131 research outputs found
Normalized Wolfe-Powell-type local minimax method for finding multiple unstable solutions of nonlinear elliptic PDEs
The local minimax method (LMM) proposed in [Y. Li and J. Zhou, SIAM J. Sci.
Comput., 23(3), 840--865 (2001)] and [Y. Li and J. Zhou, SIAM J. Sci. Comput.,
24(3), 865--885 (2002)] is an efficient method to solve nonlinear elliptic
partial differential equations (PDEs) with certain variational structures for
multiple solutions. The steepest descent direction and the Armijo-type
step-size search rules are adopted in [Y. Li and J. Zhou, SIAM J. Sci. Comput.,
24(3), 865--885 (2002)] and play a significant role in the performance and
convergence analysis of traditional LMMs. In this paper, a new algorithm
framework of the LMMs is established based on general descent directions and
two normalized (strong) Wolfe-Powell-type step-size search rules. The
corresponding algorithm framework named as the normalized Wolfe-Powell-type LMM
(NWP-LMM) is introduced with its feasibility and global convergence rigorously
justified for general descent directions. As a special case, the global
convergence of the NWP-LMM algorithm combined with the preconditioned steepest
descent (PSD) directions is also verified. Consequently, it extends the
framework of traditional LMMs. In addition, conjugate gradient-type (CG-type)
descent directions are utilized to speed up the NWP-LMM algorithm. Finally,
extensive numerical results for several semilinear elliptic PDEs are reported
to profile their multiple unstable solutions and compared for different
algorithms in the LMM's family to indicate the effectiveness and robustness of
our algorithms. In practice, the NWP-LMM combined with the CG-type direction
indeed performs much better than its known LMM companions.Comment: 27 pages, 9 figures; Accepted by SCIENCE CHINA Mathematics on January
17, 202
Nonmonotone local minimax methods for finding multiple saddle points
In this paper, by designing a normalized nonmonotone search strategy with the
Barzilai--Borwein-type step-size, a novel local minimax method (LMM), which is
a globally convergent iterative method, is proposed and analyzed to find
multiple (unstable) saddle points of nonconvex functionals in Hilbert spaces.
Compared to traditional LMMs with monotone search strategies, this approach,
which does not require strict decrease of the objective functional value at
each iterative step, is observed to converge faster with less computations.
Firstly, based on a normalized iterative scheme coupled with a local peak
selection that pulls the iterative point back onto the solution submanifold, by
generalizing the Zhang--Hager (ZH) search strategy in the optimization theory
to the LMM framework, a kind of normalized ZH-type nonmonotone step-size search
strategy is introduced, and then a novel nonmonotone LMM is constructed. Its
feasibility and global convergence results are rigorously carried out under the
relaxation of the monotonicity for the functional at the iterative sequences.
Secondly, in order to speed up the convergence of the nonmonotone LMM, a
globally convergent Barzilai--Borwein-type LMM (GBBLMM) is presented by
explicitly constructing the Barzilai--Borwein-type step-size as a trial
step-size of the normalized ZH-type nonmonotone step-size search strategy in
each iteration. Finally, the GBBLMM algorithm is implemented to find multiple
unstable solutions of two classes of semilinear elliptic boundary value
problems with variational structures: one is the semilinear elliptic equations
with the homogeneous Dirichlet boundary condition and another is the linear
elliptic equations with semilinear Neumann boundary conditions. Extensive
numerical results indicate that our approach is very effective and speeds up
the LMMs significantly.Comment: 32 pages, 7 figures; Accepted by Journal of Computational Mathematics
on January 3, 202
Convergence analysis of a spectral-Galerkin-type search extension method for finding multiple solutions to semilinear problems
In this paper, we develop an efficient spectral-Galerkin-type search
extension method (SGSEM) for finding multiple solutions to semilinear elliptic
boundary value problems. This method constructs effective initial data for
multiple solutions based on the linear combinations of some eigenfunctions of
the corresponding linear eigenvalue problem, and thus takes full advantage of
the traditional search extension method in constructing initials for multiple
solutions. Meanwhile, it possesses a low computational cost and high accuracy
