Fertilization and early embryology: Use of lasers in assisted fertilization and hatching

The erbium-yttrium-aluminium-garnet (Er: YAG) laser has been applied to micromanipulation in humans. It was used in the fertilization process for both subzonal insemination (SUZI) and for partial zona dissection (PZD). Laser-assisted micromanipulation achieved significantly higher fertilization rates (34.8%) when compared to mechanical SUZI (16.1%), but use of the laser did not improve the PZD results (laser 14.8% versus mechanical 14%). The Er: YAG laser was used to assist hatching. In the mouse it significantly improved the hatching rate (80 versus 29.3%) 110 h after administration of human chorionic gonadotrophin. This technique was applied in two different centres to patients with previous in-vitro fertilization (IVF) failures. The implantation rate per embryo (14.4% laser-assisted hatching versus 6% control group) and the pregnancy rate per transfer (40 versus 16.2%) were improve

An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

MUBs inequivalence and affine planes

There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is standard that there is a superficial similarity between complete sets of MUBs and finite affine planes, there is an intimate relationship between these large families and affine planes. This note briefly summarizes "old" results that do not appear to be well-known concerning known families of complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical Physics 53, 032204 (2012) except for format changes due to the journal's style policie

Symmetric Informationally Complete Quantum Measurements

We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d. SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions two, three, and four. We further conjecture that a particular kind of group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.Comment: 8 page

Restricted Isometries for Partial Random Circulant Matrices

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisition process that proceeds by convolution with a random pulse followed by (nonrandom) subsampling. At present, the theoretical analysis of this measurement technique is lacking. This paper demonstrates that the $s$th order restricted isometry constant is small when the number $m$ of samples satisfies $m \gtrsim (s \log n)^{3/2}$, where $n$ is the length of the pulse. This bound improves on previous estimates, which exhibit quadratic scaling

The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

Observation of Hadronic W Decays in t-tbar Events with the Collider Detector at Fermilab

We observe hadronic W decays in t-tbar -> W (-> l nu) + >= 4 jet events using a 109 pb-1 data sample of p-pbar collisions at sqrt{s} = 1.8 TeV collected with the Collider Detector at Fermilab (CDF). A peak in the dijet invariant mass distribution is obtained that is consistent with W decay and inconsistent with the background prediction by 3.3 standard deviations. From this peak we measure the W mass to be 77.2 +- 4.6 (stat+syst) GeV/c^2. This result demonstrates the presence of two W bosons in t-tbar candidates in the W (-> l nu) + >= 4 jet channel.Comment: 20 pages, 4 figures, submitted to PR

Search for charged Higgs decays of the top quark using hadronic tau decays

We present the result of a search for charged Higgs decays of the top quark, produced in $p\bar{p}$ collisions at $\surd s =$ 1.8 TeV. When the charged Higgs is heavy and decays to a tau lepton, which subsequently decays hadronically, the resulting events have a unique signature: large missing transverse energy and the low-charged-multiplicity tau. Data collected in the period 1992-1993 at the Collider Detector at Fermilab, corresponding to 18.7$\pm$0.7~pb$^{-1}$, exclude new regions of combined top quark and charged Higgs mass, in extensions to the standard model with two Higgs doublets.Comment: uuencoded, gzipped tar file of LaTeX and 6 Postscript figures; 11 pp; submitted to Phys. Rev.