Expected shannon entropy and shannon differentiation between subpopulations for neutral genes under the finite island model

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information ("Shannon differentiation") between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.

On the security of compressed sensing-based signal cryptosystem

With the development of the cyber-physical systems (CPS), the security analysis of the data therein becomes more and more important. Recently, due to the advantage of joint encryption and compression for data transmission in CPS, the emerging compressed sensing (CS)-based cryptosystem has attracted much attention, where security is of extreme importance. The existing methods only analyze the security of the plaintext under the assumption that the key is absolutely safe. However, for sparse plaintext, the prior sparsity knowledge of the plaintext could be exploited to partly retrieve the key, and then the plaintext, from the ciphertext. So, the existing methods do not provide a satisfactory security analysis. In this paper, it is conducted in the information theory frame, where the plaintext sparsity feature and the mutual information of the ciphertext, key, and plaintext are involved. In addition, the perfect secrecy criteria (Shannon-sense and Wyner-sense) are extended to measure the security. While the security level is given, the illegal access risk is also discussed. It is shown that the CS-based cryptosystem achieves the extended Wyner-sense perfect secrecy, but when the key is used repeatedly, both the plaintext and the key could be conditionally accessed.

Sudden death of entanglement and teleportation fidelity loss via the Unruh effect

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the impact of disproportional samples in credit scoring models: An application to a Brazilian bank data

Statistical methods have been widely employed to assess the capabilities of credit scoring classification models in order to reduce the risk of wrong decisions when granting credit facilities to clients. The predictive quality of a classification model can be evaluated based on measures such as sensitivity, specificity, predictive values, accuracy, correlation coefficients and information theoretical measures, such as relative entropy and mutual information. In this paper we analyze the performance of a naive logistic regression model (Hosmer & Lemeshow, 1989) and a logistic regression with state-dependent sample selection model (Cramer, 2004) applied to simulated data. Also, as a case study, the methodology is illustrated on a data set extracted from a Brazilian bank portfolio. Our simulation results so far revealed that there is no statistically significant difference in terms of predictive capacity between the naive logistic regression models and the logistic regression with state-dependent sample selection models. However, there is strong difference between the distributions of the estimated default probabilities from these two statistical modeling techniques, with the naive logistic regression models always underestimating such probabilities, particularly in the presence of balanced samples. (C) 2012 Elsevier Ltd. All rights reserved.

Indicatori di correlazione e di disordine basati sul concetto di entropia

The aim of this work is to carry out an applicative, comparative and exhaustive study between several entropy based indicators of independence and correlation. We considered some indicators characterized by a wide and consolidate literature, like mutual information, joint entropy, relative entropy or Kullback Leibler distance, and others, more recently introduced, like Granger, Maasoumi and racine entropy, also called Sρ, or utilized in more restricted domains, like Pincus approximate entropy or ApEn. We studied the behaviour of such indicators applying them to binary series. The series was designed to simulate a wide range of situations in order to characterize indicators limit and capability and to identify, case by case, the more useful and trustworthy ones. Our target was not only to study if such indicators were able to discriminate between dependence and independence because, especially for mutual information and Granger, Maasoumi and Racine, that was already demonstrated and reported in literature, but also to verify if and how they were able to provide information about structure, complexity and disorder of the series they were applied to. Special attention was paid on Pincus approximate entropy, that is said by the author to be able to provide information regarding the level of randomness, regularity and complexity of a series. By means of a focused and extensive research, we furthermore tried to clear the meaning of ApEn applied to a couple of different series. In such situation the indicator is named in literature as cross-ApEn. The cross-ApEn meaning and the interpretation of its results is often not simple nor univocal and the matter is scarcely delved into by literature, thereby users can easily leaded up to a misleading conclusion, especially if the indicator is employed, as often unfortunately it happens, in uncritical manner. In order to plug some cross-ApEn gaps and limits clearly brought out during the experimentation, we developed and applied to the already considered cases a further indicator we called “correspondence index”. The correspondence index is perfectly integrated into the cross-ApEn computational algorithm and it is able to provide, at least for binary data, accurate information about the intensity and the direction of an eventual correlation, even not linear, existing between two different series allowing, in the meanwhile, to detect an eventual condition of independence between the series themselves.

Il processo migratorio come determinante della salute mentale: l'esperienza del Centro di Consultazione Socio-Culturale nel Distretto di Pianura Est, AUSL di Bologna.

