The Pythagoras number and the uu-invariant of Laurent series fields in several variables

We show that every sum of squares in the three-variable Laurent series field $\mathbb{R}((x,y,z))$ is a sum of 4 squares, as was conjectured in a paper of Choi, Dai, Lam and Reznick in the 1980's. We obtain this result by proving that every sum of squares in a finite extension of $\mathbb{R}((x,y))$ is a sum of $3$ squares. It was already shown in Choi, Dai, Lam and Reznick's paper that every sum of squares in $\mathbb{R}((x,y))$ itself is a sum of two squares. We give a generalization of this result where $\mathbb{R}$ is replaced by an arbitrary real field. Our methods yield similar results about the $u$-invariant of fields of the same type.Comment: final version, major revisions in the style of writing (abstract and introduction rewritten) compared to v.

Numerical and analytical research of the impact of decoherence on quantum circuits

Three different levels of noisy quantum schemes modeling are considered: vectors, density matrices and Choi-Jamiolkowski related states. The implementations for personal computers and supercomputers are described, and the corresponding results are shown. For the level of density matrices, we present the technique of the fixed rank approximation and show some analytical estimates of the fidelity level.Comment: 11 pages, 9 figures, report for the International Symposium "Quantum Informatics-2014" (QI-2014), Zvenigorod, Moscow region, October 06-10, 201

The tenth order mock theta functions revisited

In this paper we consider the first four of the eight identities between the tenth order mock theta functions, found in Ramanujan's lost notebook. These were originally proved by Choi. Here we give an alternative (much shorter) proof.Comment: 11 pages; preprint, submitted for publicatio

Voicing Back: The Poetics and Politics of Ping Chong's Ethno-Historiographic Fables

In spite of Ping Chong¡¯s reputation in the American theatre scene, little has been done to explore his artistic works from a fully theorized perspective. In this dissertation, I propose a category of ¡°cultural narrative texts¡± to investigate cultural and historical themes of ¡°culture and the other¡± in Chong¡¯s fascinating ethno-historiographic fables. The poetics and politics of Chong¡¯s narrative texts are the subject of this dissertation. The frames of myth and narratology in their constructive aspects (how the mythic narratives are expressed) provide the poetics part. I adopt the literary approaches of Northrop Frye and Kenneth Burke for their intense studies on image (narrative unit), rhetoric (narrative signification), and emplotment (narrative sequence). In a connective linkage from poetics, the politics part engages the cultural and historical thematics through which I read what is expressed in Chong¡¯s (counter-) myths on people, cultures, and histories. For this complex thematic part, I construe a theoretical bricolage of a broad range of disciplines and methodologies, from psychoanalysis, cognitive science, anthropology, historiography, sociology, to poststructuralism, postcolonialism, and feminism.This dissertation deals with Chong¡¯s ethno-historiographic fables throughout his theatrical career over three decades, examining how his deconstructive myth-making wrestles with the problematic notion of ¡°the other¡± in both local (national) and global aspects. Borrowing Julia Kristeva¡¯s socially informed psychoanalysis, I approach Chong¡¯s concept of ¡°the other¡± as ¡°social abject¡± inhibiting at the margins. I argue that through Chong¡¯s (counter-) myth-making which destabilizes the authority of hegemonic narratives of the incompatible split between the self and the other, multiple voices of the marginalized return, and the monologue of the hegemonic culture is interrupted. In this dissertation, I demonstrate how the performance of Chong¡¯s (counter-) narratives, what I call ¡°voicing back,¡± resist the silence, enabling the marginalized abject to become the subjects of their own desires and histories. This ¡°voicing back¡± in its shared political languages of respect, equality, and justice (toward the others) prepares for the performance of a democracy which is based on the complete modes of speech acts, speaking and listening

Can the rapid braking of the white dwarf in AE Aquarii be explained in terms of the gravitational wave emitter mechanism?

The spin-down power of the white dwarf in the close binary AE Aquarii significantly exceeds the bolometric luminosity of the system. The interpretation of this phenomenon in terms of the gravitational-wave emitter mechanism has been recently suggested by Choi & Yi. The basic assumption of their interpretation is that the spatially limited blobs or mounds of the mass \delta m ~ 10^{-3} M_sun, are present at the magnetic poles of the white dwarf. We show that the mounds of this mass can be confined by the magnetic field of the white dwarf only if the dipole magnetic moment of the star exceeds 4x10^{37} G cm^3. Under these conditions, however, the magnetodipole losses of the white dwarf would exceed the evaluated spin-down power 6 orders of magnitude. On this basis we discard a possibility that the observed rapid braking of the white dwarf in AE Aquarii can be explained in terms of the mechanism proposed by Choi & Yi.Comment: 6 pages, published in ApJ, 576, L5

Powers opposed and intrinsic finks

Philosophers disagree over whether dispositions can be intrinsically finked or masked. Choi suggests that there are no clear, relevant differences between cases where intrinsic finks would be absurd and those where they seem plausible, and as a result rejects them wholesale. Here, I highlight two features of dispositional properties which, when considered together, provide a plausible explanation for when dispositions can be subject to intrinsic finks and when not

Parameterized Construction of Program Representations for Sparse Dataflow Analyses

Data-flow analyses usually associate information with control flow regions. Informally, if these regions are too small, like a point between two consecutive statements, we call the analysis dense. On the other hand, if these regions include many such points, then we call it sparse. This paper presents a systematic method to build program representations that support sparse analyses. To pave the way to this framework we clarify the bibliography about well-known intermediate program representations. We show that our approach, up to parameter choice, subsumes many of these representations, such as the SSA, SSI and e-SSA forms. In particular, our algorithms are faster, simpler and more frugal than the previous techniques used to construct SSI - Static Single Information - form programs. We produce intermediate representations isomorphic to Choi et al.'s Sparse Evaluation Graphs (SEG) for the family of data-flow problems that can be partitioned per variables. However, contrary to SEGs, we can handle - sparsely - problems that are not in this family