Some Topological Approaches for Generalized Rough Sets and Their Decision-Making Applications

The rough set principle was proposed as a methodology to cope with vagueness or uncertainty of data in the information systems. Day by day, this theory has proven its efficiency in handling and modeling many real-life problems. To contribute to this area, we present new topological approaches as a generalization of Pawlak’s theory by using j-adhesion neighborhoods and elucidate the relationship between them and some other types of approximations with the aid of examples. Topologically, we give another generalized rough approximation using near open sets. Also, we generate generalized approximations created from the topological models of j-adhesion approximations. Eventually, we compare the approaches given herein with previous ones to obtain a more affirmative solution for decision-making problems.

Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions

We introduce a family of inhomogeneous XX spin chains whose squared couplings are a polynomial of degree at most four in the site index. We show how to obtain an asymptotic approximation for the Rényi entanglement entropy of all such chains in a constant magnetic field at half filling by exploiting their connection with the conformal field theory of a massless Dirac fermion in a suitably curved static background. We study the above approximation for three particular chains in the family, two of them related to well-known quasi-exactly solvable quantum models on the line and the third one to classical Krawtchouk polynomials, finding an excellent agreement with the exact value obtained numerically when the Rényi parameter α is less than one. When α ≥ 1 we find parity oscillations, as expected from the homogeneous case, and show that they are very accurately reproduced by a modification of the Fagotti-Calabrese formula. We have also analyzed the asymptotic behavior of the Rényi entanglement entropy in the non-standard situation of arbitrary filling and/or inhomogeneous magnetic field. Our numerical results show that in this case a block of spins at each end of the chain becomes disentangled from the rest. Moreover, the asymptotic approximation for the case of half filling and constant magnetic field, when suitably rescaled to the region of non-vanishing entropy, provides a rough approximation to the entanglement entropy also in this general case.

DyScore: A Boosting Scoring Method with Dynamic Properties for Identifying True Binders and Non-binders in Structure-based Drug Discovery

The accurate prediction of protein-ligand binding affinity is critical for the success of computer-aided drug discovery. However, the accuracy of current scoring functions is usually unsatisfactory due to their rough approximation or sometimes even omittance of many factors involved in protein-ligand binding. For instance, the intrinsic dynamic of the protein-ligand binding state is usually disregarded in scoring function because these rapid binding affinity prediction approaches are only based on a representative complex structure of the protein and ligand in the binding state. That is, the dynamic protein-ligand binding complex ensembles are simplified as a static snapshot in calculation. In this study, two novel features were proposed for characterizing the dynamic properties of protein-ligand binding based on the static structure of the complex, which is expected to be a valuable complement to the current scoring functions. The two features demonstrate the geometry-shape matching between a protein and a ligand as well as the dynamic stability of protein-ligand binding. We further combined these two novel features with several classical scoring functions to develop a binary classification model called DyScore that uses the Extreme Gradient Boosting algorithm to classify compound poses as binders or non-binders. We have found that DyScore achieves state-of-the-art performance in distinguishing active and decoy ligands on both enhanced DUD dataset and external test set with both proposed novel features showing significant contributions to the improved performance. Especially, DyScore exhibits superior performance on early recognition, a crucial requirement for success in virtual screening and de novo drug design. The DyScore webserver is freely available to all at: http://dyscore.deepdrug.net.

Influence of smoking and other cardiovascular risk factors on heart rate circadian rhythm in normotensive and hypertensive subjects

