Pebbling, Entropy and Branching Program Size Lower Bounds

We contribute to the program of proving lower bounds on the size of branching programs solving the Tree Evaluation Problem introduced by Cook et. al. (2012). Proving a super-polynomial lower bound for the size of nondeterministic thrifty branching programs (NTBP) would separate $NL$ from $P$ for thrifty models solving the tree evaluation problem. First, we show that {\em Read-Once NTBPs} are equivalent to whole black-white pebbling algorithms thus showing a tight lower bound (ignoring polynomial factors) for this model. We then introduce a weaker restriction of NTBPs called {\em Bitwise Independence}. The best known NTBPs (of size $O(k^{h/2+1})$) for the tree evaluation problem given by Cook et. al. (2012) are Bitwise Independent. As our main result, we show that any Bitwise Independent NTBP solving $TEP_{2}^{h}(k)$ must have at least $\frac{1}{2}k^{h/2}$ states. Prior to this work, lower bounds were known for NTBPs only for fixed heights $h=2,3,4$ (See Cook et. al. (2012)). We prove our results by associating a fractional black-white pebbling strategy with any bitwise independent NTBP solving the Tree Evaluation Problem. Such a connection was not known previously even for fixed heights. Our main technique is the entropy method introduced by Jukna and Z{\'a}k (2001) originally in the context of proving lower bounds for read-once branching programs. We also show that the previous lower bounds given by Cook et. al. (2012) for deterministic branching programs for Tree Evaluation Problem can be obtained using this approach. Using this method, we also show tight lower bounds for any $k$-way deterministic branching program solving Tree Evaluation Problem when the instances are restricted to have the same group operation in all internal nodes.Comment: 25 Pages, Manuscript submitted to Journal in June 2013 This version includes a proof for tight size bounds for (syntactic) read-once NTBPs. The proof is in the same spirit as the proof for size bounds for bitwise independent NTBPs present in the earlier version of the paper and is included in the journal version of the paper submitted in June 201

Investigation of complexity dynamics in a DC glow discharge magnetized plasma using recurrence quantification analysis

The authors are thankful to BRNS-DAE, Government of India for the financial support under the project grant (Reference No. 2013/34/29/BRNS). The authors would like to express their heartfelt thanks to all the members of plasma Physics division of Saha Institute of Nuclear Physics for their help and constant support.Peer reviewedPublisher PD

Persistence in nonequilibrium surface growth

Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the molecular beam epitaxy (MBE) universality class. Both the initial transient and the long-time steady-state regimes are investigated. We show that for growth models in the MBE universality class, the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady-state regimes. For the MBE universality class, the positive and negative persistence exponents in the steady-state are found to be $\theta^S_{+} = 0.66 \pm 0.02$ and $\theta^S_{-} = 0.78 \pm 0.02$, respectively, in (1+1) dimensions, and $\theta^S_{+} = 0.76 \pm 0.02$ and $\theta^S_{-} =0.85 \pm 0.02$, respectively, in (2+1) dimensions. The noise reduction technique is applied on some of the (1+1)-dimensional models in order to obtain accurate values of the persistence exponents. We show analytically that a relation between the steady-state persistence exponent and the dynamic growth exponent, found earlier to be valid for linear models, should be satisfied by the smaller of the two steady-state persistence exponents in the nonlinear models. Our numerical results for the persistence exponents are consistent with this prediction. We also find that the steady-state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state. The dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form.Comment: 28 pages, 16 figure

Charge tunneling in fractional edge channels

We explain recent experimental observations on effective charge of edge states tunneling through a quantum point contact in the weak backscattering regime. We focus on the behavior of the excess noise and on the effective tunneling charge as a function of temperature and voltage. By introducing a minimal hierarchical model different filling factors, \nu=p/(2p+1), in the Jain sequence are treated on equal footing, in presence also of non-universal interactions. The agreement found with the experiments for \nu=2/3 and \nu=2/5 reinforces the description of tunneling of bunching of quasiparticles at low energies and quantitatively defines the condition under which one expects to measure the fundamental quasiparticle charge. We propose high-order current cumulant measurement to cross-check the validity of the above scenario and to better clarify the peculiar temperature behavior of the effective charges measured in the experiments.Comment: 6 pages, 3 figure

Pengaruh Iklan Televisi terhadap Pengambilan Keputusan Pembelian Konsumen Es Krim Magnum

According to Nielsen Advertising Information Services said the 2015 total advertising expenditure increased by 4%. This increase was also influenced by existing companies in Indonesia including PT Unilever Indonesia. Tbk with its brand advertising products Wall's Magnum Ice Cream. This study aims to identify consumer ratings of advertising done by Ice cream Magnum, analyzing the effectiveness of ads Magnum Ice Cream is able to communicate the message and analyzing consumer purchase decisions over the ads that do Magnum Ice Cream. Data processing was performed using Statistical Package For Social Science (SPSS) 19 and Minitab 14. The analysis tool used is the EPIC model and Consumer Decision Model (CDM). Based on the analysis, the measurement response television advertising and communication impact that occurs, television commercials advertising the Magnum Ice Cream edition Taste the Classic included in the category of advertising is quite effective and have an impact until the real purchase

Dissipationless transport in low density bilayer systems

In a bilayer electronic system the layer index may be viewed as the z-component of an isospin-1/2. An XY isospin-ordered ferromagnetic phase was observed in quantum Hall systems and is predicted to exist at zero magnetic field at low density. This phase is a superfluid for opposite currents in the two layers. At B=0 the system is gapless but superfluidity is not destroyed by weak disorder. In the quantum Hall case, weak disorder generates a random gauge field which probably does not destroy superfluidity. Experimental signatures include Coulomb drag and collective mode measurements.Comment: 4 pages, no figures, submitted to Phys. Rev. Let

Plasmons in coupled bilayer structures

We calculate the collective charge density excitation dispersion and spectral weight in bilayer semiconductor structures {\it including effects of interlayer tunneling}. The out-of-phase plasmon mode (the ``acoustic'' plasmon) develops a long wavelength gap in the presence of tunneling with the gap being proportional to the square root (linear power) of the tunneling amplitude in the weak (strong) tunneling limit. The in-phase plasmon mode is qualitatively unaffected by tunneling. The predicted plasmon gap should be a useful tool for studying many-body effects.Comment: 10 pages, 6 figures. to appear in Phys. Rev. Let

Chemistry of Lanthanons : Part XLIV- Isolation & Characterization of Coumarin-3- carboxylate Chelates of Lanthanons

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