arXiv subjects

Amin Shokrollahi

Publications and source records attributed to Amin Shokrollahi.

15 recordsLinked to original sources

arXiv2025

Two-phase immiscible displacement of water by gas accounting for fines migration: analytical model for vertical equilibrium

Fines migration during subterranean CO2 storage is considered as one of major contributors to formation damage and injectivity decline. The main formation damage mechanism by migrating fines is rock clogging by straining of particles in thin pore throats. The main mobilisation mechanism of attached natural reservoir fines is their detachment by capillary forces exerting from the advancing water-gas menisci. The mathematical model for displacement of water by injected CO2 from layer-cake reservoirs under fines mobilisation, migration and straining extends the classical vertical capillary-gravity equilibrium model, where hydrostatic pressure gradient is assumed in each phase. The analytical model generalises classical Buckley-Leverett problem, where the extended fractional flow accounts for permeability damage due to fines migration. We show the significant effect of fines migration on water displacement - while it decreases well injectivity, fines migration simultaneously increases reservoir sweep, increasing CO2 storage capacity.

physics.geo-ph↗

arXiv2025

Long-term propagation of CO2 plume below the seal accounting for chemical reactions and water counter-flow

Accurate prediction of long-term CO2 plume migration beneath seals is crucial for the viability of CO2 storage in deep saline aquifers. Groundwater counterflow and chemical reactions between CO2, brine, and rock significantly influence plume dynamics, dispersion, and boundary evolution. This study develops a novel analytical framework by deriving governing equations for gravity-driven gas migration and obtaining exact self-similar solutions for both pulse and continuous injection. The approach explicitly incorporates chemical reactions and water counterflow, addressing factors often neglected in existing analytical models. A sensitivity analysis is conducted to evaluate the effects of key parameters on CO2 migration. The results show that increasing the chemical reaction coefficient delays the first arrival of CO2 while accelerating its final arrival, highlighting the impact of geochemical reactions on plume migration. Additionally, higher up-dip water velocity shortens the accumulation period, thereby reducing the time required for CO2 to become trapped in geological formations. These findings improve predictive capabilities for long-term CO2 storage and provide insights for optimising sequestration strategies.

physics.geo-ph↗

arXiv2014

Convolutional Neural Associative Memories: Massive Capacity with Noise Tolerance

The task of a neural associative memory is to retrieve a set of previously memorized patterns from their noisy versions using a network of neurons. An ideal network should have the ability to 1) learn a set of patterns as they arrive, 2) retrieve the correct patterns from noisy queries, and 3) maximize the pattern retrieval capacity while maintaining the reliability in responding to queries. The majority of work on neural associative memories has focused on designing networks capable of memorizing any set of randomly chosen patterns at the expense of limiting the retrieval capacity. In this paper, we show that if we target memorizing only those patterns that have inherent redundancy (i.e., belong to a subspace), we can obtain all the aforementioned properties. This is in sharp contrast with the previous work that could only improve one or two aspects at the expense of the third. More specifically, we propose framework based on a convolutional neural network along with an iterative algorithm that learns the redundancy among the patterns. The resulting network has a retrieval capacity that is exponential in the size of the network. Moreover, the asymptotic error correction performance of our network is linear in the size of the patterns. We then ex- tend our approach to deal with patterns lie approximately in a subspace. This extension allows us to memorize datasets containing natural patterns (e.g., images). Finally, we report experimental results on both synthetic and real datasets to support our claims.

cs.NE↗

arXiv2014

Noise Facilitation in Associative Memories of Exponential Capacity

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. 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 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 surprisingly, we show that internal noise actually improves the performance of the recall phase while the pattern retrieval capacity remains intact, i.e., 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.

cs.NE↗

arXiv2013

Coupled Neural Associative Memories

We propose a novel architecture to design a neural associative memory that is capable of learning a large number of patterns and recalling them later in presence of noise. It is based on dividing the neurons into local clusters and parallel plains, very similar to the architecture of the visual cortex of macaque brain. The common features of our proposed architecture with those of spatially-coupled codes enable us to show that the performance of such networks in eliminating noise is drastically better than the previous approaches while maintaining the ability of learning an exponentially large number of patterns. Previous work either failed in providing good performance during the recall phase or in offering large pattern retrieval (storage) capacities. We also present computational experiments that lend additional support to the theoretical analysis.

cs.NE↗

arXiv2013

Neural Networks Built from Unreliable Components

Recent advances in associative memory design through strutured pattern sets and graph-based inference algorithms have allowed the reliable learning and retrieval of an exponential number of patterns. Both these and classical associative memories, however, have assumed internally noiseless computational nodes. This paper considers the setting when internal computations are also noisy. Even if all components are noisy, the final error probability in recall can often be made exceedingly small, as we characterize. There is a threshold phenomenon. We also show how to optimize inference algorithm parameters when knowing statistical properties of internal noise.

cs.NE↗

arXiv2013

A Non-Binary Associative Memory with Exponential Pattern Retrieval Capacity and Iterative Learning: Extended Results

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.

