Abstract:
In this paper by calculating carefully the capacities (defined by high order Sobolev norms on the Wiener space) for some functions of Brownian motion, we show that the dyadic approximations of the sample paths of the Brownian motion converge in the $p$-variation distance to the Brownian motion except for a slim set (i.e. except for a zero subset with respect to the capacity on the Wiener space of any order). This presents a way for studying quasi-sure properties of Wiener functionals by means of the rough path analysis.

Abstract:
The authors propose new Bayesian models to obtain individual-level and time-varying regression coefficients in longitudinal data involving a single observation per response unit at each time period. An application to explore the association between customer satisfaction and shareholder value is included in the paper. The Bayesian models allow the flexibility of incorporating industry and firm factors in the context of the application to help explain variations of the regression coefficients. Results from the analysis indicate that the effect of customer satisfaction on shareholder value is not homogeneous over time. The proposed methodology provides a powerful tool to explore the relationship between two important business concepts.

Abstract:
Structure optimizations were performed for 1 and 2 monolayers (ML) of Fe on a 5 ML W(110) substrate employing the all-electron full-potential linearized augmented plane-wave (FP-LAPW) method. The magnetic moments were also obtained for the converged and optimized structures. We find significant contractions ($\sim$ 10 %) for both the Fe-W and the neighboring Fe-Fe interlayer spacings compared to the corresponding bulk W-W and Fe-Fe interlayer spacings. Compared to the Fe bcc bulk moment of 2.2 $\mu_B$, the magnetic moment for the surface layer of Fe is enhanced (i) by 15% to 2.54 $\mu_B$ for 1 ML Fe/5 ML W(110), and (ii) by 29% to 2.84 $\mu_B$ for 2 ML Fe/5 ML W(110). The inner Fe layer for 2 ML Fe/5 ML W(110) has a bulk-like moment of 2.3 $\mu_B$. These results agree well with previous experimental data.

Abstract:
The HLLC Riemann solver, which resolves both the shock waves and contact discontinuities, is popular to the computational fluid dynamics community studying compressible flow problems with mesh methods. Although it was reported to be used in meshless methods, the crucial information and procedure to realise this scheme within the framework of meshless methods were not clarified fully. Moreover, the capability of the meshless HLLC solver to deal with compressible liquid flows is not completely clear yet as very few related studies have been reported. Therefore, a comprehensive investigation of a dimensional non-split HLLC Riemann solver for the least-square meshless method is carried out in this study. The stiffened gas equation of state is adopted to capacitate the proposed method to deal with single-phase gases and/or liquids effectively, whilst direct applying the perfect gas equation of state for compressible liquid flows might encounter great difficulties in correlating the state variables. The spatial derivatives of the Euler equations are computed by a least-square approximation and the flux terms are calculated by the HLLC scheme in a dimensional non-split pattern. Simulations of gas and liquid shock tubes, moving shock passing a cylinder, internal supersonic flows in channels and external transonic flows over aerofoils are accomplished. The current approach is verified by extensive comparisons of the produced numerical outcomes with various available data such as the exact solutions, finite volume mesh method results, experimental measurements or other reference results.

Abstract:
We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p variation, 1\leq p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLE_{\kappa} null set, where 0<\kappa\leq 4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Abstract:
The current standard for measuring tumor response using X-ray, CT and MRI is based on the response evaluation criterion in solid tumors (RECIST) which, while providing simplifications over previous (WHO) 2-D methods, stipulate four response categories: CR (complete response), PR (partial response), PD (progressive disease), SD (stable disease) based purely on percentage changes without consideration of any measurement uncertainty. In this paper, we propose a statistical procedure for tumor response assessment based on uncertainty measures of radiologist’s measurement data. We present several variance estimation methods using time series methods and empirical Bayes methods when a small number of serial observations are available on each member of a group of subjects. We use a publically available database which contains a set of over 100 CT scan images on 23 patients with annotated RECIST measurements by two radiologist readers. We show that despite of bias in each individual reader’s measurements, statistical decisions on tumor change can be made on each individual subject. The consistency of the two readers can be established based on the intra-reader change assessments. Our proposal compares favorably with the RECIST standard protocol, raising the hope that, statistically sound decision on change analysis can be made in future based on careful variability and measurement uncertainty analysis.

Abstract:
Orthotropic decks were applied to the long span bridges after World War II due to several advantages, such as light weight, high strength, few deck joints, durability, rapid construction, life-cycle economy. The fatigue problem of orthotropic decks was realized twenty years ago since fatigue failure was found. In the past two decades large amount of studies and investigations were carried out and fruitful achievements were obtained. It was found that most of the fatigue cracks were occurred at the welded connection details, such as rib-to-deck plate, rib-to-diaphragm, and rib-to-diaphragm-to-deck plate (RDDP). These connections are sensitive to fatigue cracking due to high concentrated stress and residual stress at welded connections. In this paper practical fatigue failure cases at the welded connections, ease to occur fatigue cracking, are presented, and analyzed through a numerical modeling of orthotropic deck via FE (finite element) software. Furthermore, the improvement technologies of fatigue are also discussed. The results of the analysis can be contributed to the evaluation of the fatigue design for the orthotropic deck.

Abstract:
We report on the first measurement of the differential cross section of $\phi$-meson photoproduction for the $d(\gamma,pK^{+}K^{-})n$ exclusive reaction channel. The experiment was performed using a \textcolor{black}{tagged-photon} beam and the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. A combined analysis using data from the $d(\gamma,pK^{+}K^{-})n$ channel and those from a previous publication on coherent $\phi$ production on the deuteron has been carried out to extract the $\phi-N$ total cross section, $\sigma_{\phi N}$. The extracted $\phi-N$ total cross section favors a value above 20 mb. This value is larger than the value extracted using vector-meson dominance models for $\phi$ photoproduction on the proton.

Abstract:
Intense coherent laser radiation red-detuned from absorption edge can reactively activate sizable Hall type charge and spin transport in n-doped paramagnetic semiconductors as a consequence of k-space Berry curvature transferred from valence band to photon-dressed conduction band. In the presence of disorder, the optically induced Hall conductance can change sign with laser intensity.

Abstract:
Master equation with microscopic reversibility ($q_{ij}\neq 0$ iff $q_{ji}\neq 0$) has a {\em thermodynamic superstructure} in terms of two state functions $S$, entropy, and $F$, free energy: It is discovered recently that entropy production rate $e_p=-dF/dt+Q_{hk}$ with both $-dF/dt=f_d, Q_{hk} \ge 0$. The free energy dissipation $f_d\ge 0$ reflects irreversibility in spontaneous self-organization; house-keeping heat $Q_{hk}\ge 0$ reveals broken time-symmetry in open system driven away from equilibrium. In a Riemannian geometric space, the master equation is a geodesic flow when $Q_{hk}=0$; here we show that the $e_p$ decomposition is orthogonal: $e_p$, $f_d$, $Q_{hk}$ forms a pythagorean triples. Gradient flow means {\em maximum dissipation principle} outside Onsager's regime. The presence of $Q_{hk}$ makses gradient flow no longer generally true. Thermodynamics of stochastic physics requires a new geometric perspective.