Circadian heart rate (HR) is influenced by hypertension and other cardiovascular risk factors particularly smoking, obesity and dyslipidemia. Until now, to evaluate the HR changes due to presence of these risk factors, a single HR office measure or a mean evaluated on day time or night time or 24h was used. However, since HR shows a circadian behavior, a single value represents only a rough approximation of this behavior. In this study, we analyzed the influence of smoking, obesity and dyslipidemia on the circadian rhythm in normotensive and hypertensive subject groups presenting only one of these risk factors. The 24h HR recordings of 170 normotensive (83 without risk factors, 20 smokers, 44 with dyslipidemia, 23 obese) and 353 hypertensive (169 without risk factors, 32 smokers, 99 with dyslipidemia, 53 obese) subjects were acquired using a Holter Blood Pressure Monitor. Results highlighted a specific circadian behavior with three characteristic periods presenting different HR means and rates of HR change in the eight subject groups. The slopes could be used both to estimate the morning HR surge associated with acute cardiovascular effects in the awakening and to evaluate the decline during the night. Moreover, we suggest to use three HR mean values (one for each identified period of the day) rather than two HR values to better describe the circadian HR behavior. Furthermore, smoking increased and dyslipidemia decreased mean HR values from 10:00 to 04:00, both in normotensive and hypertensive subjects in comparison with subjects without risk factors. In this time interval, hypertensive obese subjects showed higher values while normotensive ones presented quite similar values than subjects without risk factors. During the awakening (05:00–10:00) the slopes were similar among all groups with no significant difference among the mean HR values.

The Unmeritorious ‘Legality’/‘Merits’ Distinction in Singapore Administrative Law

The Singapore courts often state that judicial review of executive decision-making ought only to involve an inquiry into the ‘legality’ of a decision or the ‘decision-making process’, and not the ‘decision itself’ or its ‘merits’ – let us call this the ‘Distinction’. This article argues that the Distinction should be expunged from Singapore law. The Distinction has its roots in English case law which aimed to prevent the courts from arbitrarily substituting their decision for the executive's by reason of mere disagreement. But Singapore case law has gone further and treated the Distinction as a general principle applicable to all of administrative law. However, the Distinction is too vague for this purpose (as seen from Singapore cases which have interpreted the distinction inconsistently). It is conceptually problematic, incompatible with the practicalities of judicial review (particularly substantive review as recognised in Singapore law), and has occasionally been paid lip service but not followed in substance. The Distinction cannot form a coherent principle to guide the courts and ought to be replaced by a more nuanced application of constitutional principles relevant to determining the appropriate scope of review. Whatever these principles may be, and however they are to be balanced, the Distinction can be but an over-inclusive rough approximation of them which hampers the development of the law.

TMS Intensity and Focality Correlation with Coil Orientation at Three Non-Motor Regions

Objective: The aim of this study is to define the best transcranial magnetic stimulation (TMS) coil orientations for three clinically relevant brain areas (pre-supplementary motor area, inferior frontal gyrus, and posterior parietal cortex) by means of simulations in 12 realistic head models of current density. Methods: We computed the current densities generated by TMS in our three volumes of interest (VOI) that were delineated based on published atlases. We then analyzed the maximum intensity and spatial focality for the normal and absolute components of the current density considering different percentile thresholds. Lastly, we correlated these results with the different anatomical properties of our VOIs. Results: Overall, the spatial focality of the current density for the three VOIs varied depending on the coil’s orientation. There was major interindividual variability, and there was therefore no specific orientation that produced the best focality for all subjects. Further analysis showed that the differences in individual brain anatomy were related to the amount of focality achieved. In general, a larger percentage of sulci resulted in larger spatial focality. Moreover, larger normal current density intensity was achieved when positioning the coil axis perpendicular to the predominant orientations of the gyri of each ’s VOI. Conclusion: For a rough approximation, better coil orientations can be based on the individual’s specific brain morphology at the VOI. Moreover, TMS computational models should be employed to obtain better coil orientations in non-motor regions of interest. Significance: Finding better coil orientations in non-motor regions is a challenge in TMS and seeks to reduce interindividual variability. Our individualized TMS simulation pipeline leads to lesser interindividual variability in the focality, likely enhancing the efficacy of the stimulation and reducing the risk of stimulating adjacent, nontargeted areas. @font-face {font-family:Helvetica; panose-1:0 0 0 0 0 0 0 0 0 0; mso-font-charset:0; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:-536870145 1342208091 0 0 415 0;}@font-face {font-family:"Cambria Math"; panose-1:2 4 5 3 5 4 6 3 2 4; mso-font-charset:0; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face {font-family:Calibri; panose-1:2 15 5 2 2 2 4 3 2 4; mso-font-charset:0; mso-generic-font-family:swiss; mso-font-pitch:variable; mso-font-signature:-1610611985 1073750139 0 0 159 0;}@font-face {font-family:Times; panose-1:0 0 5 0 0 0 0 2 0 0; mso-font-alt:Times; mso-font-charset:0; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:-536870145 1342185562 0 0 415 0;}p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:""; margin-top:0cm; margin-right:0cm; margin-bottom:8.0pt; margin-left:0cm; line-height:107%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri",sans-serif; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;}.MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; font-size:11.0pt; mso-ansi-font-size:11.0pt; mso-bidi-font-size:11.0pt; font-family:"Calibri",sans-serif; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;}.MsoPapDefault {mso-style-type:export-only; margin-bottom:8.0pt; line-height:107%;}div.WordSection1 {page:WordSection1;}

