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Highlights • Proximal junctional kyphosis in adolescent idiopathic scoliosis is frequent. • Poor visualization of the sagittal plane leads to incorrect identification of curve type. • Residual or progressive symptomatic kyphosis may require surgical treatment. • Pedicle subtraction osteotomy may be an effective corrective technique., Introduction Complications in the upper thoracic spine are not uncommon after corrective surgery for deformities in adults and adolescents. Proximal junctional failure has been linked to structural osseous or ligamentous failure and proximal junctional kyphosis has been described as an increase in preoperative proximal kyphosis. Case description A 20-year-old male patient intervened after atypical development of idiopathic scoliosis, with rapid progression nearing skeletal maturity. While an increase in the magnitude of the main thoracic curve in the coronal plane was observed, the progression of structural sagittal plane deformity of the proximal thoracic curve was not identified due to poor visualization. This resulted in improper identification of curve type and choice of fusion levels, with progressive residual kyphosis across follow-up. At the age of 27, the patient was re-intervened by means of pedicle subtraction osteotomy in the apical area of the proximal thoracic deformity. Although an adequate correction was achieved, the remaining deformity of 50° and the proximal failure required extending the instrumentation and fusion to the cervical spine. This has shown itself to be an effective technique for correction of proximal residual or progressive symptomatic fixed kyphosis, thereby avoiding the morbidity of the anterior or combined approaches. Conclusions In adolescent deformity, an adequate preoperative planning including clinical and radiological study must be carried out, paying special attention to the sagittal plane to identify major and minor structural curves. The pedicle subtraction osteotomy, despite being a demanding technique and not entirely risk-free, has shown itself to be an effective corrective technique.

This paper presents a new implementation of a wattmeter based on the adding principle. Its major advantages are the very high accuracy it can reach at low power factor measurements, and the simple construction. Although the measuring method is well known, this work proposes to join analogue devices with a digital voltmeter (DMM) to get a new implementation. We use a simple switch and a binary inductive divider to implement the addition and subtraction, which practically cancels the errors due to this operation. Additionally, as the same DMM is used for measuring both conditions, its errors vanish at null power factor because the voltage is the same in both cases.

Introduction Bone density can interfere with fluoroscopy-guided tumor tracking in radiotherapy. To improve markerless tumor tracking accuracy, we developed a dual energy subtraction (DES) mechanical image mask to use with a single x-ray exposure. Methods The DES mask consists of 2-mm-thick stainless-steel with 128 pairs of slits (0.388 mm width and openings), designed to match the dynamic flat panel detector (DFPD) pixel size. This was set on the front of the DFPD. This results in a DFPD image with one containing the exposed pixels and one containing the masked pixels. The masked pixel columns were interpolated from adjacent pixels and a subtraction image was generated from the interpolated images to make a bone suppression (BS) image. A chest phantom was set on the commercially available moving table (CIRS DYNAMIC PLATFORM 008PL) and DFPD images were acquired. A reference BS image was generated by double-exposure DES with and without a 2-mm-thick stainless-steel plate. Image quality and markerless tumor tracking accuracy were then evaluated. Results The DES mask decreased most of the visible bone densities from the chest phantom image acquired with a single exposure for a peak-signal-to-noise-ratio/structural similarity index measure (PSNR/SSIM) of 25.3 db/0.685). The tracking positional error, originally 12.6 mm, was improved to 0.2 mm. Conclusions The DES mask can aid in BS image on fluoroscopic imaging and may be useful in markerless tumor tracking.

Objectives Endovascular revascularisation is the mainstay of the treatment of lower extremity peripheral arterial disease. Improvement in perfusion after treatment is often quantified by a corresponding increment in ankle or toe brachial indices. These measurements are difficult to obtain in patients with foot wounds, and have to be performed at a separate time and setting after revascularisation. This preliminary study aimed to evaluate the use of parametric colour coding and analysis of time attenuation curves as a real time quantitative measure of perfusion after endovascular revascularisation. Methods Forty-seven consecutive patients with critical limb ischaemia were retrospectively enrolled and analysed. Parametric colour coding and generation of time attenuation curves in the main pedal vessel was performed for pre- and post-intervention digital subtraction angiograms of each patient. The change in time attenuation curve parameters was compared with the change in ankle or toe brachial indices before and after intervention. Results Comparing before and after lower extremity endovascular intervention, there were significant changes in the washout parameters derived from the time attenuation curve. The percentage of contrast decay 4 seconds after peak (I4s) demonstrated the strongest correlation (R = .482) with the change in ankle or toe brachial indices. Conclusions Parametric colour coding and time attenuation curve analysis might be a helpful tool that can provide real time intra-procedural quantitative data on pedal perfusion which can improve clinical outcomes., Highlights • Analysis of time attenuation curves allows perfusion assessment in revascularization. • Percentage of contrast decay at 4 seconds is best correlated with perfusion. • This is a tool that can assess real-time perfusion and guide intervention.

