Search results for: skew%20cyclic%20LCD%20codes

Authors: Peter Joseph Basil Morris, Chhabi Nigam, S. Ramakrishnan, P. Radhakrishna

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This paper brings out the analysis of the airborne Synthetic Aperture Radar (SAR) data using the Range Migration Algorithm (RMA) for the spotlight mode of operation. Unlike in polar format algorithm (PFA), space-variant defocusing and geometric distortion effects are mitigated in RMA since it does not assume that the illuminating wave-fronts are planar. This facilitates the use of RMA for imaging scenarios involving severe differential range curvatures enabling the imaging of larger scenes at fine resolution and at shorter ranges with low center frequencies. The RMA algorithm for the spotlight mode of SAR is analyzed in this paper using the airborne data. Pre-processing operations viz: - range de-skew and motion compensation to a line are performed on the raw data before being fed to the RMA component. Various stages of the RMA viz:- 2D Matched Filtering, Along Track Fourier Transform and Slot Interpolation are analyzed to find the performance limits and the dependence of the imaging geometry on the resolution of the final image. The ability of RMA to compensate for severe differential range curvatures in the two-dimensional spatial frequency domain are also illustrated in this paper.

Keywords: range migration algorithm, spotlight SAR, synthetic aperture radar, matched filtering, slot interpolation

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Authors: Yaxian Chen, Yeonhee Park

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Driven by evolving FDA recommendations, modern clinical trials demand innovative designs that strike a balance between statistical rigor and ethical considerations. Covariate-adjusted response-adaptive (CARA) designs bridge this gap by utilizing patient attributes and responses to skew treatment allocation in favor of the treatment that is best for an individual patient’s profile. However, existing CARA designs for survival outcomes often hinge on specific parametric models, constraining their applicability in clinical practice. In this article, we address this limitation by introducing a CARA design for survival outcomes (CARAS) based on the Cox model and a variance estimator. This method addresses issues of model misspecification and enhances the flexibility of the design. We also propose a group sequential overlapweighted log-rank test to preserve type I error rate in the context of group sequential trials using extensive simulation studies to demonstrate the clinical benefit, statistical efficiency, and robustness to model misspecification of the proposed method compared to traditional randomized controlled trial designs and response-adaptive randomization designs.

Keywords: cox model, log-rank test, optimal allocation ratio, overlap weight, survival outcome

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Authors: Abootaleb Shirvani, Svetlozar Rachev

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ESG stands for Environmental, Social, and Governance and is a non-financial factor that investors use to specify material risks and growth opportunities in their analysis process. ESG ratings provide a quantitative measure of socially responsible investment, and it is essential to incorporate ESG ratings when modeling the dynamics of asset returns. In this article, we propose a triple subordinated Lévy process for incorporating numeric ESG ratings into dynamic asset pricing theory to model the time series properties of the stock returns. The motivation for introducing three layers of subordinator is twofold. The first two layers of subordinator capture the skew and fat-tailed properties of the stock return distribution that cannot be explained well by the existing Lévy subordinated model. The third layer of the subordinator introduces ESG valuation and incorporates numeric ESG ratings into dynamic asset pricing theory and option pricing. We employ the triple subordinator Lévy model for developing the ESG-valued stock return model, derive the implied ESG score surfaces for Microsoft, Apple, and Amazon stock returns, and compare the shape of the ESG implied surface scores for these stocks.

Keywords: ESG scores, dynamic asset pricing theory, multiple subordinated modeling, Lévy processes, option pricing

