Searcharxiv⌕ Search

arXiv subjects

Nithin Nagaraj

Publications and source records attributed to Nithin Nagaraj.

At least 55 records · Page 3Linked to original sources
arXiv2017

A Two-Parameter Model for Ultrasonic Tissue Characterization with Harmonic Imaging

Over the past few decades, researchers have developed several approaches such as the Reference Phantom Method (RPM) to estimate ultrasound attenuation coefficient (AC) and backscatter coefficient (BSC). AC and BSC can help to discriminate pathology from normal tissue during in-vivo imaging. In this paper, we propose a new RPM model to simultaneously compute AC and BSC for harmonic imaging and a normalized score that combines the two parameters as a measure of disease progression. The model utilizes the spectral difference between two regions of interest, the first, a proximal, close to the probe and second, a distal, away from the probe. We have implemented an algorithm based on the model and shown that it provides accurate and stable estimates to within 5% of AC and BSC for simulated received echo from post-focal depths of a homogeneous liver-like medium. For practical applications with time gain and time frequency compensated in-phase and quadrature (IQ) data from ultrasound scanner, the method has been approximated and generalized to estimate AC and BSC for tissue layer underlying a more attenuative subcutaneous layer. The angular spectrum approach for ultrasound propagation in biological tissue is employed as a virtual Reference Phantom (VRP). The VRP is calibrated with a fixed probe and scanning protocol for application to liver tissue. In a feasibility study with 16 subjects, the method is able to separate 9/11 cases of progressive non-alcoholic fatty liver disease from 5 normal. In particular, it is able to separate 4/5 cases of non-alcoholic steato-hepatitis and early fibrosis (F<=2) from normal tissue. More extensive clinical studies are needed to assess the full capability of this model for screening and monitoring disease progression in liver and other tissues.

physics.med-ph↗
arXiv2017

Simulation Study of Two Measures of Integrated Information

Background: Many authors have proposed Quantitative Theories of Consciousness (QTC) based on theoretical principles like information theory, Granger causality and complexity. Recently, Virmani and Nagaraj (arXiv:1608.08450v2 [cs.IT]) noted the similarity between Integrated Information and Compression-Complexity, and on this basis, proposed a novel measure of network complexity called Phi-Compression Complexity (Phi-C or $Φ^C$). Their computer simulations using Boolean networks showed that $Φ^C$ compares favorably to Giulio Tononi et al's Integrated Information measure $Φ$ 3.0 and exhibits desirable mathematical and computational characteristics. Methods: In the present work, $Φ^C$ was measured for two types of simulated networks: (A) Networks representing simple neuronal connectivity motifs (presented in Fig.9 of Tononi and Sporns, BMC Neuroscience 4(1), 2003); (B) random networks derived from Erdös-R ényi G(N, p)graphs. Code for all simulations was written in Python 3.6, and the library NetworkX was used to simulate the graphs. Results and discussions summary: In simulations A, for the same set of networks, $Φ^C$ values differ from the values of IIT 1.0 $Φ$ in a counter-intuitive manner. It appears that $Φ^C$ captures some invariant aspects of the interplay between information integration, network topology, graph composition and node entropy. While Virmani and Nagaraj (arXiv:1608.08450v2 [cs.IT]) sought to highlight the correlations between $Φ^C$ and IIT $Φ$, the results of simulations A highlight the differences between the two measures in the way they capture the integrated information. In simulations B, the results of simulations A are extended to the more general case of random networks. In the concluding section we outline the novel aspects of this paper, and our ongoing and future research.

q-bio.NC↗
arXiv2017

New Empirical Evidence on Disjunction Effect and Cultural Dependence

We perform new experiment using almost the same sample size considered by Tversky and Shafir to test the validity of classical probability theory in decision making. The results clearly indicate that the disjunction effect depends also on culture and more specifically on gender (females rather than males). We did more statistical analysis rather that putting the actual values done by previous authors. We propose different kind of disjunction effect i.e. strong and weak based on our statistical analysis.

