@article{3540,
abstract = {What determines the firing rate of cortical neurons in the absence of external sensory input or motor behavior, such as during sleep? Hero we report that, in a familiar environment, the discharge frequency of simultaneously recorded individual CA1 pyramidal neurons and the coactivation of cell pairs remain highly correlated across sleep-wake-steep sequences. However, both measures were affected when new sets of neurons were activated in a novel environment. Nevertheless, the grand mean firing rate of the whole pyramidal cell population remained constant across behavioral states and testing conditions. The findings suggest that long-term firing patterns of single cells can be modified by experience. We hypothesize that increased firing rates of recently used neurons are associated with a concomitant decrease in the discharge activity of the remaining population, leaving the mean excitability of the hippocampal network unaltered.},
author = {Hirase, Hajima and Leinekugel, Xavier and Czurkó, András and Jozsef Csicsvari and Buzsáki, György},
journal = {PNAS},
number = {16},
pages = {9386 -- 9390},
publisher = {National Academy of Sciences},
title = {{Firing rates of hippocampal neurons are preserved during subsequent sleep episodes and modified by novel awake experience}},
doi = {10.1073/pnas.161274398},
volume = {98},
year = {2001},
}
@article{3546,
abstract = {Local versus distant coherence of hippocampal CA1 pyramidal cells was investigated in the behaving rat. Temporal cross-correlation of pyramidal cells revealed a significantly stronger relationship among local (<140 <mu>m) pyramidal neurons compared with distant (>300 mum) neurons during non-theta-associated immobility and sleep but not during theta-associated running and walking. In contrast, cross-correlation between local pyramidal cell-interneuron pairs was significantly stronger than between distant pairs during theta oscillations but were similar during non-theta-associated behaviors. We suggest that network state-dependent functional clustering of neuronal activity emerges because of the differential contribution of the main excitatory inputs, the perforant path, and Schaffer collaterals during theta and non-theta behaviors.},
author = {Hirase, Hajima and Leinekugel, Xavier and Jozsef Csicsvari and Czurkó, András and Buzsáki, György},
journal = {Journal of Neuroscience},
number = {10},
publisher = {Society for Neuroscience},
title = {{Behavior-dependent states of the hippocampal network affect functional clustering of neurons}},
volume = {21},
year = {2001},
}
@book{3586,
abstract = {The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The original motivation for these topics was the difficulty faced (both conceptually and in the technical execution) in any attempt to combine elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains recent breakthrough solutions to meshing that fit into this category.The book should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, useful, and interesting.},
author = {Edelsbrunner, Herbert},
pages = {190},
publisher = {Cambridge University Press},
title = {{Geometry and Topology for Mesh Generation}},
doi = {10.1017/CBO9780511530067},
volume = {7},
year = {2001},
}
@misc{3596,
abstract = {Bürger has written an outstanding book. As well as discussing selection, recombination and mutation, he explains how random drift interacts with these evolutionary forces. Thus, his book covers a large fraction of population genetics, the main exception being the neutral theory of molecular evolution. Although the book is primarily theoretical, it focuses on the biological issues and includes excellent concise summaries of our present empirical knowledge.},
author = {Nicholas Barton},
booktitle = {Trends in Genetics},
pages = {420 -- 420},
publisher = {Elsevier},
title = {{Mendel and mathematics}},
doi = {10.1016/S0168-9525(01)02315-0},
volume = {17},
year = {2001},
}
@article{3622,
abstract = {The extent of genetic variation in fitness and its components and genetic variation's dependence on environmental conditions remain key issues in evolutionary biology. We present measurements of genetic variation in preadult viability in a laboratory-adapted population of Drosophila melanogaster, made at four different densities. By crossing flies heterozygous for a wild-type chromosome and one of two different balancers (TM1, TM2), we measure both heterozygous (TM1/+, TM2/+) and homozygous (+/+) viability relative to a standard genotype (TM1/TM2). Forty wild-type chromosomes were tested, of which 10 were chosen to be homozygous viable. The mean numbers produced varied significantly between chromosome lines, with an estimated between-line variance in loge numbers of 0.013. Relative viabilities also varied significantly across chromosome lines, with a variance in loge homozygous viability of 1.76 and of loge heterozygous viability of 0.165. The between-line variance for numbers emerging increased with density, from 0.009 at lowest density to 0.079 at highest. The genetic variance in relative viability increases with density, but not significantly. Overall, the effects of different chromosomes on relative viability were remarkably consistent across densities and across the two heterozygous genotypes (TM1, TM2). The 10 lines that carried homozygous viable wild-type chromosomes produced significantly more adults than the 30 lethal lines at low density and significantly fewer adults at the highest density. Similarly, there was a positive correlation between heterozygous viability and mean numbers at low density, but a negative correlation at high density.},
author = {Gardner, Michael P and Fowler, Kevin and Patridge, Linda and Nicholas Barton},
journal = {Evolution},
number = {8},
pages = {1609 -- 1620},
