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THE READ-LEHMAN LETTERS ON KINSHIP MATHEMATICS
No full textFollowing the publication of the letter from Dwight Read, (see “New Results: The Logic of Older/Younger Sibling Terms in Classificatory Terminologies” in MACT Letters, November 9 2004) Kris Lehman (F. K. L. Chit Hlaing) responded to that letter. Together Professors Read and Lehman then agreed to compile an exchange, including previous discussions, and have submitted the sequence of letters below to MACT. They offer the exchange both to record some important developments in the mathematical theory of kinship category systems as reflected in their joint work in progress, and to record the way such work develops through technical exchanges
On Read-k Projections of the Determinant
No full textWe consider read-k determinantal representations of polynomials and prove some non-expressibility results. A square matrix M whose entries are variables or field elements will be called read-k, if every variable occurs at most k times in M. It will be called a determinantal representation of a polynomial f if f = det(M). We show that
- the n × n permanent polynomial does not have a read-k determinantal representation for k ∈ o(√n/log n) (over a field of characteristic different from two). We also obtain a quantitative strengthening of this result by giving a similar non-expressibility for k ∈ o(√n/log n) for an explicit n-variate multilinear polynomial (as opposed to the permanent which is n²-variate)
A Note on Read-k Times Branching Programs
No full text. A syntactic read-k times branching program has the restriction that no variable occurs more than k times on any path (whether or not consistent) . We exhibit an explicit Boolean function f; which cannot be computed by nondeterministic syntactic read-k times branching programs of size less than exp i \Omega ip n k 2k jj ; although its complement :f has a nondeterministic syntactic read-once branching program of polynomial size. This, in particular, means that the nonuniform analogue of NLOGSPACE = co \Gamma NLOGSPACE fails for syntactic read-k times networks with k = o(log n): We also show that (even for k = 1) the syntactic model is exponentially weaker then more realistic "nonsyntactic" one. Keywords: Branching programs, read-k times networks, lower bounds y To appear in: RAIRO J. Theoretical Informatics and Application z Universitat Trier, FB Informatik, 54286 Trier, GERMANY. E--mail: [email protected] Online access for ECCC: FTP: ftp.eccc.uni-trier.de:/pub/eccc/ W..
A Note on Read-k Times Branching Programs
No full textA syntactic read-k times branching program has the restriction that no variable occurs more than k times on any path (whether or not consistent). We exhibit an explicit Boolean function f; which cannot be computed by nondeterministic syntactic read-k times branching programs of size less than exp i\Omega ip n k 2k jj ; although its complement :f has a nondeterministic syntactic read-once branching program of polynomial size. This, in particular, means that the nonuniform analogue of NLOGSPACE = co \Gamma NLOGSPACE fails for syntactic read-k times networks with k = o(log n): We also show that (even for k = 1) the syntactic model is exponentially weaker then more realistic "nonsyntactic" on
Notes on Boolean Read-k and Multilinear Circuits
No full textA monotone Boolean (OR,AND) circuit computing a monotone Boolean function f
is a read-k circuit if the polynomial produced (purely syntactically) by the
arithmetic (+,x) version of the circuit has the property that for every prime
implicant of f, the polynomial contains at least one monomial with the same set
of variables, each appearing with degree at most k. Every monotone circuit is a
read-k circuit for some k. We show that already read-1 (OR,AND) circuits are
not weaker than monotone arithmetic constant-free (+,x) circuits computing
multilinear polynomials, are not weaker than non-monotone multilinear
(OR,AND,NOT) circuits computing monotone Boolean functions, and have the same
power as tropical (min,+) circuits solving combinatorial minimization problems.
Finally, we show that read-2 (OR,AND) circuits can be exponentially smaller
than read-1 (OR,AND) circuits.Comment: A throughout revised version. To appear in Discrete Applied
Mathematic
Measurement of the ratio of branching fractions B(B0→K∗0γ )/B(B0s→φγ ) and the directCP asymmetry inB 0→K∗0γ
No full textThe ratio of branching fractions of the radiative B decays B0→K⁎0γ and B0s→ϕγ has been measured using an integrated luminosity of 1.0 fb−1 of pp collision data collected by the LHCb experiment at a centre-of-mass energy of s√=7TeV. The value obtained is
B(B0→K⁎0γ)B(B0s→ϕγ)=1.23±0.06(stat.)±0.04(syst.)±0.10(fs/fd),
where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is associated with the ratio of fragmentation fractions fs/fd. Using the world average value for B(B0→K⁎0γ), the branching fraction B(B0s→ϕγ) is measured to be (3.5±0.4)×10−5.
The direct CP asymmetry in B0→K⁎0γ decays has also been measured with the same data and found to be
ACP(B0→K⁎0γ)=(0.8±1.7(stat.)±0.9(syst.))%.
Both measurements are the most precise to date and are in agreement with the previous experimental results and theoretical expectations
DSM of Newton type for solving operator equations F(u) = f with minimal smoothness assumptions on F.
No full textThis paper is a review of the authors’ results on the DSM (Dynamical Systems Method) for solving operator equation (*) F(u) = f. It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F. It is assumed that F is continuously
Fr´echet differentiable, but no smoothness assumptions on F0(u) are imposed. The DSM for solving equation (*) is developed. Under weak assumptions global existence of the solution u(t) is proved, the existence
of u(1) is established, and the relation F(u(1)) = f is obtained. The DSM is developed for a stable solution of equation (*) when noisy data
f are given, kf − f k
The construction of Karen Karnak: The multi-author-function
No full textThis thesis is situated within the comparatively recent developments of Web 2.0 and the emergence of interactive WikiMedia, and explores the mode of authorship within a Read/Write culture compared to that of a Read/Only tradition. The hypothesis of this study is that the role of the audience has become merged with the author, and as such, represents new functions and attributes, distinct from a more conventional concept of authorship, in which the roles of audience and author are more separate. Read/Write and participatory culture, as defined by this study, is focused on collaboration, and includes the influences of D.I.Y. culture, Open-Source practices and the production of text by multiple authors. Multi-authorship presents a re-thinking of several concepts which support the notion of the individual author, since the focus of multi-authorship is not on attribution and ownership of a finished text, but on the continued malleability of a text. Modes of multi-authorship, demonstrated in the use of the pseudonyms Alan Smithee and Karen Eliot, represent declarative authors whose names signify multiple origins, whilst concurrently indicating a distinct body of work. The function of these names form an important context to this study, since primary research involves the construction of an experimental mode of multi-authorship utilising WikiMedia technology and the interaction of thirty nine participants, who are invited to create a body of work under the collective pseudonym Karen Karnak. The data generated by this experiment is analysed using aspects of Michel Foucault's author-function to identify and determine power structures inherent in the WikiMedia context. The interplay of power structures, including concepts such as identity, ownership and the body of work, affect the resulting mode of authorship and contribute to the construction of Karen Karnak, suggesting further areas of research into the emerging multi-author
K. F. C. Rose, The date and author of the Satyricon, with an introduction by J. P. Sullivan, 1971
No full textRastier Françoise. K. F. C. Rose, The date and author of the Satyricon, with an introduction by J. P. Sullivan, 1971. In: Revue des Études Anciennes. Tome 74, 1972, n°1-4. pp. 300-303
K. F. C. Rose, The Date and Author of the Satyricon. With an Introduction by J. P. Sullivan
No full textVerdière Raoul. K. F. C. Rose, The Date and Author of the Satyricon. With an Introduction by J. P. Sullivan. In: L'antiquité classique, Tome 42, fasc. 1, 1973. pp. 279-280
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