Face Size Research Articles

PARAMETERS RELATIONSHIP OF THE FACIAL AND CEREBRAL PARTS OF THE SKULL AND THE POSTERIOR FOSSA

The purpose of the study was to determine the relationship between the parameters of the facial and brain bones of the skull and the structures of the posterior cranial fossa. The most important area of medical craniology remains the complex study of the typical variability of skull structures and formations and the regularity of their interrelationships in general. These include the posterior fossa with its brain regions and vascular communications. The morphology of the posterior fossa was studied on 13 passport turtles of adults from the collection of the fundamental museum of the Department of Clinical Anatomy, Anatomy and Operative Surgery of the Dnipro State Medical University. To solve the problems, a complex of craniometric methods was used. Craniometric studies of the posterior cranial fossa, the base of the skull, were performed with a thick compass with a millimetre scale and a technical calliper with a fi ssion price of 0.01 mm, according to the standard craniology procedure. For statistical processing of data obtained as a result of craniometry the method of complex statistical analysis is applied, which includes modern methods of mathematical analysis: variation, correlation, factor and regression. Statistical analysis of the posterior fossa showed no signifi cant gender and age diff erences. The obtained data can be used both in theoretical medicine and in practical medicine, in particular in neurosurgery, to determine the volume of the posterior cranial fossa by the external size of the facial and cerebral regions of the skull. In our work, measurements were made of the skeletal structures of the posterior cranial fossa in the plane of the Frankfurt horizontal along the external dimensions of the facial and cerebral areas of the skull. The morphometric traits of «close» posterior cranial fossa (posterior cranial fossa) have been highlighted as increasing the ratio of the brain matter volume of the posterior cranial fossa to its bone volume. Craniometrically, the volume of the posterior cranial fossa has been determined to be between 110 and 218 cm3, averaging 158 cm3 with a statistical deviation of 19.14. The volume of the posterior cranial fossa in adults ranges from 140 to 230 cm3, with an average of 178 cm3. The posterior fossa volume of 178 cm3 is an indication of a «close» posterior cranial fossa. Studies of the correlation between the facial and posterior cranial lobes have shown that the posterior fossa correlates to varying degrees with individual facial size. As a result of research, V truncated cone, V ellipsoid and V cut of ball were determined. The V ellipsoid ranged from a minimum of 138,662 to a maximum of 225,688 cm3, V truncated cone from 111,562 to 169,455 cm3; the V cut of the ball from 83,694 to 192,06 cm3.

High-Performance Thin-Film Transistor with Atomic Layer Deposition (ALD)-Derived Indium-Gallium Oxide Channel for Back-End-of-Line Compatible Transistor Applications: Cation Combinatorial Approach.

In this paper, the feasibility of an indium-gallium oxide (In2(1-x)Ga2xOy) film through combinatorial atomic layer deposition (ALD) as an alternative channel material for back-end-of-line (BEOL) compatible transistor applications is studied. The microstructure of random polycrystalline In2Oy with a bixbyite structure was converted to the amorphous phase of In2(1-x)Ga2xOy film under thermal annealing at 400 °C when the fraction of Ga is ≥29 at. %. In contrast, the enhancement in the orientation of the (222) face and subsequent grain size was observed for the In1.60Ga0.40Oy film with the intermediate Ga fraction of 20 at. %. The suitability as a channel layer was tested on the 10-nm-thick HfO2 gate oxide where the natural length was designed to meet the requirement of short channel devices with a smaller gate length (<100 nm). The In1.60Ga0.40Oy thin-film transistors (TFTs) exhibited the high field-effect mobility (μFE) of 71.27 ± 0.98 cm2/(V s), low subthreshold gate swing (SS) of 74.4 mV/decade, threshold voltage (VTH) of -0.3 V, and ION/OFF ratio of >108, which would be applicable to the logic devices such as peripheral circuit of heterogeneous DRAM. The in-depth origin for this promising performance was discussed in detail, based on physical, optical, and chemical analysis.

