Optimal monomial quadratization for ODE systems

Quadratization problem is, given a system of ODEs with polynomial right-hand side, transform the system to a system with quadratic right-hand side by introducing new variables. Such transformations have been used, for example, as a preprocessing step by model order reduction methods and for transforming chemical reaction networks. We present an algorithm that, given a system of polynomial ODEs, finds a transformation into a quadratic ODE system by introducing new variables which are monomials in the original variables. The algorithm is guaranteed to produce an optimal transformation of this form (that is, the number of new variables is as small as possible), and it is the first algorithm with such a guarantee we are aware of. Its performance compares favorably with the existing software, and it is capable to tackle problems that were out of reach before

Interacting fermions in two dimensions: beyond the perturbation theory

We consider a system of 2D fermions with short-range interaction. A straightforward perturbation theory is shown to be ill-defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near the mass shell. We show that the divergences result from the interaction of fermions with the zero-sound collective mode. By re-summing the most divergent diagrams, we obtain a closed form of the self-energy near the mass shell. The spectral function exhibits a threshold feature at the onset of the emission of the zero-sound waves. We also show that the interaction with the zero sound does not affect a non-analytic, $T^{2}$-part of the specific heat.Comment: 5 pages, 4 figure

Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems

Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A quadratization reveals new variables and structures of a model, which may be easier to analyze, simulate, control, and provides a convenient parametrization for learning. This paper presents novel theory, algorithms and software capabilities for quadratization of non-autonomous ODEs. We provide existence results, depending on the regularity of the input function, for cases when a quadratic-bilinear system can be obtained through quadratization. We further develop existence results and an algorithm that generalizes the process of quadratization for systems with arbitrary dimension that retain the nonlinear structure when the dimension grows. For such systems, we provide dimension-agnostic quadratization. An example is semi-discretized PDEs, where the nonlinear terms remain symbolically identical when the discretization size increases. As an important aspect for practical adoption of this research, we extended the capabilities of the QBee software towards both non-autonomous systems of ODEs and ODEs with arbitrary dimension. We present several examples of ODEs that were previously reported in the literature, and where our new algorithms find quadratized ODE systems with lower dimension than the previously reported lifting transformations. We further highlight an important area of quadratization: reduced-order model learning. This area can benefit significantly from working in the optimal lifting variables, where quadratic models provide a direct parametrization of the model that also avoids additional hyperreduction for the nonlinear terms. A solar wind example highlights these advantages

Photon statistics from coupled quantum dots

We present an optical study of closely-spaced self-assembled InAs/GaAs quantum dots. The energy spectrum and correlations between photons subsequently emitted from a single pair provide not only clear evidence of coupling between the quantum dots but also insight into the coupling mechanism. Our results are in agreement with recent theories predicting that tunneling is largely suppressed between nonidentical quantum dots and that the interaction is instead dominated by dipole-dipole coupling and phonon-assisted energy transfer processes.Comment: 4 pages, 4 figures, to appear in Phys. Re

Remarkable Alteration of PD-L1 Expression after Immune Checkpoint Therapy in Patients with Non-Small-Cell Lung Cancer: Two Autopsy Case Reports

Pembrolizumab is an immune checkpoint inhibitor (ICI), currently recommended as thefirst-line treatment for patients with advanced non-small-cell lung cancer (NSCLC) showing 50% expression of programmed death-ligand 1 (PD-L1). Previously it was reported that platinum-based chemotherapy may change PD-L1 expression in solid cancers. However, no reports addressing alteration of PD-L1 expression after ICI therapy in NSCLC are available so far. The patients wereJapanesemales 83 and 87 years old,whowere diagnosedwithNSCLC based on the transbronchial lung biopsies showing sarcomatoid feature with high PD-L1 expression. They received Pembrolizumab,however, passed awaywith disease progression on day 27 and day 9, respectively. PD-L1, PD1, andCD8 antibodies were applied to pretreatment tumor biopsies and autopsy specimens. Immunoexpression of all themarkers was evaluated using Aperio ImageScope. We found that PD-L1 expression decreased significantly from 75.6% to 13.2% and from 100% to 58.8%, in patients 1 and 2, respectively. This alteration was less prominent in the perinecrotic tumor area. A considerable decrease of PD-L1 score was linked with a little effect of Pembrolizumab in our patients. This association might be one of the contributing mechanisms of resistance to ICI and needs further investigation in large-scale studies