These data present the 141 intracranial arterial branches' visibilities near the 72 cerebral aneurysms in postoperative 58 patients treated with titanium or cobalt-chromium-nickel-molybdenum (CCNM) alloy clips. The visibilities were evaluated using time-of-flight magnetic resonance angiography (TOF-MRA), pointwise encoding time reduction with radial acquisition (PETRA)-MRA, which uses MRA with ultrashort echo time (UTE-MRA) and subtraction technique between saturated and non-saturated images, and three-dimensional computed tomography angiography (3DCTA). We retrospectively acquired the data from the medical records of Suwa Red Cross Hospital. Each method's appearance was compared, and associations between visibility on PETRA-MRA, arterial diameter, clip numbers, clip shapes, clip materials, and amounts of hematoma were summarized. Our article on PETRA-MRA's usefulness for proximal and branched arteries evaluation after cerebral aneurysm clipping [1] was based on these data. This dataset would be useful for reference value for other neurosurgeons or radiologists for further analysis on PETRA-MRA and another UTE-MRA like SILENT-MRA after cerebral aneurysm clipping.

In EEG data acquired in the presence of fMRI, gradient-related spike artifacts contaminate the signal following the common preprocessing step of average artifact subtraction. Spike artifacts compromise EEG data quality since they overlap with the EEG signal in frequency, thereby confounding frequency-based inferences on activity. As well, spike artifacts can inflate or deflate correlations among time series, thereby confounding inferences on functional connectivity. We present Schrödinger filtering, which uses the Schrödinger equation to decompose the spike-containing input. The basis functions of the decomposition are localized and pulse-shaped, and selectively capture the various input peaks, with the spike components clustered at the beginning of the spectrum. Schrödinger filtering automatically subtracts the spike components from the data. On real and simulated data, we show that Schrödinger filtering (1) simultaneously accomplishes high spike removal and high signal preservation without affecting evoked activity, and (2) reduces spurious pairwise correlations in spontaneous activity. In these regards, Schrödinger filtering was significantly better than three other despiking techniques: median filtering, amplitude thresholding, and wavelet denoising. These results encourage the use of Schrödinger filtering in future EEG-fMRI pipelines, as well as in other spike-related applications (e.g., fMRI motion artifact removal or action potential extraction).

Publisher Summary This chapter provides an overview of limited color vision. Human color perception has both strengths and limitations. Many of those strengths and limitations are relevant to user interface design, such as the vision is optimized to detect contrasts (edges), not absolute brightness; the ability to distinguish colors depends on how colors are presented; some people have color-blindness; and the user's display and the viewing conditions affect color perception. One of the factors of color presentation that affects design principles for interactive systems is whether the colors can be distinguished by people who have common types of color-blindness. Having color-blindness does not mean an inability to see colors. It just means that one or more of the color subtraction channels don't function normally, making it difficult to distinguish certain pairs of colors. In addition, some of the guidelines for using colors are also provided.

In this chapter, we review a long-standing and comprehensive line of research on the use of the subtraction by addition (SBA) strategy when solving subtractions, in which our own research center has played an important role. We document this phenomenon in a variety of subdomains of the elementary arithmetic curriculum, ranging from single-digit mental subtraction, multidigit mental and written subtraction, to word problems in the domain of subtraction. We also review the available research that tries to link these findings about people’s use of SBA in these different curricular subdomains to their conceptual knowledge of subtraction. Taken as a whole, the reviewed research has yielded recurrent and convincing evidence for the frequent, efficient, and flexible use of SBA in the above curricular subdomains among both elementary school children and adults. Given that learners are typically taught to solve subtractions by means of direct subtraction (DS) while SBA gets little or no instructional attention, these are striking results. At the end, we reflect on some theoretical, methodological, and educational implications of these remarkable findings.