q-bio.NC↗
arXiv2016

A Compression-Complexity Measure of Integrated Information

Quantifying integrated information is a leading approach towards building a fundamental theory of consciousness. Integrated Information Theory (IIT) has gained attention in this regard due to its theoretically strong framework. However, it faces some limitations such as current state dependence, computationally expensive and inability to be applied to real brain data. On the other hand, Perturbational Complexity Index (PCI) is a clinical measure for distinguishing different levels of consciousness. Though PCI claims to capture the functional differentiation and integration in brain networks (similar to IIT), its link to integrated information theories is rather weak. Inspired by these two approaches, we propose a new measure - $Φ^C$ using a novel compression-complexity perspective that serves as a bridge between the two, for the first time. $Φ^C$ is founded on the principles of lossless data compression based complexity measures which characterize the dynamical complexity of brain networks. $Φ^{C}$ exhibits following salient innovations: (i) mathematically well bounded, (ii) negligible current state dependence unlike $Φ$, (iii) integrated information measured as compression-complexity rather than as an infotheoretic quantity, and (iv) faster to compute since number of atomic bipartitions scales linearly with the number of nodes of the network, thus avoiding combinatorial explosion. Our computer simulations show that $Φ^C$ has similar hierarchy to $<Φ>$ for several multiple-node networks and it demonstrates a rich interplay between differentiation, integration and entropy of the nodes of a network. $Φ^C$ is a promising heuristic measure to characterize the quantity of integrated information (and hence a measure of quantity of consciousness) in larger networks like human brain and provides an opportunity to test the predictions of brain complexity on real neural data.

cs.IT↗
arXiv2016

Dynamical Complexity Of Short and Noisy Time Series

Shannon Entropy has been extensively used for characterizing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs poorly. Complexity measures which are based on lossless compression algorithms are a good substitute in such scenarios. We evaluate the performance of two such Compression-Complexity Measures namely Lempel-Ziv complexity ($LZ$) and Effort-To-Compress ($ETC$) on short time series from chaotic dynamical systems in the presence of noise. Both $LZ$ and $ETC$ outperform Shannon entropy ($H$) in accurately characterizing the dynamical complexity of such systems. For very short binary sequences (which arise in neuroscience applications), $ETC$ has higher number of distinct complexity values than $LZ$ and $H$, thus enabling a finer resolution. For two-state ergodic Markov chains, we empirically show that $ETC$ converges to a steady state value faster than $LZ$. Compression-Complexity Measures are promising for applications which involve short and noisy time series.

nlin.CD↗
arXiv2016

Three Perspectives on Complexity $-$ Entropy, Compression, Subsymmetry

There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In this paper, we explore the following perspectives on complexity: "effort-to-describe" (Shannon entropy $H$, Lempel-Ziv complexity $LZ$), "effort-to-compress" ($ETC$ complexity) and "degree-of-order" (Subsymmetry or $SubSym$). While Shannon entropy and $LZ$ are very popular and widely used, $ETC$ is a recently proposed measure for time series. In this paper, we also propose a novel normalized measure $SubSym$ based on the existing idea of counting the number of subsymmetries or palindromes within a sequence. We compare the performance of these complexity measures on the following tasks: a) characterizing complexity of short binary sequences of lengths 4 to 16, b) distinguishing periodic and chaotic time series from 1D logistic map and 2D Hénon map, and c) distinguishing between tonic and irregular spiking patterns generated from the "Adaptive exponential integrate-and-fire" neuron model. Our study reveals that each perspective has its own advantages and uniqueness while also having an overlap with each other.

physics.data-an↗
arXiv2016

Cardiac Aging Detection Using Complexity Measures

As we age, our hearts undergo changes which result in reduction in complexity of physiological interactions between different control mechanisms. This results in a potential risk of cardiovascular diseases which are the number one cause of death globally. Since cardiac signals are nonstationary and nonlinear in nature, complexity measures are better suited to handle such data. In this study, non-invasive methods for detection of cardiac aging using complexity measures are explored. Lempel-Ziv (LZ) complexity, Approximate Entropy (ApEn) and Effort-to-Compress (ETC) measures are used to differentiate between healthy young and old subjects using heartbeat interval data. We show that both LZ and ETC complexity measures are able to differentiate between young and old subjects with only 10 data samples while ApEn requires at least 15 data samples.

physics.med-ph↗
arXiv2016

Neural Signal Multiplexing via Compressed Sensing

Transport of neural signals in the brain is challenging, owing to neural interference and neural noise. There is experimental evidence of multiplexing of sensory information across population of neurons, particularly in the vertebrate visual and olfactory systems. Recently, it has been discovered that in lateral intraparietal cortex of the brain, decision signals are multiplexed with decision-irrelevant visual signals. Furthermore, it is well known that several cortical neurons exhibit chaotic spiking patterns. Multiplexing of chaotic neural signals and their successful demultiplexing in the neurons amidst interference and noise, is difficult to explain. In this work, a novel compressed sensing model for efficient multiplexing of chaotic neural signals constructed using the Hindmarsh-Rose spiking model is proposed. The signals are multiplexed from a pre-synaptic neuron to its neighbouring post-synaptic neuron, in the presence of $10^4$ interfering noisy neural signals and demultiplexed using compressed sensing techniques.