TMS Intensity and Focality Correlation with Coil Orientation at Three Non-Motor Regions

Objective: The aim of this study is to define the best transcranial magnetic stimulation (TMS) coil orientations for three clinically relevant brain areas (pre-supplementary motor area, inferior frontal gyrus, and posterior parietal cortex) by means of simulations in 12 realistic head models of current density. Methods: We computed the current densities generated by TMS in our three volumes of interest (VOI) that were delineated based on published atlases. We then analyzed the maximum intensity and spatial focality for the normal and absolute components of the current density considering different percentile thresholds. Lastly, we correlated these results with the different anatomical properties of our VOIs. Results: Overall, the spatial focality of the current density for the three VOIs varied depending on the coil’s orientation. There was major interindividual variability, and there was therefore no specific orientation that produced the best focality for all subjects. Further analysis showed that the differences in individual brain anatomy were related to the amount of focality achieved. In general, a larger percentage of sulci resulted in larger spatial focality. Moreover, larger normal current density intensity was achieved when positioning the coil axis perpendicular to the predominant orientations of the gyri of each ’s VOI. Conclusion: For a rough approximation, better coil orientations can be based on the individual’s specific brain morphology at the VOI. Moreover, TMS computational models should be employed to obtain better coil orientations in non-motor regions of interest. Significance: Finding better coil orientations in non-motor regions is a challenge in TMS and seeks to reduce interindividual variability. Our individualized TMS simulation pipeline leads to lesser interindividual variability in the focality, likely enhancing the efficacy of the stimulation and reducing the risk of stimulating adjacent, nontargeted areas. @font-face {font-family:Helvetica; panose-1:0 0 0 0 0 0 0 0 0 0; mso-font-charset:0; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:-536870145 1342208091 0 0 415 0;}@font-face {font-family:"Cambria Math"; panose-1:2 4 5 3 5 4 6 3 2 4; mso-font-charset:0; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face {font-family:Calibri; panose-1:2 15 5 2 2 2 4 3 2 4; mso-font-charset:0; mso-generic-font-family:swiss; mso-font-pitch:variable; mso-font-signature:-1610611985 1073750139 0 0 159 0;}@font-face {font-family:Times; panose-1:0 0 5 0 0 0 0 2 0 0; mso-font-alt:Times; mso-font-charset:0; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:-536870145 1342185562 0 0 415 0;}p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:""; margin-top:0cm; margin-right:0cm; margin-bottom:8.0pt; margin-left:0cm; line-height:107%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri",sans-serif; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;}.MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; font-size:11.0pt; mso-ansi-font-size:11.0pt; mso-bidi-font-size:11.0pt; font-family:"Calibri",sans-serif; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;}.MsoPapDefault {mso-style-type:export-only; margin-bottom:8.0pt; line-height:107%;}div.WordSection1 {page:WordSection1;}