The constrained modified KP hierarchy and the generalized Miura transformations

In this letter, we consider the second Hamiltonian structure of the constrained modified KP hierarchy. After mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We simplify this Hamiltonian structure by factorizing the Lax operator into linear terms.Comment: 8 pages, latex, no figure

A Note on the Gauge Equivalence between the Manin-Radul and Laberge-Mathieu Super KdV Hierarchies

The gauge equivalence between the Manin-Radul and Laberge-Mathieu super KdV hierarchies is revisited. Apart from the Inami-Kanno transformation, we show that there is another gauge transformation which also possess the canonical property. We explore the relationship of these two gauge transformations from the Kupershmidt-Wilson theorem viewpoint and, as a by-product, obtain the Darboux-Backlund transformation for the Manin-Radul super KdV hierarchy. The geometrical intepretation of these transformations is also briefly discussed.Comment: 8 pages, revtex, 1 figur

Teacher-Student chain for efficient semi-supervised histology image classification

Deep learning shows great potential for the domain of digital pathology. An automated digital pathology system could serve as a second reader, perform initial triage in large screening studies, or assist in reporting. However, it is expensive to exhaustively annotate large histology image databases, since medical specialists are a scarce resource. In this paper, we apply the semi-supervised teacher-student knowledge distillation technique proposed by Yalniz et al. (2019) to the task of quantifying prognostic features in colorectal cancer. We obtain accuracy improvements through extending this approach to a chain of students, where each student's predictions are used to train the next student i.e. the student becomes the teacher. Using the chain approach, and only 0.5% labelled data (the remaining 99.5% in the unlabelled pool), we match the accuracy of training on 100% labelled data. At lower percentages of labelled data, similar gains in accuracy are seen, allowing some recovery of accuracy even from a poor initial choice of labelled training set. In conclusion, this approach shows promise for reducing the annotation burden, thus increasing the affordability of automated digital pathology systems.Comment: AI for Affordable Healthcare (AI4AH) workshop at ICLR 202

Evolutionary bi-stability in pathogen transmission mode

Many pathogens transmit to new hosts by both infection (horizontal transmission) and transfer to the infected host's offspring (vertical transmission). These two transmission modes require speci®c adap- tations of the pathogen that can be mutually exclusive, resulting in a trade-off between horizontal and vertical transmission. We show that in mathematical models such trade-offs can lead to the simultaneous existence of two evolutionary stable states (evolutionary bi-stability) of allocation of resources to the two modes of transmission. We also show that jumping between evolutionary stable states can be induced by gradual environmental changes. Using quantitative PCR-based estimates of abundance in seed and vege- tative parts, we show that the pathogen of wheat, Phaeosphaeria nodorum, has jumped between two distinct states of transmission mode twice in the past 160 years, which, based on published evidence, we interpret as adaptation to environmental change. The ®nding of evolutionary bi-stability has impli- cations for human, animal and other plant diseases. An ill-judged change in a disease control programme could cause the pathogen to evolve a new, and possibly more damaging, combination of transmission modes. Similarly, environmental changes can shift the balance between transmission modes, with adverse effects on human, animal and plant health

Plasma Neuronal Exosomal Levels of Alzheimer\u27s Disease Biomarkers in Normal Aging

Plasma neuronal exosomal levels of pathogenic Alzheimer\u27s disease (AD) proteins, cellular survival factors, and lysosomal proteins distinguish AD patients from control subjects, but changes in these exosomal proteins associated with normal aging have not been described for cognitively intact subjects. Plasma neuronal exosomal levels of P-T181-tau, P-S396-tau, Aβ1-42, cathepsin D, repressor element 1-silencing transcription factor, and neurogranin were quantified longitudinally in cognitively intact older adults using two samples collected at 3- to 11-year intervals. Except for P-S396-tau, exosomal protein levels changed significantly with aging, but were largely outside the range observed in AD patients

Selective Hybridization of a Terpyridine-Based Molecule with a Noble Metal

The electronic properties of metal-molecule interfaces can in principle be controlled by molecular design and self-assembly, yielding great potential for future nano- and optoelectronic technologies. However, the coupling between molecular orbitals and the electronic states of the surface can significantly influence molecular states. In particular, molecules designed to create metal-organic self-assembled networks have functional groups that by necessity are designed to interact strongly with metals. Here, we investigate the adsorption interactions of a terpyridine (tpy)-based molecule on a noble metal, Ag(111), by low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) together with density functional theory (DFT) calculations. By comparing the local density of states (DOS) information gained from STS for the molecule on the bare Ag(111) surface with that of the molecule decoupled from the underlying metal by a NaCl bilayer, we find that tpy-localized orbitals hybridize strongly with the metal substrate. Meanwhile, those related to the phenyl rings that link the two terminal tpy groups are less influenced by the interaction with the surface. The selective hybridization of the tpy groups provides an example of strong, orbital-specific electronic coupling between a functional group and a noble-metal surface, which may alter the intended balance of interactions and resulting electronic behavior of the molecule-metal interface

Clinically Silent Alzheimer\u27s and Vascular Pathologies Influence Brain Networks Supporting Executive Function in Healthy Older Adults

Aging is associated with declines in executive function. We examined how executive functional brain systems are influenced by clinically silent Alzheimer’s disease (AD) pathology and cerebral white matter hyperintensities (WMHs). Twenty-nine younger adults and thirty-four cognitively normal older adults completed a working memory paradigm while functional magnetic resonance imaging (fMRI) was performed. Older adults further underwent lumbar cerebrospinal fluid (CSF) draw for assessment of AD pathology and FLAIR imaging for assessment of WMHs. Accurate working memory performance in both age groups was associated with high fronto-visual functional connectivity (fC). However, in older adults, higher expression of fronto-visual fC was linked with lower levels of clinically silent AD pathology. In addition, AD pathology and WMHs were each independently related to increased fMRI response in the left dorsolateral prefrontal cortex, a pattern associated with slower task performance. Our results suggest that clinically silent AD pathology is related to lower expression of a fronto-visual fC pattern supporting executive task performance. Further, our findings suggest that AD pathology and WMHs appear to be linked with ineffective increases in frontal response in CN older adults

Nonstandard Drinfeld-Sokolov reduction

Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet (\A,\Lambda, d_1, d_0), where the $d_i$ are $\Z$-gradations of a loop algebra \A and \Lambda\in \A is a semisimple element of nonzero $d_1$-grade. A new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented. The proposal relies on splitting the $d_1$-grade zero part of \A into a vector space direct sum of two subalgebras. This permits one to interpret certain Gelfand-Dickey type systems associated with a nonstandard splitting of the algebra of pseudo-differential operators in the Drinfeld-Sokolov framework.Comment: 19 pages, LaTeX fil

Long-term prognosis for individuals with hypertension undergoing coronary artery calcium scoring

To examine the performance of coronary artery calcification (CAC) for stratifying long-term risk of death in asymptomatic hypertensive patients