Kodaira Dimension of Subvarieties

In this article we study how the birational geometry of a normal projective variety $X$ is influenced by a normal subvariety $A \subset X.$ One of the most basic examples in this context is provided by the following situation. Let $f:X\to Y$ be a surjective holomorphic map with connected fibers between compact connected complex manifolds. It is well known that given a general fiber $A$ of $f$ we have $$\kappa(X)\le \kappa(A)+\dim Y.$$ This article grew out of the realization that this result should be true with $\dim Y$ replaced by the codimension \cod_X A for a pair $(X,A)$ consisting of a normal subvariety $A$ of a compact normal variety $X$ under weak semipositivity conditions on the normal sheaf of $A$ and the weak singularity condition \cod_A (A\cap\sing X)\ge 2. We shall now state our main results in the special case of a submanifold $A$ in a projective manifold $X$ and we also simplify the semipositivity notion

Finite-Difference and Pseudospectral Time-Domain Methods Applied to Backwards-Wave Metamaterials

Backwards-wave (BW) materials that have simultaneously negative real parts of their electric permittivity and magnetic permeability can support waves where phase and power propagation occur in opposite directions. These materials were predicted to have many unusual electromagnetic properties, among them amplification of the near-field of a point source, which could lead to the perfect reconstruction of the source field in an image [J. Pendry, Phys. Rev. Lett. \textbf{85}, 3966 (2000)]. Often systems containing BW materials are simulated using the finite-difference time-domain technique. We show that this technique suffers from a numerical artifact due to its staggered grid that makes its use in simulations involving BW materials problematic. The pseudospectral time-domain technique, on the other hand, uses a collocated grid and is free of this artifact. It is also shown that when modeling the dispersive BW material, the linear frequency approximation method introduces error that affects the frequency of vanishing reflection, while the auxiliary differential equation, the Z transform, and the bilinear frequency approximation method produce vanishing reflection at the correct frequency. The case of vanishing reflection is of particular interest for field reconstruction in imaging applications.Comment: 9 pages, 8 figures, accepted by IEEE Transactions on Antennas and Propagatio

A Study on the Efficacy of Sentiment Analysis in Author Attribution

The field of authorship attribution seeks to characterize an author’s writing style well enough to determine whether he or she has written a text of interest. One subfield of authorship attribution, stylometry, seeks to find the necessary literary attributes to quantify an author’s writing style. The research presented here sought to determine the efficacy of sentiment analysis as a new stylometric feature, by comparing its performance in attributing authorship against the performance of traditional stylometric features. Experimentation, with a corpus of sci-fi texts, found sentiment analysis to have a much lower performance in assigning authorship than the traditional stylometric features

COMPARISON OF MECHANICAL vs. MANUAL MANIPULATION METHODS FOR LOW BACK PAIN

ABSTRACT:Purpose and Study Design: Prospective cohort study to explore the clinical treatment effect of mechanical vs. manual manipulation for acute low back pain.Methods: 92 patients with a history of acute low back pain were recruited from three private chiropractic offices. Two of these offices utilized manual lumbar manipulation and one used mechanical instrument manipulation (Activator) as their primary modes of treatment. The chiropractors used a "treatment as usual" protocol with the participants for a maximum of eight visits or four weeks, which ever occurred first. Primary and secondary outcome measures were the differences in pain and Oswestry scores from baseline to four weeks, respectively. Results: Socio-demographic characteristics of the two cohorts at baseline were not found to show any significant differences between the groups except for age. The Activator cohort had a significantly higher utilization of adjunctive modalities and x-rays, with a mean number of office visits about twice that of the manual manipulation cohort at four weeks. The pain scores decreased in both groups with the manual manipulation group showing a slightly greater amount of pain reduction at four weeks, but this difference did not reach statistical significance after controlling for baseline pain. The manual manipulation group also showed a slightly greater reduction in Oswestry scores from baseline to four-weeks, but this difference was not statistically significant after adjusting for baseline Oswestry score.Conclusions: In this observational study of treatment-as-usual there was no significantly greater reduction in pain scores or Oswestry scores between the manipulation and Activator groups at four weeks. There were many differences between the Activator and manual manipulation groups with respect to treatment beliefs and expectations, modality usage, and frequency/duration of care, which are potential sources of confounding in the interpretation of these results. This study provides important pilot data and research issues for the design of a future randomized clinical trial that can control for these issues of confounding variables

Projections from Subvarieties

Let $X\subset P^N$ be an n-dimensional connected projective submanifold of projective space. Let $p : P^N\to P^{N-q-1}$ denote the projection from a linear $P^q\subset P^N$. Assuming that $X\not\subset P^q$ we have the induced rational mapping $\psi:=p_X: X\to P^{N-q-1}$. This article started as an attempt to understand the structure of this mapping when $\psi$ has a lower dimensional image. In this case of necessity we have $Y := X\cap P^q$ is nonempty. We have in this article studied a closely related question, which includes many special cases including the case when the center of the projection \pn q is contained in $X$. PROBLEM. Let $Y$ be a proper connected k-dimensional projective submanifold of an $n$-dimensional projective manifold $X$. Assume that $k>0$. Let $L$ be a very ample line bundle on $X$ such that $L\otimes I_Y$ is spanned by global sections, where $I_Y$ denotes the ideal sheaf of $Y$ in $X$. Describe the structure of $(X,Y,L)$ under the additional assumption that the image of $X$ under the mapping $\psi$ associated to $| L\otimes I_Y|$ is lower dimensional

Adiabatic Preparation of a Heisenberg Antiferromagnet Using an Optical Superlattice

We analyze the possibility to prepare a Heisenberg antiferromagnet with cold fermions in optical lattices, starting from a band insulator and adiabatically changing the lattice potential. The numerical simulation of the dynamics in 1D allows us to identify the conditions for success, and to study the influence that the presence of holes in the initial state may have on the protocol. We also extend our results to two-dimensional systems.Comment: 5 pages, 4 figures + Supplementary Material (5 pages, 6 figures), published versio

The Collapse of the Wien Tail in the Coldest Brown Dwarf? Hubble Space Telescope Near-Infrared Photometry of WISE J085510.83-071442.5

We present Hubble Space Telescope (HST) near-infrared photometry of the coldest known brown dwarf, WISE J085510.83$-$071442.5 (WISE 0855$-$0714). WISE 0855$-$0714 was observed with the Wide Field Camera 3 (WFC3) aboard HST using the F105W, F125W, and F160W filters, which approximate the $Y$, $J$, and $H$ near-infrared bands. WISE 0855$-$0714 is undetected at F105W with a corresponding 2$\sigma$ magnitude limit of $\sim$26.9. We marginally detect WISE 0855$-$0714 in the F125W images (S/N $\sim$4), with a measured magnitude of 26.41 $\pm$ 0.27, more than a magnitude fainter than the $J-$band magnitude reported by Faherty and coworkers. WISE J0855$-$0714 is clearly detected in the F160W band, with a magnitude of 23.90 $\pm$ 0.02, the first secure detection of WISE 0855$-$0714 in the near-infrared. Based on these data, we find that WISE 0855$-$0714 has extremely red F105W$-$F125W and F125W$-$F160W colors relative to other known Y dwarfs. We find that when compared to the models of Saumon et al. and Morley et al., the F105W$-$F125W and F125W$-$F160W colors of WISE 0855$-$0714 cannot be accounted for simultaneously. These colors likely indicate that we are seeing the collapse of flux on the Wien tail for this extremely cold object.Comment: Accepted for publication in ApJ Letter