Highlights • Self-blame-related fMRI measures were previously validated in depressive disorders. • Reproducibility and internal consistency as a measure of reliability were examined. • Whilst simple fMRI measures exhibited fair reliability, complex measures did not. • Yet, complex measures showed reproducible clinical validity at the group level. • Connectivity measures, that balance reliability and validity better, are needed., Background In major depressive disorder (MDD), self-blame-related fMRI measures have shown the potential to be used as prognostic markers for recurrence risk. Like most potential fMRI markers, however, their reliability is unclear. Here, we probed the internal reliability of self-blame-related fMRI measures, as well as the impact of different modelling approaches on reliability metrics and validity. Methods Internal consistency (i.e. split-half reliability) was calculated for blood oxygen level-dependent (BOLD) responses and psychophysiological interactions (PPI) related to self-blame-related biases in medication-free remitted MDD participants (n = 81) and healthy controls (n = 41). Trial-length was modelled using three durations (0, 2 and 5 s), which was convolved with the haemodynamic response function (HRF) with and without time and dispersion derivatives. Intraclass correlation coefficients (ICCs) were calculated for simple contrasts examining activation to self-blaming emotions and other-blaming emotions and the more complex contrast of the subtraction-based difference between self- and other-blaming emotions within the following a priori ROIs: right superior anterior temporal lobe seed region, anterior subgenual cingulate cortex, posterior subgenual cortex and right striatum / pallidum. Results Across ROIs, we obtained fair reliability (ICC ≥ 0.40) for simple, but poor reliability (ICC

Recent advances in dual-energy imaging techniques, dual-energy subtraction radiography (DESR) and dual-energy CT (DECT), offer new and useful additional information to conventional imaging, thus improving assessment of cardiothoracic abnormalities. DESR facilitates detection and characterization of pulmonary nodules. Other advantages of DESR include better depiction of pleural, lung parenchymal, airway and chest wall abnormalities, detection of foreign bodies and indwelling devices, improved visualization of cardiac and coronary artery calcifications helping in risk stratification of coronary artery disease, and diagnosing conditions like constrictive pericarditis and valvular stenosis. Commercially available DECT approaches are classified into emission based (dual rotation/spin, dual source, rapid kilovoltage switching and split beam) and detector-based (dual layer) systems. DECT provide several specialized image reconstructions. Virtual non-contrast images (VNC) allow for radiation dose reduction by obviating need for true non contrast images, low energy virtual mono-energetic images (VMI) boost contrast enhancement and help in salvaging otherwise non-diagnostic vascular studies, high energy VMI reduce beam hardening artifacts from metallic hardware or dense contrast material, and iodine density images allow quantitative and qualitative assessment of enhancement/iodine distribution. The large amount of data generated by DECT can affect interpreting physician efficiency but also limit clinical adoption of the technology. Optimization of the existing workflow and streamlining the integration between post-processing software and picture archiving and communication system (PACS) is therefore warranted.

The 4-loop QED mass and wave function renormalization constants $Z_2$ and $Z_m$ have been evaluated in the on-shell subtraction scheme with 1100 digits of precision. We also worked out the coefficients of the five color structures of the QCD renormalization constants $Z_2^{OS}$ and $Z_m^{OS}$ which can obtained from QED-like diagrams. The results agree with lower precision results available in the literature. Analytical fits were also obtained for all these quantities., Comment: 12 pages, 1 table and 1 figure; v2: revised version accepted by Physics Letters B; v3: added the missing definition of the constant t_{63}

We describe an implementation of a subtraction scheme in the nonrelativistic-QCD treatment of heavy-quarkonium production at next-to-leading-order in the strong-coupling constant, covering $S$- and $P$-wave bound states. It is based on the dipole subtraction in the massless version by Catani and Seymour and its extension to massive quarks by Phaf and Weinzierl. Important additions include the treatment of heavy-quark bound states, in particular due to the more complicated infrared-divergence structure in the case of $P$-wave states., 29 pages, 2 figures, 3 tables, 3 formulas added, corrections and minor changes included, accepted for publication in Nucl. Phys. B