cs.NE↗

arXiv2012

Irregular Product Codes

We consider irregular product codes.In this class of codes, each codeword is represented by a matrix. The entries in each row (column) of the matrix should come from a component row (column) code. As opposed to (standard) product codes, we do not require that all component row codes nor all component column codes be the same. As we will see, relaxing this requirement can provide some additional attractive features including 1) allowing some regions of the codeword be more error-resilient 2) allowing a more refined spectrum of rates for finite-lengths and improved performance in some of these rates 3) more interaction between row and column codes during decoding. We study these codes over erasure channels. We find that for any $0 < ε< 1$, for many rate distributions on component row codes, there is a matching rate distribution on component column codes such that an irregular product code based on MDS codes with those rate distributions on the component codes has asymptotic rate $1 - ε$ and can decode on erasure channels (of alphabet size equal the alphabet size of the component MDS codes) with erasure probability $< ε$.

cs.IT↗

arXiv2011

Invertible Extractors and Wiretap Protocols

A wiretap protocol is a pair of randomized encoding and decoding functions such that knowledge of a bounded fraction of the encoding of a message reveals essentially no information about the message, while knowledge of the entire encoding reveals the message using the decoder. In this paper we study the notion of efficiently invertible extractors and show that a wiretap protocol can be constructed from such an extractor. We will then construct invertible extractors for symbol-fixing, affine, and general sources and apply them to create wiretap protocols with asymptotically optimal trade-offs between their rate (ratio of the length of the message versus its encoding) and resilience (ratio of the observed positions of the encoding and the length of the encoding). We will then apply our results to create wiretap protocols for challenging communication problems, such as active intruders who change portions of the encoding, network coding, and intruders observing arbitrary boolean functions of the encoding. As a by-product of our constructions we obtain new explicit extractors for a restricted family of affine sources over large fields (that in particular generalizes the notion of symbol-fixing sources) which is of independent interest. These extractors are able to extract the entire source entropy with zero error. Keywords: Wiretap Channel, Extractors, Network Coding, Active Intrusion, Exposure Resilient Cryptography.

cs.IT↗

arXiv2009

Analysis of the Second Moment of the LT Decoder

We analyze the second moment of the ripple size during the LT decoding process and prove that the standard deviation of the ripple size for an LT-code with length $k$ is of the order of $\sqrt k.$ Together with a result by Karp et. al stating that the expectation of the ripple size is of the order of $k$ [3], this gives bounds on the error probability of the LT decoder. We also give an analytic expression for the variance of the ripple size up to terms of constant order, and refine the expression in [3] for the expectation of the ripple size up to terms of the order of $1/k$, thus providing a first step towards an analytic finite-length analysis of LT decoding.

cs.IT↗

arXiv2009

Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynomials almost uniformly at random. The statistical distance between the output distribution of the algorithm and the uniform distribution on the set of common zeros is polynomially small in the field size, and the running time of the algorithm is polynomial in the description of the polynomials and their degrees provided that the number of the polynomials is a constant.

cs.DS↗

arXiv2009

Efficient implementation of linear programming decoding

While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the large size of the relaxed LP problem, and the inefficiency of using general-purpose LP solvers. This paper explores ideas for fast LP decoding of low-density parity-check (LDPC) codes. We first prove, by modifying the previously reported Adaptive LP decoding scheme to allow removal of unnecessary constraints, that LP decoding can be performed by solving a number of LP problems that contain at most one linear constraint derived from each of the parity-check constraints. By exploiting this property, we study a sparse interior-point implementation for solving this sequence of linear programs. Since the most complex part of each iteration of the interior-point algorithm is the solution of a (usually ill-conditioned) system of linear equations for finding the step direction, we propose a preconditioning algorithm to facilitate iterative solution of such systems. The proposed preconditioning algorithm is similar to the encoding procedure of LDPC codes, and we demonstrate its effectiveness via both analytical methods and computer simulation results.

cs.IT↗

arXiv2009

Bit Precision Analysis for Compressed Sensing

This paper studies the stability of some reconstruction algorithms for compressed sensing in terms of the bit precision. Considering the fact that practical digital systems deal with discretized signals, we motivate the importance of the total number of accurate bits needed from the measurement outcomes in addition to the number of measurements. It is shown that if one uses a $2k \times n$ Vandermonde matrix with roots on the unit circle as the measurement matrix, $O(\ell + k \log(n/k))$ bits of precision per measurement are sufficient to reconstruct a $k$-sparse signal $x \in \R^n$ with dynamic range (i.e., the absolute ratio between the largest and the smallest nonzero coefficients) at most $2^\ell$ within $\ell$ bits of precision, hence identifying its correct support. Finally, we obtain an upper bound on the total number of required bits when the measurement matrix satisfies a restricted isometry property, which is in particular the case for random Fourier and Gaussian matrices. For very sparse signals, the upper bound on the number of required bits for Vandermonde matrices is shown to be better than this general upper bound.

cs.IT↗

arXiv2005

New model for rigorous analysis of LT-codes

We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as the length of the code goes to infinity via recent results in random hypergraphs [Darling-Norris 2005]. For a code of finite length, we provide an algorithm for computing the probability of error of the decoder. This algorithm improves the one of [Karp-Luby-Shokrollahi 2004] by a linear factor.

cs.IT↗

arXiv2005

Coding Schemes for Line Networks

We consider a simple network, where a source and destination node are connected with a line of erasure channels. It is well known that in order to achieve the min-cut capacity, the intermediate nodes are required to process the information. We propose coding schemes for this setting, and discuss each scheme in terms of complexity, delay, achievable rate, memory requirement, and adaptability to unknown channel parameters. We also briefly discuss how these schemes can be extended to more general networks.

cs.IT↗