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## Über dieses Buch

This two volume set LNBI 10813 and LNBI 10814 constitutes the proceedings of the 6th International Work-Conference on Bioinformatics and Biomedical Engineering, IWBBIO 2018, held in Granada, Spain, in April 2018.The 88 regular papers presented were carefully reviewed and selected from 273 submissions. The scope of the conference spans the following areas: bioinformatics for healthcare and diseases; bioinformatics tools to integrate omics dataset and address biological question; challenges and advances in measurement and self-parametrization of complex biological systems; computational genomics; computational proteomics; computational systems for modelling biological processes; drug delivery system design aided by mathematical modelling and experiments; generation, management and biological insights from big data; high-throughput bioinformatic tools for medical genomics; next generation sequencing and sequence analysis; interpretable models in biomedicine and bioinformatics; little-big data. Reducing the complexity and facing uncertainty of highly underdetermined phenotype prediction problems; biomedical engineering; biomedical image analysis; biomedical signal analysis; challenges in smart and wearable sensor design for mobile health; and healthcare and diseases.

## Inhaltsverzeichnis

### Correction to: Textile Sensor Platform (TSP) - Development of a Textile Real-Time Electrocardiogram

The acknowledgement section of this paper was not given originally. It was added in the paper to thank some students who contributed to the work but were not authors.

Thomas Walzer, Christian Thies, Klaus Meier, Natividad Martínez Madrid

### Know-GRRF: Domain-Knowledge Informed Biomarker Discovery with Random Forests

Due to its robustness and built-in feature selection capability, random forest is frequently employed in omics studies for biomarker discovery and predictive modeling. However, random forest assumes equal importance of all features, while in reality domain knowledge may justify the prioritization of more relevant features. Furthermore, it has been shown that an antecedent feature selection step can improve the performance of random forest by reducing noises and search space. In this paper, we present a novel Know-guided regularized random forest (Know-GRRF) method that incorporates domain knowledge in a random forest framework for feature selection. Via rigorous simulations, we show that Know-GRRF outperforms existing methods by correctly identifying informative features and improving the accuracy of subsequent predictive models. Know-GRRF is responsive to a wide range of tuning parameters that help to better differentiate candidate features. Know-GRRF is also stable from run to run, making it robust to noises. We further proved that Know-GRRF is a generalized form of existing methods, RRF and GRRF. We applied Known-GRRF to a real world radiation biodosimetry study that uses non-human primate data to discover biomarkers for human applications. By using cross-species correlation as domain knowledge, Know-GRRF was able to identify three gene markers that significantly improved the cross-species prediction accuracy. We implemented Know-GRRF as an R package that is available through the CRAN archive.

Xin Guan, Li Liu

### Sampling Defective Pathways in Phenotype Prediction Problems via the Fisher’s Ratio Sampler

In this paper, we introduce the Fisher’s ratio sampler that serves to unravel the defective pathways in highly underdetermined phenotype prediction problems. This sampling algorithm first selects the most discriminatory genes, that are at the same time differentially expressed, and samples the high discriminatory genetic networks with a prior probability that it is proportional to their individual Fisher’s ratio. The number of genes of the different networks is randomly established taking into account the length of the minimum-scale signature of the phenotype prediction problem which is the one that contains the most discriminatory genes with the maximum predictive power. The likelihood of the different networks is established via leave-one-out-cross-validation. Finally, the posterior analysis of the most frequently sampled genes serves to establish the defective biological pathways. This novel sampling algorithm is much faster and simpler than Bayesian Networks. We show its application to a microarray dataset concerning a type of breast cancers with very bad prognosis (TNBC). In these kind of cancers, the breast cancer cells have tested negative for hormone epidermal growth factor receptor 2 (HER-2), estrogen receptors (ER), and progesterone receptors (PR). This lack causes that common treatments like hormone therapy and drugs that target estrogen, progesterone, and HER-2 are ineffective. We believe that the genetic pathways that are identified via the Fisher’s ratio sampler, which are mainly related to signaling pathways, provide new insights about the molecular mechanisms that are involved in this complex disease. The Fisher’s ratio sampler can be also applied to the genetic analysis of other complex diseases.

Ana Cernea, Juan Luis Fernández-Martínez, Enrique J. deAndrés-Galiana, Francisco Javier Fernández-Ovies, Zulima Fernández-Muñiz, Oscar Alvarez-Machancoses, Leorey Saligan, Stephen T. Sonis

### Sampling Defective Pathways in Phenotype Prediction Problems via the Holdout Sampler

In this paper, we introduce the holdout sampler to find the defective pathways in high underdetermined phenotype prediction problems. This sampling algorithm is inspired by the bootstrapping procedure used in regression analysis to established confidence bounds. We show that working with partial information (data bags) serves to sample the linear uncertainty region in a simple regression problem, mainly along the axis of greatest uncertainty that corresponds to the smallest singular value of the system matrix. This procedure applied to a phenotype prediction problem, considered as a generalized prediction problem between the set of genetic signatures and the set of classes in which the phenotype is divided, serves to unravel the ensemble of altered pathways in the transcriptome that are involved in the disease development. The algorithm looks for the minimum-scale genetic signature in each random holdout and the likelihood (predictive accuracy) is established using the validation dataset via a nearest-neighbor classifier. The posterior analysis serves to identify the header genes that most-frequently appear in the different hold-outs and are therefore robust to a partial lack of samples. These genes are used to establish the genetic pathways and the biological processes involved in the disease progression. This algorithm is much faster, robust and simpler than Bayesian Networks. We show its application to a microarray dataset concerning a type of breast cancers with poor prognoses (TNBC).

Juan Luis Fernández-Martínez, Ana Cernea, Enrique J. deAndrés-Galiana, Francisco Javier Fernández-Ovies, Zulima Fernández-Muñiz, Oscar Alvarez-Machancoses, Leorey Saligan, Stephen T. Sonis

### Comparison of Different Sampling Algorithms for Phenotype Prediction

In this paper, we compare different sampling algorithms used for identifying the defective pathways in highly underdetermined phenotype prediction problems. The first algorithm (Fisher’s ratio sampler) selects the most discriminatory genes and samples the high discriminatory genetic networks according to a prior probability that it is proportional to their individual Fisher’s ratio. The second one (holdout sampler) is inspired by the bootstrapping procedure used in regression analysis and uses the minimum-scale signatures found in different random hold outs to establish the most frequently sampled genes. The third one is a pure random sampler which randomly builds networks of differentially expressed genes. In all these algorithms, the likelihood of the different networks is established via leave one out cross-validation (LOOCV), and the posterior analysis of the most frequently sampled genes serves to establish the altered biological pathways. These algorithms are compared to the results obtained via Bayesian Networks (BNs). We show the application of these algorithms to a microarray dataset concerning Triple Negative Breast Cancers. This comparison shows that the Random, Fisher’s ratio and Holdout samplers are most effective than BNs, and all provide similar insights about the genetic mechanisms that are involved in this disease. Therefore, it can be concluded that all these samplers are good alternatives to Bayesian Networks which much lower computational demands. Besides this analysis confirms the insight that the altered pathways should be independent of the sampling methodology and the classifier that is used to infer them.

Ana Cernea, Juan Luis Fernández-Martínez, Enrique J. deAndrés-Galiana, Francisco Javier Fernández-Ovies, Zulima Fernández-Muñiz, Óscar Alvarez-Machancoses, Leorey Saligan, Stephen T. Sonis

### Composite Piezoelectric Material for Biomedical Micro Hydraulic System

‘Lab-on-a-chip’ is integrated micro-analytical system, which could perform sample pre-treatment, chemical reactions, analytical separation, detection and data handling. These platforms are able to convert biological, chemical or mechanical responses into electrical signals using the piezoelectric or piezoresistive materials. This paper discusses a piezoelectric composite material displaying its mechanical properties such as resonant frequencies, Young’s modulus and density. Nano composite polymer highlights the property of piezo effect and is suitable for formation of periodic micro scale patterns on it. These micro patterns are intended to be used as innovative functional elements in biomedical micro hydro mechanical systems such as micro channels. Thus by controlling surface configuration and the shape of active deformable polymer, pressure in microfluidic vessels can be changed and mobility of the transported bioparticles can be ensured.

Arvydas Palevicius, Giedrius Janusas, Elingas Cekas, YatinkumarRajeshbhai Patel

### Trabecular Bone Score in Overweight and Normal-Weight Young Women

The aim of this study was to compare Trabecular Bone Score (TBS) in overweight and normal-weight young women. This study included 14 overweight (BMI > 25 kg/m2) and 42 normal-weight (BMI < 25 kg/m2) young Lebanese women whose ages range from 18 to 32 years. Body composition, Bone Mineral Content (BMC), Bone Mineral Density (BMD), and lumbar spine (L1–L4) TBS were assessed by dual-energy X-ray asborptiometry (DXA). The DXA measurements were completed for the whole body (WB), the lumbar spine (L1–L4), the total hip (TH) and the femoral neck (FN). Physical activity, daily calcium intake, daily protein intake and sleep quality index were evaluated using validated questionnaires. Maximal oxygen consumption (VO2 max in l/mn) was measured whilst exercising on a bicycle ergometer using a specialized device. Weight, height, BMI, lean mass, fat mass, WB BMC, WB BMD, TH BMD and FN BMD were significantly higher in overweight women compared to normal-weight women. Trabecular Bone Score (TBS) was not significantly different between the two groups (overweight and normal-weight). In the whole population (n = 56), weight, height, BMI, lean mass and fat mass were positively correlated to BMC and BMD values but not to TBS values. VO2 max (l/mn) was positively correlated to BMC, BMD and TBS (p < 0.05). This study suggests that being overweight is not associated with higher trabecular bone score values in young women.