Introduction Longitudinal magnetic resonance imaging (MRI) analysis has an important role in multiple sclerosis diagnosis and follow-up. The presence of new T2-w lesions on brain MRI scans is considered a prognostic and predictive biomarker for the disease. In this study, we propose a supervised approach for detecting new T2-w lesions using features from image intensities, subtraction values, and deformation fields (DF). Methods One year apart multi-channel brain MRI scans were obtained for 60 patients, 36 of them with new T2-w lesions. Images from both temporal points were preprocessed and co-registered. Afterwards, they were registered using multi-resolution affine registration, allowing their subtraction. In particular, the DFs between both images were computed with the Demons non-rigid registration algorithm. Afterwards, a logistic regression model was trained with features from image intensities, subtraction values, and DF operators. We evaluated the performance of the model following a leave-one-out cross-validation scheme. Results In terms of detection, we obtained a mean Dice similarity coefficient of 0.77 with a true-positive rate of 74.30% and a false-positive detection rate of 11.86%. In terms of segmentation, we obtained a mean Dice similarity coefficient of 0.56. The performance of our model was significantly higher than state-of-the-art methods. Conclusions The performance of the proposed method shows the benefits of using DF operators as features to train a supervised learning model. Compared to other methods, the proposed model decreases the number of false-positives while increasing the number of true-positives, which is relevant for clinical settings., Highlights • A new framework for detecting new T2-w lesions in multiple sclerosis is proposed. • We train logistic regression classifier with subtraction and deformation features. • We analyze the effect of deformation field operators on detecting new T2-w lesions. • We show an increase in the accuracy due to the addition of deformation fields. • The proposed model decreases false-positives while increasing true-positives.

Six simple, sensitive and selective spectrophotometric methods based on mathematical filtration technique are presented for concurrent determination of aceclofenac (ACE) and paracetamol (PAR) in presence of their degradation products, namely; diclofenac sodium (DIC) and 4-aminophenol (4-AP), respectively without preliminary physical separation procedures. This technique consists of several consecutive steps applied on built-in spectrophotometer software utilizing zero and/or derivative and/or ratio spectra of the studied components. These methods, namely, dual wavelength (DW), induced dual wavelength (IDW), derivative subtraction (DS) coupled with constant multiplication (CM), ratio difference method (RD), constant center method (CC) and the novel introduced unlimited derivative ratio method (UDD). This novel method has a very powerful competence for the analysis of the challengeable mixtures lacking zero crossing point. The linearity, accuracy and precision ranges of these methods were determined and validated as per ICH guidelines. Moreover, the specificity was checked by analyzing synthetic mixtures of both drugs. These methods were applied for the determination of the cited drugs in pharmaceutical formulation and a statistical comparison of the obtained results was made with each other and with those of reported spectrophotometric method. The comparison of the results of pure powder form showed that there is no significant difference between the proposed methods and the reported method regarding both accuracy and precision.

© 2019 Elsevier Inc. In 2012, a study by Sklar et al. reported that participants could solve invisible subtractions. This notion of unconscious arithmetic has been influential because it challenges current theories of consciousness. In 2016, Karpinski et al. published a direct replication reporting evidence for unconscious addition rather than subtraction. About a year later, the study was retracted due to a computation error in the analysis pipeline. After this error was corrected, no evidence for unconscious addition nor subtraction was obtained. Recently, Karpinski et al. republished the study by applying the exclusion criteria used in Sklar et al. The reanalysis found weak evidence for unconscious subtraction. To assess the robustness of these results, we examine how sensitive the results are to data analytic decisions. We outline a set of 250 analyses that we consider justified to perform. We show that none of the analyses indicates evidence for unconscious subtraction. ispartof: Consciousness and Cognition vol:68 pages:97-106 ispartof: location:United States status: published

Microwave imaging is a promising imaging modality for the detection of early-stage breast cancer. One of the most important signal processing components of microwave radar-based breast imaging is early stage artifact removal. Several artifact removal algorithms have been reported in the literature. However, the neighbourhood-based skin subtraction and hybrid artifact removal algorithms have shown particularly promising results in different realistic 3D breast phantoms. For the first time in this paper, both algorithms have been evaluated and compared using the scan approaches of the most common microwave breast imaging prototype systems. The tests include 3D numerical as well as experimental breast phantoms scanned with hemispherical, cylindrical and adaptive scanning patterns. The efficacy of both algorithms has been evaluated across a range of appropriate performance metrics. (C) 2017 Elsevier Ltd. All rights reserved. This work is supported by Science Foundation Ireland (Grant Numbers: 11/SIRG/I2120 and 12/IP/1523), COST Action TD1301, MiMed and the Irish Research Council New Foundations Award. The authors would also like to thank Douglas Kurrant for collecting the simulation data and Jérémie Bourqui for collecting the measurement data. peer-reviewed 2018-03-02

We begin this chapter with a very powerful property of the logarithmic image processing (LIP) model, which allows for interpreting the negative elements of the gray scale as light intensifiers. The obvious consequence of this property is the ability of LIP tools (scalar multiplication and subtraction of a constant) to enhance low-light images. This is achieved by means of dynamic range expansion or histogram modification. The proposed methods are successfully generalized to color images. Moreover, we will demonstrate how to perform, at camera speed, the stabilization of images submitted to variable lighting. Four important applications are presented. An improvement of studied algorithms is realized through local lighting corrections. At the end of this chapter, some comparisons will be made with classical enhancement methods.