Influence of face grain angle, size, and moisture content on the edgewise bending strength and stiffness of birch plywood

Birch plywood exhibits outstanding mechanical properties with regards to tensile, compressive, and shear behaviors, making this engineered wood product promising in timber connection applications. However, the edgewise bending strength and stiffness, which are often critical for the design of gusset plates, have not been investigated thoroughly. Moreover, in engineering applications, the size and moisture content of the plywood plate are in general very different from those adopted in laboratory testing according to current standards. This paper aims to investigate the influence of face grain angle, size, and moisture content on the edgewise bending strength and stiffness of birch plywood. In total, 288 birch plywood specimens were tested in three-point bending at five different face grain angles to the beam longitudinal axis (from 0° (parallel) to 90° (perpendicular), with an angle step of 22.5°), with four different sizes (with the nominal depth of 20 mm, 30 mm, 40 mm, and 50 mm) and three different moisture contents (7.2 %, 11.9 %, and 21.8 %). Analytical and numerical models, both taking non-linear elasto-plastic compressive behaviors into account, were developed for the prediction of the ultimate moment capacity based on different failure definitions. Lastly, the relationships between the bending strength and elastic modulus were analyzed.

Factors influencing and long-term effects of manual myotomy phenomenon during physiotherapy for congenital muscular torticollis

PurposeTo investigate the factors influencing and long-term effects of manual myotomy (MM) occurring during physiotherapy for congenital muscular torticollis (CMT).MethodsWe retrospectively collected the clinical data of children with CMT receiving physiotherapy between 2008 and 2018. The children were divided into manual myotomy (MM) and non-manual myotomy (NMM) groups according to whether MM occurred during treatment. We assessed physiotherapy outcomes in children with CMT using craniofacial asymmetry parameters and the Cheng–Tang rating score. By measuring the ear-eye distance, ear-nose distance, eye-mouth distance, ear-mouth distance, half-head circumference, and half-head top at two sides to evaluate craniofacial asymmetry. Based on the Cheng–Tang assessment criteria, we recorded the range of rotation, range of lateral flexion, the status of the contracted muscle, the hardness of the mass, the extent of head tilting during activities and sleeping, the status of daily activities, face size, type of head shape, cranial changes, and subjective head tilting to assess the effectiveness of treatment. Clinical data and outcome indicators (craniofacial asymmetry parameters and Cheng–Tang rating score) were compared.ResultsThe MM group had a significantly higher total Cheng–Tang rating score than the NMM group (P < 0.05). Age at initial physiotherapy session was the risk factor for MM during physiotherapy.ConclusionChildren with CMT developing MM during physiotherapy generally have a good outcome, although we do not recommend MM as a goal of treatment. Physiotherapists should understand this phenomenon, assess relevant factors to predict risk, and carefully observe treatment to prevent possible complications.

Emotion recognition by web-shaped model

Emotions recognition is widely applied for many tasks in different fields, from human-computer and human-robot interaction to learning platforms. Also, it can be used as an intrinsic approach for face recognition tasks, in which an expression-independent face classifier is developed. Most approaches face the problem by designing deeper and deeper neural networks that consider an expression as a still image or, in some cases, a sequence of consecutive frames depicting the temporal component of the expression. However, these suffer the training phase’s computational burden, which can take hours or days to be completed. In this work, a Web Shaped Model is proposed, which consists of a geometrical approach for extracting discriminant features from a face, depicting the characteristics of an expression. The model does not need to be trained since it is applied on a face and centred on the nose tip, resulting in image size and face size independence. Experiments on publicly available datasets show that this approach reaches comparable and even better results than those obtained applying DNN-based approaches.

Midfacial Morphology and Neandertal-Modern Human Interbreeding.

Simple SummaryStudies of human fossils, and the DNA extracted from them, reveal a complex history of interbreeding between various human lineages over the last one hundred thousand years. Of particular interest is the nature of the population interactions between the Neandertals of Ice Age Europe and western Asia and the modern humans that eventually replaced them. Here, we used six measurements of the facial skeleton, in samples of Neandertal and early modern human fossils, in an exploratory study aimed at trying to identify geographic regions (from the Near East to western Europe) where interbreeding may have been prevalent enough to have left a signal in the facial morphology of the early modern humans of those regions. Although fossil sample sizes were in some cases very small, the results are consistent with the Near East having played an important role in the introduction of Neandertal genes into the genomes of living humans.Ancient DNA from, Neandertal and modern human fossils, and comparative morphological analyses of them, reveal a complex history of interbreeding between these lineages and the introgression of Neandertal genes into modern human genomes. Despite substantial increases in our knowledge of these events, the timing and geographic location of hybridization events remain unclear. Six measures of facial size and shape, from regional samples of Neandertals and early modern humans, were used in a multivariate exploratory analysis to try to identify regions in which early modern human facial morphology was more similar to that of Neandertals, which might thus represent regions of greater introgression of Neandertal genes. The results of canonical variates analysis and hierarchical cluster analysis suggest important affinities in facial morphology between both Middle and Upper Paleolithic early modern humans of the Near East with Neandertals, highlighting the importance of this region for interbreeding between the two lineages.

