Constant Multiplication Research Articles

Exploring Multi-Level Composition and Efficient MCM Schemes for an Energy-Efficient Wavelet Haar Architecture

This work explores multi-level fixed-point Haar transform compositions combined with MCM (multiple constant multiplication) schemes for an energy-efficient hardware architecture. We investigate a set of six lower-level Haar transforms for composing a Haar-9 architecture. The multiple-level Haar transforms use as a base M=1, M=2, and M=3 resolution levels. The processing module (PM) of the Haar explores efficient MCM schemes. The architectures were described in VHDL and synthesized employing the ST 65nm CMOS cell library. The results show that Haar-II architecture presents the lower circuit area results since this architecture requires fewer arithmetic operators. However, the most energy-efficient Haar-9 hardware architecture employs a combination of two M=2 with five M=1 blocks with a efficient MCM architecture reduced to only two arithmetic operators.

Mathematical filtration of quaternary mixture to the zero order spectra of its individual components

Simple accurate and precise validated UV spectrophotometric methods have been described here for the simultaneous determination of Tretinoin (TN) Eusolex (EX) Hydroquinone (HQ) & Hydrocortisone acetate (HC) in their dosage form. Simultaneous determination of these four drugs was a major challenge till now. Each spectrum was filtered alone to its zero-order absorption spectrum (D0) form getting spectra typical to each pure component separately. Four methods were applied depending upon constants obtained from extended regions of partially overlapped spectra in the zero or first derivative forms. The methods applied are constant multiplication coupled with spectrum subtraction method (CM-SS) derivative transformation coupled with spectrum subtraction method (DT-SS) constant value method (CV) and concentration value (conc.value) method. The partially overlapped spectra of TN and EX in the mixture were obtained by CM-SS in their zero-order form allowing direct measurement at their λmax while the resolved binary mixture of HQ and HC obtained by SS; was determined by derivatization and transformed to their zero order by DT-SS. Also Ex and HQ concentrations were determined by the graphical representation of data only without regression equation by concentration value method and the results were compared to the conventional constant value method using a regression equation. The methods applied to the quaternary mixture under study were successfully applied for the simultaneous determination of the four drugs in synthetic mixtures and in their combined dosage form Tritospot® cream. Comparing the acquired results statistically together and to official methods demonstrated no significant difference.

Evaluation of in silico and in lab sample enrichment techniques for the assessment of challengeable quaternary combination in critical ratio

A comparative study of successive spectrophotometric resolution technique for the simultaneous determination of a challengeable quaternary mixture of Chlorpheniramine maleate (CPM), Pseudoephedrine hydrochloride (PSE), Ibuprofen (IBU) and Caffeine (CAF) is presented, without preliminary physical separation steps. Several successive steps were applied on built-in spectrophotometer software utilizing zero and/or derivative and/or ratio spectra of the studied components. These methods, namely, Dual amplitude difference (DAD) as a novel method, Constant multiplication coupled with spectrum subtraction method (CM-SS), Factorized first derivative coupled with derivative transformation method (FD1 -DT) and Derivative ratio method (DD1). The calibration graphs are linear over the concentration range of 10.0–80.0 μg/mL,150.0–900.0 μg/mL, 200.0–1400.0 μg/mL and 3.0–30.0 μg/mL for CPM, PSE, IBU and CAF, respectively. The specificity of suggested methods was studied via laboratory prepared (diverse ratios) mixtures and were successfully applied for Antiflu® capsules' analysis. Moreover, sample enrichment via In Silico (via software of spectrophotometer) and In Lab (via spiking with pure sample) techniques was elected for a pharmaceutical dosage form analysis comprising CPM and PSE as minor components. Accuracy, precision and specificity were between the valid limits. Validation steps were done in accordance with the ICH guidelines. Moreover, statistical comparison was carried out between the obtained and reported results for pure powder form and no significant difference appeared.