due to the employment of an interpolated coefficient Legendre-Galerkin spectral
discretization. By applying the Schauder's fixed point theorem and other
technical strategies, the existence and spectral convergence of the numerical
solution corresponding to a specified true solution are rigorously proved. In
addition, the uniqueness of the numerical solution in a sufficiently small
neighborhood of each specified true solution is strictly verified. Numerical
results demonstrate the feasibility and efficiency of our algorithm and present
different types of multiple solutions.Comment: 23 pages, 7 figures; Chinese version of this paper is published in
SCIENTIA SINICA Mathematica, Vol. 51 (2021), pp. 1407-143
Second-order flows for approaching stationary points of a class of non-convex energies via convex-splitting schemes
The use of accelerated gradient flows is an emerging field in optimization, scientific computing and beyond. This paper contributes to the theoretical underpinnings of a recently-introduced computational paradigm known as second-order flows, which demonstrate significant performance particularly for the minimization of non-convex energy functionals defined on Sobolev spaces, and are characterized by novel dissipative hyperbolic partial differential equations. Our approach hinges upon convex-splitting schemes, a tool which is not only pivotal for clarifying the well-posedness of second-order flows, but also yields a versatile array of robust numerical schemes through temporal and spatial discretization. We prove the convergence to stationary points of such schemes in the semi-discrete setting. Further, we establish their convergence to time-continuous solutions as the time-step tends to zero, and perform a comprehensive error analysis in the fully discrete case. Finally, these algorithms undergo thorough testing and validation in approaching stationary points of non-convex variational models in applied sciences, such as the Ginzburg-Landau energy in phase-field modeling and a specific case of the Landau-de Gennes energy of the Q-tensor model for liquid crystals
On the two-distance embedding in real Euclidean space of coherent configuration of type (2,2;3)
Finding the maximum cardinality of a -distance set in Euclidean space is a
classical problem in geometry. Lison\v{e}k in 1997 constructed a maximum
-distance set in with points. That -distance set
constructed by Lison\v{e}k has a distinguished structure of a coherent
configuration of type and is embedded in two concentric spheres in
. In this paper we study whether there exists any other similar
embedding of a coherent configuration of type as a -distance set
in , without assuming any restriction on the size of the set. We
prove that there exists no such example other than that of Lison\v{e}k. The key
ideas of our proof are as follows: (i) study the geometry of the embedding of
the coherent configuration in Euclidean spaces and to drive diophantine
equations coming from this embedding. (ii) solve diophantine equations with
certain additional conditions of integrality of some parameters of the
combinatorial structure by using the method of auxiliary equations
Development and validation of prognostic index based on purine metabolism genes in patients with bladder cancer
BackgroundBladder cancer (BLCA) is a prevalent malignancy affecting the urinary system and is associated with significant morbidity and mortality worldwide. Dysregulation of tumor metabolic pathways is closely linked to the initiation and proliferation of BLCA. Tumor cells exhibit distinct metabolic activities compared to normal cells, and the purine metabolism pathway, responsible for providing essential components for DNA and RNA synthesis, is believed to play a crucial role. However, the precise involvement of Purine Metabolism Genes (PMGs) in the defense mechanism against BLCA remains elusive.MethodsThe integration of BLCA samples from the TCGA and GEO datasets facilitated the quantitative evaluation of PMGs, offering potential insights into their predictive capabilities. Leveraging the wealth of information encompassing mRNAsi, gene mutations, CNV, TMB, and clinical features within these datasets further enriched the analysis, augmenting its robustness and reliability. Through the utilization of Lasso regression, a prediction model was developed, enabling accurate prognostic assessments within the context of BLCA. Additionally, co-expression analysis shed light on the complex relationship between gene expression patterns and PMGs, unraveling their functional