Effective masses are calculated for a large variety of perovskites of the form ABX 3 differing in chemical composition (A= Na, Li, Cs; B = Pb, Sn; X= Cl, Br, I) and crystal structure. In addition, the effects of some defects and dopants are assessed. We show that the effective masses are highly correlated with the energies of the valence-band maximum, conduction-band minimum, and band gap. Using the k•p theory for the bottom of the conduction band and a tight-binding model for the top of the valence band, this trend can be rationalized in terms of the orbital overlap between halide and metal (B cation). Most of the compounds studied in this work are good charge-carrier transporters, where the effective masses of the Pb compounds (0 < m h * < m e * < 1) are systematically larger than those of the Sn-based compounds (0 < m h * ≈ m e * < 0.5). The effective masses show anisotropies depending on the crystal symmetry of the perovskite, whether orthorhombic, tetragonal, or cubic, with the highest anisotropy for the tetragonal phase (ca. 40%). In general, the effective masses of the perovskites remain low for intrinsic or extrinsic defects, apart from some notable exceptions. Whereas some dopants, such as Zn(II), flatten the conduction-band edges (m e * = 1.7m 0) and introduce deep defect states, vacancies, more specifically Pb 2+ vacancies, make the valence-band edge more shallow (m h * = 0.9m 0). From a device-performance point of view, introducing modifications that increase the orbital overlap [e.g., more cubic structures, larger halides, smaller (larger) monovalent cations in cubic (tetragonal/orthorhombic) structures] decreases the band gap and, with it, effective masses of the charge carriers.

Abstract-We consider the problem of neural association for a network of non-binary neurons. Here, the task is to recall a previously memorized pattern from its noisy version using a network of neurons whose states assume values from a finite number of non-negative integer levels. Prior works in this area consider storing a finite number of purely random patterns, and have shown that the pattern retrieval capacities (maximum number of patterns that can be memorized) scale only linearly with the number of neurons in the network.In our formulation of the problem, we consider storing patterns from a suitably chosen set of patterns, that are obtained by enforcing a set of simple constraints on the coordinates (such as those enforced in graph based codes). Such patterns may be generated from purely random information symbols by simple neural operations. Two simple neural update algorithms are presented, and it is shown that our proposed mechanisms result in a pattern retrieval capacity that is exponential in terms of the network size. Furthermore, using analytical results and simulations, we show that the suggested methods can tolerate a fair amount of errors in the input.

Abstract-We consider the problem of neural association for a network of non-binary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later, the same network should be able to recall previously memorized patterns from their noisy versions. Prior work in this area consider storing a finite number of purely random patterns, and have shown that the pattern retrieval capacities (maximum number of patterns that can be memorized) scale only linearly with the number of neurons in the network.In our formulation of the problem, we concentrate on exploiting redundancy and internal structure of the patterns in order to improve the pattern retrieval capacity. Our first result shows that if the given patterns have a suitable linear-algebraic structure, i.e. comprise a sub-space of the set of all possible patterns, then the pattern retrieval capacity is in fact exponential in terms of the number of neurons. The second result extends the previous finding to cases where the patterns have weak minor components, i.e. the smallest eigenvalues of the correlation matrix tend toward zero. We will use these minor components (or the basis vectors of the pattern null space) to both increase the pattern retrieval capacity and error correction capabilities.An iterative algorithm is proposed for the learning phase, and two simple neural update algorithms are presented for the recall phase. Using analytical results and simulations, we show that the proposed methods can tolerate a fair amount of errors in the input while being able to memorize an exponentially large number of patterns.

Abstract-The problem of neural network association is to retrieve a previously memorized pattern from its noisy version using a network of neurons. An ideal neural network should include three components simultaneously: a learning algorithm, a large pattern retrieval capacity and resilience against noise. Prior works in this area usually improve one or two aspects at the cost of the third.Our work takes a step forward in closing this gap. More specifically, we show that by forcing natural constraints on the set of learning patterns, we can drastically improve the retrieval capacity of our neural network. Moreover, we devise a learning algorithm whose role is to learn those patterns satisfying the above mentioned constraints. Finally we show that our neural network can cope with a fair amount of noise.

Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns that satisfy certain subspace constraints. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate associatively, such as hippocampus and olfactory cortex. Here we consider associative memories with boundedly noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprising, we show that internal noise improves the performance of the recall phase while the pattern retrieval capacity remains intact: the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a functional benefit to noisy neurons in biological neuronal networks.