Confinement and Viscoelastic effects on Chain Closure Dynamics

Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry - the diffusion-limited cyclization of long chain polymers - is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time t_{c} of a flexible chain (no excluded volume or hydrodynamic interactions) and the length N of its contour under the following separate conditions: (a) confinement of the chain to a sphere of radius D, and (b) modulation of its dynamics by colored Gaussian noise. Among other results, we find that in case (a) when D is much smaller than the size of the chain, t_{c}\simND^{2}, and that in case (b), t_{c}\simN^{2/(2-2H)}, H being a number between 1/2 and 1 that characterizes the decay of the noise correlations. H is not known \`a priori, but values of about 0.7 have been used in the successful characterization of protein conformational dynamics. At this value of H (selected for purposes of illustration), t_{c}\simN^3.4, the high scaling exponent reflecting the slow relaxation of the chain in a viscoelastic medium

Delay Optimal Event Detection on Ad Hoc Wireless Sensor Networks

We consider a small extent sensor network for event detection, in which nodes take samples periodically and then contend over a {\em random access network} to transmit their measurement packets to the fusion center. We consider two procedures at the fusion center to process the measurements. The Bayesian setting is assumed; i.e., the fusion center has a prior distribution on the change time. In the first procedure, the decision algorithm at the fusion center is \emph{network-oblivious} and makes a decision only when a complete vector of measurements taken at a sampling instant is available. In the second procedure, the decision algorithm at the fusion center is \emph{network-aware} and processes measurements as they arrive, but in a time causal order. In this case, the decision statistic depends on the network delays as well, whereas in the network-oblivious case, the decision statistic does not depend on the network delays. This yields a Bayesian change detection problem with a tradeoff between the random network delay and the decision delay; a higher sampling rate reduces the decision delay but increases the random access delay. Under periodic sampling, in the network--oblivious case, the structure of the optimal stopping rule is the same as that without the network, and the optimal change detection delay decouples into the network delay and the optimal decision delay without the network. In the network--aware case, the optimal stopping problem is analysed as a partially observable Markov decision process, in which the states of the queues and delays in the network need to be maintained. A sufficient statistic for decision is found to be the network-state and the posterior probability of change having occurred given the measurements received and the state of the network. The optimal regimes are studied using simulation.Comment: To appear in ACM Transactions on Sensor Networks. A part of this work was presented in IEEE SECON 2006, and Allerton 201

Proper holomorphic mappings between hyperbolic product manifolds

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.Comment: 9 pages; small revisions in the abstract & on p. 1, which reflect better the major revision (in Thm. 1.5) made in v

TeV Scale Implications of Non Commutative Space time in Laboratory Frame with Polarized Beams

We analyze $e^{+}e^{-}\rightarrow \gamma\gamma$, $e^{-}\gamma \rightarrow e^{-}\gamma$ and $\gamma\gamma \rightarrow e^{+}e^{-}$ processes within the Seiberg-Witten expanded noncommutative scenario using polarized beams. With unpolarized beams the leading order effects of non commutativity starts from second order in non commutative(NC) parameter i.e. $O(\Theta^2)$, while with polarized beams these corrections appear at first order ($O(\Theta)$) in cross section. The corrections in Compton case can probe the magnetic component($\vec{\Theta}_B$) while in Pair production and Pair annihilation probe the electric component($\vec{\Theta}_E$) of NC parameter. We include the effects of earth rotation in our analysis. This study is done by investigating the effects of non commutativity on different time averaged cross section observables. The results which also depends on the position of the collider, can provide clear and distinct signatures of the model testable at the International Linear Collider(ILC).Comment: 22 pages, 19 figures, new comments and references added, few typos corrected, Published in JHE

The Schwinger SU(3) construction - I: Multiplicity problem and relation to induced representations