Evaluation of Naso-facial proportion of the Face and Their Correlation in Bangladeshi Buddhist Rakhain Ethnic Males

Background: The face and nasal dimensions are most important cephalometric parameters describing human morphology. Nose is the most important aesthetic unit of face. There is wide variation in size and shape of nose and face due to ethnic influences. Objective: The purpose of the present study was to evaluate the naso-facial proportion of the face and their correlation in adult healthy Bangladeshi Buddhist Rakhain Ethnic males. Methodology: This cross-sectional observational study was carried out in the Department of Anatomy, Bangabandhu Sheikh Mujib Medical University (BSMMU), Dhaka from January 2011 to December 2011 for a period of one (01) year. Adult Healthy Bangladeshi Buddhist Rakhain males with the age group of 18 to 30 years were included as study population. Results: This study shows mean of nose width was 41.16 (±3.03) and mean of ¼ face width was 34.80(±1.70). This study shows nose width was 41.16 (±3.03) and ¼ face width was 34.80(±1.70). Conclusion: It was observed that nose width was significantly wider than ¼ of face width in the adult healthy Bangladeshi Buddhist Rakhain. This parameter was the importance of using patients as observers, as well as clinicians, in facial attractiveness research. Journal of Current and Advance Medical Research, January 2022;9(1):32-35

Designing an AI-Based Virtual Try-On Web Application.

In the last few years, Augmented Reality, Virtual Reality, and Artificial Intelligence (AI) have been increasingly employed in different application domains. Among them, the retail market presents the opportunity to allow people to check the appearance of accessories, makeup, hairstyle, hair color, and clothes on themselves, exploiting virtual try-on applications. In this paper, we propose an eyewear virtual try-on experience based on a framework that leverages advanced deep learning-based computer vision techniques. The virtual try-on is performed on a 3D face reconstructed from a single input image. In designing our system, we started by studying the underlying architecture, components, and their interactions. Then, we assessed and compared existing face reconstruction approaches. To this end, we performed an extensive analysis and experiments for evaluating their design, complexity, geometry reconstruction errors, and reconstructed texture quality. The experiments allowed us to select the most suitable approach for our proposed try-on framework. Our system considers actual glasses and face sizes to provide a realistic fit estimation using a markerless approach. The user interacts with the system by using a web application optimized for desktop and mobile devices. Finally, we performed a usability study that showed an above-average score of our eyewear virtual try-on application.

Group Emotion Detection Based on Social Robot Perception.

Social robotics is an emerging area that is becoming present in social spaces, by introducing autonomous social robots. Social robots offer services, perform tasks, and interact with people in such social environments, demanding more efficient and complex Human–Robot Interaction (HRI) designs. A strategy to improve HRI is to provide robots with the capacity of detecting the emotions of the people around them to plan a trajectory, modify their behaviour, and generate an appropriate interaction with people based on the analysed information. However, in social environments in which it is common to find a group of persons, new approaches are needed in order to make robots able to recognise groups of people and the emotion of the groups, which can be also associated with a scene in which the group is participating. Some existing studies are focused on detecting group cohesion and the recognition of group emotions; nevertheless, these works do not focus on performing the recognition tasks from a robocentric perspective, considering the sensory capacity of robots. In this context, a system to recognise scenes in terms of groups of people, to then detect global (prevailing) emotions in a scene, is presented. The approach proposed to visualise and recognise emotions in typical HRI is based on the face size of people recognised by the robot during its navigation (face sizes decrease when the robot moves away from a group of people). On each frame of the video stream of the visual sensor, individual emotions are recognised based on the Visual Geometry Group (VGG) neural network pre-trained to recognise faces (VGGFace); then, to detect the emotion of the frame, individual emotions are aggregated with a fusion method, and consequently, to detect global (prevalent) emotion in the scene (group of people), the emotions of its constituent frames are also aggregated. Additionally, this work proposes a strategy to create datasets with images/videos in order to validate the estimation of emotions in scenes and personal emotions. Both datasets are generated in a simulated environment based on the Robot Operating System (ROS) from videos captured by robots through their sensory capabilities. Tests are performed in two simulated environments in ROS/Gazebo: a museum and a cafeteria. Results show that the accuracy in the detection of individual emotions is 99.79% and the detection of group emotion (scene emotion) in each frame is 90.84% and 89.78% in the cafeteria and the museum scenarios, respectively.

