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Despite the interest in the neuroimaging of working memory, little is still known about the neurobiology of complex working memory in tasks that require simultaneous manipulation and storage of information. In addition to the central executive network, we assumed that the recently described salience network [involving the anterior insular cortex (AIC) and the anterior cingulate cortex (ACC)] might be of particular importance to working memory tasks that require complex, effortful processing. Method: Healthy participants (n = 26) and participants suffering from working memory problems related to the Kleine–Levin syndrome (KLS) (a specific form of periodic idiopathic hypersomnia; n = 18) participated in the study. Participants were further divided into a high- and low-capacity group, according to performance on a working memory task (listening span). In a functional magnetic resonance imaging (fMRI) study, participants were administered the reading span complex working memory task tapping cognitive effort. Principal findings: The fMRI-derived blood oxygen level dependent (BOLD) signal was modulated by (1) effort in both the central executive and the salience network and (2) capacity in the salience network in that high performers evidenced a weaker BOLD signal than low performers. In the salience network there was a dichotomy between the left and the right hemisphere; the right hemisphere elicited a steeper increase of the BOLD signal as a function of increasing effort. There was also a stronger functional connectivity within the central executive network because of increased task difficulty. Conclusion: The ability to allocate cognitive effort in complex working memory is contingent upon focused resources in the executive and in particular the salience network. Individual capacity during the complex working memory task is related to activity in the salience (but not the executive) network so that high-capacity participants evidence a lower signal and possibly hence a larger dynamic response.

Title: Logic and cryptography Author: Bc.Vojtěch Wagner Department: Department of Algebra Supervisor: prof. RNDr. Jan Krajíček, DrSc. Abstract: This work is devoted to a study of a formal method of formalization of cryptographic constructions. It is based on defining a multi-sorted formal logic theory T composed of strings, integers and objects of sort k - k-ary functions. We allow some operations on them, formulate axioms, terms and formulas. We also have a special type of integers called the counting integers. It denotes the number of x from a given interval satisfying formula ϕ(x). It allows us to talk about probabilities and use terms of probability theory. The work first describes this theory and then it brings a formalization of the Goldreich-Levin theorem. The goal of this work is to adapt all needed cryptographic terms into the language of T and then prove the theorem using objects, rules and axioms of T. Presented definitions and principles are ilustrated on examples. The purpose of this work is to show that such theory is sufficiently strong to prove such cryptographic constructions and verify its correctness and security. Keywords: cryptography, protocol verifying, Soundness theorem, formal logic theory, the Goldreich-Levin theorem 1

In this study, a computer code is developed in MATLAB&reg / to compute the Radar Cross Section (RCS) of arbitrary shaped complex targets by using Physical Optics (PO) and Modified PO. To increase the computational efficiency of the code, a novel fast integration procedure for oscillatory integrals, called Levin&rsquo / s integration, is applied to PO integrals. In order to improve the performance of PO near grazing angles and to model diffraction effects, a method called PO with Modified Surface Normal Vectors is implemented. In this method, new surface normals are defined to model the diffraction mechanism. Secondary scattering mechanisms like multiple scattering and shadowing algorithms are also included into the code to obtain a complete RCS prediction tool. For this purpose, an iterative version of PO is used to account for multiple scattering effects. Indeed, accounting for multiple scattering effects automatically solves the shadowing problem with a minor modification. Therefore, a special code for shadowing problem is not developed. In addition to frequency domain solutions of scattering problems, a waveform analysis of scattered fields in time domain is also comprised into this thesis. Instead of direct time domain methods like Time Domain Physical Optics, a Fourier domain approach is preferred to obtain the time domain expressions of the scattered fields. Frequency and time domain solutions are obtained for some simple shapes and for a complex tank model for differently polarized incident fields. Furthermore, a statistical analysis for the scattered field from the tank model is conducted.