This chapter provides an introduction to algebra through learning basic principles of addition, multiplication, exponents, and radicals. The chapter shows addition, subtraction, multiplication, and division of polynomials. Also, the chapter introduces ratios, proportions, and variation.

In this chapter, the ability of organisms to use an intuitive, approximate, and abstract sense of number to represent and operate over numerical magnitudes is discussed. The literature on adding, subtracting, and ordering nonsymbolic magnitudes generated by this approximate number system is reviewed, along with evidence that the system may also support an intuitive sensitivity to the results of multiplication and division in infants, children, adults, and nonhuman animals. A proposal for a core scaling ability 0—in which approximate number representations are used to flexibly scale up or down magnitudes in a multiplicative or divisive fashion—is advanced and substantiated with findings from infants and kindergarten-aged children.

Publisher Summary A matrix is denoted by A. The i-th row of A is denoted by Ai, the i-th column by A.i, the column of the absolute terms (right sides) by A.f. To eliminate x1, one derives from Aa system B in which the first column vanishes. For this purpose, the first row is multiplied by the leading coefficient a21 of the second row and the second row by the leading coefficient a11 of the first row. On subtraction, one has a11A2. − a21A1 = B2. 0, 58, 33, - 13, 185, 4073. Therefore, the elements of B2 are the two-rowed determinants having the fixed column (a11, a21), that is, the determinants. This chapter describes the method and computation that Jordan employed for elimination in terms of the matrix.

For the reduction of exposure dose in contrast media detection with X-ray transmission measurements, the energy measurement of X-rays and the energy subtraction (ES) method have been shown to be effective. To make the ES method applicable, a novel detector for unfolding the X-ray energy distribution was proposed by the authors. As an application of this novel detector, a CT image was reconstructed with ES data and compared with the image reconstructed using electric current data.

Surgery of focal epilepsies in childhood has largely benefited from the recent advances of the noninvasive functional imaging techniques, particularly SPECT which presurgically contributes to the localization of the seizure onset zone, in order to select the patients, decide the optimal placement of intracranial electrodes, and plan the resection. Peri-ictal SPECT (ictal and postictal) proved especially useful when video-EEG is not contributory, when MRI looks normal or shows multiple abnormalities, or in cases of discrepant findings within the presurgery workup. Because of a poor temporal resolution, peri-ictal SPECT must be coupled with video-EEG. Multimodal imaging so-called SISCOM (peri-ictal – interictal SPECT subtraction image superimposed on MRI) increases the sensitivity of peri-ictal SPECT by about 70% and makes it a good predictor of seizure-free outcome after surgery. In addition, interictal SPECT occasionally provides some interesting results regarding functional cortical maturation and learning disorders in childhood.

This chapter focuses on the various matrices used in SQL. A matrix is an array with mathematical operations defined on it and can be one, two, three, or more dimensional structures. Though it is possible to do many matrix operations in SQL, it is not a good idea, as such queries and operations eat up resources and run much too long. Matrix addition and subtraction are possible only between matrices of the same dimensions. Multiplication by a scalar constant is direct and easy and the first matrix must have the same number of rows as the second matrix has columns. It is possible to do other matrix operations in SQL, but the code becomes so complex, and the execution time so long, that it is simply not worth the effort.

The electroencephalogram (EEG) recorded during magnetic resonance imaging (MRI) inside the scanner is obstructed by the MRI gradient artefact (MGA) originating from the electromagnetic interference of the MRI with the sensitive measurement of electrical scalp potentials. Post-processing algorithms based on average artefact subtraction (AAS) have proven to be efficient in removing the MGA. However, the residual MGA after AAS still limits the quality and usable bandwidth of the EEG data despite further reduction through re-sampling, principal component analysis (PCA), and regressive filtering. We recently demonstrated that the residual MGA can largely be avoided by means of hardware synchronization. Here we present a new software synchronization method, which substitutes hardware synchronization and facilitates the removal of motion artefacts by PCA. The effectiveness of the retrospective synchronization algorithm (Resync) is demonstrated by comparison to the aforementioned techniques. For this purpose, we also developed a method for simulating the MGA and we propose new concepts for quantifying and comparing the performance of post-processing algorithms for EEG-MRI data. Results indicate that the benefits of (retrospective) synchronization and PCA depend largely on the relative contribution of timing errors and motion artefacts to the residual MGA as well as the frequency range of interest.

