Context-independent encoding of passive and active self-motion in vestibular afferent fibers during locomotion in primates

The vestibular system detects head motion to coordinate vital reflexes and provide our sense of balance and spatial orientation. A long-standing hypothesis has been that projections from the central vestibular system back to the vestibular sensory organs (i.e., the efferent vestibular system) mediate adaptive sensory coding during voluntary locomotion. However, direct proof for this idea has been lacking. Here we recorded from individual semicircular canal and otolith afferents during walking and running in monkeys. Using a combination of mathematical modeling and nonlinear analysis, we show that afferent encoding is actually identical across passive and active conditions, irrespective of context. Thus, taken together our results are instead consistent with the view that the vestibular periphery relays robust information to the brain during primate locomotion, suggesting that context-dependent modulation instead occurs centrally to ensure that coding is consistent with behavioral goals during locomotion.

A somatic UBA2 variant preceded ETV6-RUNX1 in the concordant BCP-ALL of monozygotic twins

Genetic analysis of leukemic clones in monozygotic twins with concordant ALL has proved a unique opportunity to gain insight into the molecular phylogenetics of leukemogenesis. Using whole genome sequencing, we characterized constitutional and somatic SNVs/indels and structural variants in a monozygotic twin pair with concordant ETV6-RUNX1 positive B-cell precursor acute lymphoblastic leukemia (BCP-ALL). In addition, digital PCR (dPCR) was applied to evaluate the presence of and quantify selected somatic variants at birth, diagnosis and remission. A shared somatic complex rearrangement involving chromosomes 11, 12 and 21 with identical fusion sequences in leukemias of both twins offered direct proof of a common clonal origin. The ETV6-RUNX1 fusion detected at diagnosis was found to originate from this complex rearrangement. A shared somatic frameshift deletion in UBA2 was also identified in diagnostic samples. In addition, each leukemia independently acquired analogous deletions of three genes recurrently targeted in BCP-ALLs (ETV6, ATF7IP and RAG1/RAG2) providing evidence of a convergent clonal evolution, only explained by a strong concurrent selective pressure. Quantification of the UBA2 deletion by dPCR surprisingly indicated it persisted in remission. This, for the first time to our knowledge, provided evidence of a UBA2 variant preceding the well-established initiating event ETV6-RUNX1. Further, we suggest the UBA2 deletion exerted a leukemia predisposing effect and that its essential role in SUMOylation, regulating nearly all physiological and pathological cellular processes such as DNA-repair by non-homologous end joining, may hold a mechanistic explanation for the predisposition.

The degeneration formula for stable log maps

We give a direct proof for the degeneration formula of Gromov–Witten invariants including its cycle version for degenerations with smooth singular locus in the setting of stable log maps of Abramovich-Chen, Chen, Gross–Siebert.

Classification of graded cluster algebras generated by rank 3 quivers

We consider gradings on cluster algebras generated by [Formula: see text] skew-symmetric matrices. We show that, except in one particular case, mutation-cyclic matrices give rise to gradings in which all occurring degrees are positive and have only finitely many associated cluster variables. For mutation-acyclic matrices, we prove that all occurring degrees are associated with infinitely many variables. We also give a direct proof that the gradings are balanced in this case (i.e. that there is a bijection between the cluster variables of degree [Formula: see text] and [Formula: see text] for each occurring degree [Formula: see text]).

Factorization of the Abel-Jacobi maps

As an application of the theory of Lawson homology and morphic cohomology, Walker proved that the Abel-Jacobi map factors through another regular homomorphism. In this note, we give a direct proof of the theorem.

Analytic properties of Ohno function

Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno function and study it. We consider the region of absolute convergence, give some new expressions, and show new relations of the function. We also give a direct proof of the interpolation of Ohno's relation.

Certificate complexity and symmetry of nested canalizing functions

Boolean nested canalizing functions (NCFs) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study their certificate complexity. For both Boolean values $b\in\{0,1\}$, we obtain a formula for $b$-certificate complexity and consequently, we develop a direct proof of the certificate complexity formula of an NCF. Symmetry is another interesting property of Boolean functions and we significantly simplify the proofs of some recent theorems about partial symmetry of NCFs. We also describe the algebraic normal form of $s$-symmetric NCFs. We obtain the general formula of the cardinality of the set of $n$-variable $s$-symmetric Boolean NCFs for $s=1,\dots,n$. In particular, we enumerate the strongly asymmetric Boolean NCFs.

Sources of Students’ Difficulties with Proof By Contradiction

The literature on proof by contradiction (PBC) is nearly unanimous in claiming that this proof technique is “more difficult” for students than direct proof, and offers multiple hypotheses as to why this might be the case. To examine this claim and to evaluate some of the hypotheses, we analyzed student work on proof construction problems from homework and examinations in a university “Introduction to Proof” course taught by one of the authors. We also conducted stimulated-recall interviews with student volunteers probing their thought processes while solving these problems, and their views about PBC in general. Our results suggest that the knowledge resources students bring to bear on proof problems, and how these resources are activated, explain more of their “difficulties” than does the logical structure of the proof technique, at least for this population of students.

An Entropy-based Directed Random Walk for Pathway Activity Inference Using Topological Importance and Gene Interactions

The integration of microarray technologies and machine learning methods has become popular in predicting pathological condition of diseases and discovering risk genes. The traditional microarray analysis considers pathways as simple gene sets, treating all genes in the pathway identically while ignoring the pathway network's structure information. This study, however, proposed an entropy-based directed random walk (e-DRW) method to infer pathway activity. This study aims (1) To enhance the gene-weighting method in Directed Random Walk (DRW) by incorporating t-test statistic scores and correlation coefficient values, (2) To implement entropy as a parameter variable for random walking in a biological network, and (3) To apply Entropy Weight Method (EWM) in DRW pathway activity inference. To test the objectives, the gene expression dataset was used as input datasets while the pathway dataset was used as reference datasets to build a directed graph. An equation was proposed to assess the connectivity of nodes in the directed graph via probability values calculated from the Shannon entropy formula. A direct proof of calculation based on the proposed mathematical formula was presented using e-DRW with gene expression data. Based on the results, there was an improvement in terms of sensitivity of prediction and accuracy of cancer classification between e-DRW and conventional DRW. The within-dataset experiments indicated that our novel method demonstrated robust and superior performance in terms of accuracy and number of predicted risk-active pathways compared to the other DRW methods. In conclusion, the results revealed that e-DRW not only improved prediction performance, but also effectively extracted topologically important pathways and genes that are specifically related to the corresponding cancer types.