Book reviews

Consider the perturbed harmonic oscillator Ty=-y+x²y+q(x)y in L²(), where the real potential q belongs to the Hilbert space H={q, xq L²()}. The spectrum of T is an increasing sequence of simple eigenvalues _n(q)=1+2n+_n, n 0, such that _n 0 as n. Let _n(x,q) be the corresponding eigenfunctions. Define the norming constants _n(q)=lim_xlog |_n (x,q)/_n (-x,q)|. We show that for some real Hilbert space and some subspace Furthermore, the mapping :q(q)=({_n(q)}₀, {_n(q)}₀) is a real analytic isomorphism between H and is the set of all strictly increasing sequences s={s_n}₀ such that The proof is based on nonlinear functional analysis combined with sharp asymptotics of spectral data in the high energy limit for complex potentials. We use ideas from the analysis of the inverse problem for the operator -ypy, p L²(0,1), with Dirichlet boundary conditions on the unit interval. There is no literature about the spaces We obtain their basic properties, using their representation as spaces of analytic functions in the disk.     

Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part II: Negligible handling time

In this paper we analyse a stochastic model for invertebrate predation taking account of the predator's satiation. This model approximates Holling's hungry mantid model when handling time is negligible (see Part I). For this model we derive equations from which we can calculate the functional response and the variance of the total catch. Moreover we study a number of approximations which can be used to calculate these quantities in practical cases in a relatively simple manner.List of Notation a rate constant of digestion - b maximum of rate constant of prey encounter in the mantid - c satiation threshold for search - c satiation threshold for pursuit in the mantid - c _i (w^1/2(N- N)ⁱ) - expectation operator - f rate of change of satiation during search - F functional response: mean number of prey eaten per unit of time - g rate constant of prey capture - h probability generating function of N conditional on S = s times p - H probability generating function of N - m_i ¹ - n, N number of prey caught - p probability density of S - p_n simultaneous probability (density) of N and S - q probability of strike success - r dummy variable in generating function - s, S satiation - T _s search time - T _d digestion time - v asymptotic rate of increase of var v - V asymptotic rate of increase of var N - w weight of edible part of prey - W standard Wiener process - x prey density - z (N{S = s}-N)p - rate constant of prey escape time maximum pursuit time - (v{S = + w ^1/2}-v) - present time as a fraction of the time from the start to the end of the experiment - hazard rate of T _s - mean time between (downward) passages of S through c - v w_–1/2(N-) - edible prey biomass density - probability density of , number pi - parameter of Weibull distribution of T _s = (1/2acx(-g(c)))_1/2 - w_–1/2(S -) - satiation in the guzzler approximation: solution to d/dt = f() + g(), (0)=S(0). - biomass functional response: wF - total biomass catch in the guzzler approximation: solution to d/dt = g(), (0) = 0     

Linkage relationships in the bovine MHC region. High recombination frequency between class II subregions

Class II genes of the bovine major histocompatibility complex (MHC) have been investigated by Southern blot analysis using human DNA probes. Previous studies revealed the presence of bovine DO , DQ , DQ , DR and DR genes, and restriction fragment length polymorphisms for each of these genes were documented. In the present study, the presence of three additional class II genes, designated DZ , DY , and DY , are reported. DZ was assumed to correspond to the human DZ gene while the other two were designated DY because their relationship to human class II genes could not be firmly established. The linkage relationships among bovine class II genes and two additional loci, TCP1B and C4, were investigated by family segregation analysis and analysis of linkage disequilibrium. The results clearly indicated that all these loci belong to the same linkage group. This linkage group is divided into two subregions separated by a fairly high recombination frequency. One region includes the C4, DQ , DQ , DR and DR loci and the other one is composed of the DO DY , DY , and TCPIB loci. No recombinant was observed within any of these subregions and there was a strong or fairly strong linkage disequilibrium between loci within groups. In contrast, as many as five recombinants among three different families were detected in the interval between these subregions giving a recombination frequency estimate of 0.17 ± 0.07. The fairly high recombination frequency observed between class 11 genes in cattle is strikingly different from the corresponding recombination estimates in man and mouse. The finding implies either a much larger molecular distance between some of the bovine class II genes or alternatively the presence of a recombinational hot spot in the bovine class II region.     

