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### Limit computable integer parts

Paola D'Aquino, Julia Knight, Karen Lange
2011 Archive for Mathematical Logic
We would like to know whether there is a much simpler procedure, yielding an integer part that is ∆ 0 2 (R)-limit computable relative to R.  ...  We show that for each n ∈ ω, there is a computable real closed field with no n-c.e. integer part. In fact, there is a computable real closed field with no n-c.e. integer part for any n.  ...  Computable real closed fields with no n-c.e. integer part We do not know whether ∆ 0 2 is sufficient to calculate an integer part for a computable real closed field.  ...

### Erratum to: Limit computable integer parts

Paola D'Aquino, Julia Knight, Karen Lange
2015 Archive for Mathematical Logic
However, by Theorem 3.5, a maximal Z ring for R may not be an integer part for R.  ...  Thus, finding an affirmative answer to Question 1 would not directly provide a ∆ 0 2 (R)-integer part for R, the original motivating problem for this work.  ...

### Basic Properties, Limit & Derivative Of The Greatest Integer Function

Shwaish TZ
2016 Zenodo
This paper discusses the definition and various notations used for the greatest integer and fractional part functions simply.  ...  Limit of the function is also introduced here. The derivative of the function is computed using definition which is also related to the limit and the continuity of the function.  ...  The derivative of the function is computed using definition which is also related to the limit and the continuity of the function.  ...

### A fixed-point implementation of tone mapping operation for HDR images expressed in floating-point format

Toshiyuki Dobashi, Atsushi Tashiro, Masahiro Iwahashi, Hitoshi Kiya
2014 APSIPA Transactions on Signal and Information Processing
To reduce the resources, an integer TMO which treats a floating-point number as two 8-bit integer numbers was proposed. However, this method has the limitation of available input HDR image formats.  ...  The proposed method introduces an intermediate format to relieve the limitation of input formats, and expands the integer TMO for the intermediate format.  ...  The integer TMO [21, 22] implements a global TMO with integer data and fixed-point arithmetic. Using integer data and fixed-point arithmetic reduces the memory cost and the computational cost.  ...

### [Invited Paper] An Efficient Unified-Tone-Mapping Operation for HDR Images with Various Formats

Hitoshi Kiya, Toshiyuki Dobashi
2016 ITE Transactions on Media Technology and Applications
By using both integer data and fixed-point arithmetic, the method reduces not only the memory cost but also the computational cost.  ...  However, this method has a limitation of available input HDR image formats.  ...  Moreover, using 8-bit integer data facilitates executing calculations with fixed-point arithmetic because it eases the limitation of the bit length.  ...

### Page 329 of Educational and Psychological Measurement Vol. 69, Issue 2 [page]

2009 Educational and Psychological Measurement
Part 1, with a time limit of 2 min, measures facility with integer computations (25 items); Part 2, with a time limit of 4 min, measures facility with decimal computations (25 items); and Part 3, also  ...  found only in Part 2.  ...

### Efficient Fast 1-D 8$\,\times\,$8 Inverse Integer Transform for VC-1 Application

Chih-Peng Fan, Guo-An Su
2009 IEEE transactions on circuits and systems for video technology (Print)
With the low complexity, the proposed fast algorithm is suitable to accelerate the video coding computations. Index Terms-8 8 inverse integer transform, fast algorithm, video coding, WMV9/VC-1.  ...  Therefore, the computational complexities of the proposed fast inverse transform are smaller than those of the direct method and the previous fast method.  ...  ACKNOWLEDGMENT This work is supported in part by the National Science Council, Taiwan, R.O.C., under Grant NSC96-2220-E-005-006.  ...

### Integer partitions and exclusion statistics: limit shapes and the largest parts of Young diagrams

Alain Comtet, Satya N Majumdar, Stéphane Ouvry, Sanjib Sabhapandit
2007 Journal of Statistical Mechanics: Theory and Experiment
We compute the limit shapes of the Young diagrams of the minimal difference p partitions and provide a simple physical interpretation for the limit shapes.  ...  This Gumbel statistics for the largest part remains unchanged even for general partitions of the form E=∑_i n_i i^1/ν with ν>0 where n_i is the number of times the part i appears.  ...  The distribution of the number of parts for p = 0 was computed by Erdös and Lehner  and in the appropriate scaling limit it has a Gumbel form.  ...