SIGEST

The SIGEST article in this issue is Hamiltonicity of Cubic Planar Graphs with Bounded Face Sizes, by František Kardoš. The original version of this article appeared in the SIAM Journal on Discrete Mathematics in 2020. Barnette's Conjecture is a famous problem in graph theory which asserts that every cubic bipartite 3-connected planar graph has a Hamiltonian cycle. The conjecture stems from an attempt in 1880 by P. G. Tait to solve the Four Color Theorem by establishing that every cubic 3-connected planar graph has a Hamiltonian cycle. This is a stronger statement than the Four Color Theorem and it actually turns out to be false, as shown by W. T. Tutte in 1946. Barnette's Conjecture is equivalent to the statement that every plane cubic 3-connected graph with all faces of even size has a Hamiltonian cycle. Our SIGEST paper proves a closely related conjecture of Barnette and Goodey asserting that every plane cubic 3-connected graph with all faces of size at most six has a Hamiltonian cycle; this also solves an open problem from mathematical chemistry, which posited the existence of a Hamiltonian cycle under the stronger assumption that all faces have size five or six. The proof consists of several reduction steps and eventually boils the problem down to checking a finite number of configurations, which is handled with the assistance of a computer. The derivations are accompanied by high-quality graphical illustrations, and the author has provided computer code for the automated parts of the proof.

Hamiltonicity of Cubic Planar Graphs with Bounded Face Sizes

Hamiltonicity of Cubic Planar Graphs with Bounded Face Sizes

Electrochemical Deposition of Pure-Nickel Microstructures with Controllable Size.

Pure nickel microstructures have been widely used in MEMS and have great application potential as a sacrificial mandrel for fabricating terahertz micro-cavity components. The performance of MEMS and terahertz micro-cavity components can be significantly improved through the use of high-quality pure nickel microstructures. Up to now, microfabrication techniques, such as laser micromachining, wire electrical-discharge machining, and cold-spray additive manufacturing, have been used to machine various types of such microstructures. However, huge challenges are involved in using these micromachining techniques to fabricate pure-nickel microstructures with controllable size and good dimensional accuracy, surface roughness, and edge radius. In this paper, taking the example of a pure-nickel rectangular mandrel that corresponds to the size of the end face of a 1.7-THz rectangular waveguide cavity, the machining processes for the electrochemical deposition of pure-nickel microstructures with controllable size, high dimensional accuracy, and good surface roughness and edge radius are discussed systematically. This proposed method can be used to manufacture various types of high-quality pure-nickel microstructures.

Multi-disciplinary Optimizations on Flexural Behavioural Effects on Various Advanced Aerospace Materials: A validated investigation

Generally, the importance of bending test has been employed to analyse the induction level of internal resistance of its larger face size of the test speciemens. Comparatively, stress induction is quite larger at the perpendicular face, where the bending load has been initiated its point of contact. Therefore the estimation of the location of maximum stress induction on bending test specimen must be analysed for the purpose to estimate the breaking point of test specimen, which supported a lot in the lifespan estimation of a component. In this work, three different composites are selected under the category of primary composites and thereby underwent the bending testing for the purpose of material refinement to tackle compressive load based applications. Three-Point flexural tests are conducted on the primary composites. The internal molecules bonds at peak loads are visulaized through SEM approach. Thus, the perfect inital and boundary conditions for computational strurtual analyses are found out. Ansys Workbench is an advancement tool, which is used in this work for composite generation and structural simulations. All the computational tests are effectively executed with the help of advanced coupling facility between different working environments. Finally, the numerical results are compared with experimental results and then suitable material is shortlsted based on high load withstand capacity. Additionally, the conventional analytical approaches are used to validate the flexural outcomes. Further, the advanced finite element analyses are expanded to advanced composites materials such as nanocomposites, shape memory alloys based composites, and sandwich composites. From the above all studies, the superior material is finalized based on the outcomes of this multi-inclusive investigations.