cs.IT↗
arXiv2016

Compressed Shattering

The central idea of compressed sensing is to exploit the fact that most signals of interest are sparse in some domain and use this to reduce the number of measurements to encode. However, if the sparsity of the input signal is not precisely known, but known to lie within a specified range, compressed sensing as such cannot exploit this fact and would need to use the same number of measurements even for a very sparse signal. In this paper, we propose a novel method called Compressed Shattering to adapt compressed sensing to the specified sparsity range, without changing the sensing matrix by creating shattered signals which have fixed sparsity. This is accomplished by first suitably permuting the input spectrum and then using a filter bank to create fixed sparsity shattered signals. By ensuring that all the shattered signals are utmost 1-sparse, we make use of a simple but efficient deterministic sensing matrix to yield very low number of measurements. For a discrete-time signal of length 1000, with a sparsity range of $5 - 25$, traditional compressed sensing requires $175$ measurements, whereas Compressed Shattering would only need $20 - 100$ measurements.

cs.IT↗
arXiv2013

Lossless Data Compression with Error Detection using Cantor Set

In 2009, a lossless compression algorithm based on 1D chaotic maps known as Generalized Luröth Series (or GLS) has been proposed. This algorithm (GLS-coding) encodes the input message as a symbolic sequence on an appropriate 1D chaotic map (GLS) and the compressed file is obtained as the initial value by iterating backwards on the map. For ergodic sources, it was shown that GLS-coding achieves the best possible lossless compression (in the noiseless setting) bounded by Shannon entropy. However, in the presence of noise, even small errors in the compressed file leads to catastrophic decoding errors owing to sensitive dependence on initial values. In this paper, we first show that Repetition codes $\mathcal{R}_n$ (every symbol is repeated $n$ times, where $n$ is a positive odd integer), the oldest and the most basic error correction and detection codes in literature, actually lie on a Cantor set with a fractal dimension of $\frac{1}{n}$, which is also the rate of the code. Inspired by this, we incorporate error detection capability to GLS-coding by ensuring that the compressed file (initial value on the map) lies on a Cantor set of measure zero. Even a 1-bit error in the initial value will throw it outside the Cantor set which can be detected while decoding. The error detection performance (and also the rate of the code) can be controlled by the fractal dimension of the Cantor set and could be suitably adjusted depending on the noise level of the communication channel.

cs.IT↗
arXiv2013

Comment on 'Interpretation of the Lempel-Ziv Complexity Measure in the context of Biomedical Signal Analysis'

In this Communication, we express our reservations on some aspects of the interpretation of the Lempel-Ziv Complexity measure (LZ) by Mateo et al. in "Interpretation of the Lempel-Ziv complexity measure in the context of biomedical signal analysis," IEEE Trans. Biomed. Eng., vol. 53, no. 11, pp. 2282-2288, Nov. 2006. In particular, we comment on the dependence of the LZ complexity measure on number of harmonics, frequency content and amplitude modulation. We disagree with the following statements made by Mateo et al. 1. "LZ is not sensitive to the number of harmonics in periodic signals." 2. "LZ increases as the frequency of a sinusoid increases." 3. "Amplitude modulation of a signal doesnot result in an increase in LZ." We show the dependence of LZ complexity measure on harmonics and amplitude modulation by using a modified version of the synthetic signal that has been used in the original paper. Also, the second statement is a generic statement which is not entirely true. This is true only in the low frequency regime and definitely not true in moderate and high frequency regimes.

nlin.CD↗
arXiv2012

Classification of Periodic, Chaotic and Random Sequences using NSRPS Complexity Measure

Data compression algorithms are generally perceived as being of interest for data communication and storage purposes only. However, their use in the field of data classification and analysis is also of equal importance. Automatic data classification and analysis finds use in varied fields like bioinformatics, language and sequence recognition and authorship attribution. Different complexity measures proposed in literature like Shannon entropy, Relative entropy, Kolmogrov and Algorithmic complexity have drawbacks that make these methods ineffective in analyzing short sequences that are typical in population dynamics and other fields. In this paper, we study Non-Sequential Recursive Pair Substitution (NSRPS), a lossless compression algorithm first proposed by Ebeling {\it et al.} [Math. Biosc. 52, 1980] and Jiménez-Montaño {\it et al.} [arXiv:cond-mat/0204134, 2002]). Using this algorithm, a new complexity measure was recently proposed (Nagaraj {\it et al.} [arXiv:nlin.CD/1101.4341v1, 2011]). In this work, we use NSRPS complexity measure for analyzing and classifying symbolic sequences generated by 1D chaotic dynamical systems. Even with learning data-sets of length as small as 25 and test data-sets of length as small as 10, NSRPS measure is able to accurately classify the test sequence as periodic, chaotic or random. For such short data lengths, methods which use entropy measure and traditional lossless compression algorithm like LZ77 [A.Lempel and J.Ziv, IEEE Trans. Inform. Theory {\bf 22}, 75 (1976)] (used for instance by {\it Gzip}, {\it Winzip} etc.) fails.

