Conditioned stochastic particle systems and integrable quantum spin systems

We consider from a microscopic perspective large deviation properties of several stochastic interacting particle systems, using their mapping to integrable quantum spin systems. A brief review of recent work is given and several new results are presented: (i) For the general disordered symmectric exclusion process (SEP) on some finite lattice conditioned on no jumps into some absorbing sublattice and with initial Bernoulli product measure with density $\rho$ we prove that the probability $S_\rho(t)$ of no absorption event up to microscopic time $t$ can be expressed in terms of the generating function for the particle number of a SEP with particle injection and empty initial lattice. Specifically, for the symmetric simple exclusion process on $\mathbb Z$ conditioned on no jumps into the origin we obtain the explicit first and second order expansion in $\rho$ of $S_\rho(t)$ and also to first order in $\rho$ the optimal microscopic density profile under this conditioning. For the disordered ASEP on the finite torus conditioned on a very large current we show that the effective dynamics that optimally realizes this rare event does not depend on the disorder, except for the time scale. For annihilating and coalescing random walkers we obtain the generating function of the number of annihilated particles up to time $t$, which turns out to exhibit some universal features.Comment: 25 page

The relationship between the systemic inflammatory response, tumour proliferative activity, T-lymphocytic infiltration and COX-2 expression and survival in patients with transitional cell carcinoma of the urinary bladder

The relationship between the systemic inflammatory response, tumour proliferative activity, T-lymphocytic infiltration, and COX-2 expression and survival was examined in patients with transitional cell carcinoma of the urinary bladder (n=103). Sixty-one patients had superficial disease and 42 patients had invasive disease. Cancer-specific survival was shorter in those patients with invasive compared with superficial bladder cancer (P<0.001). On univariate analysis, stratified by stage, increased Ki-67 labelling index (P<0.05), increased COX-2 expression (P<0.05), C-reactive protein (P<0.05) and adjuvant therapy (P<0.01) were associated with poorer cancer-specific survival. On multivariate analysis of these significant factors, stratified by stage, only C-reactive protein (HR 2.89, 95% CI 1.42–5.91, P=0.004) and adjuvant therapy (HR 0.29, 95% CI 0.14–0.62, P=0.001) were independently associated with poorer cancer-specific survival. These results would suggest that tumour-based factors such as grade, COX-2 expression or T-lymphocytic infiltration are subordinate to systemic factors such as C-reactive protein in determining survival in patients with transitional cell carcinoma of the urinary bladder