Cloning and comparison of Aα mating-type alleles of the basidiomycete Schizophyllum commune

Summary An A mating-type allele (A4) was isolated by walking the chromosome from the closely linked PAB1 gene. A cosmid clone containing the A1 allele isolated from the walk was used as a probe to recover the A1 allele from another cosmid library. Cosmids encoding mating-type activity were identified by transforming Schizophyllum cells and screening for activation of A-regulated development. Putative mating-type transformants were confirmed in mating tests and genetic analyses of progeny. The identity of the specific alleles isolated was demonstrated by showing that their effectiveness in transforming for mating type is limited to recipient strains possessing an A allele different from the one encoded by the cloned sequences. Transforming DNA is active in trans, suggesting that A encodes a diffusible product. Restriction mapping shows that A1 and A4 are coded in the same physical region of the genome, but within a subregion that contains extensive sequence divergence. In addition, Southern analyses show that there is only one copy of A1 or A4 per haploid genome, and that they do not cross-hybridize to one another or to any of the other A alleles. A1 and A4 were subcloned as 2.8 and 1.2 kb fragments, respectively, retaining in transformation all the mating-type activity demonstrated of the original cosmids.     

Formation ofα,ω-dodecanedioic acid andα,ω-tridecanedioic acid from different substrates by immobilized cells of a mutant ofCandida tropicalis

Summary The metabolic formation of either,-dodecanedioic acid or,-tridecanedioic acid from the individual n-alkane, n-alcohol, n-monoacid and,-diol with corresponding carbon chain length using K-carrageenan entrapped mutants S76 ofCandida tropicalis was studied. The immobilized cells of S76 could also directly produce-hydroxy acid and,-dioic acid from,-diol. With n-alcohol and n-monoacid as substrate, the amount of-hydroxy acid and,-dioic acid produced was also a function of the incubation time.The results demonstrated that in the immobilized cells of S76 the formation of,-dioic acid from n-alcohol can also run both via n-monoacid and via,-diol as well as in the normal cells of S76.     

Leaf water potential,component potentials and relative water content in a xeric grass,Agropyron dasystachyum (Hook.) Scribn.

Summary Leaf water potential ( _l ), osmotic potential ( _s ), pressure potential ( _p , turgor pressure), relative water content (R) and their interrelationships were determined for a xeric grass (Agropyron dasystachyum) found in the grasslands of Canada. Thermocouple psychrometers were used to measure _l and _s ; _p was obtained by subtraction. _l dropped from near 0 bars to about-28 bars as R went from 90% to 75%. R greater than 90% was not observed, perhaps because of a systematic error in determination of turgid water content. R remained relatively high in A. dasystachyum, even at low _l . The slope of the _l -R relationship was similar to other species which are generally considered to be drought tolerant. _p as high as 14 bars was observed. Most of the decrease in _l was accounted for by a decline in _p . The ability of A. dasystachyum to adjust to fluctuating water stress over the growing season is probably as much related to changes in tissue structure and turgor relationships as to simple changes in osmotic potential.     

An H-2 haplotype possibly derived by crossing-over between the (A α A β ) duplex and the E βlocus

The B10.STA62 strain carries the H-2 ^w27 haplotype derived from a wild mouse captured in the vicinity of Ann Arbor, Michigan. Products of two class II loci composing this haplotype, A and A , are serologically, biochemically (by tryptic peptide mapping), and functionally indistinguishable from products controlled by the A ^b and A ^/b genes of the B10.A(5R) strain. In contrast, the polypeptide chain controlled by the third class II locus, E , is different from that controlled by the E ^/b gene. This E ^/w27 chain lacks an antigenic determinant present on the E^b molecule and carries determinants lacking on the E^b molecule, the E ^/b and E ^/w27 peptide maps differ in at least six peptides, and cytotoxic T cells specific for the E ^b chains do not react with B10.STA62 target cells. This great difference between the E ^/b and E ^/w27 chains suggests that the corresponding genes have not been derived from one another by a direct mutational conversion; instead, H-2 ^w27 appears to be a recombinant haplotype derived by crossing-over between the A A duplex and the E locus. This is the first recombinant discovered separating these class II loci.     

Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations

In this paper we use a dynamical systems approach to prove the existence of a unique critical value c ^* of the speed c for which the degenerate density-dependent diffusion equation u _ct = [D(u)u _x ] _x + g(u) has: 1. no travelling wave solutions for 0 < c < c ^*, 2. a travelling wave solution u(x, t) = (x - c ^* t) of sharp type satisfying (– ) = 1, () = 0 ^*; '(^*–) = – c ^*/D'(0), '(^*+) = 0 and 3. a continuum of travelling wave solutions of monotone decreasing front type for each c > c ^*. These fronts satisfy the boundary conditions (– ) = 1, '(– ) = (+ ) = '(+ ) = 0. We illustrate our analytical results with some numerical solutions.     

