Fock-Sobolev spaces and their Carleson measures

We consider the Fock-Sobolev space $F^{p,m}$ consisting of entire functions $f$ such that $f^{(m)}$, the $m$-th order derivative of $f$, is in the Fock space $F^p$. We show that an entire function $f$ is in $F^{p,m}$ if and only if the function $z^mf(z)$ is in $F^p$. We also characterize the Carleson measures for the spaces $F^{p,m}$, establish the boundedness of the weighted Fock projection on appropriate $L^p$ spaces, identify the Banach dual of $F^{p,m}$, and compute the complex interpolation space between two $F^{p,m}$ spaces.Comment: A revised version has been published in Journal of Functional Analysi

Learning to Skim Text

Recurrent Neural Networks are showing much promise in many sub-areas of natural language processing, ranging from document classification to machine translation to automatic question answering. Despite their promise, many recurrent models have to read the whole text word by word, making it slow to handle long documents. For example, it is difficult to use a recurrent network to read a book and answer questions about it. In this paper, we present an approach of reading text while skipping irrelevant information if needed. The underlying model is a recurrent network that learns how far to jump after reading a few words of the input text. We employ a standard policy gradient method to train the model to make discrete jumping decisions. In our benchmarks on four different tasks, including number prediction, sentiment analysis, news article classification and automatic Q\&A, our proposed model, a modified LSTM with jumping, is up to 6 times faster than the standard sequential LSTM, while maintaining the same or even better accuracy

Pulsed Laser Deposition of Functionally Gradient Diamond-Like Carbon (DLC) Films Using a Picosecond Laser

Mechanical EngineeringIn the part 1, functionally gradient diamond-like carbon (FGDLC) films are fabricated using a novel pulsed laser deposition technique to enhance adhesion strength. A 355 nm picosecond laser beam is split into two beams, and the power of each split beam is changed individually by a motorized beam attenuator as a function of time. In this way, two laser beams with customized time-varying powers are available for ablating two different target materials. Two beams are irradiated on graphite and 316L stainless steel targets, respectively, in a vacuum chamber, and the produced dissimilar plasmas are mixed in space before they are deposited on a stainless steel 316L substrate. Using this method, we have built FGDLC films with a thickness of ~510 nm, where the composition changes gradually from stainless steel to DLC in the direction of deposition. We have confirmed that FGDLC films show much higher adhesion strength than normal DLC films. In the part 2, we experiment about nine different materials when laser irradiates each material. During laser ablation process two mass removal modes exist, melting and vaporization. Evaporation and homogeneous boiling are consist of vaporization. After the boiling temperature, evaporation starts from boiling point and homogeneous boiling starts near 90% of the critical point. From this theoretical background some experiments are conducted. And also we have found many properties for each material and sorted elements, which have similar properties except critical point. From this experiment, we observed different shapes of different materials.ope

PURR: Efficiently Editing Language Model Hallucinations by Denoising Language Model Corruptions

The remarkable capabilities of large language models have been accompanied by a persistent drawback: the generation of false and unsubstantiated claims commonly known as "hallucinations". To combat this issue, recent research has introduced approaches that involve editing and attributing the outputs of language models, particularly through prompt-based editing. However, the inference cost and speed of using large language models for editing currently bottleneck prompt-based methods. These bottlenecks motivate the training of compact editors, which is challenging due to the scarcity of training data for this purpose. To overcome these challenges, we exploit the power of large language models to introduce corruptions (i.e., noise) into text and subsequently fine-tune compact editors to denoise the corruptions by incorporating relevant evidence. Our methodology is entirely unsupervised and provides us with faux hallucinations for training in any domain. Our Petite Unsupervised Research and Revision model, PURR, not only improves attribution over existing editing methods based on fine-tuning and prompting, but also achieves faster execution times by orders of magnitude

Design of exceptionally strong and conductive Cu alloys beyond the conventional speculation via the interfacial energy-controlled dispersion of gamma-Al2O3 nanoparticles

The development of Cu-based alloys with high-mechanical properties (strength, ductility) and electrical conductivity plays a key role over a wide range of industrial applications. Successful design of the materials, however, has been rare due to the improvement of mutually exclusive properties as conventionally speculated. In this paper, we demonstrate that these contradictory material properties can be improved simultaneously if the interfacial energies of heterogeneous interfaces are carefully controlled. We uniformly disperse γ-Al2O3 nanoparticles over Cu matrix, and then we controlled atomic level morphology of the interface γ-Al2O3 //Cu by adding Ti solutes. It is shown that the Ti dramatically drives the interfacial phase transformation from very irregular to homogeneous spherical morphologies resulting in substantial enhancement of the mechanical property of Cu matrix. Furthermore, the Ti removes impurities (O and Al) in the Cu matrix by forming oxides leading to recovery of the electrical conductivity of pure Cu. We validate experimental results using TEM and EDX combined with first-principles density functional theory (DFT) calculations, which all consistently poise that our materials are suitable for industrial applications.1

Mapping of Passive Turbulence Control to Flow Induced Motions of Circular Cylinders.

Passive turbulence control (PTC) in the form of selectively distributed surface roughness is applied on a rigid circular cylinder on two end-springs. The cylinder is placed horizontally with its axis perpendicular to a uniform steady flow and is allowed one degree of freedom in the vertical direction. PTC consists of two roughness strips placed parallel to the cylinder axis and symmetrically to the flow with thickness on the order of the boundary layer thickness. Broad field-of-view flow visualization is used to study the wake vortex patterns. Amplitude and frequency response are measured experimentally in the range of 3×10^4≤Re≤1.2×10^5 for broad ranges of the main PTC parameters. Lift force and force-displacement lag are calculated from the time history of the displacement. Different flow induced motion (FIM) is observed depending primarily on the circumferential location of the two strips. A PTC-to-FIM Map is developed showing six distinct FIM zones: two weak-suppression and one strong-suppression zones in vortex induced vibration, a soft galloping zone and two hard galloping zones in galloping. All zones exhibit robustness with respect to roughness strip width and thickness, and even change in strip configuration. In galloping, amplitudes of oscillation reach 2.9 times the cylinder diameter limited only by the free-surface and bottom-boundary of the experimental flow channel. Visualization shows some of the conventional, low Reynolds number patterns like 2S and 2P, as well as more complex patterns with up to ten vortices per cycle. The developed PTC-to-FIM Map is useful in suppressing FIM to prevent structural damage as well as enhancing FIM to convert more hydrokinetic energy to mechanical and subsequently to electrical energy. Based on the PTC-to-FIM Map, suppression models using PTC are designed for flow-direction dependence and independence for a single cylinder. Both the amplitude and synchronization range were reduced. Two cylinder systems were also tested for FIM interference.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/93914/1/hrpark_1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/93914/2/hrpark_2.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/93914/3/hrpark_3.pd

Extending QGrams to Estimate Selectivity of String Matching with Low Edit Distance ∗ ABSTRACT

There are many emerging database applications that require accurate selectivity estimation of approximate string matching queries. Edit distance is one of the most commonly used string similarity measures. In this paper, we study the problem of estimating selectivity of string matching with low edit distance. Our framework is based on extending q-grams with wildcards. Based on the concepts of replacement semilattice, string hierarchy and a combinatorial analysis, we develop the formulas for selectivity estimation and provide the algorithm BasicEQ. We next develop the algorithm OptEQ by enhancing BasicEQ with two novel improvements. Finally we show a comprehensive set of experiments using three benchmarks comparing OptEQ with the stateof-the-art method SEPIA. Our experimental results show that OptEQ delivers more accurate selectivity estimations. 1