Structure and Properties of Hughston's Stochastic Extension of the Schr\"odinger Equation

Hughston has recently proposed a stochastic extension of the Schr\"odinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics.Comment: Plain Tex, no figure

Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips $S$-matrix is unitarily related to the $S$-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $\sigma$ of the Lax-Phillips theory. Analytic continuation in $\sigma$ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision

Gravitational Repulsion within a Black-Hole using the Stueckelberg Quantum Formalism

We wish to study an application of Stueckelberg's relativistic quantum theory in the framework of general relativity. We study the form of the wave equation of a massive body in the presence of a Schwarzschild gravitational field. We treat the mathematical behavior of the wavefunction also around and beyond the horizon (r=2M). Classically, within the horizon, the time component of the metric becomes spacelike and distance from the origin singularity becomes timelike, suggesting an inevitable propagation of all matter within the horizon to a total collapse at r=0. However, the quantum description of the wave function provides a different understanding of the behavior of matter within the horizon. We find that a test particle can almost never be found at the origin and is more probable to be found at the horizon. Matter outside the horizon has a very small wave length and therefore interference effects can be found only on a very small atomic scale. However, within the horizon, matter becomes totally "tachionic" and is potentially "spread" over all space. Small location uncertainties on the atomic scale become large around the horizon, and different mass components of the wave function can therefore interfere on a stellar scale. This interference phenomenon, where the probability of finding matter decreases as a function of the distance from the horizon, appears as an effective gravitational repulsion.Comment: 20 pages, 6 figure

Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics

We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses, to find the approximate dynamical equation for the kinetic state of any nonequilibrium system to the relativistic case, and obtain a manifestly covariant Boltzmann-type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation is then used to prove the $H$-theorem for evolution in $\tau .$ In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential $V(q),$ where $q$ is an invariant distance in the Minkowski space-time. The two-body correlations are taken to have the support in a relative $O( 2,1)$-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit

Streptococcal pharyngitis and systemic lupus erythematosus

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Could the classical relativistic electron be a strange attractor?

We review the formulation of the problem of the electromagnetic self-interaction of a relativistic charged particle in the framework of the manifestly covariant classical mechanics of Stueckelberg, Horwitz and Piron. The gauge fields of this theory, in general, cause the mass of the particle to change. We show that the non-linear Lorentz force equation for the self-interaction resulting from the expansion of the Green's function has chaotic solutions. We study the autonomous equation for the off-shell particle mass here, for which the effective charged particle mass achieves a macroscopic average value determined by what appears to be a strange attractor.Comment: 19 pages PLain TeX, 1 page Captions, 18 figure (.eps files

The ECHELON-2 trial: 5-year results of a randomized, phase III study of brentuximab vedotin with chemotherapy for CD30-positive peripheral T-cell lymphoma