relevance and potential implications in BLCA.ResultsPMGs exhibited increased expression levels in the high-risk cohort of BLCA patients, even in the absence of other clinical indicators, suggesting their potential as prognostic markers. GSEA revealed enrichment of immunological and tumor-related pathways specifically in the high-risk group. Furthermore, notable differences were observed in immune function and m6a gene expression between the low- and high-risk groups. Several genes, including CLDN6, CES1, SOST, SPRR2A, MYBPH, CGB5, and KRT1, were found to potentially participate in the oncogenic processes underlying BLCA. Additionally, CRTAC1 was identified as potential tumor suppressor genes. Significant discrepancies in immunological function and m6a gene expression were observed between the two risk groups, further highlighting the distinct molecular characteristics associated with different prognostic outcomes. Notably, strong correlations were observed among the prognostic model, CNVs, SNPs, and drug sensitivity profiles.ConclusionPMGs have been implicated in the etiology and progression of bladder cancer (BLCA). Prognostic models corresponding to this malignancy aid in the accurate prediction of patient outcomes. Notably, exploring the potential therapeutic targets within the tumor microenvironment (TME) such as PMGs and immune cell infiltration holds promise for effective BLCA management, albeit necessitating further research. Moreover, the identification of a gene signature associated with purine Metabolism presents a credible and alternative approach for predicting BLCA, signifying a burgeoning avenue for targeted therapeutic investigations in the field of BLCA
PD-1/PD-L1 Axis, Rather Than High-Mobility Group Alarmins or CD8+ Tumor-Infiltrating Lymphocytes, Is Associated With Survival in Head and Neck Squamous Cell Carcinoma Patients Who Received Surgical Resection
In current studies, the influence of tumor immune microenvironment on tumorigenesis and tumor progression has been widely explored. In the present study, we investigated the expression and significance of high mobility group box 1 (HMGB1), HMG nucleosome-binding protein 1 (HMGN1), the receptor programmed cell death 1 (PD-1) and its ligand programmed cell death ligand 1 (PD-L1) in head and neck squamous cell carcinoma (HNSCC). We explored whether HMGB1 and HMGN1 take part in recruiting T cells to HNSCC microenvironment. Furthermore, we assessed the prognostic value of HMG proteins, TILs, and PD-1/PD-L1 in postoperative patients. Tumor tissue sections were collected from 81 cases of patients with resectable HNSCC. All patients' information was integrated with clinical and pathological records, as well as follow-up data. We used immunohistochemistry to examine the subcellular localization and expression levels of HMGB1 and HMGN1, as well as tumor CD3+, CD8+, FOXP3+ lymphocyte infiltration, and the expression of immune inhibiting molecules PD-1/PD-L1. Results showed that there was no significant difference in the number of CD8+ and FOXP3+ T cells between the two groups with or without HMGB1 cytoplasmic expression in tumor tissues. The number of CD3+ T cells in HMGB1 cytoplasmic expression group (339.39 ± 230.76) was more than that in group without HMGB1 cytoplasmic expression (233.30 ± 230.91, P < 0.05). The number of CD3+, CD8+, and FOXP3+ T cells in HMGN1 cytoplasmic expression group [400.74 ± 224.04, 158.10 ± 112.10, 36.00(15.00, 69.00)] was more than that in group without HMGN1-cytoplasmic expression [222.84 ± 217.78, P < 0.01; 105.10 ± 108.25, P < 0.05; 13.00(6.75, 32.25), P < 0.01]. The positive rates of PD-1 and PD-L1 in tumor tissues were 29.6 and 67.9%, respectively. Multivariate analysis suggested that tumor expression of PD-L1 was an independent prognostic factor and PD-L1 overexpression indicated a poor overall survival (OS) and disease-free survival (DFS). Taken together, we concluded that HMGB1 and HMGN1 secreted by cancer cells may relate to recruitment of tumor infiltrating lymphocytes (TILs) in HNSCC. PD-1/PD-L1 axis, rather than HMG proteins or CD8+ tumor-infiltrating lymphocytes, has a critical role in tumor immune microenvironment and could predict the outcome of HNSCC patients who received surgical resection
Multi-strategy engineering greatly enhances provitamin A carotenoid accumulation and stability in Arabidopsis seeds