Publisher Summary This chapter introduces outline the importance of complex numbers and exponentials which are an integral part of digital communications and digital signal processing (DSP). The reason of delving deep into this area leads the readers to two-dimensional number plane which help to understand DSP. The operators such as addition, subtraction, multiplication take people through the complex side of numbers which are explained in two dimensions. The use of complex conjugate and complex exponential—in the number plane—allows readers understand the relationship of basic characteristics of numbers and its treatment. The chapter further looks into measuring angles in radians which leads to the use of pi and the equivalence of the degrees and radians in measuring angles. DSP therefore uses this concept in later stages to understand the clockwise and anticlockwise movement around the circle.

Publisher Summary Unsigned binary numbers don’t have the concept of a sign (plus or minus), which means they can be used to represent only positive values. Each “ x ” character represents a single bit; the right-hand bit is known as the Least Significant Bit (LSB) because it represents the smallest value. Two unsigned binary numbers may be added together using a process identical to that used for decimal addition. First, the two least significant bits are added together to give a sum and, possibly, a carry-out to the next stage. This process is repeated for the remaining bits, progressing toward the most significant. In the case of binary (base-2) numbers, the radix complement is known as the twos’ complement and the diminished radix complement is known as the ones’ complement. Once again, the standard way of performing the operation would be to subtract the subtrahend (00011110 2) from the minuend (00111001 2), which may require the use of one or more borrow operations. In standard decimal arithmetic, numbers are typically represented in a form known as sign-magnitude, which means prefixing values with plus or minus signs (by default, numbers without signs are assumed to represent positive values). Signed binary numbers have the concept of a sign, and they can be used to represent both positive and negative values. The end result of using signed binary numbers is to greatly reduce the complexity of operations within a computer. Binary numbers may be multiplied together by means of a shift-and-add technique.

We present a novel unified core design which is extended to realize Montgomery multiplication in the fields GF(2(n)), GF(3(m)). and GF(p). Our unified design supports RSA and elliptic Curve schemes, as well as the identity-based encryption which requires a pairing computation on an elliptic Curve. The architecture is pipelined and is highly scalable. The unified core utilizes the redundant signed digit representation to reduce the critical path delay. While the carry-save representation used in classical Unified architectures is only good for addition and Multiplication operations, the redundant signed digit representation also facilitates efficient computation of comparison and subtraction operations besides addition and multiplication. Thus, there is no need for a transformation between the redundant and the non-redundant representations of held elements, which Would be required in the classical unified architectures to realize the subtraction and comparison operations. We also quantify the benefits of the unified architectures in terms of area and critical path delay. We provide detailed implementation results. The metric shows that the new unified architecture provides an improvement over a hypothetical non-unified architecture of at least 24.88%, while the improvement over a classical unified architecture is at least 32.07%. (C) 2008 Elsevier Ltd. All rights reserved.

Publisher Summary This chapter provides the information that had been obtained from an assessment involving a dyscalculia test battery. It aims to analyze the children's numerical difficulties and to provide a remedial approach that would help them to learn the multiplication tables. Also, the facilitation of more mature development was expected in relation to number concepts and numerical skills through the establishment of flexible associations between specialized areas or modules as emphasized by Dehaene (1997). It is apparent from the results obtained that a detailed assessment with the aid of a dyscalculia test battery provided clear information concerning the numerical difficulties experienced by the participants. After taking part in the remedial sessions, the children could access any item from the multiplication tables, obtain the answers more quickly and retrieve them more often by direct recall. Also, they could use other approaches such as locating an item near the correct answer as a cue and then recall the required item or count up or down in various ways to reach the appropriate answer. Alternatively, they might use some arithmetical knowledge involving addition or subtraction, perhaps that associated with doubles or make use of commutativity as an aid to retrieving the correct answer.