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Authors: Natália Maria Rego

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ALeibnizn-algebraGis aK-vector space endowed whit a n-linearbracket operation [-,…-] : GG … G→ Gsatisfying the fundamental identity, which can be expressed saying that the right multiplication map Ry2, …, ᵧₙ: Gn→ G, Rᵧ₂, …, ᵧₙn(ˣ¹, …, ₓₙ) = [[ˣ¹, …, ₓₙ], ᵧ₂, …, ᵧₙ], is a derivation. This structure, together with its skew-symmetric version, named as Lie n-algebra or Filippov algebra, arose in the setting of Nambumechanics, an n-ary generalization of the Hamiltonian mechanics. Thefirst goal of this work is to provide a characterization of various classes of central extensions of Leibniz n-algebras in terms of homological properties. Namely, Commutator extension, Quasi-commutator extension, Stem extension, and Stem cover. These kind of central extensions are characterized by means of the character of the map *(E): nHL1(G) → M provided by the five-term exact sequence in homology with trivial coefficients of Leibniz n-algebras associated to an extension E : 0 → M → K → G → 0. For a free presentation 0 →R→ F →G→ 0of a Leibniz n-algebra G,the term M(G) = (R[F,…n.., F])/[R, F,..n-1..,F] is called the Schur multiplier of G, which is a Baer invariant, i.e., it does not depend on the chosen free presentation, and it is isomorphic to the first Leibniz n-algebras homology with trivial coefficients of G. A central extension of Leibniz n-algebras is a short exact sequenceE : 0 →M→K→G→ 0such that [M, K,.. ⁿ⁻¹.., K]=0. It is said to be a stem extension if M⊆[G, .. n.., G]. Additionally, if the induced map M(K) → M(G) is the zero map, then the stem extension Eis said to be a stem cover. The second aim of this work is to analyze the interplay between stem covers of Leibniz n-algebras and the Schur multiplier. Concretely, in the case of finite-dimensional Leibniz n-algebras, we show the existence of coverings, and we prove that all stem covers with finite-dimensional Schur multiplier are isoclinic. Additionally, we characterize stem covers of perfect Leibniz n-algebras.

Keywords: leibniz n-algebras, central extensions, Schur multiplier, stem cover

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Authors: Mark R. Skopec, Hamdi M. Issa, Henock B. Taddese, Kate Ippolito, Matthew J. Harris

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In peer review, there is a skew toward research from high-income countries, otherwise known as geographic bias. Research from well-known and prestigious institutions is often favored in the peer review process and is more frequently cited in biomedical research. English clinicians have been found to rate research from low-income countries worse compared to the same research presented as if from high-income countries. This entrenched bias, which is rooted in the perceived superiority of academic institutions in high-income countries is damaging in many regards. Crucially, it reinforces colonial roots by strengthening the dominance of knowledge bases in high-income contexts and perpetuates the perceived inferiority of research from low-income settings. We report on the interventions that Imperial College London is conducting to “decolonize” the higher education curriculum – a root and branch review of reading material in the Masters of Public Health course; identification of unconscious bias against low-income country research in faculty and staff; in-depth interviews with faculty members on their experiences and practices with respect to inclusion of low-income country research in their own teaching and learning practice; and exploring issues surrounding entrenched biases and structural impediments for enabling desirable changes. We intend to use these findings to develop frameworks and approaches, including workshops and online resources, to effect sustainable changes to diversify the curriculum at Imperial College London.

Keywords: curriculum design, diversity, geographic bias, higher education, implicit associations, inclusivity

Procedia PDF Downloads 137

Authors: Kazumasa Kawasaki, Isamu Tsuji, Hiroshi Gunbara

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A face gear drive is actually composed of a spur or helical pinion that is in mesh with a face gear and transfers power and motion between intersecting or skew axes. Due to the peculiarity of the face gear drive in shunt and confluence drive, it shows potential advantages in the application in the helicopter transmission. The advantages of such applications are the possibility of the split of the torque that appears to be significant where a pinion drives two face gears to provide an accurate division of power and motion. This mechanism greatly reduces the weight and cost compared to conventional design. Therefore, this has been led to revived interest and the face gear drive has been utilized in substitution for bevel and hypoid gears in limited cases. The face gear drive with a spur or a helical pinion is newly designed in order to determine an effective meshing area under the design parameters and specific design dimensions. The face gear has two unique dimensions which control the face width of the tooth, and the outside and inside diameters of the face gear. On the other hand, it is necessary to modify the tooth surfaces of face gear drive in order to avoid the influences of alignment errors on the tooth contact patterns in practical use. In this case, the pinion tooth surfaces are usually modified in the conventional method. However, it is hard to control the tooth contact pattern intentionally and adjust the position of the pinion axis in meshing of the gear pair. Therefore, a method of the modification of the tooth surfaces of the face gear is proposed. Moreover, based on tooth contact analysis, the tooth contact pattern and transmission errors of the designed face gear drive are analyzed, and the influences of alignment errors on the tooth contact patterns and transmission errors are investigated. These results showed that the tooth contact patterns and transmission errors were controllable and the face gear drive which is insensitive to alignment errors can be obtained.

