Let and be independent Wiener processes, consider the task of estimating a diffusion solving stochastic DE dx t =f(x )dt+dw on basis noisy observations defined bydy =x dt+db . This problem is governed by filtering equation for unnormalized conditional density with A * forwarded operator Theorem: if then fundamental solution can written explicity in terms small number statistics satisfying matrixvector equation. The Lie algebraic interpretation this result studied described. Extensions to...

We find the explicit solution to several new problems in stochastic control, among them finite-fuel problem of optimally tracking a standard Wiener process x+w t started at x by nonanticipating ξ having ξ0=0 and total variation (fuel) so as minimize expected discounted cost . In n dimensions, optimal is given thus: fuel expended singular way force x+w–ξ reach stay region remaining time t, f′ Bessel (n even) or an elementary function odd). Except for possible initial jump degenerate diffusion...

A rearrangeable connecting network is one whose permitted states realize every assignment of inlets to outlets — that is, in which it possible rearrange existing calls so as put any new call. In the effort provide adequate telephone service with efficient networks interest be able select (from suitable classes) having a minimum number crosspoints. This problem fully resolved for class built stages identical square switches arranged symmetrically around center stage: roughly, optimal should...

Abstract Objective To evaluate the effectiveness and safety of sonolysis using a low intensity 2 MHz pulsed wave ultrasound beam during carotid endarterectomy. Design Multicentre, phase 3, double blind, randomised controlled trial. Setting 16 European centres. Participants 1004 patients (mean age 68 years; 312 (31%) female) were enrolled in study between 20 August 2015 14 October 2020 until interim analysis was performed. Interventions Sonolysis (n=507) versus sham procedure (n=497). Main...

We give an approach to optimal control of systems described by stochastic functional-differential equations Itô's type : $dx(t) = f(t,x,u(t,x))dt + dw(t))$, $0 \leqq t 1$, with a cost functional $k(u) E\int_0^1 {c(t,x,u(t,x))dt} $ be minimized. Here $w( \cdot )$ is Brownian motion, f and c are nonanticipative functionals describing system dynamics rate respectively, $u(t, causal law, chosen, taking values in space $\Gamma points, depending at most on given information about the past $\{...

A class of three-stage connecting networks proven rearrangeable by D. Slepian is considered. Bounds on the number calls that must be moved are obtained some simple new methods.

The existence of admissible strategies $\gamma ( \cdot , )$ minimizing a function $E\int_0^1 {c(t,x,\gamma (t,x))dt} $ is studied, with $x = x( ,\omega continuous stochastic process, and defined as those utilizing specified pattern information about x, here described by $\sigma $-algebras $G_t included in the "past" $\{ {x(s),s \leqq t} \}$. Conclusion: Moment conditions on growth c, continuity c its third variable (the control) ensure that an optimal strategy exists. method proof depends...

The main aim of this study was to compare clinical and radiological outcomes after stabilization by a percutaneous transpedicular system from the standard open approach for thoracolumbar spine injury.Thirty-seven consecutive patients were enrolled in over period 16 months. Patients included if they experienced 1 fracture (A3.1-A3.3, according AO/Magerl classification), had an absence neurological deficits, no other significant injuries, willing participate. Eighteen treated short-segment,...

The system to be studied consists of a service unit and queue customers waiting served. Service-times are independent, nonnegative variates with the common distribution $B(v)$ having finite first moment $b_1$. Customers arrive in Poisson process (see Feller [4], p. 364) intensity $\lambda$; they form served order arrival, no defections from queue. For previous work on this queueing see for instance Pollaczek [11], Khintchine [9], Lindley [10], Kendall [7], [8], Smith [12], Bailey [1], Takacs...

This paper describes the construction of a permutation network which is advantageous for optical switching. The switching architecture planar and does not require path crossovers between crosspoints. can be partitioned if necessary to ease fabrication difficulties. An algorithm given set binary cells in achieve any specified permutation, it shown that no N x such rearrangeability with fewer than N(N - l)/2 crosspoints used here.

In the interest of providing good telephone service with efficient connecting networks, it is desirable to have at hand a knowledge some combinatorial properties such networks. One these rearrangeability: network rearrangeable if its permitted states realize every assignment inlets outlets, or alternatively, given any state x network, inlet idle in x, and outlet there way assigning new routes (if necessary) calls progress so that can be connected outlet. A natural algebraic approach study...

Tumor cell migration through the extracellular space (ECS) might be affected by its pore size and matrix molecule content. ECS volume fraction alpha (alpha = volume/total tissue volume), tortuosity lambda (lambda(2) free/apparent diffusion coefficient) nonspecific uptake k' were studied real-time tetramethylammonium method in acute slices of human tissue. The parameters temporal cortical resected during surgical treatment lobe epilepsy (control) compared with those brain tumors....

A significant minority of aneurysms treated by endovascular means undergo additional subsequent therapy to treat aneurysm recurrence. Our study was undertaken determine the risk coil embolization recurring following therapy.Patients were identified during a 10-year period from prospectively collated data bases at 2 different neuroscience institutions. Patient outcome obtained or patient's neurosurgical records. Occlusion grade assessed time treatment and follow-up angiography as complete,...

In Brief Study Design. A prospective study. Objective. The aim of this study was to compare clinical and radiological efficacy anterior cervical microdiscectomy fusion done by the newly designed low-profile interbody spacer in cases symptomatic spine spondylosis. Summary Background Data. There are basically 2 ways provide degenerative spine; first is way an unanchored “stand-alone” bone graft or cage, second with a cage anchored plate. Both concepts have their own benefits as well potential...