Abstract:
The voltage clamp method, pioneered by Hodgkin, Huxley, and Katz, laid the foundations to neurophysiological research. Its core rationale is the use of closed-loop control as a tool for system characterization. A recently introduced method, the response clamp, extends the voltage clamp rationale to the functional, phenomenological level. The method consists of on-line estimation of a response variable of interest (e.g., the probability of response or its latency) and a simple feedback control mechanism designed to tightly converge this variable toward a desired trajectory. In the present contribution I offer a perspective on this novel method and its applications in the broader context of system identification and characterization. First, I demonstrate how internal state variables are exposed using the method, and how the use of several controllers may allow for a detailed, multi-variable characterization of the system. Second, I discuss three different categories of applications of the method: (1) exploration of intrinsically generated dynamics, (2) exploration of extrinsically generated dynamics, and (3) generation of input–output trajectories. The relation of these categories to similar uses in the voltage clamp and other techniques is also discussed. Finally, I discuss the method's limitations, as well as its possible synthesis with existing complementary approaches.

Abstract:
En el discurso inaugural de la Conferencia Berkshire sobre Historia de las Mujeres, celebradaen la Universidad de Connecticut, Storrs, en junio de 2002, Joan Wallach Scott reflexiona sobrelas analíticas feministas del poder y las aplica a una interpretación crítica de la crisis desatadapor la guerra contra el terrorismo, la historia de las mujeres y el género y el conocimientoglobal y local —este último, tema central de la conferencia. Con el concepto de reverberaciones—ecos de sucesos, teorías, estrategias, etc., que viajan en el espacio y en el tiempoy que producen efectos— la autora da unidad a su reflexión sobre temáticas tan dispares.

Abstract:
We show that trial-to-trial variability in sensory detection of a weak visual stimulus is dramatically diminished when rather than presenting a fixed stimulus contrast, fluctuations in a subject’s judgment are matched by fluctuations in stimulus contrast. This attenuation of fluctuations does not involve a change in the subject’s psychometric function. The result is consistent with the interpretation of trial-to-trial variability in this sensory detection task being a high-level meta-cognitive control process that explores for something that our brains are so used to: subject–object relational dynamics.

Abstract:
The purpose of this note is to give a generalization of Gleason's theorem inspired by recent work in quantum information theory on "nonlocality without entanglement." For multipartite quantum systems, each of dimension three or greater, the only nonnegative frame functions over the set of unentangled states are those given by the standard Born probability rule. However, if one system is of dimension 2 this is not necessarily the case.

Abstract:
In this paper, Part II, of a two part paper we apply the results of [KW], Part I, to establish, with an explicit dual coordinate system, a commutative analogue of the Gelfand-Kirillov theorem for M(n), the algebra of $n\times n$ complex matrices. The function field F(n) of M(n) has a natural Poisson structure and an exact analogue would be to show that F(n) is isomorphic to the function field of a $n(n-1)$-dimensional phase space over a Poisson central rational function field in $n$ variables. Instead we show that this the case for a Galois extension, $F(n, {\frak e})$, of F(n). The techniques use a maximal Poisson commutative algebra of functions arising from Gelfand-Zeitlin theory, the algebraic action of a $n(n-1)/2$--dimensional torus on $F(n, {\frak e})$, and the structure of a Zariski open subset of M(n) as a $n(n-1)/2$--dimensional torus bundle over a $n(n+1)/2$--dimensional base space of Hessenberg matrices.

Abstract:
Let Delta_{n-1} denote the (n-1)-dimensional simplex. Let Y be a random k-dimensional subcomplex of Delta_{n-1} obtained by starting with the full (k-1)-dimensional skeleton of Delta_{n-1} and then adding each k-simplex independently with probability p. Let H_{k-1}(Y;R) denote the (k-1)-dimensional reduced homology group of Y with coefficients in a finite abelian group R. Let R and k \geq 1 be fixed. It is shown that p=(k \log n)/n is a sharp threshold for the vanishing of H_{k-1}(Y;R).

Abstract:
In this paper we classify the four dimensional gradient shrinking solitons under certain curvature conditions satisfied by all solitons arising from finite time singularities of Ricci flow on compact four manifolds with positive isotropic curvature. As a corollary we generalize a result of Perelman on three dimensional gradient shrinking solitons to dimension four.

Abstract:
The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. In dimension three we also generalize the result by removing the $\kappa$-non-collapsing assumption. In high dimension this new method allows us to prove a classification result on gradient shrinking solitons with vanishing Weyl curvature tensor, which includes the rotationally symmetric ones.

Abstract:
A holomorphic continuation of Jacquet type integrals for parabolic subgroups with abelian nilradical is studied. Complete results are given for generic characters with compact stabilizer and arbitrary representations induced from admissible representations. A description of all of the pertinent examples is given. These results give a complete description of the Bessel models corresponding to compact stabilizer.

Abstract:
Let $G$ be a complex simple Lie group and let $\g = \hbox{\rm Lie}\,G$. Let $S(\g)$ be the $G$-module of polynomial functions on $\g$ and let $\hbox{\rm Sing}\,\g$ be the closed algebraic cone of singular elements in $\g$. Let ${\cal L}\s S(\g)$ be the (graded) ideal defining $\hbox{\rm Sing}\,\g$ and let $2r$ be the dimension of a $G$-orbit of a regular element in $\g$. Then ${\cal L}^k = 0$ for any $k