Abdel-Jalil Berro, Marie-Louise Ayoub, Antonio Pinti, Said Ahmaidi, Georges El Khoury, César El Khoury, Eddy Zakhem, Bernard Cortet, Rawad El Hage

### Sarcopenia and Hip Structure Analysis Variables in a Group of Lebanese Postmenopausal Women

The aim of the present study was to compare hip structural analysis variables in postmenopausal women with sarcopenia and postmenopausal women with normal skeletal muscle mass index. This study included 8 postmenopausal women (aged between 65 and 84 years) with sarcopenia and 60 age-matched controls (with normal skeletal muscle mass index (SMI)). Body composition and bone mineral density (BMD) were assessed by dual-energy X-ray absorptiometry (DXA). Weight, lean mass, Body mass index, femoral neck cross-sectional area (FN CSA), FN section modulus (Z), FN cross sectional moment of inertia (CSMI), intertrochanteric (IT) CSA, IT Z, IT CSMI, IT cortical thickness (CT), femoral shaft (FS) CSA, FS Z and FS CSMI were significantly higher (p < 0.05) in women with normal SMI compared to women with sarcopenia. In the whole population, SMI was positively correlated to IT CSA, IT Z, IT CSMI, IT CT, FS CSA, FS Z, FS CSMI, FS CT but negatively correlated to IT buckling ratio (BR) and FS BR. The present suggests that sarcopenia negatively affects hip bone strength indices in postmenopausal women.

Riad Nasr, Eric Watelain, Antonio Pinti, Hayman Saddik, Ghassan Maalouf, Abdel-Jalil Berro, Abir Alwan, César El Khoury, Ibrahim Fayad, Rawad El Hage

### Feet Fidgeting Detection Based on Accelerometers Using Decision Tree Learning and Gradient Boosting

Detection of fidgeting activities is a field which has not been much explored as of now. Studies have shown that fidgeting has a beneficial impact on people’s healthiness as it burns a significant amount of energy. Being able to detect when someone is fidgeting would allow to study more closely the health impact of fidgeting. The purpose of this work is to propose an algorithm being able to detect feet fidgeting period of subjects while sitting using 3-D accelerometers on both shoes. Initial results on data from 5 subjects collected during this work shows an accuracy of 95% for a classification between sitting with fidgeting and sitting without fidgeting.

Julien Esseiva, Maurizio Caon, Elena Mugellini, Omar Abou Khaled, Kamiar Aminian

### Matching Confidence Masks with Experts Annotations for Estimates of Chromosomal Copy Number Alterations

Structural aberrations (SAs), gains or losses in large segments of genomes, are associated with several genetic disorders. The SAs are commonly called the copy number alterations (CNAs) and their identification/classification is required to identify diseases. Many methods have been proposed to estimate the breakpoints and segmental constants in the CNAs with highest precision using the most powerful technologies of hybridization. However, locations and lengths of CNAs estimated using well-elaborated methods are often contradictory due to extensive variability of measurements and performance of the algorithms. Still much less attention is given to the estimation accuracy and it is difficult to select the best estimator. In this work, we propose to modify the confidence masks replacing the skew Laplace distribution with the asymmetric exponential power distribution (AEP) to approximate the jitter distribution in CNAs. Next, the estimates obtained using different algorithms are matched with the annotations made by experts employing the improved masks. Finally, we specify the match confidence probability of each CNAs detector algorithm respect the experts estimates.

Jorge Muñoz-Minjares, Yuriy S. Shmaliy, Tatiana Popova, R. J. Perez–Chimal

### Using Orientation Sensors to Control a FES System for Upper-Limb Motor Rehabilitation

Contralaterally controlled functional electrical stimulation (CCFES) is a recent therapy aimed at improving the recovery of impaired limbs after stroke. For hemiplegic patients, CCFES uses a control signal from the non-impaired side of the body to regulate the intensity of electrical stimulation delivered to the affected muscles of the homologous limb on the opposite side of the body. CCFES permits an artificial muscular contraction synchronized with the patient’s intentionality to carry out functional tasks, which is a way to enhance neuroplasticity and to promote motor learning. This work presents an upper extremity motor rehabilitation system based on CCFES, using orientation sensors for control. Thus, the stimulation intensity (current amplitude) delivered to the paretic extremity is proportional to the degree of joint amplitude of the unaffected extremity. The implemented controller uses a control strategy that allows the delivered electrical stimulation intensity, to be comparable to the magnitude of movement. It was carried out a set of experiments to validate the overall system, for executing five bilateral mirror movements that include human wrist and elbow joints. Obtained results showed that movements voluntary signals acquired from right upper-limb were replicated successfully on left upper-limb using the FES system.

Andrés F. Ruíz-Olaya, Alberto López-Delis, Adson Ferreira da Rocha

### A Real-Time Research Platform for Intent Pattern Recognition: Implementation, Validation and Application

Despite multiple advances with myoelectric control, currently there is still an important need to develop more effective methods for controlling prosthesis and exoskeletons in a natural way. This work describes the design and development of a research tool for the design, development and evaluation of algorithms of myoelectric control which base on intention detection from neuromuscular activation patterns. This platform provides integrated hardware and software tools for real-time acquisition, preprocessing, visualization, storage and analysis of biological signals. It is composed of a bio-instrumentation system controlled by a real-time software created in Simulink and executed on the xPC-target platform and, a Java based software application that allows to manage the acquisition and storage processes by a system operator. System evaluation was performed by the comparison with reference signals provided by a function generator and, as an example of the application of the developed acquisition platform, it was carried out a set of experiments to decode movements at the upper-limb level.

Andres F. Ruiz-Olaya, Gloria M. Díaz, Alberto López-Delis

### Augmented Visualization and Touchless Interaction with Virtual Organs

The actual trend in surgery is the transition from open procedures to minimally invasive interventions and revolutionary changes in computer-aided surgery have been obtained thanks to the introduction of the augmented reality technology that can support the doctor during the surgery. A realistic three-dimensional visualization of the patient’s organs can be obtained by means of specific algorithms of segmentation and classification of medical images and advanced modalities of touchless interaction and innovative gesture-control devices permit surgeon to have a natural and simple way of fruition of the patient’s data preserving the surgical environment from the danger of contamination.

Lucio Tommaso De Paolis

### Decreased Composite Indices of Femoral Neck Strength in Young Obese Women

The aim of the current study was to compare compression strength index (CSI), bending strength index (BSI) and impact strength index (ISI) among obese, overweight and normal-weight young women. 117 young women (20 obese, 36 overweight and 61 normal-weight) whose ages range from 18 to 35 years participated in this study. Body composition and BMD were evaluated by dual-energy X-ray absorptiometry (DXA). CSI, BSI and ISI values were significantly lower in obese and overweight women compared to normal-weight women (p < 0.001). In the whole population (n = 117), body mass index (BMI) was negatively correlated to CSI (r = −0.66; p < 0.001), BSI (r = −0.56; p < 0.001) and ISI (r = −0.54; p < 0.001). This study suggests that obesity is associated with lower CSI, BSI and ISI values in young women.

Abdel-Jalil Berro, Said Ahmaidi, Antonio Pinti, Abir Alwan, Hayman Saddik, Joseph Matta, Fabienne Frenn, Maroun Rizkallah, Ghassan Maalouf, Rawad El Hage

### On the Use of Decision Trees Based on Diagnosis and Drug Codes for Analyzing Chronic Patients

Diabetes mellitus (DM) and essential hypertension (EH) are chronic diseases more prevalent every year, both independently and jointly. To gain insights about the particularities of these chronic conditions, we study the use of decision trees as a tool for selecting discriminative features and making predictive analyses of the health status of this kind of chronic patients. We considered gender, age, ICD9 codes for diagnosis and ATC codes for drugs associated with the diabetic and/or hypertensive population linked to the University Hospital of Fuenlabrada (Madrid, Spain) during 2012. Results show a relationship among DM/EH and diseases/drugs related to the respiratory system, mental disorders, or the musculoskeletal system. We conclude that drugs are quite informative, collecting information about the disease when the diagnosis code is not registered. Regarding predictive analyses, when discriminating patients with EH-DM and just one of these chronic conditions, better accuracy is obtained for EH (85.4%) versus DM (80.1%).

Cristina Soguero-Ruiz, Ana Alberca Díaz-Plaza, Pablo de Miguel Bohoyo, Javier Ramos-López, Manuel Rubio-Sánchez, Alberto Sánchez, Inmaculada Mora-Jiménez

### Stochastic Geometry for Automatic Assessment of Ki-67 Index in Breast Cancer Preparations

Proliferative activity of cells is one of the most critical factors in breast cancer diagnosis. It is used to evaluate tumor cell progression and to predict treatment responses in chemotherapy. Ki-67 is a nuclear biomarker commonly used to measure cellular proliferation rate. The ratio between the number of Ki-67 positive tumor nuclei and all tumor nuclei defines Ki-67 index. However, manual cell counting is tedious and time consuming because hundreds of nuclei must be labeled. To speed up the analysis process, nuclei can be segmented automatically and then classified based on staining color. Unfortunately, segmentation of individual nuclei is a big challenge because they often create complex clusters comprised of many touching and overlapping nuclei. To deal with complexities and ambiguities of cytological material we propose a generative model which approximates nuclei using ellipses. We assume that the process of generating a cytological sample has stochastic nature. Therefore it is possible to reconstruct this process using marked point process tuned according to observed cytological sample. To verify the potential of the proposed method, we applied it to determine Ki-67 index in breast cancer immunochemistry samples. The results of experiments have shown that Ki-67 indices determined by proposed approach correlate well with those computed manually.

Marek Kowal, Marcin Skobel, Józef Korbicz, Roman Monczak

### Detection Methods of Static Microscopic Objects

The article deals with selected methods of automated detection of microscopic objects in video sequences obtained by high-speed cinematography and light microscopy. The objects of interest are represented by cilia of airways and also artefact generating objects (gas bubbles and erythrocytes). The main idea of this work is to create complex diagnostic tool for evaluation of ciliated epithelium in airways, where the ratio between moving and static cilia helps to search proper diagnosis (confirmation of PCD – primary ciliary dyskinesia). Methods for automated segmentation of static cilia creates a big challenge for image analysis against the dynamic ones due to character and parameters of obtained images. This work is supported by medical specialists from Jessenius Faculty of Medicine in Martin (Slovakia) and proposed tools would fill the gap in the diagnostics in the field of respirology in Slovakia.

