Optimizing condition numbers

In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite $n\times n$ matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function. We prove that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program. This asymptotic analysis provides a valuable tool for designing an implementable algorithm for solving the problem of minimizing condition numbers

Wigner crystalization about ν\nu=3

We measure a resonance in the frequency dependence of the real diagonal conductivity, Re[$\sigma_{xx}$], near integer filling factor, $\nu=3$. This resonance depends strongly on $\nu$, with peak frequency $f_{pk} \approx 1.7$ GHz at $\nu=3.04$ or 2.92 close to integer $\nu$, but $f_{pk} \approx$ 600 MHz at $\nu=3.19$ or 2.82, the extremes of where the resonance is visible. The dependence of $f_{pk}$ upon $n^*$, the density of electrons in the partially filled level, is discussed and compared with similar measurments by Chen {\it et al.}\cite{yong} about $\nu=1$ and 2. We interpret the resonance as due to a pinned Wigner crystal phase with density $n^*$ about the $\nu=3$ state.Comment: for proceedings of EP2DS-15 (Nara) to appear in Physica

Engineering spin squeezing in a 3D optical lattice with interacting spin-orbit-coupled fermions

One of the most important tasks in modern quantum science is to coherently control and entangle many-body systems, and to subsequently use these systems to realize powerful quantum technologies such as quantum-enhanced sensors. However, many-body entangled states are difficult to prepare and preserve since internal dynamics and external noise rapidly degrade any useful entanglement. Here, we introduce a protocol that counterintuitively exploits inhomogeneities, a typical source of dephasing in a many-body system, in combination with interactions to generate metrologically useful and robust many-body entangled states. Motivated by current limitations in state-of-the-art three-dimensional (3D) optical lattice clocks (OLCs) operating at quantum degeneracy, we use local interactions in a Hubbard model with spin-orbit coupling to achieve a spin-locking effect. In addition to prolonging inter-particle spin coherence, spin-locking transforms the dephasing effect of spin-orbit coupling into a collective spin-squeezing process that can be further enhanced by applying a modulated drive. Our protocol is fully compatible with state-of-the-art 3D OLC interrogation schemes and may be used to improve their sensitivity, which is currently limited by the intrinsic quantum noise of independent atoms. We demonstrate that even with realistic experimental imperfections, our protocol may generate $\sim10$--$14$ dB of spin squeezing in $\sim1$ second with $\sim10^2$--$10^4$ atoms. This capability allows OLCs to enter a new era of quantum enhanced sensing using correlated quantum states of driven non-equilibrium systems.Comment: 20 pages, 12 figure

AC Magnetotransport in Reentrant Insulating Phases of Two-dimensional Electrons near 1/5 and 1/3 Landau fillings

We have measured high frequency magnetotransport of a high quality two-dimensional electron system (2DES) near the reentrant insulating phase (RIP) at Landau fillings ($\nu$) between 1/5 and 2/9. The magneto\textit{conductivity} in the RIP has resonant behavior around 150 MHz, showing a \textit{peak} at $\nu$$\sim$0.21. Our data support the interpretation of the RIP as due to some pinned electron solid. We have also investigated a narrowly confined 2DES recently found to have a RIP at 1/3$<$$\nu$$<$1/2 and we have revealed features, not seen in DC transport, that suggest some intriguing interplay between the 1/3 FQHE and RIP.Comment: 4 pages and 1 figure (amsart format), 16th International Conference on High Magnetic Fields in Semiconductor Physics (SemiMag16), August 2-6, 2004, Tallahasse

Microwave resonances of the bubble phases in 1/4 and 3/4 filled higher Landau levels

We have measured the diagonal conductivity in the microwave regime of an ultrahigh mobility two dimensional electron system. We find a sharp resonance in Re[sigma_{xx}] versus frequency when nu > 4 and the partial filling of the highest Landau level, nu^*, is ~ 1/4 or 3/4 and temperatures < 0.1 K. The resonance appears for a range of nu^* from 0.20 to 0.37 and again from 0.62 to 0.82. the peak frequency, f_{pk} changes from ~ 500 to ~ 150 as nu^* = 1/2 is approached. This range of f_{pk} shows no dependence on nu where the resonance is observed. The quality factor, Q, of the resonance is maximum at ~ nu^* = 0.25 and 0.74. We interpret the resonance as due to a pinning mode of the bubble phase crystal.Comment: revtex 4, 3 figures, minor corrections made. Accepted by pr

