Estimating the effective degrees of freedom in univariate multiple regression analysis

The general linear model provides the most widely applied statistical framework for analyzing functional MRI (fMRI) data. With the increasing temporal resolution of recent scanning protocols, and more elaborate data preprocessing schemes, data independency is no longer a valid assumption. In this paper, we revise the statistical background of the general linear model in the presence of temporal autocorrelations. First, when detecting the activation signal, we explicitly account for the temporal autocorrelation structure, which yields a generalized F-test and the associated corrected (or effective) degrees of freedom (DOF). The proposed approach is data driven and thus independent of any specific preprocessing method. Then, for event-related protocols, we propose a new model for the temporal autocorrelations (“damped oscillator” model) and compare this model to another, previously used in the field (first-order autoregressive model, or AR(1) model). In the case of long fMRI time series, an efficient approximation for the number of effective DOF is provided for both models. Finally, the validity of our approach is assessed using simulated and real fMRI data and is compared with more conventional methods

Light Deflection by Rotating Regular Black Holes with a Cosmological Constant

Using the Gauss-Bonnet theorem, we compute and examine the deflection angle of light rays by rotating regular black holes with a cosmological constant. By the help of optical geometries, we first deal with the Hayward black holes with cosmological contributions. Then, we reconsider the study of the Bardeen solutions. We inspect the cosmological constant effect on the deflection angle of light rays. Concretely, we find extra cosmological correction terms generalizing certain obtained findings. Using graphical analysis, we provide a comparative discussion with respect to the Kerr solutions. The results confirm that the non-linear electrodynamic charges affect the space-time geometry by decreasing the deflection angle of light rays by such cosmological black holes.Comment: latex, 16 pages, 4 figures. Accepted for publication in Chin. J. Phys 202

Light Behaviors around Black Holes in M-theory

We study the deflection angle and the trajectory of the light rays around black holes in M-theory scenarios. Using the Gauss-Bonnet theorem, we first compute and examine the deflection angle of the light rays near four and seven-dimensional AdS black holes obtained from the M-theory compactifications on the real spheres on $S^7$ and $S^4$, respectively. We discuss the effect of the M-theory brane number and the rotating parameter on such an optical quantity. We then investigate the trajectories of the light rays using the equation of motion associated with $M2$ and $M5$ branes.Comment: Latex, 22 pages, 8 figure

Deflection angle and Shadows by Black Holes in Starobinsky-Bel-Robinson Gravity from M-theory

Motivated by M-theory compactifications, we investigate optical properties of black holes in the Starobinsky-Bel-Robinsion gravity. Precisely, we study the shadows and the deflection angle of light rays by non-rotating and rotating black holes in such a novel gravity. We start by discussing the shadows of the Schwarzschild-type solutions. As expected, we obtain perfect circular shadows where the size decreases with a stringy gravity parameter denoted by $\beta$. We show that this parameter is constrained by the shadow existence. Combining the Newman-Janis algorithm and the Hamilton-Jacobi mechanism, we examine the shadow behaviors of the rotating solutions in terms of one-dimensional real curves. Essentially, we find various sizes and shapes depending on the rotating parameter and the stringy gravity parameter $a$ and $\beta$, respectively. To inspect the shadow geometric deformations, we investigate the astronomical observables and the energy emission rate. As envisaged, we reveal that $a$ and $\beta$ have an impact on such shadow behaviors. For specific values of $a$, we remark that the obtained shadow shapes share certain similarities with the ones of the Kerr black holes in plasma backgrounds. Using the Event Horizon Telescope observational data, we provide predictions for the stringy gravity parameter $\beta$ which could play a relevant role in M-theory compactifications. We finish this work by a discussion on the behaviors of the light rays near to such four dimensional black holes by computing the deflection angle in terms of a required moduli space.Comment: Latex, 27 pages, 10 figures. Authors in alphabetical orde

Retrospective study of epidemiological, clinicopathological and biological profils of 62 colorectal cancers cases in Jijel provence (Algeria)

In Algeria, the CRC wing and become the first digestive cancer in both sexes,  outperforming stomach cancer. To enrich the Algerian cancer registries, we analyzed the profiles of patients with these cancers in Jijel Willaya. This was a retrospective and descriptive analysis of epidemiological, clinicopathological and biological profiles of 62 CRC cases. We found that the CRC represented the first type of digestive cancers in which the three quarters were colon cancers. The most affected age group was 60-70 years with a male predominance and an average age of 56.20 years. The bleeding and abdominal pain were the majority telltale signs. The combined chemotherapy has been standardized with all patients and the Lieberkühnien adenocarcinoma was the major histological form. The disease issue and the choice of therapy depended on the K-RAS gene mutations. Our results were often compatible with the available literature and may provide reliable and relevant data on this disease.Key words: Colorectal cancer; Epidemiology; Therapy; Adenocarcinoma; K-RAS gen