Spectral manipulation of ratio data for simultaneous determination of binary mixture of Paracetamol and Phenylephrine Hydrochloride

Three ratio spectra manipulating spectrophotometric methods have been developed for determination of Paracetamol (PAR) and Phenylephrine HCl (PHE) in bulk powder and in pharmaceutical formulation. Linear correlations were obtained over the concentration range of 1.0–25.0 µg/mL and 5.0–50.0 µg/mL for PAR and PHE, respectively. The first method is the ratio subtraction method (RS) coupled with constant multiplication (CM) in which PHE was determined by ratio subtraction and PAR was determined by constant multiplication. The second method is the ratio difference method (RD) which depends on measuring the difference between the amplitudes of the ratio spectra at two selected wavelengths. The third method is the first derivative of the ratio spectra (1DD), which allows the determination of PAR at 238.8 and 243 nm and PHE at 213.2, 222.2, 271.8 and 286 nm. The proposed methods are simple, accurate and precise (RSD does not exceed 2%). The applicability of the proposed methods was successfully verified by the analysis of PAR and PHE in pharmaceutical formulation without interference of the dosage form additives. Furthermore, the developed methods were validated according to ICH guidelines, so they are considered to be potential competitors for the analysis of the mixture in quality control labs and pharmaceutical factories.

Quantum Circuit Design of Toom 3-Way Multiplication

In classical computation, Toom–Cook is one of the multiplication methods for large numbers which offers faster execution time compared to other algorithms such as schoolbook and Karatsuba multiplication. For the use in quantum computation, prior work considered the Toom-2.5 variant rather than the classically faster and more prominent Toom-3, primarily to avoid the nontrivial division operations inherent in the latter circuit. In this paper, we investigate the quantum circuit for Toom-3 multiplication, which is expected to give an asymptotically lower depth than the Toom-2.5 circuit. In particular, we designed the corresponding quantum circuit and adopted the sequence proposed by Bodrato to yield a lower number of operations, especially in terms of nontrivial division, which is reduced to only one exact division by 3 circuit per iteration. Moreover, to further minimize the cost of the remaining division, we utilize the unique property of the particular division circuit, replacing it with a constant multiplication by reciprocal circuit and the corresponding swap operations. Our numerical analysis shows that the resulting circuit indeed gives a lower asymptotic complexity in terms of Toffoli depth and qubit count compared to Toom-2.5 but with a large number of Toffoli gates that mainly come from realizing the division operation.

High Speed FIR Filter Using Radix-2r Multiplier and Its Application for Denoising EOG Signal

In this paper, a modified finite impulse response (FIR) filter design has been proposed for the denoising bio-electrical signals like Electrooculography(EOG). The proposed filter architecture uses modified multiplier block, which is implemented using modified Radix-[Formula: see text] arithmetic-based representation for minimizing the multiple constant multiplication and conventional ripple carry adders are replaced with [Formula: see text] compressors. This proposed architecture is implemented by using Radix-[Formula: see text]-based multiplier and [Formula: see text] compressor architectures for achieving better improvement in the critical path delay. The Radix-[Formula: see text]-based arithmetic bit recording is used in order to reduce the design complexity of the multiplication. The proposed architecture significantly reduced the delay when compared to existing and conventional architectures.

A Study of The Plied Yarn Twist Factor.(Dept.T)

This paper presents a new formula of twist multiplier for plied yarns. The study concerned the influence of several parameters such as: Fiber parameters, the bottom twist, single yarn liear density of plies. The experiments carried out on Ring-Spun plied cotton yarns and theoretical analysis based on the idealized yarn structure. The results obtained with predicted formula show a constant twist multiplier for all plied yarns.

Rigidity, creep and dynamic strength of plastics for three-dimensional printing of machine parts

Increasingly, parts of complex shapes are made using three-dimensional printing. This technique is also used in the design of equipment at the stage of physical modeling of their structures to determine certain properties of the product as a whole and its individual parts (details) on the corresponding models. The necessary conditions for physical modeling are the geometric and physical similarity of the model and kind. The presence of such proportionality makes it possible to recalculate the experimental results obtained for the model in kind by multiplying each of the determined values by a constant multiplier for all values of this dimension – the similarity coefficient. However, to study the physical characteristics of a product, it is necessary to take into account the mechanical properties of the material of its model. From various sources, you can find the main mechanical characteristics of plastic threads or samples made on a 3-D printer. Their values vary greatly depending on the manufacturing technology of models and are determined under conditions of static loading only, which is not enough to study the stress-strain state of parts that are affected by suddenly applied, long-term and dynamic loads during machine operation. This paper presents the results of a study of the physical and mechanical properties of polylactide (PLA) and polyethylene tereflatate (PET-G), which are used in the manufacture of parts by three-dimensional printing. The specific stiffness of polymers was for PLA 1.61…2.18 MPa·m3/kg, for PET-G – 1.15…1.41 MPa·m3/kg. The specific impact strength for PLA is 751.6…774.2 J·m/kg, for PET-G – 571.6…583.0 J·m/kg. The specific endurance for PLA was 1.75…2.76 kPa·m3/kg, for PET-G – 3.0…3.10 kPa·m3/kg.