Evidence for Two Different Solid Phases of Two Dimensional Electrons in High Magnetic Fields

We have performed RF spectroscopy on very high quality two dimensional electron systems in the high magnetic field insulating phase, usually associated with a Wigner solid (WS) pinned by disorder. We have found two different resonances in the frequency dependent real diagonal conductivity spectrum and we interpret them as coming from \textit{two} different pinned solid phases (labeled as "WS-A" and "WS-B"). The resonance of WS-A is observable for Landau level filling $\nu$$<$2/9 (but absent around the $\nu$=1/5 fractional quantum Hall effect (FQHE)); it then \textit{crosses over} for $\nu$$<$0.18 to the different WS-B resonance which dominates the spectrum at $\nu$$<$0.125. Moreover, WS-A resonance is found to show dispersion with respect to the size of transmission line, indicating that WS-A has a large correlation length (exceeding $\sim$100 $\mu$m); in contrast no such behavior is found for WS-B. We suggest that quantum correlations such as those responsible for FQHE may play an important role in giving rise to such different solids.Comment: 4 pages, 3 figure

Development of Functional Microfold (M) Cells from Intestinal Stem Cells in Primary Human Enteroids.

Background &amp; aimsIntestinal microfold (M) cells are specialized epithelial cells that act as gatekeepers of luminal antigens in the intestinal tract. They play a critical role in the intestinal mucosal immune response through transport of viruses, bacteria and other particles and antigens across the epithelium to immune cells within Peyer's patch regions and other mucosal sites. Recent studies in mice have demonstrated that M cells are generated from Lgr5+ intestinal stem cells (ISCs), and that infection with Salmonella enterica serovar Typhimurium increases M cell formation. However, it is not known whether and how these findings apply to primary human small intestinal epithelium propagated in an in vitro setting.MethodsHuman intestinal crypts were grown as monolayers with growth factors and treated with recombinant RANKL, and assessed for mRNA transcripts, immunofluorescence and uptake of microparticles and S. Typhimurium.ResultsFunctional M cells were generated by short-term culture of freshly isolated human intestinal crypts in a dose- and time-dependent fashion. RANKL stimulation of the monolayer cultures caused dramatic induction of the M cell-specific markers, SPIB, and Glycoprotein-2 (GP2) in a process primed by canonical WNT signaling. Confocal microscopy demonstrated a pseudopod phenotype of GP2-positive M cells that preferentially take up microparticles. Furthermore, infection of the M cell-enriched cultures with the M cell-tropic enteric pathogen, S. Typhimurium, led to preferential association of the bacteria with M cells, particularly at lower inoculum sizes. Larger inocula caused rapid induction of M cells.ConclusionsHuman intestinal crypts containing ISCs can be cultured and differentiate into an epithelial layer with functional M cells with characteristic morphological and functional properties. This study is the first to demonstrate that M cells can be induced to form from primary human intestinal epithelium, and that S. Typhimurium preferentially infect these cells in an in vitro setting. We anticipate that this model can be used to generate large numbers of M cells for further functional studies of these key cells of intestinal immune induction and their impact on controlling enteric pathogens and the intestinal microbiome

Dynamics of disordered quantum Hall crystals

Charge density waves are thought to be common in two-dimensional electron systems in quantizing magnetic fields. Such phases are formed by the quasiparticles of the topmost occupied Landau level when it is partially filled. One class of charge density wave phases can be described as electron solids. In weak magnetic fields (at high Landau levels) solids with many particles per unit cell - bubble phases - predominate. In strong magnetic fields (at the lowest Landau level) only crystals with one particle per unit cell - Wigner crystals - can form. Experimental identification of these phases is facilitated by the fact that even a weak disorder influences their dc and ac magnetotransport in a very specific way. In the ac domain, a range of frequencies appears where the electromagnetic response is dominated by magnetophonon collective modes. The effect of disorder is to localize the collective modes and to create an inhomogeneously broadened absorption line, the pinning mode. In recent microwave experiments pinning modes have been discovered both at the lowest and at high Landau levels. We present the theory of the pinning mode for a classical two-dimensional electron crystal collectively pinned by weak impurities. We show that long-range Coulomb interaction causes a dramatic line narrowing, in qualitative agreement with the experiments.Comment: 6 pages, 3 figures. To be presented at EP2DS-15, Nara, Japan. One typo correcte