On Words with the Zero Palindromic Defect

We study the set of finite words with zero palindromic defect, i.e., words rich in palindromes. This set is factorial, but not recurrent. We focus on description of pairs of rich words which cannot occur simultaneously as factors of a longer rich word

Are suprapectineal quadrilateral surface buttressing plates performances superior to traditional fixation? A finite element analysis

Acetabular fractures have a high impact on patient’s quality of life, and because acetabular fractures are high energy injuries, they often co-occur with other pathologies such as damage to cartilage that could increase related morbidity; thus, it appears of primary importance developing reliable treatments for this disease. This work aims at the evaluation of the biomechanical performances of non-conservative treatments of acetabular fractures through a finite element approach. Two pelvic plates models (the standard suprapectineal plate—SPP, and a suprapectineal quadrilateral surface buttressing plate—SQBP) were analyzed when implanted on transverse or T-shaped fractures. The plates geometries were adapted to the specific hemipelvis, mimicking the bending action that the surgeon performs on the plate intraoperatively. Implemented models were tested in a single leg stance condition. The obtained results show that using the SQBP plate in transverse and T-shaped acetabular fractures generates lower bone stress if compared to the SPP plate. Interfragmentary movement analysis shows that the SQBP plate guarantees greater stability in transverse fractures. In conclusion, the SQBP plate seems worthy of further clinical analysis, having resulted as a promising option in the treatment of transverse and T-shaped acetabular fractures, able to reduce bone stress values and to get performances comparable, and in some cases superior, to traditional fixation

An Optimal Algorithm for Tiling the Plane with a Translated Polyomino

We give a $O(n)$-time algorithm for determining whether translations of a polyomino with $n$ edges can tile the plane. The algorithm is also a $O(n)$-time algorithm for enumerating all such tilings that are also regular, and we prove that at most $\Theta(n)$ such tilings exist.Comment: In proceedings of ISAAC 201

Repetitions in infinite palindrome-rich words

Rich words are characterized by containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting open problems. We address lower bounds on the repetition threshold of infinite rich words over 2 and 3-letter alphabets, and construct a candidate infinite rich word over the alphabet $\Sigma_2=\{0,1\}$ with a small critical exponent of $2+\sqrt{2}/2$. This represents the first progress on an open problem of Vesti from 2017.Comment: 12 page

Multivariate risks and depth-trimmed regions

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this abstract axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from the multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship.Comment: 26 pages. Substantially revised version with a number of new results adde

Homologs of the small RNA SgrS are broadly distributed in enteric bacteria but have diverged in size and sequence

Sugar phosphate stress in Escherichia coli is sensed and managed by the transcriptional regulator SgrR and the small RNA (sRNA) SgrS. SgrS is a dual function RNA that performs base pairing-dependent regulation of mRNA targets and encodes a small protein, SgrT. Homologs of SgrR were analyzed for gene synteny and inter-homolog identity to identify those that are likely to be functionally analogous. These 22 SgrR homologs were used to manually locate adjacent sRNAs functionally analogous to SgrS. SgrS homologs shared little sequence identity with E. coli SgrS, but most shared several structural features. The most conserved feature of SgrS homologs was the base pairing region while the most variable feature was the sgrT-coding sequence. Analyses of predicted interactions between SgrS:ptsG mRNA pairs in different organisms revealed interesting differences in the patterns of base pairing interactions. RNA pairs with more interrupted regions of complementarity had a higher proportion of G:C base pairs than those with longer contiguous stretches of complementarity. The identification of this set of homologous sRNAs and their targets sets the stage for future studies to further elucidate the molecular requirements for regulation by SgrS

Holocene climate variations in the western Antarctic Peninsula: evidence for sea ice extent predominantly controlled by changes in insolation and ENSO variability

n/