Small models, large cardinals, and induced ideals

: The field of nanosensors has been gaining a lot of attention due to its properties such as mechanical and electrical ever since its first discovery by Dr. Wolter and first mechanical sensor in 1994. The rapidly growing demand of nanosensors has become profitable for a multidisciplinary approach in designing and fabrication of materials and strategies for potential applications. Frequent stimulating advancements are being suggested and established in recent years and thus heading towards multiple applications including food safety, healthcare, environmental monitoring, and biomedical research. Nanofabrication being an efficient method has been used in different industries like medical pharmaceutical for their complex functional geometry at a lower scale. These nanofabrications apply through different methods. There are five most commonly known methods which are frequently used, including top-down lithography, molecular self-assembly, bottom-up assembly, heat and pull method for fabrication of biosensors, etching for fabrication of nanosensors etc. Nanofabrication help at the nanoscale to design and work with small models. But these models due to their small size and being sensitive need more care for use as well as more training and experience to do work with. All methods used for nanofabrication are good and helpful. But more preferred is molecular self-assembly as it is helpful in mass production. Nanofabrication has become an emerging and developing field and it assumed that in near future our world is known by the new devices of nanofabrication.

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Efficient Binarized Convolutional Layers for Visual Inspection Applications on Resource-Limited FPGAs and ASICs

Electronics ◽

10.3390/electronics10131511 ◽

2021 ◽

Vol 10 (13) ◽

pp. 1511

Author(s):

Taylor Simons ◽

Dah-Jye Lee

Keyword(s):

Neural Networks ◽

Visual Inspection ◽

Deep Neural Networks ◽

Computational Cost ◽

Quality Inspection ◽

Agricultural Produce ◽

Resource Limited ◽

Inspection Tasks ◽

Computational Resources ◽

Small Models

There has been a recent surge in publications related to binarized neural networks (BNNs), which use binary values to represent both the weights and activations in deep neural networks (DNNs). Due to the bitwise nature of BNNs, there have been many efforts to implement BNNs on ASICs and FPGAs. While BNNs are excellent candidates for these kinds of resource-limited systems, most implementations still require very large FPGAs or CPU-FPGA co-processing systems. Our work focuses on reducing the computational cost of BNNs even further, making them more efficient to implement on FPGAs. We target embedded visual inspection tasks, like quality inspection sorting on manufactured parts and agricultural produce sorting. We propose a new binarized convolutional layer, called the neural jet features layer, that learns well-known classic computer vision kernels that are efficient to calculate as a group. We show that on visual inspection tasks, neural jet features perform comparably to standard BNN convolutional layers while using less computational resources. We also show that neural jet features tend to be more stable than BNN convolution layers when training small models.

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Choosing between identification schemes in noisy-news models

Studies in Nonlinear Dynamics & Econometrics ◽

10.1515/snde-2020-0016 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Joshua C. C. Chan ◽

Eric Eisenstat ◽

Gary Koop

Keyword(s):

Bayesian Methods ◽

Moving Average ◽

Autoregressive Moving Average ◽

Structural Shocks ◽

Vector Autoregressive ◽

Identification Scheme ◽

Identification Schemes ◽

The One ◽

Small Models ◽

Structural Vector

AbstractThis paper is about identifying structural shocks in noisy-news models using structural vector autoregressive moving average (SVARMA) models. We develop a new identification scheme and efficient Bayesian methods for estimating the resulting SVARMA. We discuss how our identification scheme differs from the one which is used in existing theoretical and empirical models. Our main contributions lie in the development of methods for choosing between identification schemes. We estimate specifications with up to 20 variables using US macroeconomic data. We find that our identification scheme is preferred by the data, particularly as the size of the system is increased and that noise shocks generally play a negligible role. However, small models may overstate the importance of noise shocks.

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Two Applications of Inner Model Theory to the Study of Sets

Bulletin of Symbolic Logic ◽

10.2307/421049 ◽

1996 ◽

Vol 2 (1) ◽

pp. 94-107 ◽

Cited By ~ 3

Author(s):

Greg Hjorth

Keyword(s):

Los Angeles ◽

Set Theory ◽

Model Theory ◽

Large Cardinals ◽

Descriptive Set Theory ◽

Inner Model Theory ◽

Regular Cardinals ◽

Inner Model ◽

Definable Sets ◽

Descriptive Set

§0. Preface. There has been an expectation that the endgame of the more tenacious problems raised by the Los Angeles ‘cabal’ school of descriptive set theory in the 1970's should ultimately be played out with the use of inner model theory. Questions phrased in the language of descriptive set theory, where both the conclusions and the assumptions are couched in terms that only mention simply definable sets of reals, and which have proved resistant to purely descriptive set theoretic arguments, may at last find their solution through the connection between determinacy and large cardinals.Perhaps the most striking example was given by [24], where the core model theory was used to analyze the structure of HOD and then show that all regular cardinals below ΘL(ℝ) are measurable. John Steel's analysis also settled a number of structural questions regarding HODL(ℝ), such as GCH.Another illustration is provided by [21]. There an application of large cardinals and inner model theory is used to generalize the Harrington-Martin theorem that determinacy implies )determinacy.However, it is harder to find examples of theorems regarding the structure of the projective sets whose only known proof from determinacy assumptions uses the link between determinacy and large cardinals. We may equivalently ask whether there are second order statements of number theory that cannot be proved under PD–the axiom of projective determinacy–without appealing to the large cardinal consequences of the PD, such as the existence of certain kinds of inner models that contain given types of large cardinals.

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Large cardinals and gap-1 morasses

Annals of Pure and Applied Logic ◽

10.1016/j.apal.2008.10.007 ◽

2009 ◽

Vol 159 (1-2) ◽

pp. 71-99 ◽

Cited By ~ 7

Author(s):

Andrew D. Brooke-Taylor ◽

Sy-David Friedman

Keyword(s):

Large Cardinals

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Co-stationarity of the ground model

Journal of Symbolic Logic ◽

10.2178/jsl/1154698589 ◽

2006 ◽

Vol 71 (3) ◽

pp. 1029-1043 ◽

Cited By ~ 3

Author(s):

Natasha Dobrinen ◽

Sy-David Friedman

Keyword(s):

Large Cardinals ◽

Partial Ordering ◽

Proper Class ◽

Ground Model ◽

Covering Theorem ◽

Uncountable Cardinal ◽

Cohen Forcing ◽

Measurable Cardinals

AbstractThis paper investigates when it is possible for a partial ordering ℙ to force Pk(Λ)\V to be stationary in Vℙ. It follows from a result of Gitik that whenever ℙ adds a new real, then Pk(Λ)\V is stationary in Vℙ for each regular uncountable cardinal κ in Vℙ and all cardinals λ ≥ κ in Vℙ [4], However, a covering theorem of Magidor implies that when no new ω-sequences are added, large cardinals become necessary [7]. The following is equiconsistent with a proper class of ω1-Erdős cardinals: If ℙ is ℵ1-Cohen forcing, then Pk(Λ)\V is stationary in Vℙ, for all regular κ ≥ ℵ2and all λ ≩ κ. The following is equiconsistent with an ω1-Erdős cardinal: If ℙ is ℵ1-Cohen forcing, then is stationary in Vℙ. The following is equiconsistent with κ measurable cardinals: If ℙ is κ-Cohen forcing, then is stationary in Vℙ.

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