Nonlinear Integral-Equation Formulation of Orthogonal Polynomials

The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P(x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial solutions is orthogonal with respect to the measure x w(x). The nonlinear integral equation can be used to specify all orthogonal polynomials in a simple and compact way. This integral equation provides a natural vehicle for extending the theory of orthogonal polynomials into the complex domain. Generalizations of the integral equation are discussed.Comment: 7 pages, result generalized to include integration in the complex domai

cis-Acting and trans-acting modulation of equine infectious anemia virus alternative RNA splicing

AbstractEquine infectious anemia virus (EIAV), a lentivirus distantly related to HIV-1, encodes regulatory proteins, EIAV Tat (ETat) and Rev (ERev), from a four-exon mRNA. Exon 3 of the tat/rev mRNA contains a 30-nucleotide purine-rich element (PRE) which binds both ERev and SF2/ASF, a member of the SR family of RNA splicing factors. To better understand the role of this element in the regulation of EIAV pre-mRNA splicing, we quantified the effects of mutation or deletion of the PRE on exon 3 splicing in vitro and on alternative splicing in vivo. We also determined the branch point elements upstream of exons 3 and 4. In vitro splicing of exon 3 to exon 4 was not affected by mutation of the PRE, and addition of purified SR proteins enhanced splicing independently of the PRE. In vitro splicing of exon 2 to exon 3 was dependent on the PRE; under conditions of excess SR proteins, either the PRE or the 5′ splice site of exon 3 was sufficient to activate splicing. We applied isoform-specific primers in real-time RT-PCR reactions to quantitatively analyze alternative splicing in cells transfected with rev-minus EIAV provirus constructs. In the context of provirus with wild-type exon 3, greater than 80% of the viral mRNAs were multiply spliced, and of these, less than 1% excluded exon 3. Deletion of the PRE resulted in a decrease in the relative amount of multiply spliced mRNA to about 40% of the total and approximately 39% of the viral mRNA excluded exon 3. Ectopic expression of ERev caused a decrease in the relative amount of multiply spliced mRNA to approximately 50% of the total and increased mRNAs that excluded exon 3 to about 4%. Over-expression of SF2/ASF in cells transfected with wild-type provirus constructs inhibited splicing but did not significantly alter exon 3 skipping

Smoothing-Based Relative Navigation and Coded Aperture Imaging

This project will develop an efficient smoothing software for incremental estimation of the relative poses and velocities between multiple, small spacecraft in a formation, and a small, long range depth sensor based on coded aperture imaging that is capable of identifying other spacecraft in the formation. The smoothing algorithm will obtain the maximum a posteriori estimate of the relative poses between the spacecraft by using all available sensor information in the spacecraft formation.This algorithm will be portable between different satellite platforms that possess different sensor suites and computational capabilities, and will be adaptable in the case that one or more satellites in the formation become inoperable. It will obtain a solution that will approach an exact solution, as opposed to one with linearization approximation that is typical of filtering algorithms. Thus, the algorithms developed and demonstrated as part of this program will enhance the applicability of small spacecraft to multi-platform operations, such as precisely aligned constellations and fractionated satellite systems

The Incremental Garbage Collection of Processes

Key Words and Phrases: garbage collection, multiprocessing systems, processor scheduling. "lazy evaluation, "eager" evaluation. CR Categories: 3.60, 3.80, 4.13, 4.22, 4.32. This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-75-C-0522. This paper was presented at the AI*PL Conference at Rochester, N.Y. in August, 1977.This paper investigates some problems associated with an argument evaluation order that we call "future" order, which is different from both call-by-name and call-by-value. In call-by-future, each formal parameter of a function is bound to a separate process (called a "future") dedicated to the evaluation of the corresponding argument. This mechanism allows the fully parallel evaluation of arguments to a function, and has been shown to augment the expressive power of a language. We discuss an approach to a problem that arises in this context: futures which were thought to be relevant when they were created become irrelevant through being ignored in the body of the expression where they were bound. The problem of irrelevant processes also appears in multiprocessing problem-solving systems which start several processors working on the same problem but with different methods, and return with the solution which finishes first. This parallel method strategy has the drawback that the processes which are investigating the losing methods must be identified, stopped, and re-assigned to more useful tasks. The solution we propose is that of garbage collection. We propose that the goal structure of the solution plan be explicitly represented in memory as part of the graph memory (like Lisp's heap) so that a garbage collection algorithm can discover which processes are performing useful work, and which can be recycled for a new task. An incremental algorithm for the unified garbage collection of storage and processes is described.MIT Artificial Intelligence Laboratory Department of Defense Advanced Research Projects Agenc

