Universal compression of Gaussian sources with unknown parameters

For a collection of distributions over a countable support set, the worst case universal compression formulation by Shtarkov attempts to assign a universal distribution over the support set. The formulation aims to ensure that the universal distribution does not underestimate the probability of any element in the support set relative to distributions in the collection. When the alphabet is uncountable and we have a collection $\cal P$ of Lebesgue continuous measures instead, we ask if there is a corresponding universal probability density function (pdf) that does not underestimate the value of the density function at any point in the support relative to pdfs in $\cal P$. Analogous to the worst case redundancy of a collection of distributions over a countable alphabet, we define the \textit{attenuation} of a class to be $A$ when the worst case optimal universal pdf at any point $x$ in the support is always at least the value any pdf in the collection $\cal P$ assigns to $x$ divided by $A$. We analyze the attenuation of the worst optimal universal pdf over length-$n$ samples generated \textit{i.i.d.} from a Gaussian distribution whose mean can be anywhere between $-\alpha/2$ to $\alpha/2$ and variance between $\sigma_m^2$ and $\sigma_M^2$. We show that this attenuation is finite, grows with the number of samples as ${\cal O}(n)$, and also specify the attentuation exactly without approximations. When only one parameter is allowed to vary, we show that the attenuation grows as ${\cal O}(\sqrt{n})$, again keeping in line with results from prior literature that fix the order of magnitude as a factor of $\sqrt{n}$ per parameter. In addition, we also specify the attenuation exactly without approximation when only the mean or only the variance is allowed to vary

Spectral fluctuations and 1/f noise in the order-chaos transition regime

Level fluctuations in quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate level fluctuations to the classical dynamics in the regular and chaotic limit. In this we show that the spectrum of the system undergoing order to chaos transition displays a characteristic $f^{-\gamma}$ noise and $\gamma$ is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles respectively of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.Comment: 4 pages, 5 figures. Modified version. To appear in Phys. Rev. Let

Extreme events and event size fluctuations in biased random walks on networks

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power black-outs which take place on networks. In this work, we study extreme events in a generalized random walk model in which the walk is preferentially biased by the network topology. The walkers preferentially choose to hop toward the hubs or small degree nodes. In this setting, we show that extremely large fluctuations in event-sizes are possible on small degree nodes when the walkers are biased toward the hubs. In particular, we obtain the distribution of event-sizes on the network. Further, the probability for the occurrence of extreme events on any node in the network depends on its 'generalized strength', a measure of the ability of a node to attract walkers. The 'generalized strength' is a function of the degree of the node and that of its nearest neighbors. We obtain analytical and simulation results for the probability of occurrence of extreme events on the nodes of a network using a generalized random walk model. The result reveals that the nodes with a larger value of 'generalized strength', on average, display lower probability for the occurrence of extreme events compared to the nodes with lower values of 'generalized strength'

Data driven consistency (working title)

We are motivated by applications that need rich model classes to represent them. Examples of rich model classes include distributions over large, countably infinite supports, slow mixing Markov processes, etc. But such rich classes may be too complex to admit estimators that converge to the truth with convergence rates that can be uniformly bounded over the entire model class as the sample size increases (uniform consistency). However, these rich classes may still allow for estimators with pointwise guarantees whose performance can be bounded in a model dependent way. The pointwise angle of course has the drawback that the estimator performance is a function of the very unknown model that is being estimated, and is therefore unknown. Therefore, even if the estimator is consistent, how well it is doing may not be clear no matter what the sample size is. Departing from the dichotomy of uniform and pointwise consistency, a new analysis framework is explored by characterizing rich model classes that may only admit pointwise guarantees, yet all the information about the model needed to guage estimator accuracy can be inferred from the sample at hand. To retain focus, we analyze the universal compression problem in this data driven pointwise consistency framework.Comment: Working paper. Please email authors for the current versio

THE POTENTIAL OF CANARIUM ODONTOPHYLLUM MIQ. (DABAI) AS ANTI-METHICILLIN RESISTANT STAPHYLOCOCCUS AUREUS AGENT

Objective: The present study evaluates the antimicrobial potential of C. Odontophyllum leaves against Methicillin-resistant Staphylococcus aureus, Candida albicans, Candida glabrata, Candida krusei, Candida tropicalis,  Aspergillus fumigatus, Aspergillus niger and Aspergillus flavus. Materials: The extracts from C. odontophyllum leaf were prepared using acetone, methanol and distilled waterprior to screening at concentrations from12.5 mg/ml to 100 mg/ml against the test microorganisms using disc diffusion method. The Minimum Inhibitory Concentration (MIC) and Minimum Bactericidal Concentration (MBC) of the extracts against susceptible organisms were determined using microbroth dilution method and streak-plate technique, respectively. Results: Water produced the highest yield of extract (5.03%) followed by methanol (2.65%) and acetone (1.79%). Out of all the microbes tested, only MRSA was found to be susceptible towards acetone and methanol extracts of C. odontophyllum leaves which showed concentration-dependent growth inhibitory effect against MRSA. Despite the highest extractive potential of water, no antimicrobial activity was observed by the aqueous extract from the screening assay. The MIC values for methanol and acetone extracts were respectively,6.25 mg/ml and 3.125 mg/ml. The MBC value of methanol extract was twice its MIC value which was 12.5 mg/ml whereas the MIC and MBC values of acetone extract against MRSA were the same (3.125 mg/ml). Conclusion: C. odontophyllum leaves have the potential to be developed as an alternative phytotherapeutic agent against MRSA infection

Zero delay synchronization of chaos in coupled map lattices

We show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice. We analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent. The zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices and we analytically estimate the synchronization error bounds.Comment: 9 pages, 9 figures ; To appear in Phys. Rev.

Quantum spectrum as a time series : Fluctuation measures

The fluctuations in the quantum spectrum could be treated like a time series. In this framework, we explore the statistical self-similarity in the quantum spectrum using the detrended fluctuation analysis (DFA) and random matrix theory (RMT). We calculate the Hausdorff measure for the spectra of atoms and Gaussian ensembles and study their self-affine properties. We show that DFA is equivalent to $\Delta_3$ statistics of RMT, unifying two different approaches.We exploit this connection to obtain theoretical estimates for the Hausdorff measure.Comment: 4+ pages. 2 figure

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include

The deuterium effect on electrochemiluminescence efficiencies of anthracene and phenanthrene

The effect of deuteration on the electrochemiluminescence (ECL) efficiencies of the mixed systems containing anthracene or phenathrene has been examined using the single light pulse in the double potential programme. Deuteration of anthracene or phenanthrene decreases the ECL efficiencies by factors of 1·2-16·0. This decrease appears to arise from the quenching of the triplets by radical ions in solution. The quenching factors are estimated by using Marcus theory of electron transfer reactions