On the Stringy Hartle-Hawking State

We argue that non-perturbative $\alpha'$ stringy effects render the Hartle-Hawking state associated with the $SL(2)/U(1)$ eternal black hole singular at the horizon. We discuss implications of this observation on firewalls in string theory

Enhancement of the AC RPA

The overall goal of this research project is to improve the response and sensitivity of the AC Retarding Potential Analyzer (RPA). The AC RPA can accurately measure the flux, energy, and energy distribution of charged particles in a space environment. The enhancement of the sensor derives from changes that increase sensitivity of flux measurements through reduction of the baseline noise. The enhanced AC RPA sensor allows diagnosis of required charge particle beams necessary for tests of materials, instruments and subsystems, for future exploration missions

Generalised Bose-Einstein phase transition in large-mm component spin glasses

It is proposed to understand finite dimensional spin glasses using a $1/m$ expansion, where $m$ is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which the expansion is made, the infinite-$m$ limit, has been studied in the mean-field limit in detail and has a very unusual phase transition, rather similar to a Bose-Einstein phase transition but with $N^{2/5}$ macroscopically occupied low-lying states.Comment: 4 pages (plus a few lines), 3 figures. v2: minor error corrected. v3: numerics supplemented by analytical arguments, references added, figure of density of states adde

The geometry of basic, approximate, and minimum-norm solutions of linear equations

AbstractThe basic solutions of the linear equations Ax = b are the solutions of subsystems corresponding to maximal nonsingular submatrices of A. The convex hull of the basic solutions is denoted by C = C(A, b). Given 1 ≤ p ≤ ∞, the lp-approximate solutions of Ax = b, denoted x{p}, are minimizers of ∥Ax − b∥p. Given M ∈ Dm, the set of positive diagonal m × m matrices, the solutions of minx ∥M(Ax − b)∥p are called scaledlp-approximate solutions. For 1 ≤ p1, p2 ≤ ∞, the minimum-lp2-norm lp1-approximate solutions are denoted x{p1}{p2}. Main results: 1.(1) If A ∈ Rm × nm, then C contains all [some] minimum lp-norm solutions, for 1 ≤ p < ∞ [p = ∞].2.(2) For general A and any 1 ≤ p1, p2 < ∞ the set C contains all x{p1}{p2}.3.(3) The set of scaled lp-approximate solutions, with M ranging over Dm, is the same for all 1 < p < ∞.4.(4) The set of scaled least-squares solutions has the same closure as the set of solutions of minx f (|Ax − b|), where f:Rm+ → R ranges over all strictly isotone functions

Characterization of the Oblique Projector U(VU)+VU(VU)^+V with Application to Constrained Least Squares

We provide a full characterization of the oblique projector $U(VU)^+V$ in the general case where the range of $U$ and the null space of $V$ are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization.Comment: v1: 6 pages v2: 7 pages. Minor changes (formatting, references) in sections 1-2. Extra statement in Theorem 3.1. Substantial revision of section 4 v3: 7 pages. A minor change (more explicit formula for \Xi) in Corollary 4.2. Changed + to direct sum at the bottom of p.5 v4: 7 pages. Removed typo in eq. (17) which was present in v2 and v

An Improved Experiment to Determine the `Past of a Particle' in the Nested Mach-Zehnder Interferometer

We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32, 050303 (2015)] to the experiment of Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] does not test the past of the photon as characterised by local weak traces. Instead of answering the questions: (i) Were the photons in A? (ii) Were the photons in B? (iii) Were the photons in C? the proposed experiment measures a degenerate operator answering the questions: (i) Were the photons in A? (ii) Were the photons in B and C together? A negative answer to the last question does not tell us if photons were present in B or C. A simple variation of the modified experiment does provide good evidence for the past of the photon in agreement with the results Danan et al. obtained.Comment: 3 pages, accepted for publication in Chinese Physics Letter

Asymptotic duality over closed convex sets

AbstractThe asymptotic duality theory of linear programming over closed convex cones [4] is extended to closed convex sets, by embedding such sets in appropriate cones. Applications to convex programming and to approximation theory are given

Integrating Groupware Activities into Workflow Management Systems

Computer supported cooperative work (CSCW) has been recognized as a crucial enabling technology for multi-user computer-based systems, particularly in cases where synchronous human-human interaction is required between geographically dispersed users. Workflow is an emerging technology that supports complex business processes in modern corporations by allowing to explicitly define the process, and by supporting its execution in a workflow management system (WFMS). Since workflow inherently involves humans carrying out parts of the process, it is only natural to explore how to synergize these two technologies. We analyze the relationships between groupware and workflow management, present our general approach to integrating synchronous groupware tools into a WFMS, and conclude with an example process that was implemented in the Oz WFMS and integrated such tools. Our main contribution lies in the integration and synchronization of individual groupware activities into modeled workflow processes, as opposed to being a built-in part of the workflow WFMS