Investigation of the main mechanical characteristics of plastics for three-dimensional printing of machine parts models

Today, new methods of manufacturing complex parts using three-dimensional printing are being introduced in engineering, including in the mechanical engineering of agricultural machinery. This technique is also used in the design of agricultural machinery at the stage of physical modeling of their structures to determine certain properties of the product as a whole and its individual parts (details) on the corresponding models. Physical modeling is used when it is difficult to perform full-scale tests of the product, as well as for economic reasons. The necessary conditions for physical modeling are the geometric and physical similarity of the model and kind. The presence of such proportionality allows us to recalculate the experimental results obtained for the model in kind by multiplying each of the determined values by a constant multiplier for all values of this dimension – the similarity coefficient. However, to study the physical characteristics of a product, it is necessary to take into account the mechanical properties of the material of its model. From various sources, you can find the main mechanical characteristics of plastic threads or samples made on a 3-D printer. Their values vary greatly depending on the model manufacturing technology. The paper presents the results of a study of the physical and mechanical properties of polylactide (PLA) and polyethylene tereflatate (PET-G), which are used in the manufacture of parts by three-dimensional printing. The specific strength of polymers was respectively: for PLA 65.6…12.2 kPa·m3/kg, for PET-G 36.7…95.4 kPa·m3/kg. Specific plasticity for PLA is equal to 60.,3 %· cm3/kg, for PET-G – 468.2 %· cm3/kg. The specific plasticity for PLA is 608.3 %· cm3/kg, for PET-G – 468.2 %· cm3/kg. Mechanical properties are investigated and the obtained mechanical characteristics must be taken into account when calculating and physically modeling plastic products for three-dimensional printing.

An approach in studying gyrostat motion with variable gyrostatic moment

The problem of the motion of a gyrostat with a fixed point and a variable gyrostatic moment under the action of gravity force is considered. A new method for integrating the equations of motion of a system consisting of a carrier body and three rotors that rotate around the main axes is proposed. The method can be attributed to the method of variation of the constant in the function for the gyrostatic moment, which linearly depends on the vector of vertical. In case of a constant multiplier, the gyrostatic moment satisfies the Poisson equation, and its variation is found from the integral of areas. The original equations have been reduced to a fifth-order system. New solutions of these equations are obtained in the case of a spherical mass distribution for the gyrostat and for the precessional motions of a carrier body. An explicit form of the gyrostatic moment is established for the case of three invariant relations.

Sumsets of semiconvex sets

AbstractWe investigate additive properties of sets$A,$where$A=\{a_1,a_2,\ldots ,a_k\}$is a monotone increasing set of real numbers, and the differences of consecutive elements are all distinct. It is known that$|A+B|\geq c|A||B|^{1/2}$for any finite set of numbers$B.$The bound is tight up to the constant multiplier. We give a new proof to this result using bounds on crossing numbers of geometric graphs. We construct examples showing the limits of possible improvements. In particular, we show that there are arbitrarily large sets with different consecutive differences and sub-quadratic sumset size.

IMCA: An Efficient In-Memory Convolution Accelerator

Traditional convolutional neural network (CNN) architectures suffer from two bottlenecks: computational complexity and memory access cost. In this study, an efficient in-memory convolution accelerator (IMCA) is proposed based on associative in-memory processing to alleviate these two problems directly. In the IMCA, the convolution operations are directly performed inside the memory as in-place operations. The proposed memory computational structure allows for a significant improvement in computational metrics, namely, TOPS/W. Furthermore, due to its unconventional computation style, the IMCA can take advantage of many potential opportunities, such as constant multiplication, bit-level sparsity, and dynamic approximate computing, which, while supported by traditional architectures, require extra overhead to exploit, thus reducing any potential gains. The proposed accelerator architecture exhibits a significant efficiency in terms of area and performance, achieving around 0.65 GOPS and 1.64 TOPS/W at 16-bit fixed-point precision with an area less than 0.25 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