### The Size of the Largest Part of Random Weighted Partitions of Large Integers

LJUBEN MUTAFCHIEV
2013 Combinatorics, probability & computing
Assuming that a weighted partition of n is selected uniformly at random from the set of all such partitions, we study the limiting distribution of the largest part size X n as n → ∞.  ...  A weighted partition of the positive integer n is a multiset of size n whose decomposition into a union of disjoint components (parts) satisfies the following condition: for a given sequence of non-negative  ...

### Evolutionary based moving target cyber defense

David J. John, Robert W. Smith, William H. Turkett, Daniel A. Cañas, Errin W. Fulp
2014 Proceedings of the 2014 conference companion on Genetic and evolutionary computation companion - GECCO Comp '14
computers at any point in time • Difficult, but is it possible to search for multiple secure configurations?  ...  vector ssh password AV:N/AC:L/Au:N/C:P/I:P/A:P 7.2 (high) -Forms the basis for EA fitness Chromosome/Configuration Fitness • Three levels used to score each CVSS vector part AV/AC/Au/C/Therefore best  ...  LimitRequestBody Positive integer Limit the size of message body. LimitRequestFields Positive integer Limit number of request HTTP header fields allowed.  ...

### Probabilistic model of error in fixed-point arithmetic Gaussian pyramid

Antoine Meler, John A. Ruiz-Hernandez, James L. Crowley
2009 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops
However, the use of repeated convolutions using integer coefficients imposes limits on the minimum number of bits that must be used for representing image data.  ...  The existence of a fast algorithm with linear computational complexity makes it feasible to implement the half-octave Gaussian pyramid in embedded computing systems using only integer arithmetic.  ...  Error Generation and Propagatioñ x is a fixed point number with n i bits of integer part and n f bits of fractional part.  ...

### An integer tone mapping operation for HDR images in OpenEXR with denormalized numbers

Tatsuya Murofushi, Toshiyuki Dobashi, Masahiro Iwahashi, Hitoshi Kiya
2014 2014 IEEE International Conference on Image Processing (ICIP)
Moreover, the exponent part and the mantissa part are processed separately as two integer numbers. As a result, an integer TMO with less numerical range is achieved by our method.  ...  Index Termshigh dynamic range, tone mapping, OpenEXR, denormalized number, integer operation  ...  The integer TMO processes the exponent part and the mantissa part separately as two integer numbers; therefore, the numerical range in the tone mapping process is greatly reduced.  ...

### Odd Ramanujan Sums of Complex Roots of Unity

Soo-Chang Pei, Kuo-Wei Chang
2007 IEEE Signal Processing Letters
(DFT) integer-valued coefficients.  ...  A special class of odd-symmetric length-4N periodic signals is studied, and it is shown how the odd Ramanujan sums are used as weighting coefficients to compute their pure imaginary discrete Fourier transform  ...  Since there is an odd part, we must deal with the imaginary integer-valued coefficients and the real one, which becomes a Gaussian integer, while in  , only real integer-valued coefficients are considered  ...

### How to Use Koblitz Curves on Small Devices? [chapter]

Kimmo Järvinen, Ingrid Verbauwhede
2015 Lecture Notes in Computer Science
Typically elliptic curve cryptosystems, such as ECDSA, also require the scalar as an integer.  ...  This results in a need for conversions between integers and the τ -adic domain, which are costly and prevent from using Koblitz curves on very constrained devices, such as RFID tags or wireless sensors  ...  The arithmetic part can be computed using the original integer k. The first method for conversion was given by Koblitz  .  ...

### COMPUTING CONVEX HULLS BY AUTOMATA ITERATION

FRANÇOIS CANTIN, AXEL LEGAY, PIERRE WOLPER
2009 International Journal of Foundations of Computer Science
This paper considers the problem of computing the real convex hull of a finite set of n-dimensional integer vectors.  ...  The proposed method consists in computing a sequence of automata representing approximations of the convex hull and using extrapolation techniques to compute the limit of this sequence.  ...  Computing the real convex hull of a finite set of integer vectors can thus be reduced to compute the topological closure of the limit of its median sequence.  ...
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