Mirror-Curves and Knot Mosaics

Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot mosaics [23], mirror-curves, and grid diagrams [3,7,22,24]. Hence, we introduce codes for mirror-curves treated as knot or link diagrams placed in rectangular square grids, suitable for software implementation. We provide tables of minimal mirror-curve codes for knots and links obtained from rectangular grids of size 3x3 and px2 (p<5), and describe an efficient algorithm for computing the Kauffman bracket and L-polynomials [18,19,20] directly from mirror-curve representations

ε\varepsilon-Almost collision-flat universal hash functions and mosaics of designs

We introduce, motivate and study $\varepsilon$-almost collision-flat (ACFU) universal hash functions $f:\mathcal X\times\mathcal S\to\mathcal A$. Their main property is that the number of collisions in any given value is bounded. Each $\varepsilon$-ACFU hash function is an $\varepsilon$-almost universal (AU) hash function, and every $\varepsilon$-almost strongly universal (ASU) hash function is an $\varepsilon$-ACFU hash function. We study how the size of the seed set $\mathcal S$ depends on $\varepsilon,|\mathcal X|$ and $|\mathcal A|$. Depending on how these parameters are interrelated, seed-minimizing ACFU hash functions are equivalent to mosaics of balanced incomplete block designs (BIBDs) or to duals of mosaics of quasi-symmetric block designs; in a third case, mosaics of transversal designs and nets yield seed-optimal ACFU hash functions, but a full characterization is missing. By either extending $\mathcal S$ or $\mathcal X$, it is possible to obtain an $\varepsilon$-ACFU hash function from an $\varepsilon$-AU hash function or an $\varepsilon$-ASU hash function, generalizing the construction of mosaics of designs from a given resolvable design (Gnilke, Greferath, Pav{\v c}evi\'c, Des. Codes Cryptogr. 86(1)). The concatenation of an ASU and an ACFU hash function again yields an ACFU hash function. Finally, we motivate ACFU hash functions by their applicability in privacy amplification

Generalized Inpainting Method for Hyperspectral Image Acquisition

A recently designed hyperspectral imaging device enables multiplexed acquisition of an entire data volume in a single snapshot thanks to monolithically-integrated spectral filters. Such an agile imaging technique comes at the cost of a reduced spatial resolution and the need for a demosaicing procedure on its interleaved data. In this work, we address both issues and propose an approach inspired by recent developments in compressed sensing and analysis sparse models. We formulate our superresolution and demosaicing task as a 3-D generalized inpainting problem. Interestingly, the target spatial resolution can be adjusted for mitigating the compression level of our sensing. The reconstruction procedure uses a fast greedy method called Pseudo-inverse IHT. We also show on simulations that a random arrangement of the spectral filters on the sensor is preferable to regular mosaic layout as it improves the quality of the reconstruction. The efficiency of our technique is demonstrated through numerical experiments on both synthetic and real data as acquired by the snapshot imager.Comment: Keywords: Hyperspectral, inpainting, iterative hard thresholding, sparse models, CMOS, Fabry-P\'ero

Review of Robert D. Morris' Class Notes for Advanced Atonal Music Theory.

This review of Class Notes for Advanced Atonal Music Theory by Robert D. Morris (Lebanon, N.H.: Frog Peak Music, 2001) describes the book’s organization, content, and applicability for pedagogical and research uses

Ecosystem services auctions: the last decade of research

ReviewAuctions offer potential cost-effectiveness improvements over other mechanisms for payments for ecosystem services (PES) contract allocation. However, evidence-based guidance for matching design to application is scarce and research priorities are unclear. To take stock of the current state of the art, we conducted a systematic review and thematic content analysis of 56 peer-reviewed journal articles discussing ES auctions published in the last decade. Auctions were approached from three overlapping perspectives: mechanism design, PES, and policy analysis. Five major themes emerged: (1) performance, including measures like cost-effectiveness and PES criteria like additionality; (2) information dynamics like price discovery and communication effects; (3) design innovations like risk-integrating and spatially coordinated mechanisms; (4) contextual variables like policy context and cultural values; and (5) participation factors. Additional attention from policymakers and continued efforts to coordinate research in this diverse and interdisciplinary subfield may be beneficialinfo:eu-repo/semantics/publishedVersio