Libor Hargaš, Zuzana Loncová, Dušan Koniar, František Jablončík, Jozef Volák

### Parkinson’s Disease Database Analysis of Stereotactic Coordinates Related to Clinical Outcomes

Parkinson’s Disease is one of the leading movement disorder diseases. It is the fourth most common neurological disease, after migraine, stroke and epilepsy. The motor symptoms of the disease significantly impair daily living and quality of life and exact a high burden on both patients and their caregivers. Deep Brain Stimulation is a proven therapy for this disease, getting positive outcomes while reducing medication. In this paper, stereotactic system used for Deep Brain Stimulation (DBS) procedures will be described. Different planning methods will be observed and compared to the gold standard normally used, neurophysiological coordinates recorded intra-operatively. MRI, CT scan and direct calculation of stereotactic coordinates will be compared and group in three different groups, according to DBS therapy outcomes: “very good DBS therapy”, “good DBS therapy” and “not major improvement”.Database of 72 DBS electrodes implanted in Parkinson’s Disease patients will be studied. Most potentially beneficial ranges of deviation within planning and neurophysiological coordinates from the operating room will be assessed, in order to provide neurosurgeons with more landmarks in order to achieve the best outcomes within a millimetric technique.We could confirm three main highlights out of this study: the neurophysiological length of the Subthalamic Nucleus does not play a major role in outcomes while being within normal range; CT scan calculations were the most accurate; direct calculations should not be used as major deviations were observed.

Francisco Estella, Esther Suarez, Beatriz Lozano, Elena Santamarta, Antonio Saiz, Fernando Rojas, Ignacio Rojas, Fernando Seijo

### Quantitative Ultrasound of Tumor Surrounding Tissue for Enhancement of Breast Cancer Diagnosis

Breast cancer is one of the leading causes of cancer-related death in female patients. The quantitative ultrasound techniques being developed recently provide useful information facilitating the classification of tumors as malignant or benign. Quantitative parameters are typically determined on the basis of signals scattered within the tumor. The present paper demonstrates the utility of quantitative data estimated based on signal backscatter in the tissue surrounding the tumor. Two quantitative parameters, weighted entropy and Nakagami shape parameter were calculated from the backscatter signal envelope. The ROC curves and the AUC parameter values were used to assess their ability to classify neoplastic lesions. Results indicate that data from tissue surrounding the tumor may characterize it better than data from within the tumor. AUC values were on average 18% higher for parameters calculated from data collected from the tissue surrounding the lesion than from the data from the lesion itself.

Ziemowit Klimonda, Katarzyna Dobruch-Sobczak, Hanna Piotrzkowska-Wróblewska, Piotr Karwat, Jerzy Litniewski

### A Texture Analysis Approach for Spine Metastasis Classification in T1 and T2 MRI

This paper presents a learning based approach for the classification of pathological vertebrae. The proposed method is applied to spine metastasis, a malignant tumor that develops inside bones and requires a rapid diagnosis for an effective treatment monitoring. We used multiple texture analysis techniques to extract useful features from two co-registered MR images sequences (T1, T2). These MRIs are part of a diagnostic protocol for vertebral metastases follow up. We adopted a slice by slice MRI analysis of 153 vertebra region of interest. Our method achieved a classification accuracy of $$90.17\% \pm 5.49$$, using only a subset of 67 relevant selected features from the initial 142.

Mohamed Amine Larhmam, Saïd Mahmoudi, Stylianos Drisis, Mohammed Benjelloun

### Parametric Variations of Anisotropic Diffusion and Gaussian High-Pass Filter for NIR Image Preprocessing in Vein Identification

Near infrared (NIR) imaging is one of the promising methods for identification of superficial veins and widely researched and used in clinical medicine and biomedical studies. However, just like imaging in visible spectrum, NIR imaging is not adequate for exact recognition of the vein system as it is, therefore nearly every research starts with preprocessing to prepare the images for identification. Two major filtering methods are anisotropic diffusion and Gaussian high-pass filter which both consist of mandatory parametric adjustments for better visualization of the images and for revealing the vein system. Therefore in this paper we deal with parametric variations of these two methods on a NIR image to give ideas for choosing proper preprocessing techniques and parameters, excluding edge detection and vein detection methodologies.

Ayca Kirimtat, Ondrej Krejcar

### FLIR vs SEEK in Biomedical Applications of Infrared Thermography

This article aims to compare the results of two different infrared cameras through revealing the irregular temperature distribution on an injured toe. Since the inhomogeneous body temperature is the key indicator of severe injuries, wounds, and illnesses, infrared thermography is the strongest method among other conventional methods to map the skin temperature variations. The current utility of infrared cameras in biomedical applications is also presented to comprehend the relationship between the nature of thermal radiation and human body temperature. In the article, the presented biomedical applications include skin cancer screening, wound detection in a diabetic foot, muscle activation assessment during an exercise, or thermal mapping of healthy human bodies. Along with the developments in infrared thermography, this article focuses on analyzing temperature distribution on the injured toe of a subject with two different smartphone-based infrared camera models namely FLIR One and SEEK Compact Pro. In addition, the results obtained from the presented infrared camera models are compared regarding to the thermal images of the injured toe.

Ayca Kirimtat, Ondrej Krejcar

### Advances in Homotopy Applied to Object Deformation

This work explores novel alternatives to conventional linear homotopy to enhance the quality of resulting transitions from object deformation applications. Studied/introduced approaches extend the linear mapping to other representations that provides smooth transitions when deforming objects while homotopy conditions are fulfilled. Such homotopy approaches are based on transcendental functions (TFH) in both simple and parametric versions. As well, we propose a variant of an existing quality indicator based on the ratio between the coefficients curve of resultant homotopy and that of a less-realistic, reference homotopy. Experimental results depict the effect of proposed TFH approaches regarding its usability and benefit for interpolating images formed by homotopic objects with smooth changes.

Jose Alejandro Salazar-Castro, Ana Cristina Umaquinga-Criollo, Lilian Dayana Cruz-Cruz, Luis Omar Alpala-Alpala, Catalina González-Castaño, Miguel A. Becerra-Botero, Diego Hernán Peluffo-Ordóñez, Cesar Germán Castellanos-Domínguez

### Thermal Imaging for Localization of Anterior Forearm Subcutaneous Veins

The anterior forearm recognition systems are very popular identify the subcutaneous veins, mostly by devices operating real-time. Real time projection systems are carried out by handheld devices with a near infrared (NIR) camera and a laser projector to choose venipuncture sites; however what we propose in this paper is an easier and more reliable way using infrared thermal (IR-T) camera. At the forearm some veins like Cephalic vein are mostly so concealed to detect by NIR cameras, therefore we propose an alternative method for localization of the whole vein system without preprocessing. Briefly in the thermograms, the forearm is segmented from the surrounding by crisp 2- means and the vein system is reconstructed on blank images by directional curvature method. All directional curvatures are combined by addition for merging the layers and highlighting mutual veins. The preliminary results are promising since all the vein system is revealed with invisible veins without any preprocessing.

Orcan Alpar, Ondrej Krejcar

### Detection of Irregular Thermoregulation in Hand Thermography by Fuzzy C-Means

From numbness to acral necrosis, vasospasms confining to the fingers are stimulating a wide variety of symptoms. Induced by several reasons, the constriction of small arteries is a severe disorder and should be diagnosed as early as possible. The major indicator of a mild vasospasm is reduced blood flow creating a nonhomogeneous radiation patterns in hand thermography before a total discoloration of the fingers. Therefore, in this paper, an identification methodology of the vasospasms is discussed, through the fuzzy c-means. Since the pseudocolored thermograms give crucial information of radiation variety, we segmented the hands from the images by hard k-means for subsequent analysis of low-radiated regions determined by fuzzy c-means. The isolated low-radiated regions in red-channel converted images also reveals ischemia as well as thermoregulation even in very milder cases.

Orcan Alpar, Ondrej Krejcar

### Medical Image Classification with Hand-Designed or Machine-Designed Texture Descriptors: A Performance Evaluation

Accurate diagnosis and early detection of various disease conditions are key to improving living conditions in any community. The existing framework for medical image classification depends largely on advanced digital image processing and machine (deep) learning techniques for significant improvement. In this paper, the performance of traditional hand-designed texture descriptors within the image-based learning paradigm is evaluated in comparison with machine-designed descriptors (extracted from pre-trained Convolution Neural Networks). Performance is evaluated, with respect to speed, accuracy and storage requirements, based on four popular medical image datasets. The experiments reveal an increased accuracy with machine-designed descriptors in most cases, though at a higher computational cost. It is therefore necessary to consider other parameters for tradeoff depending on the application being considered.

Joke A. Badejo, Emmanuel Adetiba, Adekunle Akinrinmade, Matthew B. Akanle

### Classification of Breast Cancer Histopathological Images Using KAZE Features

Breast cancer (BC) is a public health problem of first importance, being the second most common cancer worldwide. BC represents 30.4% of all new cancer cases in the European female population. The diagnosis and differential diagnosis of BC is based on the clinical presentations, physical examinations combined with imaging studies, and confirmed by histopathologic findings. Pathologists’ examination is a time-consuming analysis, susceptible to an interpretation bias mainly caused by the experience of the pathologist and the decrease of attention due to fatigue. Currently, computer-aided detection and diagnosis techniques applied to digital images are assisting the specialists.In this work, the performance of a pattern recognition system based on KAZE features in combination with Bag-of-Features (BOF) to discriminate between benign and malignant tumours is evaluated on the BreakHis database (7909 images). During the training stage, KAZE keypoints are extracted for every image in the training set. Keypoints are mapped into a histogram vector using K-means clustering. This histogram represents the input to build a binary SVM classifier. In the testing stage, the KAZE keypoints are extracted for every image in the test set, and fed into the cluster model to map them into a histogram vector. This vector is finally fed into the binary SVM training classifier to classify the image.The experimental evaluation shows the feasibility and effectiveness, in terms of classification accuracy, of the proposed scheme for the binary classification of breast cancer histopathological images with a low magnification factor.