Keywords: alignment error, face gear, gear design, helicopter transmission, tooth contact analysis

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Authors: Yong Min You

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The study on the torque ripple of Permanent Magnet Synchronous Motors (PMSMs) has been rapidly progressed, which effects on the noise and vibration of the electric vehicle. There are several ways to reduce torque ripple, which are the increase in the number of slots and poles, the notch of the rotor and stator teeth, and the skew of the rotor and stator. However, the conventional methods have the disadvantage in terms of material cost and productivity. The demagnetization characteristic of PMSMs must be attained for electric vehicle application. Due to rare earth supply issue, the demand for Dy-free permanent magnet has been increasing, which can be applied to PMSMs for the electric vehicle. Dy-free permanent magnet has lower the coercivity; the demagnetization characteristic has become more significant. To improve the torque ripple as well as the demagnetization characteristics, which are significant parameters for electric vehicle application, an unequal air-gap model is proposed for a PMSM. A shape optimization is performed to optimize the design variables of an unequal air-gap model. Optimal design variables are the shape of an unequal air-gap and the angle between V-shape magnets. An optimization process is performed by Latin Hypercube Sampling (LHS), Kriging Method, and Genetic Algorithm (GA). Finite element analysis (FEA) is also utilized to analyze the torque and demagnetization characteristics. The torque ripple and the demagnetization temperature of the initial model of 45kW PMSM with unequal air-gap are 10 % and 146.8 degrees, respectively, which are reaching a critical level for electric vehicle application. Therefore, the unequal air-gap model is proposed, and then an optimization process is conducted. Compared to the initial model, the torque ripple of the optimized unequal air-gap model was reduced by 7.7 %. In addition, the demagnetization temperature of the optimized model was also increased by 1.8 % while maintaining the efficiency. From these results, a shape optimized unequal air-gap PMSM has shown the usefulness of an improvement in the torque ripple and demagnetization temperature for the electric vehicle.

Keywords: permanent magnet synchronous motor, optimal design, finite element method, torque ripple

Procedia PDF Downloads 250

Authors: Kayode A. Olaniyi, Tola. M. Osifeko, Adeola A. Ogunleye

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Text line segmentation is an important step in document image processing. It represents a labeling process that assigns the same label using distance metric probability to spatially aligned units. Text line detection techniques have successfully been implemented mainly in printed documents. However, processing of the handwritten texts especially unconstrained documents has remained a key problem. This is because the unconstrained hand-written text lines are often not uniformly skewed. The spaces between text lines may not be obvious, complicated by the nature of handwriting and, overlapping ascenders and/or descenders of some characters. Hence, text lines detection and segmentation represents a leading challenge in handwritten document image processing. Text line detection methods that rely on the traditional global projection profile of the text document cannot efficiently confront with the problem of variable skew angles between different text lines. Hence, the formulation of a horizontal line as a separator is often not efficient. This paper presents a technique to segment a handwritten document into distinct lines of text. The proposed algorithm starts, by partitioning the initial text image into columns, across its width into chunks of about 5% each. At each vertical strip of 5%, the histogram of horizontal runs is projected. We have worked with the assumption that text appearing in a single strip is almost parallel to each other. The algorithm developed provides a sliding window through the first vertical strip on the left side of the page. It runs through to identify the new minimum corresponding to a valley in the projection profile. Each valley would represent the starting point of the orientation line and the ending point is the minimum point on the projection profile of the next vertical strip. The derived text-lines traverse around any obstructing handwritten vertical strips of connected component by associating it to either the line above or below. A decision of associating such connected component is made by the probability obtained from a distance metric decision. The technique outperforms the global projection profile for text line segmentation and it is robust to handle skewed documents and those with lines running into each other.