La ricerca in oggetto ha analizzato le relazioni tra migrazione e salute mentale nel Distretto di Pianura Est dell'AUSL di Bologna. Attraverso un dispositivo d’indagine multi-disciplinare basato sui quadri teorici dell'Antropologia Medica Critica, della Salute Pubblica e della Psichiatria, la ricerca si è inserita nell’ampio contesto di sperimentazione di un innovativo modello di assistenza per pazienti migranti, denominato Centro di Consultazione Socio- Culturale. L'architettura dello studio si rifà a un modello di Ricerca-Azione Partecipata e Multi-Situata fondato su un approccio analitico e auto-riflessivo, il quale ha consentito di problematizzare, oltre alle azioni e alle traiettorie dei vari soggetti che operano nel campo della ricerca, anche le categorie oggetto della ricerca stessa. L'analisi, profondamente radicata nel dato empirico, è stata condotta a partire dall'esperienza degli attori sociali coinvolti. Le esperienze, le informazioni e le rappresentazioni reciproche sono state co-costruite in forma partecipativa attraverso l'uso combinato di metodologie quali-quantitative proprie sia delle discipline sanitarie sia di quelle sociali. Come materiali della ricerca sono stati utilizzati: dati primari e secondari prodotti dalle istituzioni e dalle organizzazioni del territorio stesso; informazioni provenienti dall'osservazione partecipante; colloqui con informatori-chiave; interviste semi-strutturate con decisori politici, amministratori, organizzazioni del territorio, operatori dei servizi, cittadini e pazienti. La ricerca ha dimostrato la validità delle prospettive teoriche utilizzate e delle strategie di lavoro proposte. Il modello di lavoro multi-disciplinare e multi-metodologico si è rivelato produttivo nell'indagare congiuntamente le prospettive degli attori coinvolti insieme alle loro traiettorie, alle reciproche interconnessioni e alle relazioni tra processi locali e globali. L’analisi auto-riflessiva ha consentito di analizzare le attività del Centro di Consultazione evidenziandone vantaggi e limiti. Infine, la collaborazione tra Salute Pubblica e Antropologia Medica Critica ha dimostrato una grande potenzialità e produttività sia sul versante della ricerca scientifica sia su quello dell'assistenza sanitaria.

Genome characterization through a mathematical model of the genetic code: an analysis of the whole chromosome 1 of A. thaliana

The objective of this work is to characterize the genome of the chromosome 1 of A.thaliana, a small flowering plants used as a model organism in studies of biology and genetics, on the basis of a recent mathematical model of the genetic code. I analyze and compare different portions of the genome: genes, exons, coding sequences (CDS), introns, long introns, intergenes, untranslated regions (UTR) and regulatory sequences. In order to accomplish the task, I transformed nucleotide sequences into binary sequences based on the definition of the three different dichotomic classes. The descriptive analysis of binary strings indicate the presence of regularities in each portion of the genome considered. In particular, there are remarkable differences between coding sequences (CDS and exons) and non-coding sequences, suggesting that the frame is important only for coding sequences and that dichotomic classes can be useful to recognize them. Then, I assessed the existence of short-range dependence between binary sequences computed on the basis of the different dichotomic classes. I used three different measures of dependence: the well-known chi-squared test and two indices derived from the concept of entropy i.e. Mutual Information (MI) and Sρ, a normalized version of the “Bhattacharya Hellinger Matusita distance”. The results show that there is a significant short-range dependence structure only for the coding sequences whose existence is a clue of an underlying error detection and correction mechanism. No doubt, further studies are needed in order to assess how the information carried by dichotomic classes could discriminate between coding and noncoding sequence and, therefore, contribute to unveil the role of the mathematical structure in error detection and correction mechanisms. Still, I have shown the potential of the approach presented for understanding the management of genetic information.

A Hybrid Multimodal Non-Rigid Registration of MR Images Based on Diffeomorphic Demons

n this paper we present a novel hybrid approach for multimodal medical image registration based on diffeomorphic demons. Diffeomorphic demons have proven to be a robust and efficient way for intensity-based image registration. A very recent extension even allows to use mutual information (MI) as a similarity measure to registration multimodal images. However, due to the intensity correspondence uncertainty existing in some anatomical parts, it is difficult for a purely intensity-based algorithm to solve the registration problem. Therefore, we propose to combine the resulting transformations from both intensity-based and landmark-based methods for multimodal non-rigid registration based on diffeomorphic demons. Several experiments on different types of MR images were conducted, for which we show that a better anatomical correspondence between the images can be obtained using the hybrid approach than using either intensity information or landmarks alone.