A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue

It is proposed that distinct anatomical regions of cerebral cortex and of thalamic nuclei are functionally two-dimensional. On this view, the third (radial) dimension of cortical and thalamic structures is associated with a redundancy of circuits and functions so that reliable signal processing obtains in the presence of noisy or ambiguous stimuli.A mathematical model of simple cortical and thalamic nervous tissue is consequently developed, comprising two types of neurons (excitatory and inhibitory), homogeneously distributed in planar sheets, and interacting by way of recurrent lateral connexions. Following a discussion of certain anatomical and physiological restrictions on such interactions, numerical solutions of the relevant non-linear integro-differential equations are obtained. The results fall conveniently into three categories, each of which is postulated to correspond to a distinct type of tissue: sensory neo-cortex, archior prefrontal cortex, and thalamus.The different categories of solution are referred to as dynamical modes. The mode appropriate to thalamus involves a variety of non-linear oscillatory phenomena. That appropriate to archior prefrontal cortex is defined by the existence of spatially inhomogeneous stable steady states which retain contour information about prior stimuli. Finally, the mode appropriate to sensory neo-cortex involves active transient responses. It is shown that this particular mode reproduces some of the phenomenology of visual psychophysics, including spatial modulation transfer function determinations, certain metacontrast effects, and the spatial hysteresis phenomenon found in stereopsis.List of Symbols (t) Post-synaptic membrane potential (psp) - Maximum amplitude of psp - t Time - The neuronal membrane time constant - Threshold value of membrane potential - r Absolute refractory period - Synaptic operating delay - v Velocity of propagation of action potentil - x Cartesian coordinate - _jj (x) The probability that cells of class j are connected with cells of class j a distance x away - b _jj The mean synaptic weight of synapses of the jj-th class at x - _jj The space constant for connectivity - _e Surface density of excitatory neurons in a one-dimensional homogeneous and isotropic tissue - _i Surface density of inhibitory neurons in a one-dimensional homogeneous and isotropic tissue - E(x, t) Excitatory Activity, proportion of excitatory cells becoming active per unit time at the instant t, at the point x - I(x, t) Inhibitory Activity, proportion of inhibitory cells becoming active per unit time at the instant t, at the point x - x A small segment of tissue - t A small interval of time - P(x, t) Afferent excitation or inhibition to excitatory neurons - Q(x, t) Afferent excitation or inhibition to inhibitory neurons - N _e (x, t) Mean integrated excitation generated within excitatory neurons at x - N _i (x, t) Mean integrated excitation generated within inhibitory neurons at x - _e [N _e ] Expected proportion of excitatory neurons receiving at least threshold excitation per unit time, as a function of N _e - _i [N _i ] Expected proportion of inhibitory neurons receiving at least threshold excitation per unit time, as a function of N _i - G( _e ) Distribution function of excitatory neuronal thresholds - G( ₁ ) Distribution function of inhibitory neuronal thresholds - ₁ A fixed value of neuronal threshold - h(N _e ; ₁) Proportion per unit time of excitatory neurons at x reaching ₁ with a mean excitation N _e - 1[ ] Heaviside's step-function - R _e (x, t) Number of excitatory neurons which are sensitive at the instant t - R _i (x, t) Number of inhibitory neurons which are sensitive at the instant t - R _e Refractory period of excitatory neurons - r _i Refractory period of inhibitory neurons - E(x, t) Time coarse-grained excitatory activity - I(x, t) Time coarse-grained inhibitory activity - Spatial convolution - Threshold of a neuronal aggregate - v Sensitivity coefficient of response of a neuronal aggregate - E(t) Time coarse-grained spatially localised excitatory activity - I(t)> Time coarse-grained spatially localised inhibitory activity - L ₁,L ₂,L,Q See § 2.2.1, § 2.2.7, § 3.1 - Velocity with which retinal images are moved apart - Stimulus width - E _o, I _o Spatially homogeneous steady states of neuronal activity - k _e ,k _ij S _e S _ij See § 5.1     

Fromβ-lactams toα- andβ-amino acid derived peptides

Summary The potential of-lactams as intermediates for the access to- and-amino acid-derived peptides is shortly reviewed, with major focus on the technologies developed in our group. The two general strategies lie, on one side, in the oxidative ring expansion of 3-hydroxy-lactams toN-carboxy-amino acid anhydrides or Leuch's anhydrides and subsequent coupling with-amino acid esters and, on the other side, in the nucleophilic ring opening ofN-Boc--lactams. Both approaches have been successfully applied to the synthesis of,-diamino acid,-amino--hydroxy acid, polyhydroxylated-amino acid,,-disubstituted-amino acid,-amino acid,-amino--hydroxy acid and,-disubstituted-amino acid derived peptides. Because of the mild reaction conditions needed for the above transformations and the highly stereoselective procedures employed for the construction of the starting-lactam ring, the whole process allows the production of optically pure final products.