Bibliographic record
Abstract
The taut string problem concerns finding the function with the shortest graph length, i.e. the taut string, in a certain set Ω of continuous piecewise linear functions.It has appeared in a broad range of applications including statistics, image processing and economics.As it turns out, the taut string has besides minimal graph length also minimal energy and minimal total variation among the functions in Ω.The theory of real interpolation is based on Peetre's K-functional.In terms of the K-functional, we introduce invariant K-minimal sets and show a close connection between taut strings and invariant K-minimal sets.This insight leads to new problems of interpolation theory, gives possibility to generalize the notion of taut strings and provides new applications.The thesis consists of four papers.In paper I, connections between invariant K-minimal sets and various forms of taut strings are investigated.It is shown that the set Ω ′ of the derivatives of the functions in Ω can be interpreted as an invariant K-minimal set for the Banach couple (ℓ 1 , ℓ ∞ ) on R n .In particular, the derivative of the taut string has minimal K-functional in Ω ′ .A characterization of all bounded, closed and convex sets in R n that are invariant K-minimal for (ℓ 1 , ℓ ∞ ) is established.Paper II presents examples of invariant K-minimal sets in R n for (ℓ 1 , ℓ ∞ ).A convergent algorithm for computing the element with minimal K-functional in such sets is given.In the infinite-dimensional setting, a sufficient condition for a set to be invariant K-minimal with respect to the Banach coupleWith this condition at hand, different examples of invariant K-minimal sets for this couple are constructed.Paper III considers an application of taut strings to buffered real-time communication systems.The optimal buffer management strategy, with respect to minimization of a class of convex distortion functions, is characterized in terms of a taut string.Further, an algorithm for computing the optimal buffer management strategy is provided.In paper IV, infinite-dimensional taut strings are investigated in connection with the Wiener process.It is shown that the average energy per unit of time of the taut string in the long run converges, if it is constrained to stay within the distance r > 0 from the trajectory of a Wiener process, to a constant C 2 /r 2 where C ∈ (0, ∞).While the exact value of C is unknown, the numerical estimate C ≈ 0.63 is obtained through simulations on a super computer.These simulations are based on a certain algorithm for constructing finite-dimensional taut strings.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".