Decision-making dysregulation in first-episode schizophrenia

Studies with chronic schizophrenia patients have demonstrated that patients fluctuate between rigid and unpredictable responses in decision-making situations, a phenomenon which has been called dysregulation. The aim of this study was to investigate whether schizophrenia patients already display dysregulated behavior at the beginning of their illness. Thirty-two first-episode schizophrenia or schizophreniform patients and 30 healthy controls performed the two-choice prediction task. The decision-making behavior of first-episode patients was shown to be characterized by a high degree of dysregulation accompanied by low metric entropy and a tendency towards increased mutual information. These results indicate that behavioral abnormalities during the two-choice prediction task are already present during the early stages of the illness.

Stochastic rank correlation: a robust merit function for 2D/3D registration of image data obtained at different energies

In this article, the authors evaluate a merit function for 2D/3D registration called stochastic rank correlation (SRC). SRC is characterized by the fact that differences in image intensity do not influence the registration result; it therefore combines the numerical advantages of cross correlation (CC)-type merit functions with the flexibility of mutual-information-type merit functions. The basic idea is that registration is achieved on a random subset of the image, which allows for an efficient computation of Spearman's rank correlation coefficient. This measure is, by nature, invariant to monotonic intensity transforms in the images under comparison, which renders it an ideal solution for intramodal images acquired at different energy levels as encountered in intrafractional kV imaging in image-guided radiotherapy. Initial evaluation was undertaken using a 2D/3D registration reference image dataset of a cadaver spine. Even with no radiometric calibration, SRC shows a significant improvement in robustness and stability compared to CC. Pattern intensity, another merit function that was evaluated for comparison, gave rather poor results due to its limited convergence range. The time required for SRC with 5% image content compares well to the other merit functions; increasing the image content does not significantly influence the algorithm accuracy. The authors conclude that SRC is a promising measure for 2D/3D registration in IGRT and image-guided therapy in general.

Hierarchical segmentation-assisted multimodal registration for MR brain images

Information theory-based metric such as mutual information (MI) is widely used as similarity measurement for multimodal registration. Nevertheless, this metric may lead to matching ambiguity for non-rigid registration. Moreover, maximization of MI alone does not necessarily produce an optimal solution. In this paper, we propose a segmentation-assisted similarity metric based on point-wise mutual information (PMI). This similarity metric, termed SPMI, enhances the registration accuracy by considering tissue classification probabilities as prior information, which is generated from an expectation maximization (EM) algorithm. Diffeomorphic demons is then adopted as the registration model and is optimized in a hierarchical framework (H-SPMI) based on different levels of anatomical structure as prior knowledge. The proposed method is evaluated using Brainweb synthetic data and clinical fMRI images. Both qualitative and quantitative assessment were performed as well as a sensitivity analysis to the segmentation error. Compared to the pure intensity-based approaches which only maximize mutual information, we show that the proposed algorithm provides significantly better accuracy on both synthetic and clinical data.

Multifactor effects and evidence of potential interaction between complement factor H Y402H and LOC387715 A69S in age-related macular degeneration.

BACKGROUND: Variants in the complement cascade genes and the LOC387715/HTRA1, have been widely reported to associate with age-related macular degeneration (AMD), the most common cause of visual impairment in industrialized countries. METHODS/PRINCIPAL FINDINGS: We investigated the association between the LOC387715 A69S and complement component C3 R102G risk alleles in the Finnish case-control material and found a significant association with both variants (OR 2.98, p = 3.75 x 10(-9); non-AMD controls and OR 2.79, p = 2.78 x 10(-19), blood donor controls and OR 1.83, p = 0.008; non-AMD controls and OR 1.39, p = 0.039; blood donor controls), respectively. Previously, we have shown a strong association between complement factor H (CFH) Y402H and AMD in the Finnish population. A carrier of at least one risk allele in each of the three susceptibility loci (LOC387715, C3, CFH) had an 18-fold risk of AMD when compared to a non-carrier homozygote in all three loci. A tentative gene-gene interaction between the two major AMD-associated loci, LOC387715 and CFH, was found in this study using a multiplicative (logistic regression) model, a synergy index (departure-from-additivity model) and the mutual information method (MI), suggesting that a common causative pathway may exist for these genes. Smoking (ever vs. never) exerted an extra risk for AMD, but somewhat surprisingly, only in connection with other factors such as sex and the C3 genotype. Population attributable risks (PAR) for the CFH, LOC387715 and C3 variants were 58.2%, 51.4% and 5.8%, respectively, the summary PAR for the three variants being 65.4%. CONCLUSIONS/SIGNIFICANCE: Evidence for gene-gene interaction between two major AMD associated loci CFH and LOC387715 was obtained using three methods, logistic regression, a synergy index and the mutual information (MI) index.

