A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs

In this paper we provide a complete theoretical analysis of a two-dimensional degenerate nonconvex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control, and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and the smooth fit condition holds there

Experimental demonstration of enhanced self-amplified spontaneous emission by an optical klystron.

We report the first experimental evidence of enhancement of self-amplified spontaneous emission, due to the use of an optical klystron. In this free-electron laser scheme, a relativistic electron beam passes through two undulators, separated by a dispersive section. The latter converts the electron-beam energy modulation produced in the first undulator in density modulation, thus enhancing the free-electron laser gain. The experiment has been carried out at the FERMI facility in Trieste. Powerful radiation has been produced in the extreme ultraviolet range, with an intensity a few orders of magnitude larger than in pure self-amplified spontaneous emission mode. Data have been benchmarked with an existing theoretical model. © 2015 American Physical Society

The Algebra of Physical Observables in Nonlinearly Realized Gauge Theories

We classify the physical observables in spontaneously broken nonlinearly realized gauge theories in the recently proposed loopwise expansion governed by the Weak Power-Counting (WPC) and the Local Functional Equation. The latter controls the non-trivial quantum deformation of the classical nonlinearly realized gauge symmetry, to all orders in the loop expansion. The Batalin-Vilkovisky (BV) formalism is used. We show that the dependence of the vertex functional on the Goldstone fields is obtained via a canonical transformation w.r.t. the BV bracket associated with the BRST symmetry of the model. We also compare the WPC with strict power-counting renormalizability in linearly realized gauge theories. In the case of the electroweak group we find that the tree-level Weinberg relation still holds if power-counting renormalizability is weakened to the WPC condition.Comment: 20 pages, 1 figur

Singularities of N=1 Supersymmetric Gauge Theory and Matrix Models

In N=1 supersymmetric U(N) gauge theory with adjoint matter $\Phi$ and polynomial tree-level superpotential $W(\Phi)$, the massless fluctuations about each quantum vacuum are generically described by $U(1)^n$ gauge theory for some n. However, by tuning the parameters of $W(\Phi)$ to non-generic values, we can reach singular vacua where additional fields become massless. Using both the matrix model prescription and the strong-coupling approach, we study in detail three examples of such singularities: the singularities of the n=1 branch, intersections of n=1 and n=2 branches, and a class of N=1 Argyres-Douglas points. In all three examples, we find that the matrix model description of the low-energy physics breaks down in some way at the singularity.Comment: 29 pages, 1 figure. Revised section 1, fixed misprints in section 3.1, added clarifications and reference

Stem cell plasticity: time for a reappraisal?

n recent years an increasing number of publications have claimed that adult mammalian stem cells (SC) may be capable of differentiating across tissue lineage boundaries and that this plasticity may represent a novel therapeutic strategy for tissue regeneration. However, after a first phase of excitement, the issue of somatic SC plasticity remains controversial and the therapeutic perspectives are still elusive. In this review, we examine the general mechanisms which govern the function of SC, the identification and functional characterization of adult SC of different tissues and their putative capacity to transdifferentiate into mature cells of different origin. The potential clinical applications of adult SC for regenerative medicine are also discussed in each chapter. The method employed for preparing this review was the informal consensus development. Members of the Working Group on SC met four times and discussed the single points, previously assigned by the Chairman (S.T.), in order to achieve an agreement on different opinions and approve the final manuscript. All the authors of the present review have been working in the field of SC and have contributed original papers to peer-reviewed journals. In addition to the authors' own work, the present review examines articles published in journals covered by the Science Citation Index and Medline