Remarks on the Extended Characteristic Uncertainty Relations

Three remarks concerning the form and the range of validity of the state-extended characteristic uncertainty relations (URs) are presented. A more general definition of the uncertainty matrix for pure and mixed states is suggested. Some new URs are provided.Comment: LaTex, 4 pages, no figure

Comment on "On the uncertainty relations and squeezed states for the quantum mechanics on a circle"

It is shown by examples that the position uncertainty on a circle, proposed recently by Kowalski and Rembieli\'nski [J. Phys. A 35 (2002) 1405] is not consistent with the state localization. We argue that the relevant uncertainties and uncertainty relations (UR's) on a circle are that based on the Gram-Robertson matrix. Several of these generalized UR's are displayed and related criterions for squeezed states are discussed.Comment: 5 pages, LaTex2e, 3 figures.ep

CLINICAL ASPECTS AND SURGICAL TREATMENT OF TUMOURS OF THE MEDIASTINUM

No abstrac

Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions

The Barut-Girardello coherent states (BG CS) representation is extended to the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson realizations. The sp(N,R) BG CS take the form of multimode ordinary Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode Hilbert space and the relation between the canonical CS and the u(p,q) BG-type CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and their discrete superpositions contain many states studied in quantum optics (even and odd N-mode CS, pair CS) and provide an approach to quadrature squeezing, alternative to that of intelligent states. New subsets of weakly and strongly nonclassical states are pointed out and their statistical properties (first- and second-order squeezing, photon number distributions) are discussed. For specific values of the angle parameters and small amplitude of the canonical CS components these states approaches multimode Fock states with one, two or three bosons/photons. It is shown that eigenstates of a squared non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of the quadratures of A.Comment: 29 pages, LaTex, 5 figures. Improvements in text, corrections in some formulas. To appear in J. Phys. A, v. 3

Nucleation at the DNA supercoiling transition

Twisting DNA under a constant applied force reveals a thermally activated transition into a state with a supercoiled structure known as a plectoneme. Using transition state theory, we predict the rate of this plectoneme nucleation to be of order 10^4 Hz. We reconcile this with experiments that have measured hopping rates of order 10 Hz by noting that the viscosity of the bead used to manipulate the DNA limits the measured rate. We find that the intrinsic bending caused by disorder in the base-pair sequence is important for understanding the free energy barrier that governs the transition. Both analytic and numerical methods are used in the calculations. We provide extensive details on the numerical methods for simulating the elastic rod model with and without disorder.Comment: 18 pages, 15 figure

A volume inequality for quantum Fisher information and the uncertainty principle

Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$det(Cov_\rho(A_h,A_j)) \geq det(- \frac{i}{2} Tr(\rho [A_h,A_j]))$$ gives a bound for the quantum generalized covariance in terms of the commutators $[A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $_{\rho,f}$ be the associated quantum Fisher information. In this paper we conjecture the inequality $$det (Cov_\rho(A_h,A_j)) \geq det (\frac{f(0)}{2} _{\rho,f})$$ that gives a non-trivial bound for any natural number $N$ using the commutators $i[\rho, A_h]$. The inequality has been proved in the cases $N=1,2$ by the joint efforts of many authors. In this paper we prove the case N=3 for real matrices

Uncertainty Relations in Deformation Quantization

Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson, Robertson-Schr\"odinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.Comment: 28+1 pages, harvmac file, no figures, typos correcte

On misspecifications in regularity and properties of estimators

The problem of parameter estimation by the continuous time observations of a deterministic signal in white Gaussian noise is considered. The asymptotic properties of the maximum likelihood estimator are described in the asymptotic of small noise (large signal-to-noise ratio). We are interested in the situation when there is a misspecification in the regularity conditions. In particular it is supposed that the statistician uses a discontinuous (change-point type) model of signal, when the true signal is continuously differentiable function of the unknown parameter

The features of Drosophila core promoters revealed by statistical analysis

BACKGROUND: Experimental investigation of transcription is still a very labor- and time-consuming process. Only a few transcription initiation scenarios have been studied in detail. The mechanism of interaction between basal machinery and promoter, in particular core promoter elements, is not known for the majority of identified promoters. In this study, we reveal various transcription initiation mechanisms by statistical analysis of 3393 nonredundant Drosophila promoters. RESULTS: Using Drosophila-specific position-weight matrices, we identified promoters containing TATA box, Initiator, Downstream Promoter Element (DPE), and Motif Ten Element (MTE), as well as core elements discovered in Human (TFIIB Recognition Element (BRE) and Downstream Core Element (DCE)). Promoters utilizing known synergetic combinations of two core elements (TATA_Inr, Inr_MTE, Inr_DPE, and DPE_MTE) were identified. We also establish the existence of promoters with potentially novel synergetic combinations: TATA_DPE and TATA_MTE. Our analysis revealed several motifs with the features of promoter elements, including possible novel core promoter element(s). Comparison of Human and Drosophila showed consistent percentages of promoters with TATA, Inr, DPE, and synergetic combinations thereof, as well as most of the same functional and mutual positions of the core elements. No statistical evidence of MTE utilization in Human was found. Distinct nucleosome positioning in particular promoter classes was revealed. CONCLUSION: We present lists of promoters that potentially utilize the aforementioned elements/combinations. The number of these promoters is two orders of magnitude larger than the number of promoters in which transcription initiation was experimentally studied. The sequences are ready to be experimentally tested or used for further statistical analysis. The developed approach may be utilized for other species