Active Testing for Face Detection and Localization

We provide a novel search technique which uses a hierarchical model and a mutual information gain heuristic to efficiently prune the search space when localizing faces in images. We show exponential gains in computation over traditional sliding window approaches, while keeping similar performance levels.

Prognostic and diagnostic value of EEG signal coupling measures in coma.

OBJECTIVE Our aim was to assess the diagnostic and predictive value of several quantitative EEG (qEEG) analysis methods in comatose patients. METHODS In 79 patients, coupling between EEG signals on the left-right (inter-hemispheric) axis and on the anterior-posterior (intra-hemispheric) axis was measured with four synchronization measures: relative delta power asymmetry, cross-correlation, symbolic mutual information and transfer entropy directionality. Results were compared with etiology of coma and clinical outcome. Using cross-validation, the predictive value of measure combinations was assessed with a Bayes classifier with mixture of Gaussians. RESULTS Five of eight measures showed a statistically significant difference between patients grouped according to outcome; one measure revealed differences in patients grouped according to the etiology. Interestingly, a high level of synchrony between the left and right hemisphere was associated with mortality on intensive care unit, whereas higher synchrony between anterior and posterior brain regions was associated with survival. The combination with the best predictive value reached an area-under the curve of 0.875 (for patients with post anoxic encephalopathy: 0.946). CONCLUSIONS EEG synchronization measures can contribute to clinical assessment, and provide new approaches for understanding the pathophysiology of coma. SIGNIFICANCE Prognostication in coma remains a challenging task. qEEG could improve current multi-modal approaches.