Daniel Sanchez-Morillo, Jesús González, Marcial García-Rojo, Julio Ortega

### Low Data Fusion Framework Oriented to Information Quality for BCI Systems

The evaluation of the data/information fusion systems does not have standard quality criteria making the reuse and optimization of these systems a complex task. In this work, we propose a complete low data fusion (DF) framework based on the Joint Director of Laboratories (JDL) model, which considers contextual information alongside information quality (IQ) and performance evaluation system to optimize the DF process according to the user requirements. A set of IQ criteria was proposed by level. The model was tested with a brain-computer interface (BCI) system multi-environment to prove its functionality. The first level makes the selection and preprocessing of electroencephalographic signals. In level one feature extraction is carried out using discrete wavelet transform (DWT), nonlinear and linear statistical measures, and Fuzzy Rough Set – FRS algorithm for selecting the relevant features; finally, in the same level a classification process was conducted using support vector machine – SVM. A Fuzzy Inference system is used for controlling different processes based on the results given by an IQ evaluation system, which applies quality measures that can be weighted by the users of the system according to their requirements. Besides, the system is optimized based on the results given by the cuckoo search algorithm, which uses the IQ traceability for maximizing the IQ criteria according to user requirements. The test was carried out with different type and levels of noise applied to the signals. The results showed the capability and functionality of the model.

Miguel Alberto Becerra, Karla C. Alvarez-Uribe, Diego Hernán Peluffo-Ordoñez

### New Parameter Available in Phonocardiogram for Blood Pressure Estimation

Continuous and non-invasive measurement of blood pressure (BP) is of great importance. To achieve continuous and cuffless BP monitoring, pulse transit time (PTT) has been reported as a potential parameter. Nevertheless, this approach remains very sensitive, cumbersome and disagreeable for patients. This study proposes a new parameter available in phonocardiogram (PCG) to measure blood pressure. The PCG is processed and analyzed in order to measure the systolic and diastolic durations in order to study their correlation with an estimated PTT. The proposed approach evaluated on a developed data base of 37 subjects shows linear regression of two classes in distribution of diastolic duration with PTT estimated. Where, a good correlation coefficient is found for each class (class1: R = 0.87, class2: R = 0.85. This technic has significant potential to develop a new approach to measure blood pressure using PCG signal.

Omari Tahar, Ouacif Nadia, Benali Redouane, Dib Nabil, Bereksi-Reguig Fethi

### Some False ECG Waves Detections Revised by Fractal Dimensions

In this paper, we used the fractal dimensions in ECG signals to identify the wave’s detections failure. We check for the sensitivities and the importance of QRS and ST detection because different false wave’s detections caused by the various types of interference and artefact are detected for some ECG signals presenting pathologies.The fractal dimension is very sensitive to variations: if irregularities degree is great, the fractal dimension is high and vice versa. Different cases of pathologies decreased irregularities on the ECG signal so it causes a decrease in fractal dimension. However decreasing in irregularities is not necessarily pathological: a bad detection can also train it, because we have not the exact location of the beginning and the end of QRS complex or the end of the T wave, it causes a new variation in the dimension fractal which can skew the result.For that reason and in order to get good results from algorithm detection, the fractal dimensions are calculated for each QRS complex and ST segment, for some ECG signals, to check their sensitivities in heart rate irregularities and false wave’s detections so that make ECG interpretation system more effective.

Ibticeme Sedjelmaci, Fethi Bereksi Reguig

### Reconstruction of Equivalent Electrical Sources on Heart Surface

We consider the problem of increasing the informative value of electrocardiographic (ECG) surveys using data from multichannel electrocardiographic leads, that include both recorded electrocardiosignals and the coordinates of the electrodes placed on the surface of the human torso. In this area, we were interested in reconstruction of the surface distribution of the equivalent sources during the cardiac cycle at relatively low hardware cost. In our work, we propose to reconstruct the equivalent electrical sources by numerical methods, based on integral connection between the density of electrical sources and potential in a conductive medium. We consider maps of distributions of equivalent electric sources on the heart surface (HSSM), presenting source distributions in the form of a simple or double electrical layer. We indicate the dynamics of the heart electrical activity by the space-time mapping of equivalent electrical sources in HSSM.

Galina V. Zhikhareva, Mikhail N. Kramm, Oleg N. Bodin, Ralf Seepold, Anton I. Chernikov, Yana A. Kupriyanova, Natalija A. Zhuravleva

### WearIT - A Rapid Prototyping Platform for Wearables

Rapid Prototyping Platforms reduce development time by allowing quick prototyping of a prototype idea and achieve more time for actual application development with user interfaces. This approach has long been followed in technical platforms, such as the Arduino. To transfer this form of prototyping to wearables, WearIT is presented in this paper. WearIT consists of four components as a wearable prototyping platform: (1) a vest, (2) sensor and actuator shields, (3) its own library and (4) a motherboard consisting of Arduino, Raspberry Pi, a board and a GPS module. As a result, a wearable prototype can be quickly developed by attaching sensor and actuator shields to the WearIT vest. These sensor and actuator shields can then be programmed through the WearIT library. Via Virtual Network Computing (VNC) with a remote computer, the screen contents of the Raspberry Pi can be accessed and the Arduino be programmed.

Isabel Leber, Natividad Martínez Madrid

### A Review of Health Monitoring Systems Using Sensors on Bed or Cushion

How technology can answer the challenge that currently population ageing is facing to the healthcare system? In this work, systems and devices related to “smart” bed and cushion, that are commercially available or matter of research works, are reviewed.

Massimo Conti, Simone Orcioni, Natividad Martínez Madrid, Maksym Gaiduk, Ralf Seepold

### Textile Sensor Platform (TSP) - Development of a Textile Real-Time Electrocardiogram

Being able to monitor the heart activity of patients during their daily life in a reliable, comfortable and affordable way is one main goal of the personalized medicine. Current wearable solutions lack either on the wearing comfort, the quality and type of the data provided or the price of the device. This paper shows the development of a Textile Sensor Platform (TSP) in the form of an electrocardiogram (ECG)-measuring T-shirt that is able to transmit the ECG signal to a smartphone. The development process includes the selection of the materials, the design of the textile electrodes taking into consideration their electrical characteristics and ergonomy, the integration of the electrodes on the garment and their connection with the embedded electronic part. The TSP is able to transmit a real-time streaming of the ECG-signal to an Android smartphone through Bluetooth Low Energy (BLE). Initial results show a good electrical quality in the textile electrodes and promising results in the capture and transmission of the ECG-signal. This is still a work-in-progress and it is the result of an interdisciplinary master project between the School of Informatics and the School of Textiles & Design of the Reutlingen University.

Thomas Walzer, Christian Thies, Klaus Meier, Natividad Martínez Madrid

### Sensor-Mesh-Based System with Application on Sleep Study

The process of restoring our body and brain from fatigue is directly depending on the quality of sleep. It can be determined from the report of the sleep study results. Classification of sleep stages is the first step of this study and this includes the measurement of biovital data and its further processing.In this work, the sleep analysis system is based on a hardware sensor net, namely a grid of 24 pressure sensors, supporting sleep phase recognition. In comparison to the leading standard, which is polysomnography, the proposed approach is a non-invasive system. It recognises respiration and body movement with only one type of low-cost pressure sensors forming a mesh architecture. The nodes implement as a series of pressure sensors connected to a low-power and performant microcontroller. All nodes are connected via a system wide bus with address arbitration. The embedded processor is the mesh network endpoint that enables network configuration, storing and pre-processing of the data, external data access and visualization.The system was tested by executing experiments recording the sleep of different healthy young subjects. The results obtained have indicated the potential to detect breathing rate and body movement. A major difference of this system in comparison to other approaches is the innovative way to place the sensors under the mattress. This characteristic facilitates the continuous using of the system without any influence on the common sleep process.

Maksym Gaiduk, Bruno Vunderl, Ralf Seepold, Juan Antonio Ortega, Thomas Penzel

### Wearable Pneumatic Sensor for Non-invasive Continuous Arterial Blood Pressure Monitoring

The paper discusses a new type of active sensors for continuous non-invasive monitoring of arterial blood pressure based on the local pressure compensation. Practical implementation of this sensor became possible due to the effective use of modern radio-electronic element base, focused on low power consumption, miniaturization of sizes and built-in computing and communication components (microcontrollers). These characteristics are inherent in modern wearable medical devices, so the sensor proposed can be reliably attributed to this category of appliances. The use of miniature measuring unit, its arrangement close to the working area and the possibility of processing digitized data in real time directly in the microcontroller of the sensor made it possible to carry out a unique method of pressure compensation at very small (1 mm$$^{2}$$ or less) areas of elastic surfaces, such as the surface tissues of the human body. The technical implementation of the principle of local pressure compensation in the form of a pneumatic sensor, features of blood pressure measurement regimes, the results obtained and some theoretical recommendations are considered in the paper. The problem of stability of measurement modes is discussed in detail. Experimentally discovered causes of stability disturbance are considered and their theoretical analysis is carried out. The conclusion summarizes the results and outlines the ways of further research.

Viacheslav Antsiperov, Gennady Mansurov

### Gene-Gene Interaction Analysis: Correlation, Relative Entropy and Rough Set Theory Based Approach

Logical interaction between every pair of genes in a gene interaction network affects the observable behavior of any organism. This genetic interaction helps us to identify pathways of associated genes for various diseases and also finds the level of interaction between the genes in the network. In this paper, at first we have used three correlation measures, like Pearson, Spearman and Kendall-Tau to find the interaction level in a gene interaction network. Rough set can also be used to find the level of interaction, as well as direction of interaction between every pair of genes. That’s why in the second phase of the experiment, entropy measure & Rough set theory are also used to determine the level of interaction between every pair of genes as well as finds the direction of interaction that indicates which gene regulates which other genes. Experiments are done on normal & diseased samples of Colorectal Cancer dataset (GDS4382) separately. At the end we try to find out those interactions responsible for this cancer disease to take place. To validate the experimental results biologically we compare it with interactions given in NCBI database.

Sujay Saha, Sukriti Roy, Anupam Ghosh, Kashi Nath Dey

### A Transferable Belief Model Decision Support Tool over Complementary Clinical Conditions

This paper presents an algorithm for decision support over two complementary clinical conditions given a large features data base. The algorithm is mainly divided in two parts, the first one aims at identifying relevant features from a large dimension data base using a heuristic method based on a discriminating power. The second part is a tool based on the Transferable Belief Model (TBM) which combines information extracted from the selected features to provide decision results with probabilities along with a result’s consistency measure so that decision could be made carefully. The proposed algorithm is tested on a downloaded feature data base. The TBM based decision support tool showed consistent results w.r.t provided outcomes by combining data from two relevant features identified after using the heuristic feature ranking method.

