Sleeping beauty overture

Thesis (M.A.)--Boston Universit

Evidence for String Substructure

We argue that the behavior of string theory at high temperature and high longitudinal boosts, combined with the emergence of p-branes as necessary ingredients in various string dualities, point to a possible reformulation of strings, as well as p-branes, as composites of bits. We review the string-bit models, and suggest generalizations to incorporate p-branes.Comment: Latex file, 21 pages, 11 postscript figure

Strong subgroup chains and the Baer-Specker group

Examples are given of non-elementary properties that are preserved under C-filtrations for various classes C of Abelian groups. The Baer-Specker group is never the union of a chain of proper subgroups with cotorsionfree quotients. Cotorsion-free groups form an abstract elementary class (AEC). The Kaplansky invariants of the Baer-Specker group are used to determine the AECs defined by the perps of the Baer-Specker quotient groups that are obtained by factoring the Baer-Specker group B of a ZFC extension by the Baer-Specker group A of the ground model, under various hypotheses, yielding information about its stability spectrum.Comment: 12 page

Ptychographic reconstruction algorithm for frequency resolved optical gating: super-resolution and supreme robustness

Frequency-resolved optical gating (FROG) is probably the most popular technique for complete characterization of ultrashort laser pulses. In FROG, a reconstruction algorithm retrieves the pulse from a measured spectrogram, yet current FROG reconstruction algorithms require and exhibit several restricting features that weaken FROG performances. For example, the delay step must correspond to the spectral bandwidth measured with large enough SNR a condition that limits the temporal resolution of the reconstructed pulse, obscures measurements of weak broadband pulses, and makes measurement of broadband mid-IR pulses hard and slow because the spectrograms become huge. We develop a new approach for FROG reconstruction, based on ptychography (a scanning coherent diffraction imaging technique), that removes many of the algorithmic restrictions. The ptychographic reconstruction algorithm is significantly faster and more robust to noise than current FROG algorithms, which are based on generalized projections (GP). We demonstrate, numerically and experimentally, that ptychographic reconstruction works well with very partial spectrograms, e. g. spectrograms with reduced number of measured delays and spectrograms that have been substantially spectrally filtered. In addition, we implement the ptychogrpahic approach to blind second harmonic generation (SHG) FROG and demonstrate robust and complete characterization of two unknown pulses from a single measured spectrogram and power spectrum of only one of the pulses. We believe that the ptychograpy-based approach will become the standard reconstruction procedure in FROG and related diagnostics methods, allowing successful reconstructions from so far unreconstructable spectrograms.Comment: 11 pages, 9 figure

Multiple Derived Lagrangian Intersections

We give a new way to produce examples of Lagrangians in shifted symplectic derived stacks, based on multiple intersections. Specifically, we show that an m-fold fiber product of Lagrangians in a shifted symplectic derived stack its itself Lagrangian in a certain cyclic product of pairwise homotopy fiber products of the Lagrangians

Confronting the Evolving Safety and Security Challenge at Colleges and Universities

[Excerpt] “Colleges and universities have long been scrutinized and confronted with lawsuits regarding safety and security measures designed and implemented to protect students and prevent dangerous incidents on campus. Under the doctrine of in loco parentis, college administrators assume responsibility for the physical safety and well-being of students as they matriculate through their academic programs. However, in recent decades, the realization that university communities are not immune to criminal activity has led to federal legislation and judicial opinions that have attempted to identify what legal duty colleges and universities have to prevent security breaches. Moreover, college and university administrators have looked to the courts and legal counsel to determine an institution’s exposure to legal liability and strategies that might be used to minimize such exposure. This charge has been, and remains, a daunting challenge for the higher education community. This Article reviews recent cases regarding the legal duty American colleges and universities have to protect the student community from harm or injury resulting from safety or security breaches. Moreover, this Article identifies legal challenges colleges and universities may face in response to campus surveillance efforts and negligence hiring and retention allegations. Finally, the Article offers some insight intended to advance the legal community’s efforts to counsel and advise college and university administrators regarding the issue of campus safety.

Approximating the Diameter of Planar Graphs in Near Linear Time

We present a $(1+\epsilon)$-approximation algorithm running in $O(f(\epsilon)\cdot n \log^4 n)$ time for finding the diameter of an undirected planar graph with non-negative edge lengths