Sex Differences in Adult Facial Three-Dimensional Morphology: Application to Gender-Affirming Facial Surgery.

Background: Gender-affirming facial surgery (GFS) is pursued by transgender individuals who desire facial features that better reflect their gender identity. Currently, there are a few objective guidelines to justify and facilitate effective surgical decision making. Objective: To quantify the effect of sex on adult facial size and shape through an analysis of three-dimensional (3D) facial surface images. Materials and Methods: Facial measurements were obtained by registering an atlas facial surface to 3D surface scans of 545 males and 1028 females older than 20 years of age. The differences between male and female faces were analyzed and visualized for a set of predefined surgically relevant facial regions. Results: On average, male faces are 7.3% larger than female faces (Cohen's D = 2.17). Sex is associated with significant facial shape differences (p < 0.0001) in the entire face as well as in each sub-region considered in this study. The facial regions in which sex has the largest effect on shape are the brow, jaw, nose, and cheek. Conclusions: These findings provide biologic data-driven anatomic guidance and justification for GFS, particularly forehead contouring cranioplasty, mandible and chin alterations, rhinoplasty, and cheek modifications.

Modeling of Polycrystalline Material Microstructure with 3D Grain Boundary Based on Laguerre-Voronoi Tessellation.

Voronoi tessellations are shown to be statistically representative of polycrystalline microstructures, which have been widely accepted for the modeling of microstructures of metallurgic and ceramic materials. In this paper, a new implementation of the Voronoi diagram in Laguerre geometry is presented for the generation of numerical models of polycrystalline microstructures, where the size and shape of the grains can be controlled, and the 3D grain boundaries can be modeled with a specified thickness. The distribution of grain sizes in the models is fitted to a lognormal distribution, compared with the normal distribution in the Voronoi tessellation methods. Finally, statistical analyses of grain face and grain size distribution are performed with the models, and the macroscopic elastic properties of polycrystalline ceramic materials are simulated to verify the capability of the presented method.

Driver Fatigue Detection Using Improved Deep Learning and Personalized Framework

In transportation, drivers’ state directly affects traffic safety. Therefore, an accurate driver’s fatigue detection is crucial for ensuring driving safety. Real-time and accurate technology is needed for driver fatigue detection. To address this problem, this article proposes a fatigue detection method based on an improved deep learning and personalized framework. First, clustering is applied to face size, and cluster numbers are used to determine the number of detection layers. Then, the size of anchor boxes is set according to the face size. In the proposed framework, the number of convolutional networks is set according to the principle that the receptive field should match the face size in the predicted feature map. Finally, a variety of fatigue features are learned by minimizing the loss function. In addition, a personalized face fatigue detection method is put forward for building a fatigue detection framework to judge the driver’s fatigue status more reasonably. The experimental results show that the proposed method based on an improved clustering method and local receptive field can improve the detection speed of driver’s fatigue while maintaining high detection accuracy. The proposed method can reach 125 fps by using GPU GeForce GTX TITAN, which satisfies the real-time requirement. In addition, the personalized framework can achieve high detection accuracy while keeping acceptable speed. The proposed model can accurately and timely detect driver fatigue, which can help to avoid accidents.

Determination of tightness of the filtering half-mask adhesion to a user’s face

Purpose. To determine the correlation between adhesion tightness of filtering half-masks and anthropometric indices of employees faces. Methodology. To study tightness of the half-mask adhesion to a users face, a coefficient of NaCl aerosol test was determined in accordance with the requirements by DSTU EN 149:2017 (EN 149:2001+A1:2009, IDT). Volunteers took part in the testing selected in keeping with the parametric table divided into 12 settings along the face length and across its width. The tests were carried out using Respi and Standart respirators produced in lots by SPE Standart ltd. Findings. It has been identified that the tested filtering half-masks correspond to the standards by DSTU EN 149:2017 (EN 149:2001+A1:2009, IDT) and provide adequate protection of respiratory organs of users against harmful aerosols. It has been demonstrated that the required half-mask adhesion to a face depends upon the obturator design, half-mask geometry, and stretching force of a headband. It has been proved that employees with small faces require the instrumental verification of the preferred half-mask while selecting respiratory protective equipment. In turn, for users with large faces quality control is quite sufficient by means of any suitable method described by DSTU EN 529:2006 (EN 529:2005, IDT). Individuals with large faces have demonstrated the greatest values of the tightness coefficient of filtering half-mask adhesion. Originality. It is represented by the scientific substantiation of the tightness coefficient of filtering half-mask adhesion upon the length and width of users faces. Practical value. Mathematical expressions have been derived making it possible to calculate the tightness coefficient of the half-mask adhesion relying upon the face size. The abovementioned will help assess preliminarily protective characteristics of respirators without specific laboratory equipment.