Staple grains with low levels of provitamin A carotenoids contribute to the global prevalence of vitamin A deficiency and therefore are the main targets for provitamin A biofortification. However, carotenoid stability during both seed maturation and postharvest storage is a serious concern for the full benefits of carotenoid biofortified grains. In this study, we utilized Arabidopsis as a model to establish carotenoid biofortification strategies in seeds. We discovered that manipulation of carotenoid biosynthetic activity by seed-specific expression of Phytoene synthase (PSY) increases both provitamin A and total carotenoid levels but the increased carotenoids are prone to degradation during seed maturation and storage, consistent with previous studies of provitamin A biofortified grains. In contrast, stacking with Orange (ORHis), a gene that initiates chromoplast biogenesis, dramatically enhances provitamin A and total carotenoid content and stability. Up to 65- and 10-fold increases of β-carotene and total carotenoids, respectively, with provitamin A carotenoids composing over 63% were observed in the seeds containing ORHis and PSY. Co-expression of Homogentisate geranylgeranyl transferase (HGGT) with ORHis and PSY further increases carotenoid accumulation and stability during seed maturation and storage. Moreover, knocking-out of β-carotene hydroxylase 2 (BCH2) by CRISPR/Cas9 not only potentially facilitates β-carotene accumulation but also minimizes the negative effect of carotenoid over production on seed germination. Our findings provide new insights into various processes on carotenoid accumulation and stability in seeds and establish a multiplexed strategy to simultaneously target carotenoid biosynthesis, turnover, and stable storage for carotenoid biofortification in crop seeds
Improving Generalization in Visual Reinforcement Learning via Conflict-aware Gradient Agreement Augmentation
Learning a policy with great generalization to unseen environments remains
challenging but critical in visual reinforcement learning. Despite the success
of augmentation combination in the supervised learning generalization, naively
applying it to visual RL algorithms may damage the training efficiency,
suffering from serve performance degradation. In this paper, we first conduct
qualitative analysis and illuminate the main causes: (i) high-variance gradient
magnitudes and (ii) gradient conflicts existed in various augmentation methods.
To alleviate these issues, we propose a general policy gradient optimization
framework, named Conflict-aware Gradient Agreement Augmentation (CG2A), and
better integrate augmentation combination into visual RL algorithms to address
the generalization bias. In particular, CG2A develops a Gradient Agreement
Solver to adaptively balance the varying gradient magnitudes, and introduces a
Soft Gradient Surgery strategy to alleviate the gradient conflicts. Extensive
experiments demonstrate that CG2A significantly improves the generalization
performance and sample efficiency of visual RL algorithms.Comment: accepted by iccv202
A Stress Induced Source of Phonon Bursts and Quasiparticle Poisoning
The performance of superconducting qubits is degraded by a poorly
characterized set of energy sources breaking the Cooper pairs responsible for
superconductivity, creating a condition often called "quasiparticle poisoning."
Recently, a superconductor with one of the lowest average quasiparticle
densities ever measured exhibited quasiparticles primarily produced in bursts
which decreased in rate with time after cooldown. Similarly, several cryogenic
calorimeters used to search for dark matter have also observed an unknown
source of low-energy phonon bursts that decrease in rate with time after
cooldown. Here, we show that a silicon crystal glued to its holder exhibits a
rate of low-energy phonon events that is more than two orders of magnitude
larger than in a functionally identical crystal suspended from its holder in a
low-stress state. The excess phonon event rate in the glued crystal decreases
with time since cooldown, consistent with a source of phonon bursts which
contributes to quasiparticle poisoning in quantum circuits and the low-energy
events observed in cryogenic calorimeters. We argue that relaxation of
thermally induced stress between the glue and crystal is the source of these
events, and conclude that stress relaxation contributes to quasiparticle
poisoning in superconducting qubits and the athermal phonon background in a
broad class of rare-event searches.Comment: 13 pages, 6 figures. W. A. Page and R. K. Romani contributed equally
to this work. Correspondence should be addressed to R. K. Roman
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