Minimal Permutations and 2-Regular Skew Tableaux

Bouvel and Pergola introduced the notion of minimal permutations in the study of the whole genome duplication-random loss model for genome rearrangements. Let $\mathcal{F}_d(n)$ denote the set of minimal permutations of length $n$ with $d$ descents, and let $f_d(n)= |\mathcal{F}_d(n)|$. They derived that $f_{n-2}(n)=2^{n}-(n-1)n-2$ and $f_n(2n)=C_n$, where $C_n$ is the $n$-th Catalan number. Mansour and Yan proved that $f_{n+1}(2n+1)=2^{n-2}nC_{n+1}$. In this paper, we consider the problem of counting minimal permutations in $\mathcal{F}_d(n)$ with a prescribed set of ascents. We show that such structures are in one-to-one correspondence with a class of skew Young tableaux, which we call $2$-regular skew tableaux. Using the determinantal formula for the number of skew Young tableaux of a given shape, we find an explicit formula for $f_{n-3}(n)$. Furthermore, by using the Knuth equivalence, we give a combinatorial interpretation of a formula for a refinement of the number $f_{n+1}(2n+1)$.Comment: 19 page

Coccidiomycosis infection of the patella mimicking a neoplasm - two case reports.

BackgroundCoccidioidomycosis is an endemic fungal infection in the southwestern of United States. Most infections are asymptomatic or manifest with mild respiratory complaints. Rare cases may cause extrapulmonary or disseminated disease. We report two cases of knee involvement that presented as isolated lytic lesions of the patella mimicking neoplasms.Case presentationThe first case, a 27 year-old immunocompetent male had progressive left anterior knee pain for four months. The second case was a 78 year-old male had left anterior knee pain for three months. Both of them had visited general physicians without conclusive diagnosis. A low attenuation lytic lesion in the patella was demonstrated on their image studies, and the initial radiologist's interpretation was suggestive of a primary bony neoplasm. The patients were referred for orthopaedic oncology consultation. The first case had a past episode of pulmonary coccioidomycosis 2 years prior, while the second case had no previous coccioidal infection history but lived in an endemic area, the central valley of California. Surgical biopsy was performed in both cases due to diagnostic uncertainty. Final pathologic examination revealed large thick walled spherules filled with endospores establishing the final diagnosis of extrapulmonary coccidioidomycosis.ConclusionsThough history and laboratory findings are supportive, definitive diagnosis still depends on growth in culture or endospores identified on histology. We suggest that orthopaedic surgeons and radiologists keep in mind that chronic fungal infections can mimic osseous neoplasm by imaging

Microprocessor of microRNAs: regulation and potential for therapeutic intervention

MicroRNAs (miRNAs) are a class of small, noncoding RNAs critically involved in a wide spectrum of normal and pathological processes of cells or tissues by fine-tuning the signals important for stem cell development, cell differentiation, cell cycle regulation, apoptosis, and transformation. Considerable progress has been made in the past few years in understanding the transcription, biogenesis and functional regulation of miRNAs. Numerous studies have implicated altered expression of miRNAs in human cancers, suggesting that aberrant expression of miRNAs is one of the hallmarks for carcinogenesis. In this review, we briefly discuss most recent discoveries on the regulation of miRNAs at the level of microprocessor-mediated biogenesis of miRNAs

Hybrid fuzzy and sliding-mode control for motorised tether spin-up when coupled with axial vibration

A hybrid fuzzy sliding mode controller is applied to the control of motorised tether spin-up coupled with an axial oscillation phenomenon. A six degree of freedom dynamic model of a motorised momentum exchange tether is used as a basis for interplanetary payload exchange. The tether comprises a symmetrical double payload configuration, with an outrigger counter inertia and massive central facility. It is shown that including axial elasticity permits an enhanced level of performance prediction accuracy and a useful departure from the usual rigid body representations, particularly for accurate payload positioning at strategic points. A special simulation program has been devised in MATLAB and MATHEMATICA for a given initial condition data case

Wedge impact with the influence of ice

This work presents a canonical study on a wedge entering water near a single piece of ice using computational-fluid-dynamics (CFD) and a Wagner-type theoretical model with corrections for non-linear effects. Calculations for a series of conditions with ice of different sizes and locations relative to the wedge are conducted. The hydrodynamic force due to impact, the pressure distribution on the wedge surface, and the pile-up phenomenon are examined to study the role of ice in the impact process. The theoretical model is shown to be accurate and can serve as a useful method to assess slamming loads under the influence of ice. It is shown that even for the case of a small piece of ice, the slamming force on the wedge can increase by 30%