Multimodal non-rigid image registration methods for therapy and surgery planning

La planificación pre-operatoria se ha convertido en una tarea esencial en cirugías y terapias de marcada complejidad, especialmente aquellas relacionadas con órgano blando. Un ejemplo donde la planificación preoperatoria tiene gran interés es la cirugía hepática. Dicha planificación comprende la detección e identificación precisa de las lesiones individuales y vasos así como la correcta segmentación y estimación volumétrica del hígado funcional. Este proceso es muy importante porque determina tanto si el paciente es un candidato adecuado para terapia quirúrgica como la definición del abordaje a seguir en el procedimiento. La radioterapia de órgano blando es un segundo ejemplo donde la planificación se requiere tanto para la radioterapia externa convencional como para la radioterapia intraoperatoria. La planificación comprende la segmentación de tumor y órganos vulnerables y la estimación de la dosimetría. La segmentación de hígado funcional y la estimación volumétrica para planificación de la cirugía se estiman habitualmente a partir de imágenes de tomografía computarizada (TC). De igual modo, en la planificación de radioterapia, los objetivos de la radiación se delinean normalmente sobre TC. Sin embargo, los avances en las tecnologías de imagen de resonancia magnética (RM) están ofreciendo progresivamente ventajas adicionales. Por ejemplo, se ha visto que el ratio de detección de metástasis hepáticas es significativamente superior en RM con contraste Gd–EOB–DTPA que en TC. Por tanto, recientes estudios han destacado la importancia de combinar la información de TC y RM para conseguir el mayor nivel posible de precisión en radioterapia y para facilitar una descripción precisa de las lesiones del hígado. Con el objetivo de mejorar la planificación preoperatoria en ambos escenarios se precisa claramente de un algoritmo de registro no rígido de imagen. Sin embargo, la gran mayoría de sistemas comerciales solo proporcionan métodos de registro rígido. Las medidas de intensidad de voxel han demostrado ser criterios de similitud de imágenes robustos, y, entre ellas, la Información Mutua (IM) es siempre la primera elegida en registros multimodales. Sin embargo, uno de los principales problemas de la IM es la ausencia de información espacial y la asunción de que las relaciones estadísticas entre las imágenes son homogéneas a lo largo de su domino completo. La hipótesis de esta tesis es que la incorporación de información espacial de órganos al proceso de registro puede mejorar la robustez y calidad del mismo, beneficiándose de la disponibilidad de las segmentaciones clínicas. En este trabajo, se propone y valida un esquema de registro multimodal no rígido 3D usando una nueva métrica llamada Información Mutua Centrada en el Órgano (Organ-Focused Mutual Information metric (OF-MI)) y se compara con la formulación clásica de la Información Mutua. Esto permite mejorar los resultados del registro en áreas problemáticas incorporando información regional al criterio de similitud, beneficiándose de la disponibilidad real de segmentaciones en protocolos estándares clínicos, y permitiendo que la dependencia estadística entre las dos modalidades de imagen difiera entre órganos o regiones. El método propuesto se ha aplicado al registro de TC y RM con contraste Gd–EOB–DTPA así como al registro de imágenes de TC y MR para planificación de radioterapia intraoperatoria rectal. Adicionalmente, se ha desarrollado un algoritmo de apoyo de segmentación 3D basado en Level-Sets para la incorporación de la información de órgano en el registro. El algoritmo de segmentación se ha diseñado específicamente para la estimación volumétrica de hígado sano funcional y ha demostrado un buen funcionamiento en un conjunto de imágenes de TC abdominales. Los resultados muestran una mejora estadísticamente significativa de OF-MI comparada con la Información Mutua clásica en las medidas de calidad de los registros; tanto con datos simulados (p<0.001) como con datos reales en registro hepático de TC y RM con contraste Gd– EOB–DTPA y en registro para planificación de radioterapia rectal usando OF-MI multi-órgano (p<0.05). Adicionalmente, OF-MI presenta resultados más estables con menor dispersión que la Información Mutua y un comportamiento más robusto con respecto a cambios en la relación señal-ruido y a la variación de parámetros. La métrica OF-MI propuesta en esta tesis presenta siempre igual o mayor precisión que la clásica Información Mutua y consecuentemente puede ser una muy buena alternativa en aplicaciones donde la robustez del método y la facilidad en la elección de parámetros sean particularmente importantes. Abstract Pre-operative planning has become an essential task in complex surgeries and therapies, especially for those affecting soft tissue. One example where soft tissue preoperative planning is of high interest is liver surgery. It involves the accurate detection and identification of individual liver lesions and vessels as well as the proper functional liver segmentation and volume estimation. This process is very important because it determines whether the patient is a suitable candidate for surgical therapy and the type of procedure. Soft tissue radiation therapy is a second example where planning is required for both conventional external and intraoperative radiotherapy. It involves the segmentation of the tumor target and vulnerable organs and the estimation of the planned dose. Functional liver segmentations and volume estimations for surgery planning are commonly estimated from computed tomography (CT) images. Similarly, in radiation therapy planning, targets to be irradiated and healthy and vulnerable tissues to be protected from irradiation are commonly delineated on CT scans. However, developments in magnetic resonance imaging (MRI) technology are progressively offering advantages. For instance, the hepatic metastasis detection rate has been found to be significantly higher in Gd–EOB–DTPAenhanced MRI than in CT. Therefore, recent studies highlight the importance of combining the information from CT and MRI to achieve the highest level of accuracy in radiotherapy and to facilitate accurate liver lesion description. In order to improve those two soft tissue pre operative planning scenarios, an accurate nonrigid image registration algorithm is clearly required. However, the vast majority of commercial systems only provide rigid registration. Voxel intensity measures have been shown to be robust measures of image similarity, and among them, Mutual Information (MI) is always the first candidate in multimodal registrations. However, one of the main drawbacks of Mutual Information is the absence of spatial information and the assumption that statistical relationships between images are the same over the whole domain of the image. The hypothesis of the present thesis is that incorporating spatial organ information into the registration process may improve the registration robustness and quality, taking advantage of the clinical segmentations availability. In this work, a multimodal nonrigid 3D registration framework using a new Organ- Focused Mutual Information metric (OF-MI) is proposed, validated and compared to the classical formulation of the Mutual Information (MI). It allows improving registration results in problematic areas by adding regional information into the similitude criterion taking advantage of actual segmentations availability in standard clinical protocols and allowing the statistical dependence between the two modalities differ among organs or regions. The proposed method is applied to CT and T1 weighted delayed Gd–EOB–DTPA-enhanced MRI registration as well as to register CT and MRI images in rectal intraoperative radiotherapy planning. Additionally, a 3D support segmentation algorithm based on Level-Sets has been developed for the incorporation of the organ information into the registration. The segmentation algorithm has been specifically designed for the healthy and functional liver volume estimation demonstrating good performance in a set of abdominal CT studies. Results show a statistical significant improvement of registration quality measures with OF-MI compared to MI with both simulated data (p<0.001) and real data in liver applications registering CT and Gd–EOB–DTPA-enhanced MRI and in registration for rectal radiotherapy planning using multi-organ OF-MI (p<0.05). Additionally, OF-MI presents more stable results with smaller dispersion than MI and a more robust behavior with respect to SNR changes and parameters variation. The proposed OF-MI always presents equal or better accuracy than the classical MI and consequently can be a very convenient alternative within applications where the robustness of the method and the facility to choose the parameters are particularly important.