publisher = {Wiley-Blackwell},
title = {{Genetic variation for preadult viability in Drosophila melanogaster}},
volume = {55},
year = {2001},
}
@article{4200,
abstract = {Zebrafish embryos homozygous for the masterblind (mb1) mutation exhibit a striking phenotype in which the eyes and telencephalon are reduced or absent and diencephalic fates expand to the front of the brain. Here we show that mb1(-/-) embryos carry an amino-acid change at a conserved site in the Wnt pathway scaffolding protein, Axin1. The amino-acid substitution present in the mbl allele abolishes the binding of Axin to Gsk3 and affects Tcf-dependent transcription. Therefore, Gsk3 activity may be decreased in mbl(-/-) embryos and in support of this possibility, overexpression of either wild-type Axin1 or Gsk3 beta can restore eye and telencephalic fates to mb1(-/-) embryos. Our data reveal a crucial role for Axin1-dependent inhibition of the Wnt pathway in the early regional subdivision of the anterior neural plate into telencephalic, diencephalic, and eye-forming territories.},
author = {Heisenberg, Carl-Philipp J and Houart, Corinne and Take Uchi, Masaya and Rauch, Gerd and Young, Neville and Coutinho, Pedro and Masai, Ichiro and Caneparo, Luca and Concha, Miguel and Geisler, Robert and Dale, Trevor and Wilson, Stephen and Stemple, Derek},
journal = {Genes and Development},
number = {11},
pages = {1427 -- 1434},
publisher = {Cold Spring Harbor Laboratory Press},
title = {{A mutation in the Gsk3-binding domain of zebrafish Masterblind/Axin1 leads to a fate transformation of telencephalon and eyes to diencephalon}},
doi = {10.1101/gad.194301},
volume = {15},
year = {2001},
}
@article{8522,
abstract = {For diffeomorphisms of smooth compact manifolds, we consider the problem of how fast the number of periodic points with period $n$grows as a function of $n$. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the first author has shown that arbitrarily fast growth is topologically (Baire) generic for $C^2$ or smoother diffeomorphisms. In the present work we show that, by contrast, for a measure-theoretic notion of genericity we call ``prevalence'', the growth is not much faster than exponential. Specifically, we show that for each $\delta > 0$, there is a prevalent set of ( $C^{1+\rho}$ or smoother) diffeomorphisms for which the number of period $n$ points is bounded above by $\operatorname{exp}(C n^{1+\delta})$ for some $C$ independent of $n$. We also obtain a related bound on the decay of the hyperbolicity of the periodic points as a function of $n$. The contrast between topologically generic and measure-theoretically generic behavior for the growth of the number of periodic points and the decay of their hyperbolicity shows this to be a subtle and complex phenomenon, reminiscent of KAM theory.},
author = {Kaloshin, Vadim and Hunt, Brian R.},
issn = {1079-6762},
journal = {Electronic Research Announcements of the American Mathematical Society},
keywords = {General Mathematics},
number = {4},
pages = {17--27},
publisher = {American Mathematical Society},
title = {{A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I}},
doi = {10.1090/s1079-6762-01-00090-7},
volume = {7},
year = {2001},
}
@article{8524,
abstract = {A number α∈R is diophantine if it is not well approximable by rationals, i.e. for some C,ε>0 and any relatively prime p,q∈Z we have |αq−p|>Cq−1−ε. It is well-known and is easy to prove that almost every α in R is diophantine. In this paper we address a noncommutative version of the diophantine properties. Consider a pair A,B∈SO(3) and for each n∈Z+ take all possible words in A, A -1, B, and B - 1 of length n, i.e. for a multiindex I=(i1,i1,…,im,jm) define |I|=∑mk=1(|ik|+|jk|)=n and \( W_n(A,B ) = \{W_{\cal I}(A,B) = A^{i_1} B^{j_1} \dots A^{i_m} B^{j_m}\}_{|{\cal I|}=n \).¶Gamburd—Jakobson—Sarnak [GJS] raised the problem: prove that for Haar almost every pair A,B∈SO(3) the closest distance of words of length n to the identity, i.e. sA,B(n)=min|I|=n∥WI(A,B)−E∥, is bounded from below by an exponential function in n. This is the analog of the diophantine property for elements of SO(3). In this paper we prove that s A,B (n) is bounded from below by an exponential function in n 2. We also exhibit obstructions to a “simple” proof of the exponential estimate in n.},
author = {Kaloshin, Vadim and Rodnianski, I.},
issn = {1016-443X},
journal = {Geometric And Functional Analysis},
number = {5},
pages = {953--970},
publisher = {Springer Nature},
title = {{Diophantine properties of elements of SO(3)}},
doi = {10.1007/s00039-001-8222-8},
volume = {11},
year = {2001},
}
@article{8521,
abstract = {We continue the previous article's discussion of bounds, for prevalent diffeomorphisms of smooth compact manifolds, on the growth of the number of periodic points and the decay of their hyperbolicity as a function of their period $n$. In that article we reduced the main results to a problem, for certain families of diffeomorphisms, of bounding the measure of parameter values for which the diffeomorphism has (for a given period $n$) an almost periodic point that is almost nonhyperbolic. We also formulated our results for $1$-dimensional endomorphisms on a compact interval. In this article we describe some of the main techniques involved and outline the rest of the proof. To simplify notation, we concentrate primarily on the $1$-dimensional case.},
author = {Kaloshin, Vadim and Hunt, Brian R.},
issn = {1079-6762},
journal = {Electronic Research Announcements of the American Mathematical Society},
keywords = {General Mathematics},
number = {5},
pages = {28--36},
publisher = {American Mathematical Society},
title = {{A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II}},
doi = {10.1090/s1079-6762-01-00091-9},
volume = {7},
year = {2001},
}