Robust effective ground state in a nonintegrable Floquet quantum circuit

An external periodic (Floquet) drive is believed to bring any initial state to the featureless infinite temperature state in generic nonintegrable isolated quantum many-body systems. However, numerical or analytical evidence either proving or disproving this hypothesis is very limited and the issue has remained unsettled. Here, we study the initial state dependence of Floquet heating in a nonintegrable kicked Ising chain of length up to $L=30$ with an efficient quantum circuit simulator, showing a possible counterexample: The ground state of the effective Floquet Hamiltonian is exceptionally robust against heating, and could stay at finite energy density even after infinitely many Floquet cycles, if the driving period is shorter than a threshold value. This sharp energy localization transition/crossover does not happen for generic excited states. Our finding paves the way for engineering Floquet protocols with finite driving periods realizing long-lived, or possibly even perpetual, Floquet phases by initial state design.Comment: 5+6 pages, 4+6 figure

Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks

We identify hidden layers inside a deep neural network (DNN) with group actions on the data domain, and formulate a formal deep network as a dual voice transform with respect to the Koopman operator, a linear representation of the group action. Based on the group theoretic arguments, particularly by using Schur's lemma, we show a simple proof of the universality of DNNs.Comment: NeurReps 202

Joint Group Invariant Functions on Data-Parameter Domain Induce Universal Neural Networks

The symmetry and geometry of input data are considered to be encoded in the internal data representation inside the neural network, but the specific encoding rule has been less investigated. In this study, we present a systematic method to induce a generalized neural network and its right inverse operator, called the ridgelet transform, from a joint group invariant function on the data-parameter domain. Since the ridgelet transform is an inverse, (1) it can describe the arrangement of parameters for the network to represent a target function, which is understood as the encoding rule, and (2) it implies the universality of the network. Based on the group representation theory, we present a new simple proof of the universality by using Schur's lemma in a unified manner covering a wide class of networks, for example, the original ridgelet transform, formal deep networks, and the dual voice transform. Since traditional universality theorems were demonstrated based on functional analysis, this study sheds light on the group theoretic aspect of the approximation theory, connecting geometric deep learning to abstract harmonic analysis.Comment: NeurReps 202

Structured Hammerstein-Wiener Model Learning for Model Predictive Control

This paper aims to improve the reliability of optimal control using models constructed by machine learning methods. Optimal control problems based on such models are generally non-convex and difficult to solve online. In this paper, we propose a model that combines the Hammerstein-Wiener model with input convex neural networks, which have recently been proposed in the field of machine learning. An important feature of the proposed model is that resulting optimal control problems are effectively solvable exploiting their convexity and partial linearity while retaining flexible modeling ability. The practical usefulness of the method is examined through its application to the modeling and control of an engine airpath system.Comment: 6 pages, 3 figure

Impact of hypoxia on the pathogenesis and therapy resistance in multiple myeloma

Multiple myeloma (MM) is a refractory plasma cell tumor. In myeloma cells, the transcription factor IRF4, the master regulator of plasma cells, is aberrantly upregulated and plays an essential role in oncogenesis. IRF4 forms a positive feedback loop with MYC, leading to additional tumorigenic properties. In recent years, molecular targeted therapies have contributed to a significant improvement in the prognosis of MM. Nevertheless, almost all patients experience disease progression, which is thought to be a result of treatment resistance induced by various elements of the bone marrow microenvironment. Among these, the hypoxic response, one of the key processes for cellular homeostasis, induces hypoxia-adapted traits such as undifferentiation, altered metabolism, and dissemination, leading to drug resistance. These inductions are caused by ectopic gene expression changes mediated by the activation of hypoxia-inducible factors (HIFs). By contrast, the expression levels of IRF4 and MYC are markedly reduced by hypoxic stress. Notably, an anti-apoptotic capability is usually acquired under both normoxic and hypoxic conditions, but the mechanism is distinct. This fact strongly suggests that myeloma cells may survive by switching their dependent regulatory factors from IRF4 and MYC (normoxic bone marrow region) to HIF (hypoxic bone marrow microenvironment). Therefore, to achieve deep remission, combination therapeutic agents, which are complementarily effective against both IRF4-MYC-dominant and HIF-dominated fractions, may become an important therapeutic strategy for MM

Minimum Trotterization Formulas for a Time-Dependent Hamiltonian

When a time propagator $e^{\delta t A}$ for duration $\delta t$ consists of two noncommuting parts $A=X+Y$, Trotterization approximately decomposes the propagator into a product of exponentials of $X$ and $Y$. Various Trotterization formulas have been utilized in quantum and classical computers, but much less is known for the Trotterization with the time-dependent generator $A(t)$. Here, for $A(t)$ given by the sum of two operators $X$ and $Y$ with time-dependent coefficients $A(t) = x(t) X + y(t) Y$, we develop a systematic approach to derive high-order Trotterization formulas with minimum possible exponentials. In particular, we obtain fourth-order and sixth-order Trotterization formulas involving seven and fifteen exponentials, respectively, which are no more than those for time-independent generators. We also construct another fourth-order formula consisting of nine exponentials having a smaller error coefficient. Finally, we numerically benchmark the fourth-order formulas in a Hamiltonian simulation for a quantum Ising chain, showing that the 9-exponential formula accompanies smaller errors per local quantum gate than the well-known Suzuki formula

乳癌術前化学療法において腋窩リンパ節転移が陰性化するための効果予測因子の検討

Purpose: We investigated the role of tumor-infiltrating lymphocytes (TILs) in pretreatment primary breast cancer to predict pathological response to neoadjuvant chemotherapy (NAC) in patients with clinical node-positive disease (cN +). Methods: The subjects of this study were 60 patients with cN + , who received NAC followed by breast surgery with axillary lymph node dissection (ALND). We conducted a semi-quantitative assessment of TILs in pretreatment primary tumors and their association with clinicopathological factors and axillary lymph node metastasis. Results: We observed a higher number of TILs in tumors with negative hormone receptors, positive human epidermal growth factor receptor 2, or high Ki67. TILs were associated with a favorable response to NAC in primary tumors. The rate of axillary pathologic complete response (Ax-pCR) was significantly higher in patients with a high number of TILs than in patients with a low number of TILs (72.0% versus 17.1%, p < 0.001). In multivariable analysis, a high number of TILs was a significant predictor of Ax-pCR as well as of pCR of the primary tumor after NAC. Importantly, all patients with HER2-positive tumors in the high TILs group showed Ax-pCR on ALND. Conclusion: TILs in pretreatment primary breast cancer had the potential to predict therapeutic efficacy of NAC in patients with clinical node-positive disease.博士（医学）・乙第1498号・令和3年3月15日© Springer Nature Singapore Pte Ltd. 2020This is a post-peer-review, pre-copyedit version of an article published in Surgery today. The final authenticated version is available online at: https://doi.org/10.1007/s00595-020-02157-6