In vivo NMR imaging and T1 measurements of water protons in the human brain

Nuclear magnetic resonance (NMR) proton density images of the human brain have been made by the FONAR method. Spin-lattice relaxation times, T₁, of water hydrogen protons have been determined at random positions within frontal and temporal regions of the human brain. The primary purpose of this ongoing research is to accumulate a large data base of normal T₁ values for water protons in normal human brain tissue. Our experience to data includes 31 measurements on 18 volunteer subjects, and the mean value ± standard deviation is 215 ± 42 msec. In addition, two metastatic lesions of the brain were studied and found to have T₁ values longer than those for normal brain tissue.     

A central limit theorem for the sojourn times of strongly ergodic Markov chains

Let X_n be an irreducible aperiodic recurrent Markov chain with countable state space I and with the mean recurrence times having second moments. There is proved a global central limit theorem for the properly normalized sojourn times. More precisely, if $\text{t}{}^{\mathrm{(n}}\text{)}{}_{\mathrm{i}}\text{=Σ}{}^{\mathrm{n}}{}_{\mathrm{k=1}}\text{i}\text{?}{}_{\mathrm{i}}\text{(X}{}_{\mathrm{k}}\text{)}$, then the probability measures induced by {t⁽ⁿ⁾_i/√n?√nπ_i}_i?I(π_i being the ergotic distribution) on the Hilbert-space of square summable I-sequences converge weakly in this space to a Gaussian measure determined by a certain weak potential operator.     

A note on occupation times of random walks

In this note I show that some asymptotic results on the average occupancy time of an interval derived for lattice random walks with negative exponential transition probabilities are true for all random walks whose transition probabilities have a finite variance. The proof is based on the continuum limit.     

On first passage time structure of random walks

For continuous time birth-death processes on {0,1,2,…}, the first passage time T⁺_n from n to n + 1 is always a mixture of (n + 1) independent exponential random variables. Furthermore, the first passage time T_0,n+1 from 0 to (n + 1) is always a sum of (n + 1) independent exponential random variables. The discrete time analogue, however, does not necessarily hold in spite of structural similarities. In this paper, some necessary and sufficient conditions are established under which T⁺_n and T_0,n+1 for discrete time birth-death chains become a mixture and a sum, respectively, of (n + 1) independent geometric random variables on {1,2,…};. The results are further extended to conditional first passage times.     

Qualitative and quantitative ultrashort echo time (UTE) imaging of cortical bone

We describe the use of two-dimensional ultrashort echo time (2D UTE) sequences with minimum TEs of 8 μs to image and quantify cortical bone on a clinical 3T scanner. An adiabatic inversion pulse was used for long T(2) water and fat signal suppression. Adiabatic inversion prepared UTE acquisitions with varying TEs were used for T(2) measurement. Saturation recovery UTE acquisitions were used for T(1) measurement. Bone water concentration was measured with the aid of an external reference phantom. UTE techniques were evaluated on cadaveric specimens and healthy volunteers. A signal-to-noise ratio of around 30, contrast-to-noise ratio of around 27/20 between bone and muscle/fat were achieved in tibia in vivo with a nominal voxel size of 0.23 × 0.23 × 6.0 mm(3) in a scan time of 5 min. A mean T(1) of 223 ± 11 ms and mean T(2) of 390 ± 19 μs were found. Mean bone water concentrations of 23.3 ± 1.6% with UTE and 21.7 ± 1.3% with adiabatic inversion prepared UTE sequences were found in tibia in five normal volunteers. The results show that in vivo qualitative and quantitative evaluation of cortical bone is feasible with 2D UTE sequences.     

ON THE HITTING PROBABILITY AND POLARITY FOR A CLASS OF SELF-SIMILAR MARKOV PROCESSES

1IntroductionSelf-similarMarkoyprocesseson(0,co)wereintroducedbyLamperti[ZI.AnormalMarkovprocessX=(fi,F,R,Xt,ot,p")withstatespace(0,co)iscalledself-similarMarkovprocessoforderorjor>0,ifitstransitionfunctionPt(x,A)satisfiesPt(x,A)=Pa,(a"x,a"A)Vt>9,a>0,x>0,AEB(0,co).Itwasshownin[2]and[11]thateveryself-similarMarkovprocesson(0,co)automaticllyisstronglyMarkovianandhasanicepath",soitisaHuntprocessinthesenseof[1].Thefractalpropertiesoftheprocesseswerestudiedin[6]and[8].TheitoExcursiontheor…     

A one-dimensional version of the random interlacements

We base ourselves on the construction of the two-dimensional random interlacements (Comets et al., 2016) to define the one-dimensional version of the process. For this, we consider simple random walks conditioned on never hitting the origin. We compare this process to the conditional random walk on the ring graph. Our results are the convergence of the vacant set on the ring graph to the vacant set of one-dimensional random interlacements, a central limit theorem for the interlacements’ local time and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements’ local times.     

On uniform closeness of local times of Markov chains and i.i.d. sequences

In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of $n$ i.i.d. random variables with law given by the invariant measure of that Markov chain. The proof of this result uses a refinement of the soft local time method of Popov and Teixeira (2015).     

A search method for optimal control of a flow shop system of traditional machines

We consider a convex and nondifferentiable optimization problem for deterministic flow shop systems in which the arrival times of the jobs are known and jobs are processed in the order they arrive. The decision variables are the service times that are to be set only once before processing the first job, and cannot be altered between processes. The cost objective is the sum of regular costs on job completion times and service costs inversely proportional to the controllable service times. A finite set of subproblems, which can be solved by trust-region methods, are defined and their solutions are related to the optimal solution of the optimization problem under consideration. Exploiting these relationships, we introduce a two-phase search method which converges in a finite number of iterations. A numerical study is held to demonstrate the solution performance of the search method compared to a subgradient method proposed in earlier work.