Octal Bent Generalized Boolean Functions

In this paper we characterize (octal) bent generalized Boolean functions defined on \BBZ_2^n with values in \BBZ_8. Moreover, we propose several constructions of such generalized bent functions for both $n$ even and $n$ odd

Developing Critical Thinking Military Officers

Critical thinking is frequently identified as an important trait for military officers. This paper examines critical thinking from a historical, pedagogical, and warfighting perspective. The author uses his experience teaching mathematical reasoning at the Naval Postgraduate School to provide helpful advice for educators charged with teaching deductive and inductive reasoning. The paper argues that critical thinking should be taught early in an officer\u27s career. It emphasizes a systematic and Socratic instructional approach along with the importance of equipping students with the necessary tools to evaluate problem-solving techniques and critique their associated solutions. Finally, the paper discusses Augmented Intelligence and the growing need to adopt a more holistic view of the combined Human and Machine-Learning decision making system

Remarks on the Occasion of the Retirement of Distinguished Professor Guillermo Owen

The article is a tribute to Distinguished Professor Guillermo Owen who recently retired from the Naval Postgraduate School after 40 years of service

Decomposing generalized bent and hyperbent functions

In this paper we introduce generalized hyperbent functions from $F_{2^n}$ to $Z_{2^k}$, and investigate decompositions of generalized (hyper)bent functions. We show that generalized (hyper)bent functions from $F_{2^n}$ to $Z_{2^k}$ consist of components which are generalized (hyper)bent functions from $F_{2^n}$ to $Z_{2^{k^\prime}}$ for some $k^\prime < k$. For odd $n$, we show that the Boolean functions associated to a generalized bent function form an affine space of semibent functions. This complements a recent result for even $n$, where the associated Boolean functions are bent.Comment: 24 page

Robustness and Vulnerability Measures of Deep Learning Methods for Cyber Defense

NPS NRP Technical ReportNavy networks and infrastructures are under frequent cyberattack. One developing area of application of Artificial Intelligence (AI) and Machine Learning (ML) is cybersecurity. However, some weakness of machine learning, such as the lack of interpretability and the susceptibility to adversarial data, are important issues that must be studied for reliable and safe applications of AI tools. The robustness of deep learning (DL) techniques used in computer vision and language processing have been extensively studied. However, less is currently known about the vulnerabilities and robustness of DL methods suitable in cybersecurity applications. The goal of this research is to investigate mathematical concepts and quantitative measures of robustness and vulnerability to adversarial data for cybersecurity DL and to create computational algorithms capable of quantitatively evaluating the robustness and vulnerability of DL tools. The tasks of the project include literature review, an innovative study of mathematical concepts, the development of computational algorithms, the validation of the concepts and algorithms through examples. The deliverables of the project include technical reports, student thesis, and technical papers for publication. This work will enhance understanding of vulnerabilities of deep learning systems that could be incorporated in future DoN networks, and provide the US Navy with computational tools capable of measuring the robustness of the AI enabled systems.Navy Cyber Defense Operations CommandN2/N6 - Information WarfareThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

Robustness and Vulnerability Measures of Deep Learning Methods for Cyber Defense

NPS NRP Executive SummaryNavy networks and infrastructures are under frequent cyberattack. One developing area of application of Artificial Intelligence (AI) and Machine Learning (ML) is cybersecurity. However, some weakness of machine learning, such as the lack of interpretability and the susceptibility to adversarial data, are important issues that must be studied for reliable and safe applications of AI tools. The robustness of deep learning (DL) techniques used in computer vision and language processing have been extensively studied. However, less is currently known about the vulnerabilities and robustness of DL methods suitable in cybersecurity applications. The goal of this research is to investigate mathematical concepts and quantitative measures of robustness and vulnerability to adversarial data for cybersecurity DL and to create computational algorithms capable of quantitatively evaluating the robustness and vulnerability of DL tools. The tasks of the project include literature review, an innovative study of mathematical concepts, the development of computational algorithms, the validation of the concepts and algorithms through examples. The deliverables of the project include technical reports, student thesis, and technical papers for publication. This work will enhance understanding of vulnerabilities of deep learning systems that could be incorporated in future DoN networks, and provide the US Navy with computational tools capable of measuring the robustness of the AI enabled systems.Navy Cyber Defense Operations CommandN2/N6 - Information WarfareThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

Faces of NPS: Cmdr. Thor Martinsen

Faces of NPS features Interviews spotlighting the students, faculty, staff and alumni of our Nation’s premier defense education and research institution

Bisecting binomial coefficients

In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit nontrivial bisections, and a class with only trivial bisections. As a byproduct of this last construction, we show conjectures Q2 and Q4 of Cusick and Li [7]. We next find several bounds for the number of nontrivial bisections and further compute (using a supercomputer) the exact number of such bisections for n ≤ 51

Ledererfaringer med innføring og bruk av etisk refleksjon som arbeidsmetode

Drammen kommunes deltakelse i det nasjonale prosjektet ”Samarbeid om etisk kompetanseheving” er bakgrunn for denne oppgaven. Kommunen har deltatt siden 2008 og et stort antall ansatte har fått opplæring og mange virksomheter mange aktive refleksjonsgrupper. Mye fokus rettes mot de ansatte, men hvilken erfaringer har lederne gjort med dette arbeidet. Det gir grunnlaget for problemstillingen for denne studien som er : Hvilke erfaringer har lederne med innføring og bruk av etisk refleksjon som arbeidsmetode blant ansatte