Abderraouf Hadj Henni, David Pasquier, Nacim Betrouni

### An Online Viewer of FHR Signal for Research, E-Learning and Tele-Medicine

This paper presents a web viewer of Fetal Heart Rate (FHR) signals developed on HTML5/JavaScript. It provides an easy solution to remotely consult an FHR signal on a web browser without installing any specific software and it can be used either on a computer or on mobile device. There are three major applications of this tool. First, it is used to build up our FHR database used for research on signal processing and analysis. Secondly, it is used on our E-learning website e.RCF in order to train midwives and obstetricians to interpret FHR signals. At last, it could be used on telemedicine either on tele-monitoring to remotely check the fetal welfare, or on tele-expertise to enable practitioners to ask for specialists’ opinion. This viewer is designed to correspond to practitioners’ habits while including tools to ease the interpretation the FHR signal.

Samuel Boudet, Agathe Houzé de l’Aulnoit, Antonio Pinti, Romain Demailly, Michael Genin, Regis Beuscart, Jessica Schiro, Laurent Peyrodie, Denis Houzé de l’Aulnoit

### Modeling Spread of Infectious Diseases at the Arrival Stage of Hajj

During the 2009 H1N1 influenza pandemic, there was rising concern about the potential contribution of international travel and global mass gatherings on the dynamic of the virus. The travel patterns after global mass gatherings can cause a rapid spread of infections. Studying the impact of travel patterns, high population density, and social mixing on disease transmission in these events could help public health authorities assess the risk of global epidemics and evaluate various prevention measures. There have been many studies on computational modeling of epidemic spread in various settings, but few of them address global mass gatherings. In this paper, we develop a stochastic susceptible-exposed-infected-recovered agent-based model to predict early stage of a disease epidemic among international participants in the annual Hajj or pilgrimage to Makkah (also called Mecca). The epidemic model is used to explore several scenarios with initial reproduction number R0 range from 1.3 to 1.7, and various initial proportions of infections range from 0.5% to 1% of total arriving pilgrims. Following an epidemic with one infectious per flight, the model results predict an average of 30% infectious and 20% exposed individuals in Makkah by the end of the arrival period. The proposed model can be used to assess various intervention measures during the arrival of international participants to control potential epidemics in different global mass gatherings.

Sultanah M. Alshammari, Armin R. Mikler

### Exploring In-Game Reward Mechanisms in Diaquarium – A Serious Game for Children with Type 1 Diabetes

When developing serious games for health, the main goal is to use game mechanisms in a way that the users decide to extend their playing time, complete all levels within the game, and thereby gain progression and intended learning with regard to disease management. One major concern when developing games for health is, therefore, the possibility of users who withdraw from the game before completed. A game, with a rapid descending popularity and users quitting gameplay early, fails to provide medical education to patients and is thus useless. For that reason, motivational game elements, such as in-game rewards, have been heavily used when designing serious games. This paper identifies and suggests several reinforcement mechanisms within serious games and explores how they can be applied in diabetes. The game called Diaquarium, a serious game for children with Type 1 diabetes, provides knowledge regarding how nutrition, blood glucose levels, and insulin interplay for this patient group. A prototype has been developed to demonstrate its concept and some game mechanisms with help of Unity 3D game engine and the C# programming language. Game design, requirements and suggestions for the project, were gathered through literature review, attending workshops, meetings and discussions with experts, as well as feedback from a related user group through a questionnaire. The questionnaire was distributed to an elementary school class, involving nine 9-year-old children. The questionnaire examined and collected feedback regarding the game outline, usability, and preferred reward mechanisms in the Diaquarium game. Despite a short period of testing and a limited test group with non-diabetic children, the game was recognized as attractive and moderately difficult within the potential user group. The analysis suggests that rewards are highly a matter of preference. Simultaneously, there were indications that some of the rewards were more favorable than others. It appears that rewards serving a purpose within the game, e.g., potentially effect progression in the gameplay, are more favorable than the opposite rewards serving no purpose. The findings were highly valued and taken into consideration during the design process of exploring the in-game rewards of the Diaquarium.

Ida Charlotte Rønningen, Eirik Årsand, Gunnar Hartvigsen

### An “Awareness” Environment for Clinical Decision Support in e-Health

The notion of cross-boundary decision support has the potential to transform the design of future work environments for e-health through a connected system that allows for harnessing of healthcare information and expert knowledge across geographical boundaries for more effective decision-making. The trouble, however, is that the use of healthcare information in decision-making usually occurs within the context of a complex structure of clinical work practices that is often shaped by a wide range of factors, including organisational culture, local work contexts, socially constructed traditions of actions, experiences and patients’ circumstances. They vary across geographical and organisational boundaries, and have remained to date largely unaccounted for in the design of e-health systems. As a result, achieving the e-health vision of ‘open’ clinical decision support requires a rethinking of key clinical and organisational processes in a manner that accommodates clinical work practice as a fundamental part of how clinicians work and make decisions in real-world settings. Drawing on the theories of human activity system and situation awareness as well as the belief-desire-intention architecture in AI, this paper presents the design of an awareness environment for cross-boundary clinical decision support in e-health that takes account of the concept of work practice as a design requirement. The proposed system shows that incorporating practice information into the design of e-health systems enhances their usefulness for ‘open’ clinical decision support.

Obinna Anya, Hissam Tawfik

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 Title: Dense matter and the compressible liquid drop model Author(s): Lorenz, Carl Philip Doctoral Committee Chair(s): Ravenhall, D. G. Department / Program: Physics Discipline: Physics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Physics, Astronomy and Astrophysics Physics, Nuclear Abstract: We explore the equation of state of dense matter at densities up to nuclear matter density using the compressible liquid drop model. We consider two primary areas of application: the collapsing core of supernovae and the inner crust of a cooled neutron star. The model is generalized to include a refined description of the nuclear surface properties as well as a number of smaller physical effects. We also adapt it to accommodate droplet shapes other than the customary spherical clusters in order to study the phase character of matter in these astrophysical situations.We present the results of a Hartree-Fock finite-temperature calculation of nuclear surface and curvature thermodynamic potentials, using phenomenological forces. These are the requisite ingredients needed for the model. For our purposes, we calculate these properties over the complete range of proton fraction (0 to 0.5). The self-consistent method is exploited to extract an approximation for neutron evaporation rates from hot nuclear surfaces.Dense matter at fixed overall proton fraction of $Y\sb p$ = 0.3 is considered at densities up to nuclear saturation density at low temperatures. We lay the framework, however, to explore matter at temperatures that one would expect in the collapsing supernova core. Matter in beta equilibrium is considered at low temperatures; this is the character of the matter that one expects to exist in the inner crust of a cooled neutron star. We obtain for the first time the density range occupied by the non-spherical nuclear shapes. Issue Date: 1991 Type: Text Language: English URI: http://hdl.handle.net/2142/20263 Rights Information: Copyright 1991 Lorenz, Carl Philip Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9210900 OCLC Identifier: (UMI)AAI9210900

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# Show view over existing view in same activity

I am newbie Android developer, and I am starting out with a simple Sudoku game. The problem I am facing right now is that I have my game showing on a dedicated Activity, which is displaying a custom View class. I have the code within the onDraw function. Now I want to show a custom keypad view, which is a separate class extending View, whenever a user clicks on a block in the Sudoku grid.

I am extremely confused as to how I should go about doing this. I am reluctant to create a dedicated activity for just this keypad, and want to show this keypad over the Sudoku grid view that the activity is currently displaying.

The activity is using setContentView(myCustomGridViewClass) to show the grid. Now I want something to the equivalent of

onTouch -> setContentView(myCustomKeypadView), though this should appear over the previous view.

I have tried reading about the LayoutInflater, but did not understand how to use it to show the keypad within this same activity. This is probably a very noob question, but any help, including any other questions, or sources I could refer to for an answer would be highly appreciated.

Regards,

You could place both views in a FrameLayout or a RelativeLayout and control the keypad's visibility (http://developer.android.com/reference/android/view/View.html#setVisibility(int)) when needed.


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# Checking whether a coin is fair

(Redirected from Checking if a coin is fair)

In statistics, the question of checking whether a coin is fair is one whose importance lies, firstly, in providing a simple problem on which to illustrate basic ideas of statistical inference and, secondly, in providing a simple problem that can be used to compare various competing methods of statistical inference, including decision theory. The practical problem of checking whether a coin is fair might be considered as easily solved by performing a sufficiently large number of trials, but statistics and probability theory can provide guidance on two types of question; specifically those of how many trials to undertake and of the accuracy an estimate of the probability of turning up heads, derived from a given sample of trials.

A fair coin is an idealized randomizing device with two states (usually named "heads" and "tails") which are equally likely to occur. It is based on the coin flip used widely in sports and other situations where it is required to give two parties the same chance of winning. Either a specially designed chip or more usually a simple currency coin is used, although the latter might be slightly "unfair" due to an asymmetrical weight distribution, which might cause one state to occur more frequently than the other, giving one party an unfair advantage.[1] So it might be necessary to test experimentally whether the coin is in fact "fair" – that is, whether the probability of the coin falling on either side when it is tossed is approximately 50%. It is of course impossible to rule out arbitrarily small deviations from fairness such as might be expected to affect only one flip in a lifetime of flipping; also it is always possible for an unfair (or "biased") coin to happen to turn up exactly 10 heads in 20 flips. As such, any fairness test must only establish a certain degree of confidence in a certain degree of fairness (a certain maximum bias). In more rigorous terminology, the problem is of determining the parameters of a Bernoulli process, given only a limited sample of Bernoulli trials.

## Preamble

This article describes experimental procedures for determining whether a coin is fair or not fair. There are many statistical methods for analyzing such an experimental procedure. This article illustrates two of them.

Both methods prescribe an experiment (or trial) in which the coin is tossed many times and the result of each toss is recorded. The results can then be analysed statistically to decide whether the coin is "fair" or "probably not fair".