Keywords: connected-component, projection-profile, segmentation, text-line

Procedia PDF Downloads 93

Authors: Mancho Manev

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The concept of almost paracontact Riemannian manifolds (abbr., apcR manifolds) was introduced by I. Sato in 1976 as an analogue of almost contact Riemannian manifolds. The notion of an apcR manifold of type (p,q) was defined by S. Sasaki in 1980, where p and q are respectively the numbers of the multiplicity of the structure eigenvalues 1 and -1. It also has a simple eigenvalue of 0. In our work, we consider (2n+1)-dimensional apcR manifolds of type (n,n), i.e., the paracontact distribution of the studied manifold can be considered as a 2n-dimensional almost paracomplex Riemannian distribution with almost paracomplex structure and structure group O(n) × O(n). The aim of the present study is to introduce a new class of apcR manifolds. Such a manifold is obtained using the construction of a certain Riemannian cone over it, and the resulting manifold is a paraholomorphic paracomplex Riemannian manifold (abbr., phpcR manifold). We call it a para-Sasaki-like Riemannian manifold (abbr., pSlR manifold) and give some explicit examples. We study the structure of pSlR spaces and find that the paracontact form η is closed and each pSlR manifold locally can be considered as a certain product of the real line with a phpcR manifold, which is locally a Riemannian product of two equidimensional Riemannian spaces. We also obtain that the curvature of the pSlR manifolds is completely determined by the curvature of the underlying local phpcR manifold. Moreover, the ξ-directed Ricci curvature is equal to -2n, while in the Sasaki case, it is 2n. Accordingly, the pSlR manifolds can be interpreted as the counterpart of the Sasaki manifolds; the skew-symmetric part of ∇η vanishes, while in the Sasaki case, the symmetric part vanishes. We define a hyperbolic extension of a (complete) phpcR manifold that resembles a certain warped product, and we indicate that it is a (complete) pSlR manifold. In addition, we consider the hyperbolic extension of a phpcR manifold and prove that if the initial manifold is a complete Einstein manifold with negative scalar curvature, then the resulting manifold is a complete Einstein pSlR manifold with negative scalar curvature. In this way, we produce new examples of a complete Einstein Riemannian manifold with negative scalar curvature. Finally, we define and study para contact conformal/homothetic deformations by deriving a subclass that preserves the para-Sasaki-like condition. We then find that if we apply a paracontact homothetic deformation of a pSlR space, we obtain that the Ricci tensor is invariant.

Keywords: almost paracontact Riemannian manifolds, Einstein manifolds, holomorphic product manifold, warped product manifold

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Authors: Andrew Green, Jiaming Liu, Kellathur Srinivasan, Raymond Chua

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Introduction: The size of Singapore’s online health product (HP) market (e-commerce) is largely unknown. However, it is recognized that a large majority comes from overseas and thus, unregulated. As buying HP from unauthorized sources significantly compromises public health safety, understanding e-commerce users’ demographics and their perceptions on online HP purchasing becomes a pivotal first step to form a basis for recommendations in Singapore’s pharmacovigilance efforts. Objective: To assess the prevalence of online HP purchasing behaviour among Singaporean e-commerce users. Methodology: This is a cross-sectional study targeting Singaporean e-commerce users recruited from various local websites and online forums. Participants were not randomized into study arms but instead stratified by random sampling method based on participants’ age. A self-administered anonymous questionnaire was used to explore participants' demographics, online HP purchasing behaviour, knowledge and attitude. The association of different variables with online HP purchasing behaviour was analysed using logistic regression statistics. Main outcome measures: Prevalence of HP e-commerce users in Singapore (%) and variables that contribute to the prevalence (adjusted prevalent ratio). Results: The study recruited 372 complete and valid responses. The prevalence of online HP consumers among e-commerce users in Singapore is estimated to be 55.9% (1.7 million consumers). Online purchasing of complementary HP (46.9%) was the most prevalent, followed by medical devices (21.6%) and Western medicine (20.5%). Multivariate analysis showed that age is an independent variable that correlates with the likelihood of buying HP online. The prevalence of HP e-commerce users is highest in the 35-44 age group (64.1%) and lowest among the 16-24 age group (36.4%). The most bought HP through the internet are vitamins and minerals (21.5%), non-herbal (15.9%), herbal (13.9%), weight loss (8.7%) and sports (8.4%) supplements. While the top 3 products are distributed equally between the genders, there is a skew towards female respondents (12.4% in females vs. 4.9% in males) for weight loss supplements and towards males (13.2% in males vs. 3.7% in females) for sports supplements. Even though online consumers are in the younger age brackets, our study found that up to 72.0% of HP bought online are bought for others (buyer’s family and/or friends). Multivariate analysis showed a statistically significant association between purchasing HP through online means and the perceptions that 'internet is safe' (adjusted Prevalence Ratio=1.15, CI 1.03-1.28), 'buying HP online is time saving' (PR=1.17, CI 1.01-1.36), and 'recognition of HP brand' (PR=1.21 CI 1.06-1.40). Conclusions: This study has provided prevalence data for online HP market in Singapore, and has allowed the country’s regulatory body to formulate a targeted pharmacovigilance approach to this growing problem.