The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an $Sp(2,R)$ unitary representation commuting with the SU(3) representation, the infinity of occurrences of each SU(3) irreducible representation can be handled in complete detail. A natural `generating representation' for SU(3), containing each irreducible representation exactly once, is identified within a subspace of the Schwinger construction; and this is shown to be equivalent to an induced representation of SU(3).Comment: Latex, 25 page

Programmable quantum state discriminator by Nuclear Magnetic Resonance

In this paper a programmable quantum state discriminator is implemented by using nuclear magnetic resonance. We use a two qubit spin-1/2 system, one for the data qubit and one for the ancilla (programme) qubit. This device does the unambiguous (error free) discrimination of pair of states of the data qubit that are symmetrically located about a fixed state. The device is used to discriminate both, linearly polarized states and elliptically polarized states. The maximum probability of the successful discrimination is achieved by suitably preparing the ancilla qubit. It is also shown that, the probability of discrimination depends on angle of unitary operator of the protocol and ellipticity of the data qubit state.Comment: 22 pages and 9 figure

Optimal Database Search: Waves and Catalysis

Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic oscillators, which can be exactly solved in both classical and quantum domains. Classical wave algorithms are far more stable against decoherence compared to their quantum counterparts. In addition to providing convenient demonstration models, they may have a role in practical situations, such as catalysis.Comment: 4 pages (v2) 6 pages, RevTeX4. Title changed. Substantially expanded to include stability considerations, quantum domain analysis, application to catalysis. (v3) Version accepted for publication. (v4) Error in Eqs.(10,11) corrected by replacing \omega by \omega^2. No change in implementation and applicatio

Quantum Random Walks do not need a Coin Toss

Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete quantum random walks, studied in the literature, have nonetheless used both superposition and a quantum coin toss instruction. This is not necessary, and a discrete quantum random walk without a quantum coin toss instruction is defined and analyzed here. Our construction eliminates quantum entanglement from the algorithm, and the results match those obtained with a quantum coin toss instruction.Comment: 6 pages, 4 figures, RevTeX (v2) Expanded to include relation to quantum walk with a coin. Connection with Dirac equation pointed out. Version to be published in Phys. Rev.

Critical behavior at de-pinning of a driven disordered vortex matter in 2H-NbS2

We report unusual jamming in driven ordered vortex flow in 2H-NbS2. Reinitiating movement in these jammed vortices with a higher driving force, and halting it thereafter once again with a reduction in drive, unfolds a critical behavior centered around the de-pinning threshold via divergences in the lifetimes of transient states, validating the predictions of a recent simulation study, which also pointed out a correspondence between plastic de-pinning in vortex matter and the notion of random organization proposed in the context of sheared colloids undergoing diffusive motion.Comment: Phys. Rev. B (in press, 2012). The paper has 14 pages of Text+ Refs. with 4 figures. (Note as some of the figure files are large in size, to enable faster download, the file size has been kept small and the figure resolution are low. The online version of the paper to appear in PRB will contain the higher resolution figures

Possible Neutrino-Antineutrino Oscillation Under Gravity and its Consequences

We show that under gravity the effective masses for neutrino and antineutrino are different which opens a possible window of neutrino-antineutrino oscillation even if the rest masses of the corresponding eigenstates are same. This is due to CPT violation and possible to demonstrate if the neutrino mass eigenstates are expressed as a combination of neutrino and antineutrino eigenstates, as of the neutral kaon system, with the plausible breaking of lepton number conservation. In early universe, in presence of various lepton number violating processes, this oscillation might lead to neutrino-antineutrino asymmetry which resulted baryogenesis from the B-L symmetry by electro-weak sphaleron processes. On the other hand, for Majorana neutrinos, this oscillation is expected to affect the inner edge of neutrino dominated accretion disks around a compact object by influencing the neutrino sphere which controls the accretion dynamics, and then the related type-II supernova evolution and the r-process nucleosynthesis.Comment: 3 pages; contribution to appear in the Proceedings of the MG11 Meeting on General Relativity, Berlin, July 23-29, 2006; prepared on the basis of the talk presented in the meeting; new version with updated reference