Knowledge of the response of the primary visual cortex to the various spatial frequencies and orientations in the visual scene should help us understand the principles by which the brain recognizes patterns. Current information about the cortical layout of spatial frequency response is still incomplete because of difficulties in recording and interpreting adequate data. Here, we report results from a study of the cat primary visual cortex in which we employed a new image-analysis method that allows improved separation of signal from noise and that we used to examine the neurooptical response of the primary visual cortex to drifting sine gratings over a range of orientations and spatial frequencies. We found that (i) the optical responses to all orientations and spatial frequencies were well approximated by weighted sums of only two pairs of basis pictures, one pair for orientation and a different pair for spatial frequency; (ii) the weightings of the two pictures in each pair were approximately in quadrature (1͞4 cycle apart); and (iii) our spatial frequency data revealed a cortical map that continuously assigns different optimal spatial frequency responses to different cortical locations over the entire spatial frequency range.

We study the dynamics of a repulsively coupled array of phase oscillators. For an array of globally coupled identical oscillators, repulsive coupling results in a family of synchronized regimes characterized by zero mean field. If the number of oscillators is sufficiently large, phase locking among oscillators is destroyed, independently of the coupling strength, when the oscillators' natural frequencies are not the same. In locally coupled networks, however, phase locking occurs even for nonidentical oscillators when the coupling strength is sufficiently strong.

Explicit asymptotic analytical results are derived for the motion of scroll wave filaments in the complex Ginzburg-Landau equation. Good agreement with numerical tests is obtained. The analysis highlights the necessity of allowing for previously ignored small wave-number shifts in the propagation of the waves away from the filament. [S0031-9007(97) PACS numbers: 82.40.Ck, 47.32.Cc Rotating spiral waves are observed in a variety of physical, chemical, and biological settings including the Belousov-Zhabotinsky (BZ) reaction, thermal convection in a thin fluid layer, slime mold on a nutrient-supplied medium, and waves of electrical activity in heart tissue [1,2]. While much attention has been devoted to spiral waves in two dimensions, there has also been increasing interest in the study of spiral waves in three dimensions or "scroll waves" [2]. The simple point singularity or "defect" at the center of a two-dimensional (2D) spiral wave now becomes a line defect known as the scroll wave filament which can be straight, curved, closed to form a loop, knotted, or interlinked with other loops. The scroll wave can be given a "twist" by allowing for a relative phase difference of the spirals along the filament. Scroll waves have been observed experimentally in the BZ reaction [3], in slime mold [4], and they are also believed to occur in the heart [5]. For a large class of extended systems in the vicinity of a Hopf bifurcation, expansion of the relevant equations [6] leads to a universal equation called the complex Ginzburg-Landau equation (CGLE),where A is a complex scalar field, and a and b are real parameters. (For example, in a system of diffusing chemically reacting constituents, a nonzero b arises due to unequal diffusion coefficients of the chemicals.) Equation (1) exhibits spiral waves in two dimensions and scroll waves in three dimensions. In this paper, we shall study the fundamental problem of obtaining the dynamical behavior of a three-dimensional (3D) CGLE scroll wave filament [7].In a pioneering work by Keener [8], analysis techniques and results for the evolution of scroll wave filaments for general systems of reaction-diffusion equations were formulated. The results are based on certain hypotheses concerning the asymptotic form of the solution and the number of solutions of an adjoint equation that results from the analysis. Quantitative tests of the theory against numerical or laboratory experiments have never been made in the generic case of unequal diffusion coefficients [analogous to b fi 0 in (1)]. This is because coefficients in Keener's general theory are expressed in terms of inner products with solutions of the adjoint equation, which has never been solved. In our paper, by focusing on the simpler CGLE, we are able to derive explicit results and to quantitatively test them numerically. Our solution, while adopting some of Keener's techniques, also makes evident a defect in the hypotheses utilized in the previous theory. In particular, we find that it is necessary to include the possibility of w...

When rebels make alliances, what informs their choice of allies? Civil wars are rarely simple contests between rebels and incumbent regimes. Rather, rival militant networks provide the context in which these fragmented conflicts unfold. Alliances that emerge within this competitive landscape have the power to alter conflict trajectories and shape their outcomes. Yet patterns of interrebel cooperation are understudied. The existing scholarship on rebel alliances focuses on why rebels cooperate, but little attention is given to the composition of those alliances: with whom rebels cooperate. We explore how power, ideology, and state sponsorship can shape alliance choices in multiparty civil wars. Employing network analysis and an original data set of tactical cooperation among Syrian rebels, we find compelling evidence that ideological homophily is a primary driver of rebel collaboration. Our findings contribute to an emerging literature that reasserts the role of ideology in conflict processes.