Keywords: e-commerce, pharmaceuticals, pharmacovigilance, Singapore

Procedia PDF Downloads 332

Authors: Dragan Ribarić

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We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral Mindlin plate finite elements with 12 external degrees of freedom. In the problem-independent linked interpolation, the interpolation functions are independent of any problem material parameters and the rotation fields are not expressed in terms of the nodal displacement parameters. On the contrary, in the problem-dependent linked interpolation, the interpolation functions depend on the material parameters and the rotation fields are expressed in terms of the nodal displacement parameters. Two cubic 4-node quadrilateral plate elements are presented, named Q4-U3 and Q4-U3R5. The first one is modelled with one displacement and two rotation degrees of freedom in every of the four element nodes and the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form and which can be statically condensed within the element. Both elements are able to pass the constant-bending patch test exactly as well as the non-zero constant-shear patch test on the oriented regular mesh geometry in the case of cylindrical bending. In any mesh shape, the elements have the correct rank and only the three eigenvalues, corresponding to the solid body motions are zero. There are no additional spurious zero modes responsible for instability of the finite element models. In comparison with the problem-independent cubic linked interpolation implemented in Q9-U3, the nine-node plate element, significantly less degrees of freedom are employed in the model while retaining the interpolation conformity between adjacent elements. The presented elements are also compared to the existing problem-independent quadratic linked-interpolation element Q4-U2 and to the other known elements that also use the quadratic or the cubic linked interpolation, by testing them on several benchmark examples. Simple functional upgrading from the quadratic to the cubic linked interpolation, implemented in Q4-U3 element, showed no significant improvement compared to the quadratic linked form of the Q4-U2 element. Only when the additional bubble terms are incorporated in the displacement and rotation function fields, which complete the full cubic linked interpolation form, qualitative improvement is fulfilled in the Q4-U3R5 element. Nevertheless, the locking problem exists even for the both presented elements, like in all pure displacement elements when applied to very thin plates modelled by coarse meshes. But good and even slightly better performance can be noticed for the Q4-U3R5 element when compared with elements from the literature, if the model meshes are moderately dense and the plate thickness not extremely thin. In some cases, it is comparable to or even better than Q9-U3 element which has as many as 12 more external degrees of freedom. A significant improvement can be noticed in particular when modeling very skew plates and models with singularities in the stress fields as well as circular plates with distorted meshes.

Keywords: Mindlin plate theory, problem-independent linked interpolation, problem-dependent interpolation, quadrilateral displacement-based plate finite elements

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Authors: Sunil Sangwan, Narayan Chandra Nayak

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Over the last few decades, Indian banking system has achieved remarkable growth in its credit volume. However, one of the most disturbing facts about this growth is the uneven distribution of financial services across regions. Having witnessed limited success from all the earlier efforts towards financial inclusion targeting the rural poor and the underprivileged, provision of microfinance, of late, has emerged as a supplementary mechanism. There are two prominent modes of microfinance distribution in India namely Bank-SHG linkage (SBLP) and private Microfinance Institutions (MFIs). Ironically, such efforts also seem to have failed to achieve the desired targets as the microfinance services have witnessed skewed distribution across the states of the country. This study attempts to make a comparative analysis of the geographical skew of the SBLP and MFI in India and examine the factors influencing their regional distribution. The results indicate that microfinance services are largely concentrated in the southern region, accounting for about 50% of all microfinance clients and 49% of all microfinance loan portfolios. This is distantly followed by an eastern region where client outreach is close to 25% only. The north-eastern, northern, central, and western regions lag far behind in microfinance sectors, accounting for only 4%, 4%, 10%, and 7 % client outreach respectively. The penetration of SHGs is equally skewed, with the southern region accounting for 46% of client outreach and 70% of loan portfolios followed by an eastern region with 21% of client outreach and 13% of the loan portfolio. Contrarily, north-eastern, northern, central, western and eastern regions account for 5%, 5%, 10%, and 13% of client outreach and 3%, 3%, 7%, and 4% of loan portfolios respectively. The study examines the impact of literacy rate, rural poverty, population density, primary sector share, non-farm activities, loan default behavior and bank penetration on the microfinance penetration. The study is limited to 17 major states of the country over the period 2008-2014. The results of the GMM estimation indicate the significant positive impact of literacy rate, non-farm activities and population density on microfinance penetration across the states, while the rise in loan default seems to deter it. Rural poverty shows the significant negative impact on the spread of SBLP, while it has a positive impact on MFI penetration, hence indicating the policy of exclusion being adhered to by the formal financial system especially towards the poor. However, MFIs seem to be working as substitute mechanisms to banks to fill the gap. The findings of the study are a pointer towards enhancing financial literacy, non-farm activities, rural bank penetration and containing loan default for achieving greater microfinance prevalence.