• Posterior probability density function, or PDF (Bayesian approach). The true probability of obtaining a particular side when a fair coin is tossed is unknown, but the uncertainty is initially represented by the "prior distribution". The theory of Bayesian inference is used to derive the posterior distribution by combining the prior distribution and the likelihood function which represents the information obtained from the experiment. The probability that this particular coin is a "fair coin" can then be obtained by integrating the PDF of the posterior distribution over the relevant interval that represents all the probabilities that can be counted as "fair" in a practical sense.
• Estimator of true probability (Frequentist approach). This method assumes that the experimenter can decide to toss the coin any number of times. He first decides on the level of confidence required and the tolerable margin of error. These parameters determine the minimum number of tosses that must be performed to complete the experiment.

An important difference between these two approaches is that the first approach gives some weight to one's prior experience of tossing coins, while the second does not. The question of how much weight to give to prior experience, depending on the quality (credibility) of that experience, is discussed under credibility theory.

## Posterior probability density function

One method is to calculate the posterior probability density function of Bayesian probability theory.

A test is performed by tossing the coin N times and noting the observed numbers of heads, h, and tails, t. The symbols H and T represent more generalised variables expressing the numbers of heads and tails respectively that might have been observed in the experiment. Thus N = H+T = h+t.

Next, let r be the actual probability of obtaining heads in a single toss of the coin. This is the property of the coin which is being investigated. Using Bayes' theorem, the posterior probability density of r conditional on h and t is expressed as follows:

$f(r | H=h, T=t) = \frac {\Pr(H=h | r, N=h+t) \, g(r)} {\int_0^1 \Pr(H=h |r', N=h+t) \, g(r') \, dr'}. \!$

where g(r) represents the prior probability density distribution of r, which lies in the range 0 to 1.

The prior probability density distribution summarizes what is known about the distribution of r in the absence of any observation. We will assume that the prior distribution of r is uniform over the interval [0, 1]. That is, g(r) = 1. (In practice, it would be more appropriate to assume a prior distribution which is much more heavily weighted in the region around 0.5, to reflect our experience with real coins.)

The probability of obtaining h heads in N tosses of a coin with a probability of heads equal to r is given by the binomial distribution:

$\Pr(H=h | r, N=h+t) = {N \choose h} \, r^h \, (1-r)^t. \!$

Substituting this into the previous formula:

$f(r | H=h, T=t) = \frac{{N \choose h}\,r^h\,(1-r)^t} {\int_0^1 {N \choose h}\,r^h\,(1-r)^t\,dr} = \frac{r^h\,(1-r)^t}{\int_0^1 r^h\,(1-r)^t\,dr} .$

This is in fact a beta distribution (the conjugate prior for the binomial distribution), whose denominator can be expressed in terms of the beta function:

$f(r | H=h, T=t) = \frac{1}{\mathrm{B}(h+1,t+1)} \; r^h\,(1-r)^t. \!$

As a uniform prior distribution has been assumed, and because h and t are integers, this can also be written in terms of factorials:

$f(r | H=h, T=t) = \frac{(h+t+1)!}{h!\,\,t!} \; r^h\,(1-r)^t. \!$

### Example

For example, let N = 10, h = 7, i.e. the coin is tossed 10 times and 7 heads are obtained:

$f(r | H=7, T=3) = \frac{(10+1)!}{7!\,\,3!} \; r^7 \, (1-r)^3 = 1320 \, r^7 \, (1-r)^3 \!$

The graph on the right shows the probability density function of r given that 7 heads were obtained in 10 tosses. (Note: r is the probability of obtaining heads when tossing the same coin once.)

Plot of the probability density f(x | H = 7,T = 3) = 1320 x7 (1 - x)3 with x ranging from 0 to 1.

The probability for an unbiased coin (defined for this purpose as one whose probability of coming down heads is somewhere between 45% and 55%)

$\Pr(0.45 < r <0.55) = \int_{0.45}^{0.55} f(r | H=7, T=3) \,dr \approx 13\% \!$

is small when compared with the alternative hypothesis (a biased coin). However, it is not small enough to cause us to believe that the coin has a significant bias. Notice that this probability is slightly higher than our presupposition of the probability that the coin was fair corresponding to the uniform prior distribution, which was 10%. Using a prior distribution that reflects our prior knowledge of what a coin is and how it acts, the posterior distribution would not favor the hypothesis of bias. However the number of trials in this example (10 tosses) is very small, and with more trials the choice of prior distribution would be somewhat less relevant.)

Note that, with the uniform prior, the posterior probability distribution f(r | H = 7,T = 3) achieves its peak at r = h / (h + t) = 0.7; this value is called the maximum a posteriori (MAP) estimate of r. Also with the uniform prior, the expected value of r under the posterior distribution is

$\operatorname{E}[r] = \int_0^1 r \cdot f(r | H=7, T=3) \, \mathrm{d}r = \frac{h+1}{h+t+2} = \frac{2}{3}\,.$

## Estimator of true probability

 The best estimator for the actual value $r\,\!$ is the estimator $p\,\! = \frac{h}{h+t}$. This estimator has a margin of error (E) where $|p - r| < E$ at a particular confidence level.

Using this approach, to decide the number of times the coin should be tossed, two parameters are required:

1. The confidence level which is denoted by confidence interval (Z)
2. The maximum (acceptable) error (E)
• The confidence level is denoted by Z and is given by the Z-value of a standard normal distribution. This value can be read off a standard score statistics table for the normal distribution. Some examples are:
Z value Confidence Level Comment
0.6745 gives 50.000% level of confidence Half
1.0000 gives 68.269% level of confidence One std dev
1.6449 gives 90.000% level of confidence "One Nine"
1.9599 gives 95.000% level of confidence 95 percent
2.0000 gives 95.450% level of confidence Two std dev
2.5759 gives 99.000% level of confidence "Two Nines"
3.0000 gives 99.730% level of confidence Three std dev
3.2905 gives 99.900% level of confidence "Three Nines"
3.8906 gives 99.990% level of confidence "Four Nines"
4.0000 gives 99.993% level of confidence Four std dev
4.4172 gives 99.999% level of confidence "Five Nines"
• The maximum error (E) is defined by $|p - r| < E$ where $p\,\!$ is the estimated probability of obtaining heads. Note: $r$ is the same actual probability (of obtaining heads) as $r\,\!$ of the previous section in this article.
• In statistics, the estimate of a proportion of a sample (denoted by p) has a standard error (standard deviation of error) given by:
$s_p = \sqrt{ \frac {p \, (1-p) } {n} }$

where n is the number of trials (which was denoted by N in the previous section).

This standard error $s_p$ function of p has a maximum at $p = (1-p) = 0.5$. Further, in the case of a coin being tossed, it is likely that p will be not far from 0.5, so it is reasonable to take p=0.5 in the following:

 $s_p\,\!$ $= \sqrt{ \frac {p \, (1-p) } {n} } = \sqrt{ \frac {0.5 \times 0.5 } {n} } = \frac {1}{2 \, \sqrt{n}}$

And hence the value of maximum error (E) is given by

 $E= Z \, s_p = \frac {Z}{2 \, \sqrt{n}}$

Solving for the required number of coin tosses, n,

$n = \frac {Z^2} {4 \, E^2} \!$

### Examples

1. If a maximum error of 0.01 is desired, how many times should the coin be tossed?

$n = \frac {Z^2} {4 \, E^2} = \frac {Z^2} {4 \times 0.01^2} = 2500 \ Z^2$
$n = 2500\,$ at 68.27% level of confidence (Z=1)
$n = 10000\,$ at 95.45% level of confidence (Z=2)
$n = 27225\,$ at 99.90% level of confidence (Z=3.3)

2. If the coin is tossed 10000 times, what is the maximum error of the estimator $p\,\!$ on the value of $r\,\!$ (the actual probability of obtaining heads in a coin toss)?

$E = \frac {Z}{ 2 \, \sqrt{n} }$
$E = \frac {Z}{ 2 \, \sqrt{ 10000 } } = \frac {Z}{ 200 }$
$E = 0.0050\,$ at 68.27% level of confidence (Z=1)
$E = 0.0100\,$ at 95.45% level of confidence (Z=2)
$E = 0.0165\,$ at 99.90% level of confidence (Z=3.3)

3. The coin is tossed 12000 times with a result of 5961 heads (and 6039 tails). What interval does the value of $r\,\!$ (the true probability of obtaining heads) lie within if a confidence level of 99.999% is desired?

$p = \frac{h}{h+t} \, = \frac{5961}{12000} \, = 0.4968$

Now find the value of Z corresponding to 99.999% level of confidence.

$Z = 4.4172 \,\!$

Now calculate E

$E = \frac{Z}{2 \, \sqrt{n}} \, = \frac{4.4172}{2 \, \sqrt{12000}} \, = 0.0202$

The interval which contains r is thus:

$p - E < r < p + E \,\!$
$0.4766 < r < 0.5170 \,\!$

Hence, 99.999% of the time, the interval above would contain $r\,\!$ which is the true value of obtaining heads in a single toss.

## Other approaches

Other approaches to the question of checking whether a coin is fair are available using decision theory, whose application would require the formulation of a loss function or utility function which describes the consequences of making a given decision. An approach that avoids requiring either a loss function or a prior probability (as in the Bayesian approach) is that of "acceptance sampling".[2]

## Other applications

The above mathematical analysis for determining if a coin is fair can also be applied to other uses. For example:

• Determining the proportion of defective items for a product subjected to a particular (but well defined) condition. Sometimes a product can be very difficult or expensive to produce. Furthermore, if testing such products will result in their destruction, a minimum number of items should be tested. Using a similar analysis, the probability density function of the product defect rate can be found.
• Two party polling. If a small random sample poll is taken where there are only two mutually exclusive choices, then this is similar to tossing a single coin multiple times using a possibly biased coin. A similar analysis can therefore be applied to determine the confidence to be ascribed to the actual ratio of votes cast. (Note that if people are allowed to abstain then the analysis must take account of that, and the coin-flip analogy doesn't quite hold.)
• Determining the sex ratio in a large group of an animal species. Provided that a small random sample (i.e. small in comparison with the total population) is taken when performing the random sampling of the population, the analysis is similar to determining the probability of obtaining heads in a coin toss.


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# Proof of the formula for Euler's totient function

I read on a forum somewhere that the totient function can be calculated by finding the product of one less than each of the number's prime factors. For example, to find $\phi(30)$, you would calculate $(2-1)\times (3-1)\times (5-1) = 8$.

