Attractor neural networks storing multiple space representations: a model for hippocampal place fields

A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully connected limits are studied, and the storage capacity and the information capacity are found. The important parameters determining the performance of the network are the sparsity of the spatial representations and the degree of connectivity, as found already for the storage of individual memory patterns in the general theory of auto-associative networks. Such results suggest a quantitative parallel between theories of hippocampal function in different animal species, such as primates (episodic memory) and rodents (memory for space).Comment: 19 RevTeX pages, 8 pes figure

Multi-Qubit Joint Measurements in Circuit QED: Stochastic Master Equation Analysis

We derive a family of stochastic master equations describing homodyne measurement of multi-qubit diagonal observables in circuit quantum electrodynamics. In the regime where qubit decay can be neglected, our approach replaces the polaron-like transformation of previous work, which required a lengthy calculation for the physically interesting case of three qubits and two resonator modes. The technique introduced here makes this calculation straightforward and manifestly correct. Using this technique, we are able to show that registers larger than one qubit evolve under a non-Markovian master equation. We perform numerical simulations of the three-qubit, two-mode case from previous work, obtaining an average post-measurement state fidelity of $\sim 94\%$, limited by measurement-induced decoherence and dephasing.Comment: 22 pages, 9 figures. Comments welcom

Breather solitons in highly nonlocal media

We investigate the breathing of optical spatial solitons in highly nonlocal media. Generalizing the Ehrenfest theorem, we demonstrate that oscillations in beam width obey a fourth-order ordinary differential equation. Moreover, in actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell [Science \textbf{276}, 1538 (1997)] cannot accurately describe the dynamics of self-confined beams as the transverse size oscillations have a period which not only depends on power but also on the initial width. Modeling the nonlinear response by a Poisson equation driven by the beam intensity we verify the theoretical results against numerical simulations.Comment: 7 pages, 4 figures, resubmitted to Physical Review

The postulations á la D'Alembert and á la Cauchy for higher gradient continuum theories are equivalent. A review of existing results

In order to found continuum mechanics, two different postulations have been used. The first, introduced by Lagrange and Piola, starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients. Then, by using the divergence theorem, a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body. This method assumes an a priori notion of internal work, regards stress tensors as dual of virtual displacements and their gradients, deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts. The second method, conceived by Cauchy and based on the celebrated tetrahedron argument, starts by postulating the type of contact interactions which can be exerted on the boundary of every (suitably) regular part of a body. Then it proceeds by proving the existence of stress tensors from a balance-type postulate. In this paper, we review some relevant literature on the subject, discussing how the two postulations can be reconciled in the case of higher gradient theories. Finally, we underline the importance of the concept of contact surface, edge and wedge s-order forces

Black Hole Attractors and Pure Spinors

We construct black hole attractor solutions for a wide class of N=2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to sum_k f_k = Im(C Phi), where Phi is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, Phi=Omega and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation.Comment: 26 page

Photonic potential for TM waves

We discuss the effective photonic potential for TM waves in inhomogeneous isotropic media. The model provides an easy and intuitive comprehension of form birefringence, paving the way for a new approach on the design of graded-index optical waveguides on nanometric scales. We investigate the application to nanophotonic devices, including integrated nanoscale wave plates and slot waveguides.Comment: 4 pages, 7 figure

Ductal carcinoma in situ of the breast: the importance of morphologic and molecular interactions.

Ductal carcinoma in situ (DCIS) of the breast is a lesion characterized by significant heterogeneity, in terms of morphology, immunohistochemical staining, molecular signatures, and clinical expression. For some patients, surgical excision provides adequate treatment, but a subset of patients will experience recurrence of DCIS or progression to invasive ductal carcinoma (IDC). Recent years have seen extensive research aimed at identifying the molecular events that characterize the transition from normal epithelium to DCIS and IDC. Tumor epithelial cells, myoepithelial cells, and stromal cells undergo alterations in gene expression, which are most important in the early stages of breast carcinogenesis. Epigenetic modifications, such as DNA methylation, together with microRNA alterations, play a major role in these genetic events. In addition, tumor proliferation and invasion is facilitated by the lesional microenvironment, which includes stromal fibroblasts and macrophages that secrete growth factors and angiogenesis-promoting substances. Characterization of DCIS on a molecular level may better account for the heterogeneity of these lesions and how this manifests as differences in patient outcome and response to therapy. Molecular assays originally developed for assessing likelihood of recurrence in IDC are recently being applied to DCIS, with promising results. In the future, the classification of DCIS will likely incorporate molecular findings along with histologic and immunohistochemical features, allowing for personalized prognostic information and therapeutic options for patients with DCIS. This review summarizes current data regarding the molecular characterization of DCIS and discusses the potential clinical relevance