Keywords: bank penetration, literacy rate, microfinance, primary sector share, rural non-farm activities, rural poverty

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Authors: Savas Yildiz

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The article assesses the performance of international aid donors to determine the sub-national distribution of their aid projects dependent on recipient countries’ governance. The present paper extends the scope from a cross-country perspective to a more detailed analysis by looking at the effects of institutional qualities on the sub-national distribution of foreign aid. The analysis examines geo-referenced aid project in 37 countries and 404 regions at the first administrative division level in Sub-Saharan Africa from the World Bank (WB) and the African Development Bank (ADB) that were approved between the years 2000 and 2011. To measure the influence of institutional qualities on the distribution of aid the following measures are used: control of corruption, government effectiveness, regulatory quality and rule of law from the World Governance Indicators (WGI) and the corruption perception index from Transparency International. Furthermore, to assess the importance of ethnic heterogeneity on the sub-national distribution of aid projects, the study also includes interaction terms measuring ethnic fragmentation. The regression results indicate a general skew of aid projects towards regions which hold capital cities, however, being incumbent presidents’ birth region does not increase the allocation of aid projects significantly. Nevertheless, with increasing quality of institutions aid projects are less skewed towards capital regions and the previously estimated coefficients loose significance in most cases. Higher ethnic fragmentation also seems to impede the possibility to allocate aid projects mainly in capital city regions and presidents’ birth places. Additionally, to assess the performance of the WB based on its own proclaimed goal to aim the poor in a country, the study also includes sub-national wealth data from the Demographic and Health Surveys (DSH), and finds that, even with better institutional qualities, regions with a larger share from the richest quintile receive significantly more aid than regions with a larger share of poor people. With increasing ethnic diversity, the allocation of aid projects towards regions where the richest citizens reside diminishes, but still remains high and significant. However, regions with a larger share of poor people still do not receive significantly more aid. This might imply that the sub-national distribution of aid projects increases in general with higher ethnic fragmentation, independent of the diverse regional needs. The results provide evidence that institutional qualities matter to undermine the influence of incumbent presidents on the allocation of aid projects towards their birth regions and capital regions. Moreover, even for countries with better institutional qualities the WB and the ADB do not seem to be able to aim the poor in a country with their aid projects. Even, if one considers need-based variables, such as infant mortality and child mortality rates, aid projects do not seem to be allocated in districts with a larger share of people in need. Therefore, the study provides further evidence using more detailed information on the sub-national distribution of aid projects that aid is not being allocated effectively towards regions with a larger share of poor people to alleviate poverty in recipient countries directly. Institutions do not have any significant influence on the sub-national distribution of aid towards the poor.

