We study the ability of linear recurrent networks obeying discrete time dynamics to store long temporal sequences that are retrievable from the instantaneous state of the network. We calculate this temporal memory capacity for both distributed shift register and random orthogonal connectivity matrices. We show that the memory capacity of these networks scales with system size.
The complete connectional map (connectome) of a neural circuit is essential for understanding its structure and function. Such maps have only been obtained in Caenorhabditis elegans. As an attempt at solving mammalian circuits, we reconstructed the connectomes of six interscutularis muscles from adult transgenic mice expressing fluorescent proteins in all motor axons. The reconstruction revealed several organizational principles of the neuromuscular circuit. First, the connectomes demonstrate the anatomical basis of the graded tensions in the size principle. Second, they reveal a robust quantitative relationship between axonal caliber, length, and synapse number. Third, they permit a direct comparison of the same neuron on the left and right sides of the same vertebrate animal, and reveal significant structural variations among such neurons, which contrast with the stereotypy of identified neurons in invertebrates. Finally, the wiring length of axons is often longer than necessary, contrary to the widely held view that neural wiring length should be minimized. These results show that mammalian muscle function is implemented with a variety of wiring diagrams that share certain global features but differ substantially in anatomical form. This variability may arise from the dominant role of synaptic competition in establishing the final circuit.
In Saccharomyces cerevisiae, the mitochondrial carrier family protein Pic2 imports copper into the matrix. Deletion of PIC2 causes defects in mitochondrial copper uptake and copper-dependent growth phenotypes owing to decreased cytochrome c oxidase activity. However, copper import is not completely eliminated in this mutant, so alternative transport systems must exist. Deletion of MRS3, a component of the iron import machinery, also causes a copper-dependent growth defect on non-fermentable carbon. Deletion of both PIC2 and MRS3 led to a more severe respiratory growth defect than either individual mutant. In addition, MRS3 expressed from a high copy number vector was able to suppress the oxygen consumption and copper uptake defects of a strain lacking PIC2. When expressed in Lactococcus lactis, Mrs3 mediated copper and iron import. Finally, a PIC2 and MRS3 double mutant prevented the copper-dependent activation of a heterologously expressed copper sensor in the mitochondrial intermembrane space. Taken together, these data support a role for the iron transporter Mrs3 in copper import into the mitochondrial matrix.
Slow dynamics in disordered materials prohibits direct simulation of their rich nonequilibrium behavior at large scales. "Patchwork dynamics" is introduced to mimic relaxation over a very broad range of time scales by equilibrating or optimizing directly on successive length scales. This dynamics is used to study coarsening and to replicate memory effects for spin glasses and random ferromagnets. It is also used to find, with high confidence, exact ground states in large or toroidal samples.The term "spin glass" refers both to experimental disordered magnetic systems and to theoretical models with enough randomness and frustration in their interactions to preclude conventional magnetic order. The experimental systems exhibit a complex cluster of historydependent nonequilibrium effects [1,2]. For example, while a spin glass is "aged" at fixed temperature, its magnetic susceptibility slowly changes, even after waits 20 orders of magnitude longer than the time for single spin reorientation. Upon further cooling, the material "rejuvenates": its susceptibility reverts to what it would have been without the wait. But amazingly, the system does retain a "memory" of its history and when temperature returns to that at which aging took place, susceptibility nears its aged value. In fact, waits at multiple temperatures can be stored and recovered in [3]. Similar effects are seen in a variety of experimental systems and multiple explanations have been proposed [2,4]. Yet despite thirty years of study, the nature of spin-glass dynamics -and of aging and memory effects in other "glassy" materials -remains controversial and ill-understood. In particular, how these effects are related to the temporal evolution of correlations is an open question.In this paper, we present "patchwork dynamics", a numerical approach for studying growth of correlations and non-equilibrium effects over a wide range of length and time scales in systems with quenched disorder. Patchwork dynamics proceeds by a succession of coarse-grained equilibrations -or optimizations at zero temperatureand provides a framework for investigating the relation between the evolution of microscopic correlations and the complex nonequilibrium effects observed in experimental spin glasses. This approach therefore replaces dependence on time by dependence on length scales. It can be used to study coarsening and the persistence of the initial state, to replicate memory and rejuvenation effects, to visualize how disordered systems store their history, and also as a ground state algorithm for systems that are otherwise difficult to optimize.As an initial application, in this paper we investigate the two-dimensional (2D) Edwards-Anderson Ising spin glass model (ISG) and the 2D random bond ferromagnet (RBFM), both at zero temperature. For both models, the Hamiltonian, H, has the form H = − ij J ij s i s j , where the Ising spin variables s i = ±1 lie on a d-dimensional lattice and the J ij are mean-zero Gaussian random variables for the ISG and are random, but positive, for the...
A possible phase in short-range spin glasses exhibiting infinitely many equilibrium states is proposed and characterized in real space. Experimental signatures in equilibrating systems measured with scanning probes are discussed. Some models with correlations in their exchange interactions are argued to exhibit this phase. Questions are raised about more realistic models and related issues.
In the Materials and Methods section titled "Confocal imaging," there was an error in the second sentence. The correct sentence should read: "We used a 63× 1.4 NA oil-immersion objective and optically zoomed-in so that each pixel was 0.1 µm (Nyquist limit)."
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