Distribution of the Proportionality Coefficient of Winter Route Accounting

In previous studies it was shown that the coefficient of proportionality of the winter route count (WRC) of animals included in the formula of WRC in the form of a constant multiplier π/2, is actually a random variable – the same as the average number of intersections account route traces per unit length, and the average length of the diurnal animals. The value π/2 is the mathematical expectation value of the proportionality factor, provided that the count route equiprobably crosses the daily footprint at any place and at any angle from 0 to 2π during a winter route counting of animals. At the same time, both the nature of the distribution of the coefficient as a random variable and the values of its variance as its other statistical characteristics remained unknown. In this study, it was found that when the above-mentioned count conditions are met, the distribution of the proportionality coefficient of WRC as a random variable will be exponential or power-like. This allows calculating the values of its variance and relative statistical error in advance without collecting additional count data.

Card-based Cryptography with Dihedral Symmetry

It is known that secure computation can be done by using a deck of physical cards. This area is called card-based cryptography. Shinagawa et al. (in: Provable security—9th international conference, ProvSec 2015, Kanazawa, Japan, 2015) proposed regular n-sided polygon cards that enable to compute functions over {mathbb {Z}}/n{mathbb {Z}}. In particular, they designed efficient protocols for linear functions (e.g. addition and constant multiplication) over {mathbb {Z}}/n{mathbb {Z}}. Here, efficiency is measured by the number of cards used in the protocol. In this paper, we propose a new type of cards, dihedral cards, as a natural generalization of regular polygon cards. Based on them, we construct efficient protocols for various interesting functions such as carry of addition, equality, and greater-than, whose efficient construction has not been known before. Beside this, we introduce a new protocol framework that captures a wide class of card types including binary cards, regular polygon cards, dihedral cards, and so on.

Uniform bounds on harmonic Beltrami differentials and Weil–Petersson curvatures

Abstract In this article we show that for every finite area hyperbolic surface X of type {(g,n)} and any harmonic Beltrami differential μ on X, then the magnitude of μ at any point of small injectivity radius is uniform bounded from above by the ratio of the Weil–Petersson norm of μ over the square root of the systole of X up to a uniform positive constant multiplication. We apply the uniform bound above to show that the Weil–Petersson Ricci curvature, restricted at any hyperbolic surface of short systole in the moduli space, is uniformly bounded from below by the negative reciprocal of the systole up to a uniform positive constant multiplication. As an application, we show that the average total Weil–Petersson scalar curvature over the moduli space is uniformly comparable to {-g} as the genus g goes to infinity.

Who reacts to what information in securities analyst reports? Direct evidence from the investor trade imbalance

Using a comprehensive dataset that distinguishes the buy/sell volume of four investor types, we find that foreign institutions and domestic mutual funds are the primary users of analyst reports. Their buy–sell imbalances move in tandem with analysts' signals and significantly explain the size of cumulative abnormal returns across incidents of analyst report releases. Proprietary traders' buy/sell positions are less related to analyst opinions, and individual investors emerge as de facto liquidity providers to aggressive institutions. Institutional investors respond first to stock recommendations and then use target prices as supplementary information. Earnings forecasts, which contain nuanced information, do not elicit abnormal trade imbalances for any institutional investors. We further discover that trade reactions to target prices and earnings forecasts can be viewed more as a constant multiplier of the signal rather than as an increasing or decreasing function of the signal strength. The trade imbalance caused by analyst information is found to predict next-period stock returns, although the predictive ability is for the short-term period only.

Construction of higher-level MDS matrices in nested SPNs

This paper presents a new construction of large-scale maximum distance separable (MDS) matrices which can be used in the design of block ciphers. We extend Cauchy matrices defined over a finite field and consider these matrices on a finite commutative ring. The resulting generalized Cauchy (GC) matrices retain the advantage of a maximum branch number. We investigate the properties of such matrices in this study. First, we provide a construction of GC matrices. The proposed construction guarantees that most of the (binary) entries in a GC matrix are zero, thereby reducing the search space for cheap GC matrices considerably. Second, we minimize the number of different sub-matrices in a GC matrix to make it more suitable for lookup table implementation, we call this a compact GC matrix. We then elaborate the structure of such compact GC matrices to consider all possible matrices and thus obtain the number of compact GC matrices. Finally, we consider the involutory potential of compact GC matrices. In particular, we prove that any compact GC matrix can be modified into an involutory one through a series of column-exchanging operations and a constant matrix multiplication. Through our experiment, we discover large-scale GC matrices, which can facilitate the future design of involutory component-based ciphers. Our best constructions can reduce the number of XOR gates in the higher-level diffusion layers in Hierocrypt-L1 and Hierocrypt-3 by 35.1% and 50%, respectively, while providing the same number of active S-boxes. Moreover, compared with the existing ones, the involutory nature of the new matrices allows for equally efficient diffusion in both encryption and decryption.