nlin.CD↗
arXiv2011

Lossless Compression and Complexity of Chaotic Sequences

We investigate the complexity of short symbolic sequences of chaotic dynamical systems by using lossless compression algorithms. In particular, we study Non-Sequential Recursive Pair Substitution (NSRPS), a lossless compression algorithm first proposed by W. Ebeling et al. [Math. Biosc. 52, 1980] and Jiménez-Montaño et al. [arXiv:cond-mat/0204134, 2002]) which was subsequently shown to be optimal. NSPRS has also been used to estimate Entropy of written English (P. Grassberger [arXiv:physics/0207023, 2002]). We propose a new measure of complexity - defined as the number of iterations of NSRPS required to transform the input sequence into a constant sequence. We test this measure on symbolic sequences of the Logistic map for various values of the bifurcation parameter. The proposed measure of complexity is easy to compute and is observed to be highly correlated with the Lyapunov exponent of the original non-linear time series, even for very short symbolic sequences (as short as 50 samples). Finally, we construct symbolic sequences from the Skew-Tent map which are incompressible by popular compression algorithms like WinZip, WinRAR and 7-Zip, but compressible by NSRPS.

nlin.CD↗
arXiv2010

Sharing Graphs

Almost all known secret sharing schemes work on numbers. Such methods will have difficulty in sharing graphs since the number of graphs increases exponentially with the number of nodes. We propose a secret sharing scheme for graphs where we use graph intersection for reconstructing the secret which is hidden as a sub graph in the shares. Our method does not rely on heavy computational operations such as modular arithmetic or polynomial interpolation but makes use of very basic operations like assignment and checking for equality, and graph intersection can also be performed visually. In certain cases, the secret could be reconstructed using just pencil and paper by authorised parties but cannot be broken by an adversary even with unbounded computational power. The method achieves perfect secrecy for (2, n) scheme and requires far fewer operations compared to Shamir's algorithm. The proposed method could be used to share objects such as matrices, sets, plain text and even a heterogeneous collection of these. Since we do not require a previously agreed upon encoding scheme, the method is very suitable for sharing heterogeneous collection of objects in a dynamic fashion.

cs.CR↗
arXiv2010

How not to share a set of secrets

This note analyses one of the existing space efficient secret sharing schemes and suggests vulnerabilities in its design. We observe that the said algorithm fails for certain choices of the set of secrets and there is no reason for preferring this particular scheme over alternative schemes. The paper also elaborates the adoption of a scheme proposed by Hugo Krawczyk as an extension of Shamir's scheme, for a set of secrets. Such an implementation is space optimal and works for all choices of secrets. We also propose two new methods of attack which are valid under certain assumptions and observe that it is the elimination of random values that facilitates these kinds of attacks.

cs.CR↗
arXiv2009

Huffman Coding as a Non-linear Dynamical System

In this paper, source coding or data compression is viewed as a measurement problem. Given a measurement device with fewer states than the observable of a stochastic source, how can one capture the essential information? We propose modeling stochastic sources as piecewise linear discrete chaotic dynamical systems known as Generalized Luröth Series (GLS) which dates back to Georg Cantor's work in 1869. The Lyapunov exponent of GLS is equal to the Shannon's entropy of the source (up to a constant of proportionality). By successively approximating the source with GLS having fewer states (with the closest Lyapunov exponent), we derive a binary coding algorithm which exhibits minimum redundancy (the least average codeword length with integer codeword lengths). This turns out to be a re-discovery of Huffman coding, the popular lossless compression algorithm used in the JPEG international standard for still image compression.

nlin.CD↗
arXiv2008

Increasing Average Period Lengths by Switching of Robust Chaos Maps in Finite Precision

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits ($T$) of a dynamical system scales as a function of computer precision ($ε$) and the correlation dimension ($d$) of the chaotic attractor: $T \sim ε^{-d/2}$. In this work, we are concerned with increasing the average period length which is desirable for chaotic cryptography applications. Our experiments reveal that random and chaotic switching of deterministic chaotic dynamical systems yield higher average length of periodic orbits as compared to simple sequential switching or absence of switching. To illustrate the application of switching, a novel generalization of the Logistic map that exhibits Robust Chaos (absence of attracting periodic orbits) is first introduced. We then propose a pseudo-random number generator based on chaotic switching between Robust Chaos maps which is found to successfully pass stringent statistical tests of randomness.

nlin.CD↗