Is Storage Capacity Adequate?

published or submitted for publicationnot peer reviewe

Storage capacity of correlated perceptrons

We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A general formalism is introduced using a multi-perceptron costfunction that allows to determine the maximal number of random inputs as a function of the desired values of the correlations. Replica-symmetric results for $K=2$ and $K=3$ are compared with properties of two-layer networks of tree-structure and fixed Boolean function between hidden units and output. The results show which correlations in the hidden layer of multi-layer neural networks are crucial for the value of the storage capacity.Comment: 16 pages, Latex2

Beyond peak reservoir storage? A global estimate of declining water storage capacity in large reservoirs

Water storage is an important way to cope with temporal variation in water supply and demand. The storage capacity and the lifetime of water storage reservoirs can be significantly reduced by the inflow of sediments. A global, spatially explicit assessment of reservoir storage loss in conjunction with vulnerability to storage loss has not been done. We estimated the loss in reservoir capacity for a global data set of large reservoirs from 1901 to 2010, using modeled sediment flux data. We use spatially explicit population data sets as a proxy for storage demand and calculate storage capacity for all river basins globally. Simulations suggest that the net reservoir capacity is declining as a result of sedimentation (5% compared to the installed capacity). Combined with increasing need for storage, these losses challenge the sustainable management of reservoir operation and water resources management in many regions. River basins that are most vulnerable include those with a strong seasonal flow pattern and high population growth rates such as the major river basins in India and China. Decreasing storage capacity globally suggests that the role of reservoir water storage in offsetting sea-level rise is likely weakening and may be changing sign

Storage Capacity as an Information-Theoretic Vertex Cover and the Index Coding Rate

Motivated by applications in distributed storage, the storage capacity of a graph was recently defined to be the maximum amount of information that can be stored across the vertices of a graph such that the information at any vertex can be recovered from the information stored at the neighboring vertices. Computing the storage capacity is a fundamental problem in network coding and is related, or equivalent, to some well-studied problems such as index coding with side information and generalized guessing games. In this paper, we consider storage capacity as a natural information-theoretic analogue of the minimum vertex cover of a graph. Indeed, while it was known that storage capacity is upper bounded by minimum vertex cover, we show that by treating it as such we can get a 3/2 approximation for planar graphs, and a 4/3 approximation for triangle-free planar graphs. Since the storage capacity is intimately related to the index coding rate, we get a 2 approximation of index coding rate for planar graphs and 3/2 approximation for triangle-free planar graphs. We also show a polynomial time approximation scheme for the index coding rate when the alphabet size is constant. We then develop a general method of "gadget covering" to upper bound the storage capacity in terms of the average of a set of vertex covers. This method is intuitive and leads to the exact characterization of storage capacity for various families of graphs. As an illustrative example, we use this approach to derive the exact storage capacity of cycles-with-chords, a family of graphs related to outerplanar graphs. Finally, we generalize the storage capacity notion to include recovery from partial node failures in distributed storage. We show tight upper and lower bounds on this partial recovery capacity that scales nicely with the fraction of failures in a vertex.Comment: A shorter version of this paper in the proceedings of the IEEE International Symposium on Information Theory, 2017 contains an error. The approximation factor for index coding rate for planar graphs was wrongly claimed to be 1.923. The correct approximation factor of our method is 2, and we have corrected Theorem 3 in this versio

Influence of synaptic depression on memory storage capacity

Synaptic efficacy between neurons is known to change within a short time scale dynamically. Neurophysiological experiments show that high-frequency presynaptic inputs decrease synaptic efficacy between neurons. This phenomenon is called synaptic depression, a short term synaptic plasticity. Many researchers have investigated how the synaptic depression affects the memory storage capacity. However, the noise has not been taken into consideration in their analysis. By introducing "temperature", which controls the level of the noise, into an update rule of neurons, we investigate the effects of synaptic depression on the memory storage capacity in the presence of the noise. We analytically compute the storage capacity by using a statistical mechanics technique called Self Consistent Signal to Noise Analysis (SCSNA). We find that the synaptic depression decreases the storage capacity in the case of finite temperature in contrast to the case of the low temperature limit, where the storage capacity does not change

Note on the pumped storage potential of the Onslow-Manorburn depression, New Zealand

The Onslow-Manorburn depression in the South Island of New Zealand has possibility for development as the upper reservoir of the world's largest pumped storage scheme, as measured by an energy storage capacity of 10,200 GWh of realisable potential energy. This would more than triple the total national hydro-power energy storage capacity. It is envisaged that the scheme could either operate on a seasonal cycle or act as a passive energy reserve to buffer existing hydro-power capacity against the effect of dry years

Storage Capacity of Extremely Diluted Hopfield Model

The storage capacity of the extremely diluted Hopfield Model is studied by using Monte Carlo techniques. In this work, instead of diluting the synapses according to a given distribution, the dilution of the synapses is obtained systematically by retaining only the synapses with dominant contributions. It is observed that by using the prescribed dilution method the critical storage capacity of the system increases with decreasing number of synapses per neuron reaching almost the value obtained from mean-field calculations. It is also shown that the increase of the storage capacity of the diluted system depends on the storage capacity of the fully connected Hopfield Model and the fraction of the diluted synapses.Comment: Latex, 14 pages, 4 eps figure

Storage Capacity of Two-dimensional Neural Networks

We investigate the maximum number of embedded patterns in the two-dimensional Hopfield model. The grand state energies of two specific network states, namely, the energies of the pure-ferromagnetic state and the state of specific one stored pattern are calculated exactly in terms of the correlation function of the ferromagnetic Ising model. We also investigate the energy landscape around them by computer simulations. Taking into account the qualitative features of the phase diagrams obtained by Nishimori, Whyte and Sherrington [Phys. Rev. E {\bf 51}, 3628 (1995)], we conclude that the network cannot retrieve more than three patterns.Comment: 13pages, 7figures, revtex

Analyzing the impact of storage shortage on data availability in decentralized online social networks

Maintaining data availability is one of the biggest challenges in decentralized online social networks (DOSNs). The existing work often assumes that the friends of a user can always contribute to the sufficient storage capacity to store all data. However, this assumption is not always true in today’s online social networks (OSNs) due to the fact that nowadays the users often use the smart mobile devices to access the OSNs. The limitation of the storage capacity in mobile devices may jeopardize the data availability. Therefore, it is desired to know the relation between the storage capacity contributed by the OSN users and the level of data availability that the OSNs can achieve. This paper addresses this issue. In this paper, the data availability model over storage capacity is established. Further, a novel method is proposed to predict the data availability on the fly. Extensive simulation experiments have been conducted to evaluate the effectiveness of the data availability model and the on-the-fly prediction