny trials of Eucalyptus viminalis. The trials, located in northern, central and southern Buenos Aires Province, Argentina, comprised 148 open-pollinated families from 13 Australian native provenances and eight local Argentinean seedlots. The Australian native provenances come from a limited range of the natural distribution. Overall survival, based on the latest assessment of each trial, was 62.4%. Single-site analyses showed that statistically significant provenances differences (p?<?0.05) for at least one of the studied traits in three out of the five trials analyzed. The local land race performed inconsistently in this study. The average narrow-sense individual-tree heritability estimate $ \left( {{{\hat{h}}^2}} \right) $ was 0.27 for diameter and 0.17 for total height. Values of $ {\hat{h}^2} $ also increased with age. Pilodyn penetration, assessed at only one site, was more heritable $ \left( {{{\hat{h}}^2} = 0.32} \right) $ than the average of growth traits. Estimated individual-tree heritabilities were moderate to low for stem straightness (average of 0.20) and relative bark thickness (0.16). The estimated additive genetic correlations $ \left( {{{{r}}_{{A}}}} \right) $ between diameter and height were consistently high and positive ( $ {{r}_{^A}} $ average of 0.90). High additive genetic correlations were observed between growth variables and pilodyn penetration ( $ {{r}_{^A}} $ average of 0.58). Relative bark thickness showed a negative correlation with diameter $ \left( {{{{r}}_{^A}} = - 0.39} \right) $ and height $ \left( {{{{r}}_{^A}} = - 0.51} \right) $ . The average estimated additive genetic correlation between sites was high for diameter (0.67). The implications of all these parameter estimates for genetic improvement of E. viminalis in Argentina are discussed.     

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.

     

Pareto genealogies arising from a Poisson branching evolution model with selection

We study a class of coalescents derived from a sampling procedure out of $N$ i.i.d. Pareto $\left( \alpha \right) $ random variables, normalized by their sum, including $\beta $ –size-biasing on total length effects ( $\beta <\alpha $ ). Depending on the range of $\alpha ,$ we derive the large $N$ limit coalescents structure, leading either to a discrete-time Poisson-Dirichlet $ \left(\alpha ,-\beta \right) \Xi -$ coalescent ( $\alpha \in \left[ 0,1\right) $ ), or to a family of continuous-time Beta $\left( 2-\alpha ,\alpha -\beta \right) \Lambda -$ coalescents ( $\alpha \in \left[ 1,2\right) $ ), or to the Kingman coalescent ( $\alpha \ge 2$ ). We indicate that this class of coalescent processes (and their scaling limits) may be viewed as the genealogical processes of some forward in time evolving branching population models including selection effects. In such constant-size population models, the reproduction step, which is based on a fitness-dependent Poisson Point Process with scaling power-law $\left( \alpha \right) $ intensity, is coupled to a selection step consisting of sorting out the $N$ fittest individuals issued from the reproduction step.