相关论文: Energy of taut strings accompanying Wiener process
In the article, we find the asymptotic distribution of the derivative of the taut string accompanying a Wiener process in a strip of fixed width on long time intervals. This enables to find explicit expressions for minimal energy (averaged…
In a recent paper, M. Lifshits and E. Setterqvist introduced the taut string of a Brownian motion $w$, defined as the function of minimal quadratic energy on $[0,T]$ staying in a tube of fixed width $h>0$ around $w$. The authors showed a…
A function $f=f_T$ is called least energy approximation to a function $B$ on the interval $[0,T]$ with penalty $Q$ if it solves the variational problem $$ \int_0^T \left[ f'(t)^2 + Q(f(t)-B(t)) \right] dt \searrow \min. $$ For quadratic…
We consider the asymptotic behavior (over long time intervals) of the minimal integral energy \[ |h|_T^\psi = \int_0^T \psi(h^\prime(t)) \, \mathrm{d}t \] of majorants of the Wiener process $ W(\cdot) $ satisfying the constraints $ h(0) = r…
Dynamic Time Warping (DTW) is a widely used similarity measure for comparing strings that encode time series data, with applications to areas including bioinformatics, signature verification, and speech recognition. The standard…
The string equations of motion and constraints are solved near the horizon and near the singularity of a Schwarzschild black hole. In a conformal gauge such that $\tau = 0$ ($\tau$ = worldsheet time coordinate) corresponds to the horizon…
The inverse first-passage problem for a Wiener process $(W_t)_{t\ge0}$ seeks to determine a function $b{}:{}\mathbb{R}_+\to\mathbb{R}$ such that \[\tau=\inf\{t>0| W_t\ge b(t)\}\] has a given law. In this paper two methods for approximating…
The dynamic time warping (dtw) distance is an established tool for mining time series data. The DTW-Mean problem consists of computing a series which minimizes the so-called Fr\'echet function, that is, the sum of squared dtw-distances to a…
The classical electromagnetic modes outside a long, straight, superconducting cosmic string are calculated, assuming the string to be surrounded by a superconducting cylindric surface of radius R. Thereafter, by use of a Bogoliubov-type…
We present a calculation of the ground state energy of massive spinor fields and massive scalar fields in the background of an inhomogeneous magnetic string with potential given by a delta function. The zeta functional regularization is…
The quantum energy-momentum tensor ${\hat T}^{\mu\nu}(x)$ is computed for strings in Minkowski space-time. We compute its expectation value for different physical string states both for open and closed bosonic strings. The states considered…
A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The tau-function of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are…
We use effective string theory (EST) to describe a toroidal 2d domain wall embedded in a 3d torus. In particular, we compute the free energy of the domain wall in an expansion in inverse powers of the area, up to the second non-universal…
We study small vibrations of a string with time-dependent length $\ell(t)$ and boundary damping. The vibrations are described by a 1-d wave equation in an interval with one moving endpoint at a speed $\ell'(t)$ slower than the speed of…
Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression dW/dt=\partial H(x,t)/…
The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal $I(t)$ is related to its correlation function $\left\langle I(t)I(t+\tau)\right\rangle$. We consider non-stationary processes with the widely observed…
We study the small vibrations of axially moving strings described by a wave equation in an interval with two endpoints moving in the same direction with a constant speed. The solution is expressed by a series formula where the coefficients…
The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy,…
Dynamic time warping distance (DTW) is a widely used distance measure between time series. The best known algorithms for computing DTW run in near quadratic time, and conditional lower bounds prohibit the existence of significantly faster…
The string theory defined by gauging $\W_{\infty/2}$, the sub-algebra of $\W_{\infty}$ generated by the currents of even spin, is discussed. The critical value of the central charge is calculated using zeta-function techniques and shown to…