Publisher Summary This chapter presents the role of computerized analysis of magnetic resonance imaging (MRI) in the diagnosis of breast lesions. It is important to review the basic mechanisms of contrast uptake in the breast and the limitations of contrast-enhanced (CE) MRI to visualize this uptake in order to fully appreciate the rationale for computerized analysis of CE MRI. Magnetic resonance imaging acquisition protocols are defined by the sequences at which the radiofrequency field in the coil is turned on and off. Typical techniques are Tl-weighted spin-echo and gradient-echo imaging. The patient is examined in prone orientation using a dedicated bilateral breast coil. A series of precontrast images is made, followed by intravenous application of the contrast agent at a well-defined rate by means of a power injector. The presence of malignant disease is correlated with several temporal and morphological characteristics of the contrast enhancement at CE MRI. To visualize the enhancement, subtraction images are typically computed. The precontrast series subtracted from the postcontrast series (wash-in series) emphasize the early kinetics caused by transfer of the contrast agent from the neovascular system to the leakage space. The first postcontrast series subtracted from the last postcontrast series (washout series) visualize early departure of the contrast agent from the leakage space back to the neovascular system. The methods used to visualize the contrast enhancement are multiplanar reformatting (MPR) and maximum-intensity projection (MIP). In the first method, cross sections through the CE MRI volume are calculated at various depths and directions, and in the second method the wash-in volume is projected in one or multiple directions. The resulting MIP views allow superior assessment of multifocal enhancement patterns that extend into multiple cross sections.

We present a general subtraction method for computing radiative corrections to QCD jet cross sections at next-to-next-to-leading order accuracy. The steps needed to set up this subtraction scheme are the same as those used in next-to-leading order computations. However, all steps need non-trivial modifications, which we implement such that that those can be defined at any order in perturbation theory. We give a status report of the implementation of the method to computing jet cross sections in electron-positron annihilation at the next-to-next-to-leading order accuracy., Comment: 6 pages, talk given at the conference "Loops and Legs in Quantum Field Theory", Sondershausen, April 2008

We report on automating the Catani-Seymour dipole subtraction which is a general procedure to treat infrared divergences in real emission processes at next-to-leading order in QCD. The automatization rests on three essential steps: the creation of the dipole terms, the calculation of the color linked squared Born matrix elements, and the evaluation of different helicity amplitudes. The routines have been tested for a number of complex processes, such as the real emission process gg --> t anti-t ggg., Latex, 6 pages, 1 figure. To appear in the proceedings of `Loops and Legs in Quantum Field Theory', April 2008, Sondershausen, Germany

This chapter continues with the pre-chemometrics review of analytic geometry, noting the term “vector” in all cases can be represented by a matrix of r x c dimensions, where r = number of rows and c = number of columns. The operations defined are employed in future discussions. If M represents a vector with components (or elements) as (M x , M y ), then sM (where s is a real number, also termed a “scalar”) is defined as the vector represented by (sM x , sM y ); and the length of sM is s times the length of M. In the case when s < 0 (s is a positive, real number), the vectors sM and M have the exact same direction. For the case where s < 0 (where s is a negative, real number), then the vectors sM and M have the exact opposite directions. When s = 0, there is no definition for the vector or direction. Thus, the direction angles of M can be related to those of sM. Vector division is represented as vector multiplication by using a fractional multiplier term. This chapter presents examples of vector-vector addition and vector-vector subtraction along with their graphical representations.

Algorithms for initialization, clearing, zeroing, copying, comparing, and setting small constants are established. The next logical sets of algorithms to develop are addition, subtraction, and digit-shifting algorithms. These algorithms make use of the lower level algorithms and are the crucial building block for the multiplication algorithms. It is very important that these algorithms are highly optimized. On their own they are simple 0 (n) algorithms, but they can be called from higher level algorithms, which easily places them at 0(n 2 ) or even 0 (n 3 ) work levels. One significant difference between a logical shift and the way decimals are shifted is that digits below the zero'th position are removed from the number. For example, consider 11O1 2 > > 1; using decimal notation this would produce 110.1 2 . However, with a logical shift the result is 11O2.

This chapter explains how to write and deploy a simple stateful Web service that uses Web Services Resource Framework (WSRF) to keep state information. The first Web service is an extremely simple Math Web Service, which is referred to as MathService . It allows users to perform the addition and subtraction operations. Furthermore, MathService has the following resource properties (RPs for short): value (integer) and last operation performed (string). It also adds a “Get Value” operation to access the value RP. MathService's internal logic is very simple. Once a new resource is created, the “value” RP is initialized to zero, and the “last operation” RP is initialized to “NONE.” The addition and subtraction operations expect only one integer parameter. This parameter is added/subtracted to the “value” RP, and the “last operation” RP is changed to "ADDITION" or "SUBTRACTION" accordingly. Also, the addition and subtraction operations don't return anything. Finally, this first example is limited to having only one single resource.