BACKGROUND: For patients with peripheral T-cell lymphoma (PTCL), outcomes using frontline treatment with cyclophosphamide, doxorubicin, vincristine, and prednisone (CHOP) or CHOP-like therapy are typically poor. The ECHELON-2 study demonstrated that brentuximab vedotin plus cyclophosphamide, doxorubicin, and prednisone (A+CHP) exhibited statistically superior progression-free survival (PFS) per independent central review and improvements in overall survival versus CHOP for the frontline treatment of patients with systemic anaplastic large cell lymphoma or other CD30-positive PTCL. PATIENTS AND METHODS: ECHELON-2 is a double-blind, double-dummy, randomized, placebo-controlled, active-comparator phase III study. We present an exploratory update of the ECHELON-2 study, including an analysis of 5-year PFS per investigator in the intent-to-treat analysis group. RESULTS: A total of 452 patients were randomized (1 : 1) to six or eight cycles of A+CHP (N = 226) or CHOP (N = 226). At median follow-up of 47.6 months, 5-year PFS rates were 51.4% [95% confidence interval (CI): 42.8% to 59.4%] with A+CHP versus 43.0% (95% CI: 35.8% to 50.0%) with CHOP (hazard ratio = 0.70; 95% CI: 0.53-0.91), and 5-year overall survival (OS) rates were 70.1% (95% CI: 63.3% to 75.9%) with A+CHP versus 61.0% (95% CI: 54.0% to 67.3%) with CHOP (hazard ratio = 0.72; 95% CI: 0.53-0.99). Both PFS and OS were generally consistent across key subgroups. Peripheral neuropathy was resolved or improved in 72% (84/117) of patients in the A+CHP arm and 78% (97/124) in the CHOP arm. Among patients who relapsed and subsequently received brentuximab vedotin, the objective response rate was 59% with brentuximab vedotin retreatment after A+CHP and 50% with subsequent brentuximab vedotin after CHOP. CONCLUSIONS: In this 5-year update of ECHELON-2, frontline treatment of patients with PTCL with A+CHP continues to provide clinically meaningful improvement in PFS and OS versus CHOP, with a manageable safety profile, including continued resolution or improvement of peripheral neuropathy

A RIAM/lamellipodin-talin-integrin complex forms the tip of sticky fingers that guide cell migration.

The leading edge of migrating cells contains rapidly translocating activated integrins associated with growing actin filaments that form 'sticky fingers' to sense extracellular matrix and guide cell migration. Here we utilized indirect bimolecular fluorescence complementation to visualize a molecular complex containing a Mig-10/RIAM/lamellipodin (MRL) protein (Rap1-GTP-interacting adaptor molecule (RIAM) or lamellipodin), talin and activated integrins in living cells. This complex localizes at the tips of growing actin filaments in lamellipodial and filopodial protrusions, thus corresponding to the tips of the 'sticky fingers.' Formation of the complex requires talin to form a bridge between the MRL protein and the integrins. Moreover, disruption of the MRL protein-integrin-talin (MIT) complex markedly impairs cell protrusion. These data reveal the molecular basis of the formation of 'sticky fingers' at the leading edge of migrating cells and show that an MIT complex drives these protrusions

Model-Independent Determination of the Strong-Phase Difference Between D0 and D0 → K0S,L h+h- (h=π,K) and its Impact on the Measurement of the CKM angle γ/φ3

We report the first determination of the relative strong-phase difference between D^0 -\u3e K^0_S,L K^+ K^- and D^0-bar -\u3e K^0_S,L K^+ K^-. In addition, we present updated measurements of the relative strong-phase difference between D^0 -\u3e K^0_S,L pi^+ pi^- and D^0-bar -\u3e K^0_S,L pi^+ pi^-. Both measurements exploit the quantum coherence between a pair of D^0 and D^0-bar mesons produced from psi(3770) decays. The strong-phase differences measured are important for determining the Cabibbo-Kobayashi-Maskawa angle gamma/phi_3 in B^- -\u3e K^- D^0-tilde decays, where D^0-tilde is a D^0 or D^0-bar meson decaying to K^0_S h^+ h^- (h=pi,K), in a manner independent of the model assumed to describe the D^0 -\u3e K^0_S h^+ h^- decay. Using our results, the uncertainty in gamma/phi_3 due to the error on the strong-phase difference is expected to be between 1.7 and 3.9 degrees for an analysis using B^- K^- D^0-tilde D^0-tilde -\u3e K^0_S pi^+ pi^- decays, and between 3.2 and 3.9 degrees for an analysis based on B^- -\u3e K^- D^0-tilde, D^0-tilde -\u3e K^0_S K^+ K^- decays. A measurement is also presented of the CP-odd fraction, F_-, of the decay D^0 -\u3e K^0_S K^+ K^- in the region of the phi -\u3e K^+ K^- resonance. We find that in a region within 0.01 GeV^2/c^4 of the nominal phi mass squared F_- \u3e 0.91 at the 90% confidence level