BET inhibitors induce apoptosis through a MYC independent mechanism and synergise with CDK inhibitors to kill osteosarcoma cells

Osteosarcoma (OS) survival rates have plateaued in part due to a lack of new therapeutic options. Here we demonstrate that bromodomain inhibitors (BETi), JQ1, I-BET151, I-BET762, exert potent anti-tumour activity against primary and established OS cell lines, mediated by inhibition of BRD4. Strikingly, unlike previous observations in long-term established human OS cell lines, the antiproliferative activity of JQ1 in primary OS cells was driven by the induction of apoptosis, not cell cycle arrest. In further contrast, JQ1 activity in OS was mediated independently of MYC downregulation. We identified that JQ1 suppresses the transcription factor FOSL1 by displacement of BRD4 from its locus. Loss of FOSL1 phenocopied the antiproliferative effects of JQ1, identifying FOSL1 suppression as a potential novel therapeutic approach for OS. As a monotherapy JQ1 demonstrated significant anti-tumour activity in vivo in an OS graft model. Further, combinatorial treatment approaches showed that JQ1 increased the sensitivity of OS cells to doxorubicin and induced potent synergistic activity when rationally combined with CDK inhibitors. The greater level of activity achieved with the combination of BETi with CDK inhibitors demonstrates the efficacy of this combination therapy. Taken together, our studies show that BET inhibitors are a promising new therapeutic for OS

Supplemental data for "Bear encounters with seismic stations in Alaska and northwestern Canada"

This collection is established as a supplement to a published manuscript, "Bear encounters with seismic stations in Alaska and northwestern Canada".This project was supported by the National Science Foundation, Grant EAR-1352688

Biliary reconstructive techniques and associated anatomic variants in adult living donor liver transplantations: The adult‐to‐adult living donor liver transplantation cohort study experience

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140020/1/lt24872.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/140020/2/lt24872_am.pd

RR Lyrae variables in M32 and the disk of M31

We observed two fields near M32 with the Advanced Camera for Surveys/High Resolution Channel (ACS/HRC) on board the Hubble Space Telescope (HST). The main field, F1, is 1.8 arcmin from the center of M32; the second field, F2, constrains the M31 background, and is 5.4 arcmin distant. Each field was observed for 16-orbits in each of the F435W (narrow B) and F555W (narrow V) filters. The duration of the observations allowed RR Lyrae stars and other short-period variables to be detected. A population of RR Lyrae stars determined to belong to M32 would prove the existence of an ancient population in that galaxy, a subject of some debate. We detected 17 RR Lyrae variables in F1 and 14 in F2. A 1-sigma upper limit of 6 RR Lyrae variables belonging to M32 is inferred from these two fields alone. Use of our two ACS/WFC parallel fields provides better constraints on the M31 background, however, and implies that $7_{-3}^{+4}$ (68 % confidence interval) RR Lyrae variables in F1 belong to M32. We have therefore found evidence for an ancient population in M32. It seems to be nearly indistinguishable from the ancient population of M31. The RR Lyrae stars in the F1 and F2 fields have indistinguishable mean V-band magnitudes, mean periods, distributions in the Bailey diagram and ratios of RRc to RR(tot) types. However, the color distributions in the two fields are different, with a population of red RRab variables in F1 not seen in F2. We suggest that these might be identified with the detected M32 RR Lyrae population, but the small number of stars rules out a definitive claim.Comment: 19 pages, 18 figures, accepted Ap

L-Edge Spectroscopy of Dilute, Radiation-Sensitive Systems Using a Transition-Edge-Sensor Array

We present X-ray absorption spectroscopy and resonant inelastic X-ray scattering (RIXS) measurements on the iron L-edge of 0.5 mM aqueous ferricyanide. These measurements demonstrate the ability of high-throughput transition-edge-sensor (TES) spectrometers to access the rich soft X-ray (100-2000eV) spectroscopy regime for dilute and radiation-sensitive samples. Our low-concentration data are in agreement with high-concentration measurements recorded by conventional grating-based spectrometers. These results show that soft X-ray RIXS spectroscopy acquired by high-throughput TES spectrometers can be used to study the local electronic structure of dilute metal-centered complexes relevant to biology, chemistry and catalysis. In particular, TES spectrometers have a unique ability to characterize frozen solutions of radiation- and temperature-sensitive samples.Comment: 19 pages, 4 figure