I can't seem to get my head round why this works and don't know what to type in to google to find a formal proof. Could someone please explain in an easy to understand way why this works.

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This was mentioned in one or more answers, but just to restate as a comment: the totient function is not always the product of one less than the prime factors; if a number has n multiples of the same prime factor, you use p^n - p^(n-1); in the case where n==1, you would use p - p^0 which is p - 1. –  Foon Feb 17 '13 at 17:46

By definition, $\phi(30)$ is the count of numbers less than $30$ that are co-prime to it. Also, $\phi(abc) = \phi(a)\times \phi(b)\times \phi(c)$. Note that $\phi(p)$ for all primes is always $p - 1$ because there are $p - 1$ numbers less than any given prime $p$, and all numbers less than a prime are coprime to it.

This means $\phi(30) = \phi(2\cdot 3 \cdot 5) = \phi(2) \cdot \phi(3) \cdot \phi(5) = (2-1)(3-1)(5-1) = 8$. But $\phi(60) = 16 \ne (2 - 1)(3 - 1)(5 - 1)$ so what you said is not always true. It is true only if you have an order $1$ of all the prime divisors.

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$\phi(4) \neq \phi(2) \cdot \phi(2)$ because $gcd(2,2) \neq 1$ –  Cortizol Feb 17 '13 at 15:07
@Cortizol Reworded. –  Parth Kohli Feb 17 '13 at 15:11

First of all, the Totient Function is Multiplicative

If $N=\prod_{1\le r\le n}p_r^{a_i},\phi(N)=\prod_{1\le r\le n}\phi(p_r^{a_i})$ where $p_i$ are distinct primes and $a_i$ are positive integers.

Now, $p_r^{a_i}$ is relatively prime with any number which is not divisible by $p_r$

The number of numbers which are $\le p_r^{a_i}$ and are divisible by $p_r$ is $\frac{p_r^{a_i}}{p_r}=p_r^{a_i-1}$

So, $\phi(p_r^{a_i})$ is equal to $p_r^{a_i}-p_r^{a_i-1}=p_r^{a_i-1}(p_r-1)$

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I might be wrong, but it seems to be that what OP is asking is precisely the question of why is the function multiplicative. –  tomasz Feb 17 '13 at 15:20
@tomasz, even the accepted answer did not prove it.To me, the question was when we can write $\phi(N)=\prod(b_i-1)$ where $N=\prod b_i$ –  lab bhattacharjee Feb 17 '13 at 15:23
When it comes to the accepted answer not containing the proof, you're absolutely right. But still, the question does ask about a formal proof... nevermind. I think OP slightly derailed his question himself. –  tomasz Feb 17 '13 at 15:25
In any event, you probably meant numbers divisible by $p_r$ in the penultimate line. –  tomasz Feb 17 '13 at 15:27
If $n=p_1^{\alpha_1} p_2^{\alpha_2}\dots p_k^{\alpha_k}$ then $\phi(n)=n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)\dots \left(1-\frac{1}{p_k}\right).$ Now, proof of multiplication is pretty "easy" –  Cortizol Feb 17 '13 at 15:28

Hint $\$ Examining the units (invertibles) in the CRT decomposition $\rm\: \Bbb Z/n \cong \Bbb Z/p^j \oplus \cdots \oplus \Bbb Z/q^k \:$ shows that $\rm\:\phi(n) = \phi(p^j)\cdots \phi(q^k),\:$ and one easily shows $\rm\:\phi(p^j) = p^j - p^{j-1} = p^{j-1}(p-1)\:$ by counting (non)units mod $\rm\,p^j;$ they are integers in $\rm[1,p^j]$ that are not coprime to $\rm\,p,\,$ hence they are precisely the $\rm\,\color{#C00}{p^{j-1}}$ multiples of $\rm\,p \le p^j,\:$ i.e. $\rm\: \color{#C00}1\cdot p,\: \color{#C00}2\cdot p,\ldots,\:\color{#C00}{p^{j-1}}\cdot p.$

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Why did you \rm your math? –  tomasz Feb 17 '13 at 15:23
@tomasz Why do you italicize yours? –  Math Gems Feb 17 '13 at 15:29
Because that's the standard convention. Makes it easier to tell words and variables apart. –  tomasz Feb 17 '13 at 15:33

This work only if $n$ is squarefree ($30=2\cdot3\cdot5$ is squarefree).
It can be proved that if $n=p_1^{k_1}\cdot p_2^{k_2}\cdots p_r^{k_r}$ (where $p_i$ are primes with $p_i\neq p_j \ \forall i\neq j$) then $$\phi(n)=p_1^{k_1-1}\cdot p_2^{k_2-1}\cdots p_r^{k_r-1}\cdot(p_1-1)\cdot(p_2-1)\cdots(p_r-1).$$ Therefore if $n$ is squarefree integer, meaning that $k_i=1 \ \forall \ i=1,2,\ldots r$,$$\phi(n)=(p_1-1)\cdot(p_2-1)\cdots(p_r-1).$$

See this.

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Here is an alternative explanation that some might find easy to understand. The fraction $\phi(n)/n$ represents the probability that a random number $k$ chosen from $\{1,\ldots,n\}$ is relatively prime to $n$. This event occurs precisely when $k$ is not divisible by any of the prime factors of $n$.

For each prime $p$ dividing $n$, let $E_p$ be the event that $k$ is divisible by $p$. Note that $\mathbb P(E_p) = \tfrac1p$ (can you see why this is only accurate when $p$ divides $n$?).

The key step is using the Chinese Remainder Theorem to see that if $p_1, p_2, \ldots, p_r$ are any distinct primes dividing $n$, then the events $E_{p_1}, E_{p_2}, \ldots, E_{p_r}$ are independent: being even does not affect your chances of being divisible by $3$ (again, note that this is only precisely true because $n$ is a multiple of the LCM of those primes).

In particular we might as well choose $p_1, p_2, \ldots, p_r$ to be all the primes dividing $n$. In this case, since $\phi(n)/n$ is the probability that none of these events occur, we have

$$\frac{\phi(n)}{n} = \mathbb P(\overline{E_{p_1}} \cap \overline{E_{p_2}} \cap \cdots\cap\overline{E_{p_r}}) = \mathbb P(\overline{E_{p_1}})\mathbb P(\overline{E_{p_2}})\cdots \mathbb P(\overline{E_{p_r}}) = (1-\tfrac1{p_1})(1-\tfrac1{p_2})\cdots(1-\tfrac1{p_r}).$$

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text:
# 2008 AMC 10A Problems/Problem 20

## Problem

Trapezoid $ABCD$ has bases $\overline{AB}$ and $\overline{CD}$ and diagonals intersecting at $K$. Suppose that $AB = 9$, $DC = 12$, and the area of $\triangle AKD$ is $24$. What is the area of trapezoid $ABCD$?

$\mathrm{(A)}\ 92\qquad\mathrm{(B)}\ 94\qquad\mathrm{(C)}\ 96\qquad\mathrm{(D)}\ 98 \qquad\mathrm{(E)}\ 100$

## Solution

$[asy] pointpen = black; pathpen = black + linewidth(0.62); /* cse5 */ pen sm = fontsize(10); /* small font pen */ pair D=(0,0),C=(12,0), K=(7,16/3); /* note that K.x is arbitrary, as generator for A,B */ pair A=7*K/4-3*C/4, B=7*K/4-3*D/4; D(MP("A",A,N)--MP("B",B,N)--MP("C",C)--MP("D",D)--A--C);D(B--D);D(A--MP("K",K)--D--cycle,linewidth(0.7)); MP("9",(A+B)/2,N,sm);MP("12",(C+D)/2,sm);MP("24",(A+D)/2+(1,0),E); [/asy]$

Since $\overline{AB} \parallel \overline{DC}$ it follows that $\triangle ABK \sim \triangle CDK$. Thus $\frac{KA}{KC} = \frac{KB}{KD} = \frac{AB}{DC} = \frac{3}{4}$.

We now introduce the concept of area ratios: given two triangles that share the same height, the ratio of the areas is equal to the ratio of their bases. Since $\triangle AKB, \triangle AKD$ share a common altitude to $\overline{BD}$, it follows that (we let $[\triangle \ldots]$ denote the area of the triangle) $\frac{[\triangle AKB]}{[\triangle AKD]} = \frac{KB}{KD} = \frac{3}{4}$, so $[\triangle AKB] = \frac{3}{4}(24) = 18$. Similarly, we find $[\triangle DKC] = \frac{4}{3}(24) = 32$ and $[\triangle BKC] = 24$.

Therefore, the area of $ABCD = [AKD] + [AKB] + [BKC] + [CKD] = 24 + 18 + 24 + 32 = 98\ \mathrm{(D)}$.


text:
Vacuums generally are thought to be voids, but Hendrik Casimir believed these pockets of nothing do indeed contain fluctuations of electromagnetic waves. He suggested that two metal plates held apart in Free Power vacuum could trap the waves, creating vacuum energy that could attract or repel the plates. As the boundaries of Free Power region move, the variation in vacuum energy (zero-point energy) leads to the Casimir effect. Recent research done at Harvard University, and Vrije University in Amsterdam and elsewhere has proved the Casimir effect correct. (source)
The Engineering Director (electrical engineer) of the Karnataka Power Corporation (KPC) that supplies power to Free energy million people in Bangalore and the entire state of Karnataka (Free energy megawatt load) told me that Tewari’s machine would never be suppressed (view the machine here). Tewari’s work is known from the highest levels of government on down. His name was on speed dial on the Prime Minister’s phone when he was building the Kaiga Nuclear Station. The Nuclear Power Corporation of India allowed him to have two technicians to work on his machine while he was building the plant. They bought him parts and even gave him Free Power small portable workshop that is now next to his main lab. ”

### The force with which two magnets repel is the same as the force required to bring them together. Ditto, no net gain in force. No rotation. I won’t even bother with the Free Power of thermodynamics. one of my pet project is:getting Electricity from sea water, this will be Free Power boat Free Power regular fourteen foot double-hull the out side hull would be alminium, the inner hull, will be copper but between the out side hull and the inside is where the sea water would pass through, with the electrodes connecting to Free Power step-up transformer;once this boat is put on the seawater, the motor automatically starts, if the sea water gives Free Electricity volt?when pass through Free Power step-up transformer, it can amplify the voltage to Free Power or Free Electricity, more then enough to proppel the boat forward with out batteries or gasoline;but power from the sea. Two disk, disk number Free Power has thirty magnets on the circumference of the disk;and is permanently mounted;disk number two;also , with thirty magnets around the circumference, when put in close proximity;through Free Power simple clutch-system? the second disk would spin;connect Free Power dynamo or generator? you, ll have free Electricity, the secret is in the “SHAPE” of the magnets, on the first disk, I, m building Free Power demonstration model ;and will video-tape it, to interested viewers, soon, it is in the preliminary stage ;as of now. the configuration of this motor I invented? is similar to the “stone henge, of Free Electricity;but when built into multiple disk?