Keywords: aid allocation, georeferenced data, institutions, spatial analysis

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Authors: Ayon Mukherjee

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Covariate-adjusted response-adaptive (CARA) designs use the available responses to skew the treatment allocation in a clinical trial in towards treatment found at an interim stage to be best for a given patient's covariate profile. Extensive research has been done on various aspects of CARA designs with the patient responses assumed to follow a parametric model. However, ranges of application for such designs are limited in real-life clinical trials where the responses infrequently fit a certain parametric form. On the other hand, robust estimates for the covariate-adjusted treatment effects are obtained from the parametric assumption. To balance these two requirements, designs are developed which are free from distributional assumptions about the survival responses, relying only on the assumption of proportional hazards for the two treatment arms. The proposed designs are developed by deriving two types of optimum allocation designs, and also by using a distribution function to link the past allocation, covariate and response histories to the present allocation. The optimal designs are based on biased coin procedures, with a bias towards the better treatment arm. These are the doubly-adaptive biased coin design (DBCD) and the efficient randomized adaptive design (ERADE). The treatment allocation proportions for these designs converge to the expected target values, which are functions of the Cox regression coefficients that are estimated sequentially. These expected target values are derived based on constrained optimization problems and are updated as information accrues with sequential arrival of patients. The design based on the link function is derived using the distribution function of a probit model whose parameters are adjusted based on the covariate profile of the incoming patient. To apply such designs, the treatment allocation probabilities are sequentially modified based on the treatment allocation history, response history, previous patients’ covariates and also the covariates of the incoming patient. Given these information, an expression is obtained for the conditional probability of a patient allocation to a treatment arm. Based on simulation studies, it is found that the ERADE is preferable to the DBCD when the main aim is to minimize the variance of the observed allocation proportion and to maximize the power of the Wald test for a treatment difference. However, the former procedure being discrete tends to be slower in converging towards the expected target allocation proportion. The link function based design achieves the highest skewness of patient allocation to the best treatment arm and thus ethically is the best design. Other comparative merits of the proposed designs have been highlighted and their preferred areas of application are discussed. It is concluded that the proposed CARA designs can be considered as suitable alternatives to the traditional balanced randomization designs in survival trials in terms of the power of the Wald test, provided that response data are available during the recruitment phase of the trial to enable adaptations to the designs. Moreover, the proposed designs enable more patients to get treated with the better treatment during the trial thus making the designs more ethically attractive to the patients. An existing clinical trial has been redesigned using these methods.

Keywords: censored response, Cox regression, efficiency, ethics, optimal allocation, power, variability

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Authors: Rachid Belhachemi, Pierre Rostan, Alexandra Rostan

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This paper develops a discrete-time option pricing model for index options. The model consists of two key ingredients. First, daily stock return innovations are driven by a continuous hidden threshold mixed skew-normal (HTSN) distribution which generates conditional non-normality that is needed to fit daily index return. The most important feature of the HTSN is the inclusion of a latent state variable with a continuum of states, unlike the traditional mixture distributions where the state variable is discrete with little number of states. The HTSN distribution belongs to the class of univariate probability distributions where parameters of the distribution capture the dependence between the variable of interest and the continuous latent state variable (the regime). The distribution has an interpretation in terms of a mixture distribution with time-varying mixing probabilities. It has been shown empirically that this distribution outperforms its main competitor, the mixed normal (MN) distribution, in terms of capturing the stylized facts known for stock returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence. Second, heteroscedasticity in the model is captured by a threeexogenous-factor GARCH model (GARCHX), where the factors are taken from the principal components analysis of various world indices and presents an application to option pricing. The factors of the GARCHX model are extracted from a matrix of world indices applying principal component analysis (PCA). The empirically determined factors are uncorrelated and represent truly different common components driving the returns. Both factors and the eight parameters inherent to the HTSN distribution aim at capturing the impact of the state of the economy on price levels since distribution parameters have economic interpretations in terms of conditional volatilities and correlations of the returns with the hidden continuous state. The PCA identifies statistically independent factors affecting the random evolution of a given pool of assets -in our paper a pool of international stock indices- and sorting them by order of relative importance. The PCA computes a historical cross asset covariance matrix and identifies principal components representing independent factors. In our paper, factors are used to calibrate the HTSN-GARCHX model and are ultimately responsible for the nature of the distribution of random variables being generated. We benchmark our model to the MN-GARCHX model following the same PCA methodology and the standard Black-Scholes model. We show that our model outperforms the benchmark in terms of RMSE in dollar losses for put and call options, which in turn outperforms the analytical Black-Scholes by capturing the stylized facts known for index returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence.

Keywords: continuous hidden threshold, factor models, GARCHX models, option pricing, risk-premium

Procedia PDF Downloads 276