Time-Space Constrained Codes for Phase-Change Memories

Phase-change memory (PCM) is a promising non-volatile solid-state memory technology. A PCM cell stores data by using its amorphous and crystalline states. The cell changes between these two states using high temperature. However, since the cells are sensitive to high temperature, it is important, when programming cells, to balance the heat both in time and space. In this paper, we study the time-space constraint for PCM, which was originally proposed by Jiang et al. A code is called an \emph{$(\alpha,\beta,p)$-constrained code} if for any $\alpha$ consecutive rewrites and for any segment of $\beta$ contiguous cells, the total rewrite cost of the $\beta$ cells over those $\alpha$ rewrites is at most $p$. Here, the cells are binary and the rewrite cost is defined to be the Hamming distance between the current and next memory states. First, we show a general upper bound on the achievable rate of these codes which extends the results of Jiang et al. Then, we generalize their construction for $(\alpha\geq 1, \beta=1,p=1)$-constrained codes and show another construction for $(\alpha = 1, \beta\geq 1,p\geq1)$-constrained codes. Finally, we show that these two constructions can be used to construct codes for all values of $\alpha$, $\beta$, and $p$

Emergent geometry from q-deformations of N=4 super Yang-Mills

We study BPS states in a marginal deformation of super Yang-Mills on R x S^3 using a quantum mechanical system of q-commuting matrices. We focus mainly on the case where the parameter q is a root of unity, so that the AdS dual of the field theory can be associated to an orbifold of AdS_5x S^5. We show that in the large N limit, BPS states are described by density distributions of eigenvalues and we assign to these distributions a geometrical spacetime interpretation. We go beyond BPS configurations by turning on perturbative non-q-commuting excitations. Considering states in an appropriate BMN limit, we use a saddle point approximation to compute the BMN energy to all perturbative orders in the 't Hooft coupling. We also examine some BMN like states that correspond to twisted sector string states in the orbifold and we show that our geometrical interpretation of the system is consistent with the quantum numbers of the corresponding states under the quantum symmetry of the orbifold.Comment: 22 pages, 1 figure. v2: added references. v3:final published versio

Energy efficiency of information transmission by electrically coupled neurons

The generation of spikes by neurons is energetically a costly process. This paper studies the consumption of energy and the information entropy in the signalling activity of a model neuron both when it is supposed isolated and when it is coupled to another neuron by an electrical synapse. The neuron has been modelled by a four dimensional Hindmarsh-Rose type kinetic model for which an energy function has been deduced. For the isolated neuron values of energy consumption and information entropy at different signalling regimes have been computed. For two neurons coupled by a gap junction we have analyzed the roles of the membrane and synapse in the contribution of the energy that is required for their organized signalling. Computational results are provided for cases of identical and nonidentical neurons coupled by unidirectional and bidirectional gap junctions. One relevant result is that there are values of the coupling strength at which the organized signalling of two neurons induced by the gap junction takes place at relatively low values of energy consumption and the ratio of mutual information to energy consumption is relatively high. Therefore, communicating at these coupling values could be energetically the most efficient option

Generalized Holographic Principle, Gauge Invariance and the Emergence of Gravity a la Wilczek

We show that a generalized version of the holographic principle can be derived from the Hamiltonian description of information flow within a quantum system that maintains a separable state. We then show that this generalized holographic principle entails a general principle of gauge invariance. When this is realized in an ambient Lorentzian space-time, gauge invariance under the Poincare group is immediately achieved. We apply this pathway to retrieve the action of gravity. The latter is cast a la Wilczek through a similar formulation derived by MacDowell and Mansouri, which involves the representation theory of the Lie groups SO(3,2) and SO(4,1).Comment: 26 pages, 1 figur

Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model

Many-body localization is a unique physical phenomenon driven by interactions and disorder for which a quantum system can evade thermalization. While the existence of a many-body localized phase is now well-established in one-dimensional systems, its fate in higher dimension is an open question. We present evidence for the occurrence of a transition to a many-body localized regime in a two-dimensional quantum dimer model with interactions and disorder. Our analysis is based on the results of large-scale simulations for static and dynamical properties of a consequent number of observables. Our results pave the way for a generic understanding of occurrence of a many-body localization transition in dimension larger than one, and highlight the unusual quantum dynamics that can be present in constrained systems.Comment: 15 pages, 14 figures, published versio