Hamiltonian cycles in annular decomposable Barnette graphs

Barnette’s conjecture is an unsolved problem in graph theory. The problem states that every 3-regular (cubic), 3-connected, planar, bipartite (Barnette) graph is Hamiltonian. Partial results have been derived with restrictions on the number of vertices, several properties of face-partitions and dual graphs of Barnette graphs, while some studies focus just on structural characterizations of Barnette graphs. Noting that spider web graphs are a subclass of Annular Decomposable Barnette (ADB graphs) graphs and are Hamiltonian, we study ADB graphs and their annular-connected subclass (ADB-AC graphs). We show that ADB-AC graphs can be generated from the smallest Barnette graph (B 0) using recursive edge operations. We derive several conditions assuring the existence of Hamiltonian cycles in ADB-AC graphs without imposing restrictions on the number of vertices, face size or any other constraints on the face partitions. We show that there can be two types of annuli in ADB-AC graphs, ring annuli and block annuli. Our main result is, ADB-AC graphs having non-singular sequences of ring annuli are Hamiltonian.

Facial Achromatic Number of Triangulations with Given Guarding Number

A (not necessarily proper) $k$-coloring $c : V(G) \rightarrow \{1,2,\dots,k\}$ of a graph $G$ on a surface is a {\em facial $t$-complete $k$-coloring} if every $t$-tuple of colors appears on the boundary of some face of $G$. The maximum number $k$ such that $G$ has a facial $t$-complete $k$-coloring is called a {\em facial $t$-achromatic number} of $G$, denoted by $\psi_t(G)$. In this paper, we investigate the relation between the facial 3-achromatic number and guarding number of triangulations on a surface, where a {\em guarding number} of a graph $G$ embedded on a surface, denoted by $\gd(G)$, is the smallest size of its {\em guarding set} which is a generalized concept of guards in the art gallery problem. We show that for any graph $G$ embedded on a surface, $\psi_{\Delta(G^*)}(G) \leq \gd(G) + \Delta(G^*) - 1$, where $\Delta(G^*)$ is the largest face size of $G$. Furthermore, we investigate sufficient conditions for a triangulation $G$ on a surface to satisfy $\psi_{3}(G) = \gd(G) + 2$. In particular, we prove that every triangulation $G$ on the sphere with $\gd(G) = 2$ satisfies the above equality and that for one with guarding number $3$, it also satisfies the above equality with sufficiently large number of vertices.

Relationship between mean grain face curvature and number of faces in normal grain growth: The meaning of normalized integral mean curvature

This paper describes the physical meaning of MS norm (=MS/V1/3), the unitless grain size normalized integral mean curvature of grain faces, as a descriptor of the effect of face number on grain shape, affecting grain boundary velocity in curvature driven grain growth. MS norm has consistently been found to have a linear relationship with face class, f, among diverse experiments with real materials and simulations. Analysis of MS norm in terms of the effects of grain size and number of faces on its components, the average mean curvature H¯ and surface area S, show that combined, they reduce to a unitless term that is a function only of grain shape. Values of H¯, approximated as MS /V2/3 are shown for the first time as a function of f and grain scale. Plots of H¯ versus f show positive values at low face classes, decreasing rapidly towards zero at f∼15, and becoming increasingly negative at a decreasing rate with increasing f. Plotted versus linear grain scale, V1/3, the value of H¯ for each face class decreases in magnitude with increased scale during growth. Plots of Ms vs. face class show a continuous decrease as with H¯. Independent plots of Ms vs. linear grain scale for individual face classes were found to be linear through the origin, with slopes equal to MS norm.