In this paper, we study the problem of feature selection in cancer-related machine learning tasks. In particular, we study the accuracy and stability of different feature selection approaches within simplistic machine learning pipelines. Earlier studies have shown that for certain cases, the accuracy of detection can easily reach 100% given enough training data. Here, however, we concentrate on...

Critical processes of ideal integrable models of Hele-Shaw flows are considered. A regularization method based on multiscaling expansions of solutions of the KdV and Toda hierarchies characterized by string equations is proposed. Examples are exhibited in which the tritronquée solution of the Painlevé-I equation turns out to provide the leading term of the regularization

Critical processes of ideal integrable models of Hele-Shaw flows are considered. A regularization method based on multiscaling expansions of solutions of the KdV and Toda hierarchies characterized by string equations is proposed. Examples are exhibited in which the tritronquée solution of the Painlevé-I equation turns out to provide the leading term of the regularization

A concept of "pinched flow fractionation" for the continuous size separation and analysis of particles in microfabricated devices has been proposed and demonstrated. In this method, particles suspended in liquid were continuously introduced into a microchannel having a pinched segment and were aligned to one sidewall in the pinched segment by another liquid flow without particles. The particles...

Discovery of novel immune biomarkers for monitoring of disease prognosis and response to therapy in immune-mediated inflammatory diseases is an important unmet clinical need. Here, we establish a novel framework for immunological biomarker discovery, comparing a conventional (liquid) flow cytometry platform (CFP) and a unique lyoplate-based flow cytometry platform (LFP) in combination with adva...

We prove that the extended Toda hierarchy of [1] admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m ≥ −1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination...

A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-type is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (" positive " and " negative ") set of flows. Special solutions corresponding to topological Landau-Ginzburg models of D-type are characterized by a Riemann-Hilbert problem, which can be converted into a generalized hod...

Thermal field-flow fractionation (ThFFF) is capable of separating a wide molecular mass range of polymers by their molecular mass (Mr) and chemical composition. However, retention and resolution decrease significantly for polymers with Mr<20 kDa. Various approaches for increasing the retention of low Mr (<15 kDa) polymers were investigated. Our results showed that temperature conditions and sin...

The recently developed theory of Lagrangian flows for transport equations with low regularity coefficients enables to consider non BV vector fields. We apply this theory to prove existence and stability of global Lagrangian solutions to the repulsive Vlasov-Poisson system with only integrable initial distribution function with finite energy. These solutions have a well-defined Lagrangian flow. ...

Current flow cytometry (FCM) reagents and instrumentation allow for the measurement of an unprecedented number of parameters for any given cell within a homogenous or heterogeneous population. While this provides a great deal of power for hypothesis testing, it also generates a vast amount of data, which is typically analyzed manually through a processing called "gating." For large experiments,...