İşbirlikçi Filtreleme için Pearson Korelasyonu Üzerine Statik ve Dinamik Önem Ağırlıklandırma Çarpanları Çalışması

Recommender systems as a field of data mining and knowledge discovery have a tremendous impact on movie recommendation platforms. Proper recommendation for the audience, considering profiles, is a measurable argument. By inferencing the linear combinations between some numerical data such as user rating actions, statistical analyses can be done. Thus, any item such as a movie can be recommended or not. The numerical calculation of correlations, namely the similarity weight, should be recomputed before prediction to increase the effect of user similarities for further constant multiplications. This method is named as the significance weighting that processes one more step to stress the impact of similarities. The affinity between users can simply be the total number of co-rated items, or any further inference using more complex computations. In this work, the significance weighting method related to Pearson Correlation is inspected using comparative approaches. The MovieLens dataset, both including ML100K and ML1M releases, are used in the experiments. k-fold cross-validation method is applied in a shifting fashion to increase the number of tests. After having Pearson Correlation Coefficients for user-user similarities, weights are signified using three different approaches. Then, neighbors are sorted to choose the top-N closest users for the user in the test. Concerning experimental results, over two other techniques, an explicit method that utilizes only the co-rated item count is preferred taking its simplicity and performance into account. In the plots of experimental results section, accuracy and error metrics are presented for three different significance weighting approaches. Especially for the ML100K dataset, the simple weighting method outperforms in terms of the error metrics.

The Constant Multiplier FFT

In this paper, we present a new fast Fourier transform (FFT) hardware architecture called constant multiplier (CM) FFT. Whereas rotators in previous architectures must rotate among several different angles, the CM FFT exploits the use of constant multipliers to calculate the rotations. The paper explores the 4-parallel and 8-parallel radix-2 CM FFT, which calculates the FFT entirely by using constant multipliers. Later, radices 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> are presented, with emphasis in radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> and radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> as the best alternatives. Experimental results for a 1024-point radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> CM FFT show that the proposed approach reduces the number of block random-access memories (BRAM) and digital signal processing (DSP) slices with respect to previous approaches, while achieving the highest clock frequency for a 4-parallel FFT architecture on field-programmable gate arrays (FPGAs) reported so far.

Trade-off efficacy and data processing strategy in the power of spectral resolution of co-formulated antihypertensive pharmaceuticals.

Versatile, extraction-free univariate spectrophotometric methods have been modified to get effective spectral resolution of mixtures in accordance with their feature challenges. The proposed methods have been applied and validated for analyzing some antihypertensive medicines in their co-formulated medicinal products. Two mixtures have been used: the first one [Mix I (OLM/ADB)] is composed of Olmesartan medoxomil (OLM) and Amlodipine besylate (ADB) with partly-overlapped spectra while the second [Mix II (TEL/HCT)] is made up Telmisartan (TEL) and Hydrochlorothiazide (HCT) with total-overlapped spectra. Induced dual wavelength, absorbance correction and ratio subtraction coupled with constant multiplication methods were applied to Mix I (OLM/ADB), while dual wavelength, advanced absorbance subtraction and constant center coupled with spectrum subtraction methods were applied to Mix II (TEL/HCT). Calibration graphs were established with good correlation coefficients. The methods exhibit significant advantages as simplicity, sensitivity, minimal data manipulation besides optimum robustness. Selectivity was inspected using lab-mixtures with diverse ratios. Accuracy, precision and repeatability were found to be within the acceptable limits. The proposed methods are good enough to be used for co-assay of analytes in combined forms without any interfering from excipients. Moreover, all results were estimated in accordance with ICH criteria and successfully compared with those of the reported methods applying t-test and F-test at 95% confidence level. Generally, these methods can be used efficiently for routine quality control testing.