The terms subtraction and subtraction hybridization refer to a global identification of up- and/or down-regulated sequences, as opposed to looking at specific transcripts to determine whether or not there is any modulation of expression. Subtraction hybridization methods also differ dramatically from both antibody-mediated immunopurification of specific polysomes and generic polysome purification. Nucleic acid-based subtraction is attractive because the end point of the assay is a population of sequences partly or entirely responsible for a change in the cellular phenotype. The result of physical subtraction of commonly expressed sequences is a population of differentially expressed molecules suitable for cloning, restriction mapping, sequencing, and expression studies. Most of the newer methods for the identification of differentially expressed genes are polymerase chain reaction (PCR)-based approaches. Particularly, the method of nucleic acid subtraction coupled with suppression PCR has become a favored method for the isolation of differentially expressed messenger RNAs (mRNAs). This approach has the advantage of being a PCR-based assay, and the unique design of the nucleic adapters needed to support this assay is the key to the system. The mechanics of the assay favor a normalization of differential expressed sequences, which means, by the end of the assay all of the differentially expressed sequences are present in the ‘pool’ at similar concentrations, regardless of their abundance level in the original biological material.

This chapter discusses the role of single-photon-emission computed tomography (SPECT) in epilepsy. SPECT is a valuable clinical tool that is used in the management of patients with medically resistant partial epilepsy, who are under evaluation for surgical treatment. This technique provides useful and complementary data for localization of the seizure focus and is regularly employed in most epilepsy surgery centers. The sensitivity of SPECT for the detection of seizure focus is higher than that of structural imaging but gives little indication of the underlying pathology. The complete three-dimensional dataset provided by SPECT enables the selection of optimal image planes. Moreover, coregistration of SPECT with magnetic resonance imaging (MRI) is useful particularly for the interpretation of subtraction images. It has the advantage of an anatomic correlation and may highlight an area of relative hyperperfusion or hypoperfusion. The main role of interictal SPECT is to aid interpretation of ictal SPECT studies by providing a baseline for visual comparison or image subtraction.

Two modifications are suggested in the commonly used algorithms (such as the $O(n^2)$ Parker algorithm) for the explicit inversion of Vandermonde matrices resulting in an algorithm whose accuracy is no worse than those of the existing algorithms, but which is significantly more accurate in many pathological situations. The first modification circumvents, to some extent, the subtraction of ‘two big like-signed numbers’ which in turn reduces round-off errors, while the second modification exploits the structure of the inverse and uses two recursive formulae instead of one to bring about an increase in accuracy. Numerical results are presented to demonstrate the increase in accuracy that results from these two modifications. Although the modified algorithm is always at least as accurate as the Parker algorithm, it does, unfortunately, involve an increase in complexity from $O(n^2)$ to $O(n^3)$, so that use of this algorithm to increase the relative accuracy is recommended only in situations where the standard algorithms fail to yield accurate results.

Publisher Summary This chapter discusses the cortico–cortical coherence study in human electrocorticogram (ECoG). ECoG presents an invaluable opportunity to study the human brain function as ECoG is virtually free from volume conduction that blurs the scalp-recorded electroencephalography (EEG) signals. The chapter presents various methodological problems in the computation of scalp EEG coherence. These methodological problems are, especially troublesome for the scalp EEG analysis. The interpretation of coherence might require some caution because of the volume conduction and common reference effects. A recent study on EEG coherence combined with repetitive transcranial magnetic stimulation (rTMS) is also described. This can be regarded as an example of how one can noninvasively change the EEG coherence in vivo . With some caution and the use of additional computation, such as subtraction of coherence at rest or partial coherence, the scalp EEG coherence could be a useful method for measuring cortical connectivity. It is possible that the low-frequency rTMS could not only alter the cortical excitability but also the corticocortical coherence.

This chapter reviews the behavior of the LVQ networks closely. The LVQ architecture of the logical coordinators generalizes directly to the logical quantifiers, with the single difference of the addition of extra neurons to the competitive layer in order to cover more accurately the larger data space of the quantifiers. One of the ways in which the path of quantifier learning can be made smoother is by allowing the L1 neurons to inhibit one another. The activity-dependent weight addition tends to correlate the active neuron with its input; activity-dependent weight subtraction among neurons tends to decorrelate the active neuron from all the other neurons. The paths of competitive neurons head straight for their final position in Q7 and are separated from one another through the simulation, without the clumping together that characterized these same paths in the other simulations. The “error” created by a universal node capturing a high existential simulates the way in which people actually use the universals. It corresponds to the Labov's “loose” universal quantification.