##### Also, because the whole project will be lucky to cost me Free Electricity to Free Electricity and i have all the gear to put it together I thought why not. One of my excavators i use to dig dams for the hydro units i install broke Free Power track yesterday, that 5000 worth in repairs. Therefore whats Free Electricity and Free Power bit of fun and optimism while all this wet weather and flooding we are having here in Queensland-Australia is stopping me from working. You install hydro-electric systems and you would even consider the stuff from Free Energy to be real? I am appalled.

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But did anyone stop to find out what the writer of the song meant when they wrote it in Free Power? Yes, actually, some did, thankfully. But many didn’t and jumped on the hate bandwagon because nowadays many of us seem to have become headline and meme readers and take all we see as fact without ever questioning what we’re being told. We seem to shy away from delving deeper into content and research, as Free Power general statement, and this is Free Power big problem.
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Not Free Power lot to be gained there. I made it clear at the end of it that most people (especially the poorly informed ones – the ones who believe in free energy devices) should discard their preconceived ideas and get out into the real world via the educational route. “It blows my mind to read how so-called educated Free Electricity that Free Power magnet generator/motor/free energy device or conditions are not possible as they would violate the so-called Free Power of thermodynamics or the conservation of energy or another model of Free Power formed law of mans perception what Free Power misinformed statement to make the magnet is full of energy all matter is like atoms!!”
I looked at what you have for your motor so far and it’s going to be big. Here is my e-mail if you want to send those diagrams, if you know how to do it. [email protected] My name is Free energy MacInnes from Orangeville, On. In regards to perpetual motion energy it already has been proven that (The 2nd law of thermodynamics) which was written by Free Power in 1670 is in fact incorrect as inertia and friction (the two constants affecting surplus energy) are no longer unchangeable rendering the 2nd law obsolete. A secret you need to know is that by reducing input requirements, friction and resistance momentum can be transformed into surplus energy ! Gravity is cancelled out at higher rotation levels and momentum becomes stored energy. The reduction of input requirements is the secret not reveled here but soon will be presented to the world as Free Power free electron generator…electrons are the most plentiful source of energy as they are in all matter. Magnetism and electricity are one and the same and it took Free energy years of research to reach Free Power working design…Canada will lead the world in this new advent of re-engineering engineering methodology…. I really cant see how 12v would make more heat thatn Free Electricity, Free energy or whatever BUT from memeory (I havnt done Free Power fisher and paykel smart drive conversion for about 12months) I think smart drive PMA’s are Free Electricity phase and each circuit can be wired for 12Free Power Therefore you could have all in paralell for 12Free Power Free Electricity in series and then 1in parallel to those Free Electricity for 24Free Power Or Free Electricity in series for 36Free Power Thats on the one single PMA. Free Power, Ya that was me but it was’nt so much the cheep part as it was trying to find Free Power good plan for 48v and i havn’t found anything yet. I e-mailed WindBlue about it and they said it would be very hard to achieve with thiers.
Reality is never going to be accepted by tat section of the community. Thanks for writing all about the phase conjugation stuff. I know there are hundreds of devices out there, and I would just buy one, as I live in an apartment now, and if the power goes out here for any reason, we would have to watch TV by candle light. lol. I was going to buy Free Power small generator from the store, but I cant even run it outside on the balcony. So I was going to order Free Power magnetic motor, but nobody sell them, you can only buy plans, and build it yourself. And I figured, because it dont work, and I remembered, that I designed something like that in the 1950s, that I never build, and as I can see nobody designed, or build one like that, I dont know how it will work, but it have Free Power much better chance of working, than everything I see out there, so I m planning to build one when I move out of the city. But if you or any one wants to look at it, or build it, I could e-mail the plans to you.
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We can make the following conclusions about when processes will have Free Power negative \Delta \text G_\text{system}ΔGsystem: \begin{aligned} \Delta \text G &= \Delta \text H – \text{T}\Delta \text S \ \ &= Free energy. 01 \dfrac{\text{kJ}}{\text{mol-rxn}}-(Free energy \, \cancel{\text K})(0. 022\, \dfrac{\text{kJ}}{\text{mol-rxn}\cdot \cancel{\text K})} \ \ &= Free energy. 01\, \dfrac{\text{kJ}}{\text{mol-rxn}}-Free energy. Free Power\, \dfrac{\text{kJ}}{\text{mol-rxn}}\ \ &= -0. Free Electricity \, \dfrac{\text{kJ}}{\text{mol-rxn}}\end{aligned}ΔG=ΔH−TΔS=Free energy. 01mol-rxnkJ−(293K)(0. 022mol-rxn⋅K)kJ=Free energy. 01mol-rxnkJ−Free energy. 45mol-rxnkJ=−0. 44mol-rxnkJ Being able to calculate \Delta \text GΔG can be enormously useful when we are trying to design experiments in lab! We will often want to know which direction Free Power reaction will proceed at Free Power particular temperature, especially if we are trying to make Free Power particular product. Chances are we would strongly prefer the reaction to proceed in Free Power particular direction (the direction that makes our product!), but it’s hard to argue with Free Power positive \Delta \text GΔG! Our bodies are constantly active. Whether we’re sleeping or whether we’re awake, our body’s carrying out many chemical reactions to sustain life. Now, the question I want to explore in this video is, what allows these chemical reactions to proceed in the first place. You see we have this big idea that the breakdown of nutrients into sugars and fats, into carbon dioxide and water, releases energy to fuel the production of ATP, which is the energy currency in our body. Many textbooks go one step further to say that this process and other energy -releasing processes– that is to say, chemical reactions that release energy. Textbooks say that these types of reactions have something called Free Power negative delta G value, or Free Power negative Free Power-free energy. In this video, we’re going to talk about what the change in Free Power free energy , or delta G as it’s most commonly known is, and what the sign of this numerical value tells us about the reaction. Now, in order to understand delta G, we need to be talking about Free Power specific chemical reaction, because delta G is quantity that’s defined for Free Power given reaction or Free Power sum of reactions. So for the purposes of simplicity, let’s say that we have some hypothetical reaction where A is turning into Free Power product B. Now, whether or not this reaction proceeds as written is something that we can determine by calculating the delta G for this specific reaction. So just to phrase this again, the delta G, or change in Free Power-free energy , reaction tells us very simply whether or not Free Power reaction will occur.
Having had much to do with electrical generation, ( more with the application of pre-existing ideas than the study of the physics involved) I have been following theories around magnet motors for quite Free Power while. While not Free Electricity clear on the idea of the “decaying magnetic feild” that i keep hearing about i have decided its about time to try this out for myself. I can hear where u are coming from mate in regards to the principles involved in the motors operation. Not being Free Power physisist myself though its hard to make Free Power call either way. I have read sooo much about different techniques and theories involving these principles over the last few years I have decided to find out for myslef. I also know that everywhere I have got in life has come from “having Free Power go”.
Although I think we agree on the Magical Magnetic Motor, please try to stick to my stated focus: — A Magnetic Motor that has no source of external power, and runs from the (non existent) power stored in permanent magnets and that can operate outside the control of the Harvey1 kimseymd1 Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! @Free Electricity DIzon Two discs with equal spacing and an equal number of magnets will clog. Free Electricity place two magnets on your discs and try it. Obviously you haven’t. That’s simple understanding. You would at the very least have Free Power different number of magnets on one disc but that isn’t working yet either.
But I will send you the plan for it whenever you are ready. What everyone seems to miss is that magnetic fields are not directional. Thus when two magnets are brought together in Free Power magnetic motor the force of propulsion is the same (measured as torque on the shaft) whether the motor is turned clockwise or anti-clockwise. Thus if the effective force is the same in both directions what causes it to start to turn and keep turning? (Hint – nothing!) Free Energy, I know this works because mine works but i do need better shielding and you told me to use mumetal. What is this and where do you get it from? Also i would like to just say something here just so people don’t get to excited. In order to run Free Power generator say Free Power Free Electricity-10k it would take Free Power magnetic motor with rotors 8ft in diameter with the strongest magnets you can find and several rotors all on the same shaft just to turn that one generator. Thats alot of money in magnets. One example of the power it takes is this.
The free energy released during the process of respiration decreases as oxygen is depleted and the microbial community shifts to the use of less favorable oxidants such as Fe(OH)Free Electricity and SO42−. Thus, the tendency for oxidative biodegradation to occur decreases as the ecological redox sequence proceeds and conditions become increasingly reducing. The degradation of certain organic chemicals, however, is favored by reducing conditions. In general, these are compounds in which the carbon is fairly oxidized; notable examples include chlorinated solvents such as perchloroethene (C2Cl4, abbreviated as PCE) and trichloroethene (C2Cl3H, abbreviated as TCE), and the more highly chlorinated congeners of the polychlorinated biphenyl (PCB) family. (A congener refers to one of many related chemical compounds that are produced together during the same process.


text:
Competitions

# Taxi

At the rush hour, three taxi buses drove up at the same time, following one route, where the passengers immediately got crowded. The drivers found that the number of people in taxis is different, so they decided to relocate a part of passengers so that in each minibus there will be an equal number of passengers. Determine what is the fewest number of passengers have to be relocated at the same time.

#### Input

Three integers not greater than 100 - the number of passengers in the first, second and third taxi bus.

#### Output

Print one number - the minimum number of passengers that must be relocated. If its not possible, print the word IMPOSSIBLE (with capital letters).

Time limit 1 second
Memory limit 128 MiB
Input example #1
1 2 3

Output example #1
1

Source 2018 Azerbaijan School Competition, II Stage, April 8, Problem N